TSTP Solution File: SET646^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET646^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 17:45:21 EDT 2024
% Result : Theorem 0.42s 0.60s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET646^3 : TPTP v8.2.0. Released v3.6.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue May 28 10:39:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.21/0.51 %----Proving TH0
% 0.42/0.60 --- Run --ho-elim --full-saturate-quant at 10...
% 0.42/0.60 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.upLVOam16P/cvc5---1.0.5_32389.smt2
% 0.42/0.60 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.upLVOam16P/cvc5---1.0.5_32389.smt2
% 0.42/0.60 (assume a0 (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.42/0.60 (assume a1 (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.42/0.60 (assume a2 (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.42/0.60 (assume a3 (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.42/0.60 (assume a4 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.42/0.60 (assume a5 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.42/0.60 (assume a6 (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))))
% 0.42/0.60 (assume a7 (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.42/0.60 (assume a8 (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))
% 0.42/0.60 (assume a9 (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.42/0.60 (assume a10 (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))
% 0.42/0.60 (assume a11 (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))
% 0.42/0.60 (assume a12 (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))
% 0.42/0.60 (assume a13 (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))
% 0.42/0.60 (assume a14 (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))))
% 0.42/0.60 (assume a15 (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))))
% 0.42/0.60 (assume a16 (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))))
% 0.42/0.60 (assume a17 (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))))
% 0.42/0.60 (assume a18 (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))))
% 0.42/0.60 (assume a19 (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))))
% 0.42/0.60 (assume a20 (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))))
% 0.42/0.60 (assume a21 (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))
% 0.42/0.60 (assume a22 (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))))
% 0.42/0.60 (assume a23 (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))))
% 0.42/0.60 (assume a24 (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))))
% 0.42/0.60 (assume a25 (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))))
% 0.42/0.60 (assume a26 (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))))
% 0.42/0.60 (assume a27 (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))))
% 0.42/0.60 (assume a28 (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))))
% 0.42/0.60 (assume a29 (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))))
% 0.42/0.60 (assume a30 (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))
% 0.42/0.60 (assume a31 (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))))
% 0.42/0.60 (assume a32 (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)))))
% 0.42/0.60 (assume a33 (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))))))))
% 0.42/0.60 (assume a34 (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))))))))
% 0.42/0.60 (assume a35 (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (lambda ((X $$unsorted)) true))))))
% 0.42/0.60 (assume a36 true)
% 0.42/0.60 (step t1 (cl (not (= (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))) false)) (not (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))))) false) :rule equiv_pos2)
% 0.42/0.60 (anchor :step t2 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t2.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t3 (cl (and (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))))) (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))))) (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X))))))) (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W))))))))))))) (not (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))))))))) (not (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X)))))))) (not (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y))))) (not (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) (not (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X)))) (not (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) (not (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) (not (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) (not (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X)))))) (not (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) (not (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y)))) (not (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) (not (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) (not (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t4 (cl (not (= (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))))))) (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))))))) (not (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W))))))))))) (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W))))))))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t5 (cl (= tptp.upwards_well_founded tptp.upwards_well_founded)) :rule refl)
% 0.42/0.60 (anchor :step t2.t6 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t6.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (anchor :step t2.t6.t2 :args ((X (-> $$unsorted Bool)) (:= X X) (Z $$unsorted) (:= Z Z)))
% 0.42/0.60 (step t2.t6.t2.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t6.t2.t2 (cl (= Z Z)) :rule refl)
% 0.42/0.60 (step t2.t6.t2.t3 (cl (= (@ X Z) (@ X Z))) :rule refl)
% 0.42/0.60 (anchor :step t2.t6.t2.t4 :args ((Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t2.t6.t2.t4.t1 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t6.t2.t4.t2 (cl (= (@ X Y) (@ X Y))) :rule refl)
% 0.42/0.60 (step t2.t6.t2.t4.t3 (cl (= (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))) (forall ((W $$unsorted)) (or (not (@ (@ R Y) Y)) (not (@ X W)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t6.t2.t4.t4 (cl (= (forall ((W $$unsorted)) (or (not (@ (@ R Y) Y)) (not (@ X W)))) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t6.t2.t4.t5 (cl (= (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W)))))) :rule trans :premises (t2.t6.t2.t4.t3 t2.t6.t2.t4.t4))
% 0.42/0.60 (step t2.t6.t2.t4.t6 (cl (= (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W))))) (and (@ X Y) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W))))))) :rule cong :premises (t2.t6.t2.t4.t2 t2.t6.t2.t4.t5))
% 0.42/0.60 (step t2.t6.t2.t4 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))) (exists ((Y $$unsorted)) (and (@ X Y) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W)))))))) :rule bind)
% 0.42/0.60 (step t2.t6.t2.t5 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W)))))) (not (forall ((Y $$unsorted)) (not (and (@ X Y) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W)))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t6.t2.t6 (cl (= (forall ((Y $$unsorted)) (not (and (@ X Y) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W))))))) (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t6.t2.t7 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ X Y) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W)))))))) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))) :rule cong :premises (t2.t6.t2.t6))
% 0.42/0.60 (step t2.t6.t2.t8 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (or (not (@ (@ R Y) Y)) (forall ((W $$unsorted)) (not (@ X W)))))) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))) :rule trans :premises (t2.t6.t2.t5 t2.t6.t2.t7))
% 0.42/0.60 (step t2.t6.t2.t9 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))) :rule trans :premises (t2.t6.t2.t4 t2.t6.t2.t8))
% 0.42/0.60 (step t2.t6.t2.t10 (cl (= (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W))))))) (=> (@ X Z) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W))))))))))) :rule cong :premises (t2.t6.t2.t3 t2.t6.t2.t9))
% 0.42/0.60 (step t2.t6.t2 (cl (= (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))))) :rule bind)
% 0.42/0.60 (step t2.t6.t3 (cl (= (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t6.t4 (cl (= (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))))) :rule trans :premises (t2.t6.t2 t2.t6.t3))
% 0.42/0.60 (step t2.t6 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W))))))))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W))))))))))))) :rule bind)
% 0.42/0.60 (step t2.t7 (cl (= (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))))))) (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))))))) :rule cong :premises (t2.t5 t2.t6))
% 0.42/0.60 (step t2.t8 (cl (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W))))))))))))) :rule resolution :premises (t2.t4 t2.t7 a34))
% 0.42/0.60 (step t2.t9 (cl (not (= (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))))))) (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))))))) (not (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W))))))))))) (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t10 (cl (= tptp.well_founded tptp.well_founded)) :rule refl)
% 0.42/0.60 (anchor :step t2.t11 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t11.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (anchor :step t2.t11.t2 :args ((X (-> $$unsorted Bool)) (:= X X) (Z $$unsorted) (:= Z Z)))
% 0.42/0.60 (step t2.t11.t2.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t11.t2.t2 (cl (= Z Z)) :rule refl)
% 0.42/0.60 (step t2.t11.t2.t3 (cl (= (@ X Z) (@ X Z))) :rule refl)
% 0.42/0.60 (anchor :step t2.t11.t2.t4 :args ((Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t2.t11.t2.t4.t1 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t11.t2.t4.t2 (cl (= (@ X Y) (@ X Y))) :rule refl)
% 0.42/0.60 (step t2.t11.t2.t4.t3 (cl (= (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t11.t2.t4.t4 (cl (= (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W))))) (and (@ X Y) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))) :rule cong :premises (t2.t11.t2.t4.t2 t2.t11.t2.t4.t3))
% 0.42/0.60 (step t2.t11.t2.t4 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))) :rule bind)
% 0.42/0.60 (step t2.t11.t2.t5 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))) (not (forall ((Y $$unsorted)) (not (and (@ X Y) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t11.t2.t6 (cl (= (forall ((Y $$unsorted)) (not (and (@ X Y) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))) (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t11.t2.t7 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ X Y) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))) :rule cong :premises (t2.t11.t2.t6))
% 0.42/0.60 (step t2.t11.t2.t8 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))) :rule trans :premises (t2.t11.t2.t5 t2.t11.t2.t7))
% 0.42/0.60 (step t2.t11.t2.t9 (cl (= (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))) :rule trans :premises (t2.t11.t2.t4 t2.t11.t2.t8))
% 0.42/0.60 (step t2.t11.t2.t10 (cl (= (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W))))))) (=> (@ X Z) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))))))) :rule cong :premises (t2.t11.t2.t3 t2.t11.t2.t9))
% 0.42/0.60 (step t2.t11.t2 (cl (= (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))))) :rule bind)
% 0.42/0.60 (step t2.t11.t3 (cl (= (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t11.t4 (cl (= (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))))) :rule trans :premises (t2.t11.t2 t2.t11.t3))
% 0.42/0.60 (step t2.t11 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W))))))))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))))))))) :rule bind)
% 0.42/0.60 (step t2.t12 (cl (= (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))))))) (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))))))) :rule cong :premises (t2.t10 t2.t11))
% 0.42/0.60 (step t2.t13 (cl (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W))))))))))))) :rule resolution :premises (t2.t9 t2.t12 a33))
% 0.42/0.60 (step t2.t14 (cl (not (= (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)))) (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X))))))))) (not (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X))))) (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t15 (cl (= tptp.rel_field tptp.rel_field)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (X $$unsorted) (:= X X)))
% 0.42/0.60 (step t2.t16.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t2 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t3 (cl (and (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y))))) (not (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) (not (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X)))) (not (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) (not (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) (not (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) (not (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X)))))) (not (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) (not (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y)))) (not (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) (not (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) (not (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t16.t4 (cl (not (= (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))))) (not (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t5 (cl (= tptp.equiv_classes tptp.equiv_classes)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t6 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (S1 (-> $$unsorted Bool)) (:= S1 S1)))
% 0.42/0.60 (step t2.t16.t6.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t6.t2 (cl (= S1 S1)) :rule refl)
% 0.42/0.60 (step t2.t16.t6.t3 (cl (= (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))) (not (forall ((X $$unsorted)) (not (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t6.t4 (cl (= (forall ((X $$unsorted)) (not (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))) (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t6.t5 (cl (= (not (forall ((X $$unsorted)) (not (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) :rule cong :premises (t2.t16.t6.t4))
% 0.42/0.60 (step t2.t16.t6.t6 (cl (= (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) :rule trans :premises (t2.t16.t6.t3 t2.t16.t6.t5))
% 0.42/0.60 (step t2.t16.t6 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t7 (cl (= (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))))) :rule cong :premises (t2.t16.t5 t2.t16.t6))
% 0.42/0.60 (step t2.t16.t8 (cl (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) :rule resolution :premises (t2.t16.t4 t2.t16.t7 a30))
% 0.42/0.60 (step t2.t16.t9 (cl (not (= (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))))) (not (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y))))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t10 (cl (= tptp.rel_domain tptp.rel_domain)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t11 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (X $$unsorted) (:= X X)))
% 0.42/0.60 (step t2.t16.t11.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t11.t2 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t11.t3 (cl (= (exists ((Y $$unsorted)) (@ (@ R X) Y)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t11 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t12 (cl (= (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))))) :rule cong :premises (t2.t16.t10 t2.t16.t11))
% 0.42/0.60 (step t2.t16.t13 (cl (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule resolution :premises (t2.t16.t9 t2.t16.t12 a28))
% 0.42/0.60 (step t2.t16.t14 (cl (not (= (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))))) (not (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y))))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t15 (cl (= tptp.rel_codomain tptp.rel_codomain)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t16 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t16.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t16.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t16.t3 (cl (= (exists ((X $$unsorted)) (@ (@ R X) Y)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t16 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t17 (cl (= (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))))) :rule cong :premises (t2.t16.t15 t2.t16.t16))
% 0.42/0.60 (step t2.t16.t18 (cl (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule resolution :premises (t2.t16.t14 t2.t16.t17 a27))
% 0.42/0.60 (step t2.t16.t19 (cl (not (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))))) (not (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R))))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t20 (cl (= tptp.equiv_rel tptp.equiv_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t16.t21.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t2 (cl (and (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) (not (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X)))))) (not (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) (not (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y)))) (not (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) (not (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) (not (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t16.t21.t3 (cl (not (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t4 (cl (= tptp.transitive tptp.transitive)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t5 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t16.t21.t5.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t5.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t5 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t6 (cl (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule cong :premises (t2.t16.t21.t4 t2.t16.t21.t5))
% 0.42/0.60 (step t2.t16.t21.t7 (cl (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule resolution :premises (t2.t16.t21.t3 t2.t16.t21.t6 a25))
% 0.42/0.60 (step t2.t16.t21.t8 (cl (not (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t9 (cl (= tptp.symmetric tptp.symmetric)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t10 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t16.t21.t10.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t10.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t10 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t11 (cl (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) :rule cong :premises (t2.t16.t21.t9 t2.t16.t21.t10))
% 0.42/0.60 (step t2.t16.t21.t12 (cl (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule resolution :premises (t2.t16.t21.t8 t2.t16.t21.t11 a24))
% 0.42/0.60 (step t2.t16.t21.t13 (cl (not (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t14 (cl (= tptp.rel_composition tptp.rel_composition)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t15 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2) (X $$unsorted) (:= X X) (Z $$unsorted) (:= Z Z)))
% 0.42/0.60 (step t2.t16.t21.t15.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t15.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t15.t3 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t15.t4 (cl (= Z Z)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t15.t5 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t15.t6 (cl (= (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t15.t7 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule cong :premises (t2.t16.t21.t15.t6))
% 0.42/0.60 (step t2.t16.t21.t15.t8 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule trans :premises (t2.t16.t21.t15.t5 t2.t16.t21.t15.t7))
% 0.42/0.60 (step t2.t16.t21.t15 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t16 (cl (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) :rule cong :premises (t2.t16.t21.t14 t2.t16.t21.t15))
% 0.42/0.60 (step t2.t16.t21.t17 (cl (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule resolution :premises (t2.t16.t21.t13 t2.t16.t21.t16 a21))
% 0.42/0.60 (step t2.t16.t21.t18 (cl (not (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t19 (cl (= tptp.is_rel_on tptp.is_rel_on)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t20 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (A (-> $$unsorted Bool)) (:= A A) (B (-> $$unsorted Bool)) (:= B B)))
% 0.42/0.60 (step t2.t16.t21.t20.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t20.t2 (cl (= A A)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t20.t3 (cl (= B B)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t20.t4 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t20 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t21 (cl (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) :rule cong :premises (t2.t16.t21.t19 t2.t16.t21.t20))
% 0.42/0.60 (step t2.t16.t21.t22 (cl (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule resolution :premises (t2.t16.t21.t18 t2.t16.t21.t21 a18))
% 0.42/0.60 (step t2.t16.t21.t23 (cl (not (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t24 (cl (= tptp.sub_rel tptp.sub_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t25 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2)))
% 0.42/0.60 (step t2.t16.t21.t25.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t25.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t25.t3 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t25 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t26 (cl (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) :rule cong :premises (t2.t16.t21.t24 t2.t16.t21.t25))
% 0.42/0.60 (step t2.t16.t21.t27 (cl (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule resolution :premises (t2.t16.t21.t23 t2.t16.t21.t26 a17))
% 0.42/0.60 (step t2.t16.t21.t28 (cl (not (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t29 (cl (= tptp.pair_rel tptp.pair_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t30 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t2.t16.t21.t30.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t30.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t30.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t30.t4 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t30.t5 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t30.t6 (cl (= (= V Y) (= Y V))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t30.t7 (cl (= (or (= U X) (= V Y)) (or (= X U) (= Y V)))) :rule cong :premises (t2.t16.t21.t30.t5 t2.t16.t21.t30.t6))
% 0.42/0.60 (step t2.t16.t21.t30 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t31 (cl (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) :rule cong :premises (t2.t16.t21.t29 t2.t16.t21.t30))
% 0.42/0.60 (step t2.t16.t21.t32 (cl (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule resolution :premises (t2.t16.t21.t28 t2.t16.t21.t31 a15))
% 0.42/0.60 (step t2.t16.t21.t33 (cl (not (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t34 (cl (= tptp.misses tptp.misses)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t35 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t21.t35.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t35.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t35.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t35.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t35.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t16.t21.t35.t4))
% 0.42/0.60 (step t2.t16.t21.t35.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t16.t21.t35.t3 t2.t16.t21.t35.t5))
% 0.42/0.60 (step t2.t16.t21.t35.t7 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t16.t21.t35.t6))
% 0.42/0.60 (step t2.t16.t21.t35.t8 (cl (= (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t35.t9 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule trans :premises (t2.t16.t21.t35.t7 t2.t16.t21.t35.t8))
% 0.42/0.60 (step t2.t16.t21.t35 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t36 (cl (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t16.t21.t34 t2.t16.t21.t35))
% 0.42/0.60 (step t2.t16.t21.t37 (cl (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule resolution :premises (t2.t16.t21.t33 t2.t16.t21.t36 a13))
% 0.42/0.60 (step t2.t16.t21.t38 (cl (not (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t39 (cl (= tptp.meets tptp.meets)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t40 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t21.t40.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t40.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t40.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t40.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t40.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t16.t21.t40.t4))
% 0.42/0.60 (step t2.t16.t21.t40.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t16.t21.t40.t3 t2.t16.t21.t40.t5))
% 0.42/0.60 (step t2.t16.t21.t40 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t41 (cl (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) :rule cong :premises (t2.t16.t21.t39 t2.t16.t21.t40))
% 0.42/0.60 (step t2.t16.t21.t42 (cl (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule resolution :premises (t2.t16.t21.t38 t2.t16.t21.t41 a12))
% 0.42/0.60 (step t2.t16.t21.t43 (cl (not (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t44 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t45 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t21.t45.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t45.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t45.t3 (cl (= (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t45 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t46 (cl (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) :rule cong :premises (t2.t16.t21.t44 t2.t16.t21.t45))
% 0.42/0.60 (step t2.t16.t21.t47 (cl (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule resolution :premises (t2.t16.t21.t43 t2.t16.t21.t46 a11))
% 0.42/0.60 (step t2.t16.t21.t48 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t49 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t50 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t21.t50.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t3 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t16.t21.t50.t4 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t50.t5 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t50.t6 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t21.t50.t6.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t6.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t6.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t50.t6 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t50.t7 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t16.t21.t50.t5 t2.t16.t21.t50.t6))
% 0.42/0.60 (step t2.t16.t21.t50.t8 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t16.t21.t50.t4 t2.t16.t21.t50.t7 a4))
% 0.42/0.60 (step t2.t16.t21.t50.t9 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t50.t10 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t50.t11 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t21.t50.t11.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t11.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t11.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t11.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t50.t11.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t50.t11.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t16.t21.t50.t11.t4 t2.t16.t21.t50.t11.t5))
% 0.42/0.60 (step t2.t16.t21.t50.t11 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t50.t12 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t16.t21.t50.t10 t2.t16.t21.t50.t11))
% 0.42/0.60 (step t2.t16.t21.t50.t13 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t16.t21.t50.t9 t2.t16.t21.t50.t12 a3))
% 0.42/0.60 (step t2.t16.t21.t50.t14 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t50.t15 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t16 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t50.t17 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t16.t21.t50.t15 t2.t16.t21.t50.t16))
% 0.42/0.60 (step t2.t16.t21.t50.t18 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t16.t21.t50.t14 t2.t16.t21.t50.t17 a2))
% 0.42/0.60 (step t2.t16.t21.t50.t19 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t16.t21.t50.t3 a9 a8 a7 a6 a5 t2.t16.t21.t50.t8 t2.t16.t21.t50.t13 t2.t16.t21.t50.t18 a1 a0))
% 0.42/0.60 (step t2.t16.t21.t50.t20 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule and :premises (t2.t16.t21.t50.t19))
% 0.42/0.60 (step t2.t16.t21.t50.t21 (cl (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t2.t16.t21.t50.t19))
% 0.42/0.60 (step t2.t16.t21.t50.t22 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t23 (cl (= (@ tptp.intersection X) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X))) :rule cong :premises (t2.t16.t21.t50.t21 t2.t16.t21.t50.t22))
% 0.42/0.60 (step t2.t16.t21.t50.t24 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t50.t25 (cl (= (@ (@ tptp.intersection X) Y) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) :rule cong :premises (t2.t16.t21.t50.t23 t2.t16.t21.t50.t24))
% 0.42/0.60 (step t2.t16.t21.t50.t26 (cl (= (= tptp.emptyset (@ (@ tptp.intersection X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) :rule cong :premises (t2.t16.t21.t50.t20 t2.t16.t21.t50.t25))
% 0.42/0.60 (step t2.t16.t21.t50 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t51 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))))) :rule cong :premises (t2.t16.t21.t49 t2.t16.t21.t50))
% 0.42/0.60 (step t2.t16.t21.t52 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t53 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t21.t53.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t53.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t53.t3 (cl (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t53.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t53.t5 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t53.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y))) :rule cong :premises (t2.t16.t21.t53.t4 t2.t16.t21.t53.t5))
% 0.42/0.60 (step t2.t16.t21.t53.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t53.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule trans :premises (t2.t16.t21.t53.t6 t2.t16.t21.t53.t7))
% 0.42/0.60 (step t2.t16.t21.t53.t9 (cl (= (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) :rule cong :premises (t2.t16.t21.t53.t3 t2.t16.t21.t53.t8))
% 0.42/0.60 (step t2.t16.t21.t53 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t54 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule cong :premises (t2.t16.t21.t52 t2.t16.t21.t53))
% 0.42/0.60 (step t2.t16.t21.t55 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule trans :premises (t2.t16.t21.t51 t2.t16.t21.t54))
% 0.42/0.60 (step t2.t16.t21.t56 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule equiv_pos2)
% 0.42/0.60 (anchor :step t2.t16.t21.t57 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t21.t57.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t57.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t57.t3 (cl (= (= (@ (@ tptp.intersection X) Y) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t57 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t58 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) :rule cong :premises (t2.t16.t21.t52 t2.t16.t21.t57))
% 0.42/0.60 (step t2.t16.t21.t59 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule resolution :premises (t2.t16.t21.t56 t2.t16.t21.t58 a10))
% 0.42/0.60 (step t2.t16.t21.t60 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule resolution :premises (t2.t16.t21.t48 t2.t16.t21.t55 t2.t16.t21.t59))
% 0.42/0.60 (step t2.t16.t21.t61 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t62 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t63 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t21.t63.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t63.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t63.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t63 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t64 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t16.t21.t62 t2.t16.t21.t63))
% 0.42/0.60 (step t2.t16.t21.t65 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t16.t21.t61 t2.t16.t21.t64 a4))
% 0.42/0.60 (step t2.t16.t21.t66 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t67 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t21.t68 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t21.t68.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t68.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t68.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t68.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t68.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t68.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t16.t21.t68.t4 t2.t16.t21.t68.t5))
% 0.42/0.60 (step t2.t16.t21.t68 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t16.t21.t69 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t16.t21.t67 t2.t16.t21.t68))
% 0.42/0.60 (step t2.t16.t21.t70 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t16.t21.t66 t2.t16.t21.t69 a3))
% 0.42/0.60 (step t2.t16.t21.t71 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t21.t72 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t73 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t21.t74 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t16.t21.t72 t2.t16.t21.t73))
% 0.42/0.60 (step t2.t16.t21.t75 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t16.t21.t71 t2.t16.t21.t74 a2))
% 0.42/0.60 (step t2.t16.t21.t76 (cl (and (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t16.t21.t2 t2.t16.t21.t7 t2.t16.t21.t12 a23 a22 t2.t16.t21.t17 a20 a19 t2.t16.t21.t22 t2.t16.t21.t27 a16 t2.t16.t21.t32 a14 t2.t16.t21.t37 t2.t16.t21.t42 t2.t16.t21.t47 t2.t16.t21.t60 a9 a8 a7 a6 a5 t2.t16.t21.t65 t2.t16.t21.t70 t2.t16.t21.t75 a1 a0))
% 0.42/0.60 (step t2.t16.t21.t77 (cl (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))))) :rule and :premises (t2.t16.t21.t76))
% 0.42/0.60 (step t2.t16.t21.t78 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t21.t79 (cl (= (@ tptp.reflexive R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R))) :rule cong :premises (t2.t16.t21.t77 t2.t16.t21.t78))
% 0.42/0.60 (step t2.t16.t21.t80 (cl (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule and :premises (t2.t16.t21.t76))
% 0.42/0.60 (step t2.t16.t21.t81 (cl (= (@ tptp.symmetric R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R))) :rule cong :premises (t2.t16.t21.t80 t2.t16.t21.t78))
% 0.42/0.60 (step t2.t16.t21.t82 (cl (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule and :premises (t2.t16.t21.t76))
% 0.42/0.60 (step t2.t16.t21.t83 (cl (= (@ tptp.transitive R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R))) :rule cong :premises (t2.t16.t21.t82 t2.t16.t21.t78))
% 0.42/0.60 (step t2.t16.t21.t84 (cl (= (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)))) :rule cong :premises (t2.t16.t21.t79 t2.t16.t21.t81 t2.t16.t21.t83))
% 0.42/0.60 (step t2.t16.t21 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R))))) :rule bind)
% 0.42/0.60 (step t2.t16.t22 (cl (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)))))) :rule cong :premises (t2.t16.t20 t2.t16.t21))
% 0.42/0.60 (step t2.t16.t23 (cl (= tptp.equiv_rel tptp.equiv_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t24 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t16.t24.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t24.t2 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (forall ((X $$unsorted)) (@ (@ R X) X)))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t24.t3 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t24.t4 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t24.t5 (cl (= (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule cong :premises (t2.t16.t24.t2 t2.t16.t24.t3 t2.t16.t24.t4))
% 0.42/0.60 (step t2.t16.t24 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t25 (cl (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))))) :rule cong :premises (t2.t16.t23 t2.t16.t24))
% 0.42/0.60 (step t2.t16.t26 (cl (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))))) :rule trans :premises (t2.t16.t22 t2.t16.t25))
% 0.42/0.60 (step t2.t16.t27 (cl (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule resolution :premises (t2.t16.t19 t2.t16.t26 a26))
% 0.42/0.60 (step t2.t16.t28 (cl (not (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t29 (cl (= tptp.transitive tptp.transitive)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t30 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t16.t30.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t30.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t30 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t31 (cl (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule cong :premises (t2.t16.t29 t2.t16.t30))
% 0.42/0.60 (step t2.t16.t32 (cl (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule resolution :premises (t2.t16.t28 t2.t16.t31 a25))
% 0.42/0.60 (step t2.t16.t33 (cl (not (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t34 (cl (= tptp.symmetric tptp.symmetric)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t35 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t16.t35.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t35.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t35 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t36 (cl (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) :rule cong :premises (t2.t16.t34 t2.t16.t35))
% 0.42/0.60 (step t2.t16.t37 (cl (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule resolution :premises (t2.t16.t33 t2.t16.t36 a24))
% 0.42/0.60 (step t2.t16.t38 (cl (not (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t39 (cl (= tptp.rel_composition tptp.rel_composition)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t40 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2) (X $$unsorted) (:= X X) (Z $$unsorted) (:= Z Z)))
% 0.42/0.60 (step t2.t16.t40.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t16.t40.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t16.t40.t3 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t40.t4 (cl (= Z Z)) :rule refl)
% 0.42/0.60 (step t2.t16.t40.t5 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t40.t6 (cl (= (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t40.t7 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule cong :premises (t2.t16.t40.t6))
% 0.42/0.60 (step t2.t16.t40.t8 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule trans :premises (t2.t16.t40.t5 t2.t16.t40.t7))
% 0.42/0.60 (step t2.t16.t40 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t41 (cl (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) :rule cong :premises (t2.t16.t39 t2.t16.t40))
% 0.42/0.60 (step t2.t16.t42 (cl (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule resolution :premises (t2.t16.t38 t2.t16.t41 a21))
% 0.42/0.60 (step t2.t16.t43 (cl (not (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t44 (cl (= tptp.is_rel_on tptp.is_rel_on)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t45 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (A (-> $$unsorted Bool)) (:= A A) (B (-> $$unsorted Bool)) (:= B B)))
% 0.42/0.60 (step t2.t16.t45.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t45.t2 (cl (= A A)) :rule refl)
% 0.42/0.60 (step t2.t16.t45.t3 (cl (= B B)) :rule refl)
% 0.42/0.60 (step t2.t16.t45.t4 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t45 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t46 (cl (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) :rule cong :premises (t2.t16.t44 t2.t16.t45))
% 0.42/0.60 (step t2.t16.t47 (cl (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule resolution :premises (t2.t16.t43 t2.t16.t46 a18))
% 0.42/0.60 (step t2.t16.t48 (cl (not (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t49 (cl (= tptp.sub_rel tptp.sub_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t50 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2)))
% 0.42/0.60 (step t2.t16.t50.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t16.t50.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t16.t50.t3 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t50 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t51 (cl (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) :rule cong :premises (t2.t16.t49 t2.t16.t50))
% 0.42/0.60 (step t2.t16.t52 (cl (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule resolution :premises (t2.t16.t48 t2.t16.t51 a17))
% 0.42/0.60 (step t2.t16.t53 (cl (not (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t54 (cl (= tptp.pair_rel tptp.pair_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t55 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t2.t16.t55.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t55.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t55.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t55.t4 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t2.t16.t55.t5 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t55.t6 (cl (= (= V Y) (= Y V))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t55.t7 (cl (= (or (= U X) (= V Y)) (or (= X U) (= Y V)))) :rule cong :premises (t2.t16.t55.t5 t2.t16.t55.t6))
% 0.42/0.60 (step t2.t16.t55 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule bind)
% 0.42/0.60 (step t2.t16.t56 (cl (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) :rule cong :premises (t2.t16.t54 t2.t16.t55))
% 0.42/0.60 (step t2.t16.t57 (cl (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule resolution :premises (t2.t16.t53 t2.t16.t56 a15))
% 0.42/0.60 (step t2.t16.t58 (cl (not (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t59 (cl (= tptp.misses tptp.misses)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t60 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t60.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t60.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t60.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t60.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t60.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t16.t60.t4))
% 0.42/0.60 (step t2.t16.t60.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t16.t60.t3 t2.t16.t60.t5))
% 0.42/0.60 (step t2.t16.t60.t7 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t16.t60.t6))
% 0.42/0.60 (step t2.t16.t60.t8 (cl (= (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t60.t9 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule trans :premises (t2.t16.t60.t7 t2.t16.t60.t8))
% 0.42/0.60 (step t2.t16.t60 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t61 (cl (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t16.t59 t2.t16.t60))
% 0.42/0.60 (step t2.t16.t62 (cl (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule resolution :premises (t2.t16.t58 t2.t16.t61 a13))
% 0.42/0.60 (step t2.t16.t63 (cl (not (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t64 (cl (= tptp.meets tptp.meets)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t65 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t65.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t65.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t65.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t65.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t65.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t16.t65.t4))
% 0.42/0.60 (step t2.t16.t65.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t16.t65.t3 t2.t16.t65.t5))
% 0.42/0.60 (step t2.t16.t65 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t66 (cl (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) :rule cong :premises (t2.t16.t64 t2.t16.t65))
% 0.42/0.60 (step t2.t16.t67 (cl (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule resolution :premises (t2.t16.t63 t2.t16.t66 a12))
% 0.42/0.60 (step t2.t16.t68 (cl (not (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t69 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t70 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t70.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t70.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t70.t3 (cl (= (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t70 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule bind)
% 0.42/0.60 (step t2.t16.t71 (cl (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) :rule cong :premises (t2.t16.t69 t2.t16.t70))
% 0.42/0.60 (step t2.t16.t72 (cl (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule resolution :premises (t2.t16.t68 t2.t16.t71 a11))
% 0.42/0.60 (step t2.t16.t73 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t74 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t75 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t75.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t3 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t16.t75.t4 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t75.t5 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t75.t6 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t75.t6.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t6.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t6.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t75.t6 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t16.t75.t7 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t16.t75.t5 t2.t16.t75.t6))
% 0.42/0.60 (step t2.t16.t75.t8 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t16.t75.t4 t2.t16.t75.t7 a4))
% 0.42/0.60 (step t2.t16.t75.t9 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t75.t10 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t75.t11 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t75.t11.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t11.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t11.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t11.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t75.t11.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t75.t11.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t16.t75.t11.t4 t2.t16.t75.t11.t5))
% 0.42/0.60 (step t2.t16.t75.t11 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t16.t75.t12 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t16.t75.t10 t2.t16.t75.t11))
% 0.42/0.60 (step t2.t16.t75.t13 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t16.t75.t9 t2.t16.t75.t12 a3))
% 0.42/0.60 (step t2.t16.t75.t14 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t75.t15 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t16 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t75.t17 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t16.t75.t15 t2.t16.t75.t16))
% 0.42/0.60 (step t2.t16.t75.t18 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t16.t75.t14 t2.t16.t75.t17 a2))
% 0.42/0.60 (step t2.t16.t75.t19 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t16.t75.t3 a9 a8 a7 a6 a5 t2.t16.t75.t8 t2.t16.t75.t13 t2.t16.t75.t18 a1 a0))
% 0.42/0.60 (step t2.t16.t75.t20 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule and :premises (t2.t16.t75.t19))
% 0.42/0.60 (step t2.t16.t75.t21 (cl (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t2.t16.t75.t19))
% 0.42/0.60 (step t2.t16.t75.t22 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t23 (cl (= (@ tptp.intersection X) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X))) :rule cong :premises (t2.t16.t75.t21 t2.t16.t75.t22))
% 0.42/0.60 (step t2.t16.t75.t24 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t75.t25 (cl (= (@ (@ tptp.intersection X) Y) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) :rule cong :premises (t2.t16.t75.t23 t2.t16.t75.t24))
% 0.42/0.60 (step t2.t16.t75.t26 (cl (= (= tptp.emptyset (@ (@ tptp.intersection X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) :rule cong :premises (t2.t16.t75.t20 t2.t16.t75.t25))
% 0.42/0.60 (step t2.t16.t75 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t16.t76 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))))) :rule cong :premises (t2.t16.t74 t2.t16.t75))
% 0.42/0.60 (step t2.t16.t77 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t78 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t78.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t78.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t78.t3 (cl (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule refl)
% 0.42/0.60 (step t2.t16.t78.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t78.t5 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t78.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y))) :rule cong :premises (t2.t16.t78.t4 t2.t16.t78.t5))
% 0.42/0.60 (step t2.t16.t78.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t78.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule trans :premises (t2.t16.t78.t6 t2.t16.t78.t7))
% 0.42/0.60 (step t2.t16.t78.t9 (cl (= (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) :rule cong :premises (t2.t16.t78.t3 t2.t16.t78.t8))
% 0.42/0.60 (step t2.t16.t78 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t16.t79 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule cong :premises (t2.t16.t77 t2.t16.t78))
% 0.42/0.60 (step t2.t16.t80 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule trans :premises (t2.t16.t76 t2.t16.t79))
% 0.42/0.60 (step t2.t16.t81 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule equiv_pos2)
% 0.42/0.60 (anchor :step t2.t16.t82 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t16.t82.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t82.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t82.t3 (cl (= (= (@ (@ tptp.intersection X) Y) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t82 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t16.t83 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) :rule cong :premises (t2.t16.t77 t2.t16.t82))
% 0.42/0.60 (step t2.t16.t84 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule resolution :premises (t2.t16.t81 t2.t16.t83 a10))
% 0.42/0.60 (step t2.t16.t85 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule resolution :premises (t2.t16.t73 t2.t16.t80 t2.t16.t84))
% 0.42/0.60 (step t2.t16.t86 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t87 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t88 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t88.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t88.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t88.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t88 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t16.t89 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t16.t87 t2.t16.t88))
% 0.42/0.60 (step t2.t16.t90 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t16.t86 t2.t16.t89 a4))
% 0.42/0.60 (step t2.t16.t91 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t92 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t16.t93 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t16.t93.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t93.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t16.t93.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t16.t93.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t93.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t93.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t16.t93.t4 t2.t16.t93.t5))
% 0.42/0.60 (step t2.t16.t93 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t16.t94 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t16.t92 t2.t16.t93))
% 0.42/0.60 (step t2.t16.t95 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t16.t91 t2.t16.t94 a3))
% 0.42/0.60 (step t2.t16.t96 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t16.t97 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t16.t98 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t16.t99 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t16.t97 t2.t16.t98))
% 0.42/0.60 (step t2.t16.t100 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t16.t96 t2.t16.t99 a2))
% 0.42/0.60 (step t2.t16.t101 (cl (and (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t16.t3 a31 t2.t16.t8 a29 t2.t16.t13 t2.t16.t18 t2.t16.t27 t2.t16.t32 t2.t16.t37 a23 a22 t2.t16.t42 a20 a19 t2.t16.t47 t2.t16.t52 a16 t2.t16.t57 a14 t2.t16.t62 t2.t16.t67 t2.t16.t72 t2.t16.t85 a9 a8 a7 a6 a5 t2.t16.t90 t2.t16.t95 t2.t16.t100 a1 a0))
% 0.42/0.60 (step t2.t16.t102 (cl (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule and :premises (t2.t16.t101))
% 0.42/0.60 (step t2.t16.t103 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t16.t104 (cl (= (@ tptp.rel_domain R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R))) :rule cong :premises (t2.t16.t102 t2.t16.t103))
% 0.42/0.60 (step t2.t16.t105 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t16.t106 (cl (= (@ (@ tptp.rel_domain R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X))) :rule cong :premises (t2.t16.t104 t2.t16.t105))
% 0.42/0.60 (step t2.t16.t107 (cl (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule and :premises (t2.t16.t101))
% 0.42/0.60 (step t2.t16.t108 (cl (= (@ tptp.rel_codomain R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R))) :rule cong :premises (t2.t16.t107 t2.t16.t103))
% 0.42/0.60 (step t2.t16.t109 (cl (= (@ (@ tptp.rel_codomain R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X))) :rule cong :premises (t2.t16.t108 t2.t16.t105))
% 0.42/0.60 (step t2.t16.t110 (cl (= (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)) (or (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X)))) :rule cong :premises (t2.t16.t106 t2.t16.t109))
% 0.42/0.60 (step t2.t16 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X))))) :rule bind)
% 0.42/0.60 (step t2.t17 (cl (= (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)))) (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X)))))) :rule cong :premises (t2.t15 t2.t16))
% 0.42/0.60 (step t2.t18 (cl (= tptp.rel_field tptp.rel_field)) :rule refl)
% 0.42/0.60 (anchor :step t2.t19 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (X $$unsorted) (:= X X)))
% 0.42/0.60 (step t2.t19.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t19.t2 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t19.t3 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) (lambda ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t19.t4 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t19.t5 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (lambda ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) X))) :rule cong :premises (t2.t19.t3 t2.t19.t4))
% 0.42/0.60 (step t2.t19.t6 (cl (= (@ (lambda ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) X) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t19.t7 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) :rule trans :premises (t2.t19.t5 t2.t19.t6))
% 0.42/0.60 (step t2.t19.t8 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) (lambda ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t19.t9 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (lambda ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) X))) :rule cong :premises (t2.t19.t8 t2.t19.t4))
% 0.42/0.60 (step t2.t19.t10 (cl (= (@ (lambda ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) X) (not (forall ((X $$unsorted)) (not (@ (@ R X) X)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t19.t11 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X) (not (forall ((X $$unsorted)) (not (@ (@ R X) X)))))) :rule trans :premises (t2.t19.t9 t2.t19.t10))
% 0.42/0.60 (step t2.t19.t12 (cl (= (or (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X))))))) :rule cong :premises (t2.t19.t7 t2.t19.t11))
% 0.42/0.60 (step t2.t19 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X)))))))) :rule bind)
% 0.42/0.60 (step t2.t20 (cl (= (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))) R) X) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))) R) X)))) (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X))))))))) :rule cong :premises (t2.t18 t2.t19))
% 0.42/0.60 (step t2.t21 (cl (= (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)))) (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X))))))))) :rule trans :premises (t2.t17 t2.t20))
% 0.42/0.60 (step t2.t22 (cl (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X)))))))) :rule resolution :premises (t2.t14 t2.t21 a32))
% 0.42/0.60 (step t2.t23 (cl (not (= (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))))) (not (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t24 (cl (= tptp.equiv_classes tptp.equiv_classes)) :rule refl)
% 0.42/0.60 (anchor :step t2.t25 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (S1 (-> $$unsorted Bool)) (:= S1 S1)))
% 0.42/0.60 (step t2.t25.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t25.t2 (cl (= S1 S1)) :rule refl)
% 0.42/0.60 (step t2.t25.t3 (cl (= (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))) (not (forall ((X $$unsorted)) (not (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t25.t4 (cl (= (forall ((X $$unsorted)) (not (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))) (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t25.t5 (cl (= (not (forall ((X $$unsorted)) (not (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) :rule cong :premises (t2.t25.t4))
% 0.42/0.60 (step t2.t25.t6 (cl (= (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) :rule trans :premises (t2.t25.t3 t2.t25.t5))
% 0.42/0.60 (step t2.t25 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) :rule bind)
% 0.42/0.60 (step t2.t26 (cl (= (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))))) :rule cong :premises (t2.t24 t2.t25))
% 0.42/0.60 (step t2.t27 (cl (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y)))))))))) :rule resolution :premises (t2.t23 t2.t26 a30))
% 0.42/0.60 (step t2.t28 (cl (not (= (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))))) (not (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y))))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t29 (cl (= tptp.rel_domain tptp.rel_domain)) :rule refl)
% 0.42/0.60 (anchor :step t2.t30 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (X $$unsorted) (:= X X)))
% 0.42/0.60 (step t2.t30.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t30.t2 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t30.t3 (cl (= (exists ((Y $$unsorted)) (@ (@ R X) Y)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t30 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule bind)
% 0.42/0.60 (step t2.t31 (cl (= (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))))) :rule cong :premises (t2.t29 t2.t30))
% 0.42/0.60 (step t2.t32 (cl (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y))))))) :rule resolution :premises (t2.t28 t2.t31 a28))
% 0.42/0.60 (step t2.t33 (cl (not (= (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))))) (not (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y))))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t34 (cl (= tptp.rel_codomain tptp.rel_codomain)) :rule refl)
% 0.42/0.60 (anchor :step t2.t35 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t2.t35.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t35.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t35.t3 (cl (= (exists ((X $$unsorted)) (@ (@ R X) Y)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t35 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule bind)
% 0.42/0.60 (step t2.t36 (cl (= (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))))) :rule cong :premises (t2.t34 t2.t35))
% 0.42/0.60 (step t2.t37 (cl (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y))))))) :rule resolution :premises (t2.t33 t2.t36 a27))
% 0.42/0.60 (step t2.t38 (cl (not (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))))) (not (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R))))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t39 (cl (= tptp.equiv_rel tptp.equiv_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t40.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t40.t2 (cl (and (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) (not (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X)))))) (not (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) (not (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y)))) (not (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) (not (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) (not (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t40.t3 (cl (not (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t4 (cl (= tptp.transitive tptp.transitive)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t5 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t40.t5.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t40.t5.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t5 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule bind)
% 0.42/0.60 (step t2.t40.t6 (cl (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule cong :premises (t2.t40.t4 t2.t40.t5))
% 0.42/0.60 (step t2.t40.t7 (cl (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule resolution :premises (t2.t40.t3 t2.t40.t6 a25))
% 0.42/0.60 (step t2.t40.t8 (cl (not (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t9 (cl (= tptp.symmetric tptp.symmetric)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t10 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t40.t10.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t40.t10.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t10 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule bind)
% 0.42/0.60 (step t2.t40.t11 (cl (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) :rule cong :premises (t2.t40.t9 t2.t40.t10))
% 0.42/0.60 (step t2.t40.t12 (cl (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule resolution :premises (t2.t40.t8 t2.t40.t11 a24))
% 0.42/0.60 (step t2.t40.t13 (cl (not (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t14 (cl (= tptp.rel_composition tptp.rel_composition)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t15 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2) (X $$unsorted) (:= X X) (Z $$unsorted) (:= Z Z)))
% 0.42/0.60 (step t2.t40.t15.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t40.t15.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t40.t15.t3 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t15.t4 (cl (= Z Z)) :rule refl)
% 0.42/0.60 (step t2.t40.t15.t5 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t15.t6 (cl (= (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t15.t7 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule cong :premises (t2.t40.t15.t6))
% 0.42/0.60 (step t2.t40.t15.t8 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule trans :premises (t2.t40.t15.t5 t2.t40.t15.t7))
% 0.42/0.60 (step t2.t40.t15 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule bind)
% 0.42/0.60 (step t2.t40.t16 (cl (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) :rule cong :premises (t2.t40.t14 t2.t40.t15))
% 0.42/0.60 (step t2.t40.t17 (cl (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule resolution :premises (t2.t40.t13 t2.t40.t16 a21))
% 0.42/0.60 (step t2.t40.t18 (cl (not (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t19 (cl (= tptp.is_rel_on tptp.is_rel_on)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t20 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (A (-> $$unsorted Bool)) (:= A A) (B (-> $$unsorted Bool)) (:= B B)))
% 0.42/0.60 (step t2.t40.t20.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t40.t20.t2 (cl (= A A)) :rule refl)
% 0.42/0.60 (step t2.t40.t20.t3 (cl (= B B)) :rule refl)
% 0.42/0.60 (step t2.t40.t20.t4 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t20 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule bind)
% 0.42/0.60 (step t2.t40.t21 (cl (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) :rule cong :premises (t2.t40.t19 t2.t40.t20))
% 0.42/0.60 (step t2.t40.t22 (cl (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule resolution :premises (t2.t40.t18 t2.t40.t21 a18))
% 0.42/0.60 (step t2.t40.t23 (cl (not (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t24 (cl (= tptp.sub_rel tptp.sub_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t25 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2)))
% 0.42/0.60 (step t2.t40.t25.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t40.t25.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t40.t25.t3 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t25 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule bind)
% 0.42/0.60 (step t2.t40.t26 (cl (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) :rule cong :premises (t2.t40.t24 t2.t40.t25))
% 0.42/0.60 (step t2.t40.t27 (cl (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule resolution :premises (t2.t40.t23 t2.t40.t26 a17))
% 0.42/0.60 (step t2.t40.t28 (cl (not (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t29 (cl (= tptp.pair_rel tptp.pair_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t30 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t2.t40.t30.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t30.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t30.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t40.t30.t4 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t2.t40.t30.t5 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t30.t6 (cl (= (= V Y) (= Y V))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t30.t7 (cl (= (or (= U X) (= V Y)) (or (= X U) (= Y V)))) :rule cong :premises (t2.t40.t30.t5 t2.t40.t30.t6))
% 0.42/0.60 (step t2.t40.t30 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule bind)
% 0.42/0.60 (step t2.t40.t31 (cl (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) :rule cong :premises (t2.t40.t29 t2.t40.t30))
% 0.42/0.60 (step t2.t40.t32 (cl (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule resolution :premises (t2.t40.t28 t2.t40.t31 a15))
% 0.42/0.60 (step t2.t40.t33 (cl (not (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t34 (cl (= tptp.misses tptp.misses)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t35 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t40.t35.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t35.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t35.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t35.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t35.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t40.t35.t4))
% 0.42/0.60 (step t2.t40.t35.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t40.t35.t3 t2.t40.t35.t5))
% 0.42/0.60 (step t2.t40.t35.t7 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t40.t35.t6))
% 0.42/0.60 (step t2.t40.t35.t8 (cl (= (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t35.t9 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule trans :premises (t2.t40.t35.t7 t2.t40.t35.t8))
% 0.42/0.60 (step t2.t40.t35 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t40.t36 (cl (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t40.t34 t2.t40.t35))
% 0.42/0.60 (step t2.t40.t37 (cl (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule resolution :premises (t2.t40.t33 t2.t40.t36 a13))
% 0.42/0.60 (step t2.t40.t38 (cl (not (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t39 (cl (= tptp.meets tptp.meets)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t40 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t40.t40.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t40.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t40.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t40.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t40.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t40.t40.t4))
% 0.42/0.60 (step t2.t40.t40.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t40.t40.t3 t2.t40.t40.t5))
% 0.42/0.60 (step t2.t40.t40 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule bind)
% 0.42/0.60 (step t2.t40.t41 (cl (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) :rule cong :premises (t2.t40.t39 t2.t40.t40))
% 0.42/0.60 (step t2.t40.t42 (cl (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule resolution :premises (t2.t40.t38 t2.t40.t41 a12))
% 0.42/0.60 (step t2.t40.t43 (cl (not (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t44 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t45 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t40.t45.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t45.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t45.t3 (cl (= (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t45 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule bind)
% 0.42/0.60 (step t2.t40.t46 (cl (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) :rule cong :premises (t2.t40.t44 t2.t40.t45))
% 0.42/0.60 (step t2.t40.t47 (cl (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule resolution :premises (t2.t40.t43 t2.t40.t46 a11))
% 0.42/0.60 (step t2.t40.t48 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t49 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t50 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t40.t50.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t3 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t40.t50.t4 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t50.t5 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t50.t6 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t40.t50.t6.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t6.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t6.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t50.t6 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t40.t50.t7 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t40.t50.t5 t2.t40.t50.t6))
% 0.42/0.60 (step t2.t40.t50.t8 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t40.t50.t4 t2.t40.t50.t7 a4))
% 0.42/0.60 (step t2.t40.t50.t9 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t50.t10 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t50.t11 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t40.t50.t11.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t11.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t11.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t11.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t50.t11.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t50.t11.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t40.t50.t11.t4 t2.t40.t50.t11.t5))
% 0.42/0.60 (step t2.t40.t50.t11 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t40.t50.t12 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t40.t50.t10 t2.t40.t50.t11))
% 0.42/0.60 (step t2.t40.t50.t13 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t40.t50.t9 t2.t40.t50.t12 a3))
% 0.42/0.60 (step t2.t40.t50.t14 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t50.t15 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t16 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t50.t17 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t40.t50.t15 t2.t40.t50.t16))
% 0.42/0.60 (step t2.t40.t50.t18 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t40.t50.t14 t2.t40.t50.t17 a2))
% 0.42/0.60 (step t2.t40.t50.t19 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t40.t50.t3 a9 a8 a7 a6 a5 t2.t40.t50.t8 t2.t40.t50.t13 t2.t40.t50.t18 a1 a0))
% 0.42/0.60 (step t2.t40.t50.t20 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule and :premises (t2.t40.t50.t19))
% 0.42/0.60 (step t2.t40.t50.t21 (cl (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t2.t40.t50.t19))
% 0.42/0.60 (step t2.t40.t50.t22 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t23 (cl (= (@ tptp.intersection X) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X))) :rule cong :premises (t2.t40.t50.t21 t2.t40.t50.t22))
% 0.42/0.60 (step t2.t40.t50.t24 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t50.t25 (cl (= (@ (@ tptp.intersection X) Y) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) :rule cong :premises (t2.t40.t50.t23 t2.t40.t50.t24))
% 0.42/0.60 (step t2.t40.t50.t26 (cl (= (= tptp.emptyset (@ (@ tptp.intersection X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) :rule cong :premises (t2.t40.t50.t20 t2.t40.t50.t25))
% 0.42/0.60 (step t2.t40.t50 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t40.t51 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))))) :rule cong :premises (t2.t40.t49 t2.t40.t50))
% 0.42/0.60 (step t2.t40.t52 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t53 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t40.t53.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t53.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t53.t3 (cl (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule refl)
% 0.42/0.60 (step t2.t40.t53.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t53.t5 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t53.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y))) :rule cong :premises (t2.t40.t53.t4 t2.t40.t53.t5))
% 0.42/0.60 (step t2.t40.t53.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t53.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule trans :premises (t2.t40.t53.t6 t2.t40.t53.t7))
% 0.42/0.60 (step t2.t40.t53.t9 (cl (= (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) :rule cong :premises (t2.t40.t53.t3 t2.t40.t53.t8))
% 0.42/0.60 (step t2.t40.t53 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t40.t54 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule cong :premises (t2.t40.t52 t2.t40.t53))
% 0.42/0.60 (step t2.t40.t55 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule trans :premises (t2.t40.t51 t2.t40.t54))
% 0.42/0.60 (step t2.t40.t56 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule equiv_pos2)
% 0.42/0.60 (anchor :step t2.t40.t57 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t40.t57.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t57.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t57.t3 (cl (= (= (@ (@ tptp.intersection X) Y) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t57 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t40.t58 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) :rule cong :premises (t2.t40.t52 t2.t40.t57))
% 0.42/0.60 (step t2.t40.t59 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule resolution :premises (t2.t40.t56 t2.t40.t58 a10))
% 0.42/0.60 (step t2.t40.t60 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule resolution :premises (t2.t40.t48 t2.t40.t55 t2.t40.t59))
% 0.42/0.60 (step t2.t40.t61 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t62 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t63 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t40.t63.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t63.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t40.t63.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t63 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t40.t64 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t40.t62 t2.t40.t63))
% 0.42/0.60 (step t2.t40.t65 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t40.t61 t2.t40.t64 a4))
% 0.42/0.60 (step t2.t40.t66 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t67 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t40.t68 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t40.t68.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t40.t68.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t40.t68.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t40.t68.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t68.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t68.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t40.t68.t4 t2.t40.t68.t5))
% 0.42/0.60 (step t2.t40.t68 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t40.t69 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t40.t67 t2.t40.t68))
% 0.42/0.60 (step t2.t40.t70 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t40.t66 t2.t40.t69 a3))
% 0.42/0.60 (step t2.t40.t71 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t40.t72 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t40.t73 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t40.t74 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t40.t72 t2.t40.t73))
% 0.42/0.60 (step t2.t40.t75 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t40.t71 t2.t40.t74 a2))
% 0.42/0.60 (step t2.t40.t76 (cl (and (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t40.t2 t2.t40.t7 t2.t40.t12 a23 a22 t2.t40.t17 a20 a19 t2.t40.t22 t2.t40.t27 a16 t2.t40.t32 a14 t2.t40.t37 t2.t40.t42 t2.t40.t47 t2.t40.t60 a9 a8 a7 a6 a5 t2.t40.t65 t2.t40.t70 t2.t40.t75 a1 a0))
% 0.42/0.60 (step t2.t40.t77 (cl (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))))) :rule and :premises (t2.t40.t76))
% 0.42/0.60 (step t2.t40.t78 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t40.t79 (cl (= (@ tptp.reflexive R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R))) :rule cong :premises (t2.t40.t77 t2.t40.t78))
% 0.42/0.60 (step t2.t40.t80 (cl (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule and :premises (t2.t40.t76))
% 0.42/0.60 (step t2.t40.t81 (cl (= (@ tptp.symmetric R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R))) :rule cong :premises (t2.t40.t80 t2.t40.t78))
% 0.42/0.60 (step t2.t40.t82 (cl (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule and :premises (t2.t40.t76))
% 0.42/0.60 (step t2.t40.t83 (cl (= (@ tptp.transitive R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R))) :rule cong :premises (t2.t40.t82 t2.t40.t78))
% 0.42/0.60 (step t2.t40.t84 (cl (= (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)))) :rule cong :premises (t2.t40.t79 t2.t40.t81 t2.t40.t83))
% 0.42/0.60 (step t2.t40 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R))))) :rule bind)
% 0.42/0.60 (step t2.t41 (cl (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)))))) :rule cong :premises (t2.t39 t2.t40))
% 0.42/0.60 (step t2.t42 (cl (= tptp.equiv_rel tptp.equiv_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t43 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t43.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t43.t2 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (forall ((X $$unsorted)) (@ (@ R X) X)))) :rule all_simplify)
% 0.42/0.60 (step t2.t43.t3 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) :rule all_simplify)
% 0.42/0.60 (step t2.t43.t4 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) :rule all_simplify)
% 0.42/0.60 (step t2.t43.t5 (cl (= (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule cong :premises (t2.t43.t2 t2.t43.t3 t2.t43.t4))
% 0.42/0.60 (step t2.t43 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule bind)
% 0.42/0.60 (step t2.t44 (cl (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))) R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))) R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))))) :rule cong :premises (t2.t42 t2.t43))
% 0.42/0.60 (step t2.t45 (cl (= (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))))) :rule trans :premises (t2.t41 t2.t44))
% 0.42/0.60 (step t2.t46 (cl (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule resolution :premises (t2.t38 t2.t45 a26))
% 0.42/0.60 (step t2.t47 (cl (not (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) (not (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t48 (cl (= tptp.transitive tptp.transitive)) :rule refl)
% 0.42/0.60 (anchor :step t2.t49 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t49.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t49.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) :rule all_simplify)
% 0.42/0.60 (step t2.t49 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule bind)
% 0.42/0.60 (step t2.t50 (cl (= (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))))) :rule cong :premises (t2.t48 t2.t49))
% 0.42/0.60 (step t2.t51 (cl (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) :rule resolution :premises (t2.t47 t2.t50 a25))
% 0.42/0.60 (step t2.t52 (cl (not (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) (not (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t53 (cl (= tptp.symmetric tptp.symmetric)) :rule refl)
% 0.42/0.60 (anchor :step t2.t54 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.42/0.60 (step t2.t54.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t54.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) :rule all_simplify)
% 0.42/0.60 (step t2.t54 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule bind)
% 0.42/0.60 (step t2.t55 (cl (= (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))))) :rule cong :premises (t2.t53 t2.t54))
% 0.42/0.60 (step t2.t56 (cl (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X)))))) :rule resolution :premises (t2.t52 t2.t55 a24))
% 0.42/0.60 (step t2.t57 (cl (not (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) (not (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t58 (cl (= tptp.rel_composition tptp.rel_composition)) :rule refl)
% 0.42/0.60 (anchor :step t2.t59 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2) (X $$unsorted) (:= X X) (Z $$unsorted) (:= Z Z)))
% 0.42/0.60 (step t2.t59.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t59.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t59.t3 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t59.t4 (cl (= Z Z)) :rule refl)
% 0.42/0.60 (step t2.t59.t5 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t59.t6 (cl (= (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t59.t7 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule cong :premises (t2.t59.t6))
% 0.42/0.60 (step t2.t59.t8 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) :rule trans :premises (t2.t59.t5 t2.t59.t7))
% 0.42/0.60 (step t2.t59 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule bind)
% 0.42/0.60 (step t2.t60 (cl (= (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))))) :rule cong :premises (t2.t58 t2.t59))
% 0.42/0.60 (step t2.t61 (cl (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z)))))))) :rule resolution :premises (t2.t57 t2.t60 a21))
% 0.42/0.60 (step t2.t62 (cl (not (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) (not (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t63 (cl (= tptp.is_rel_on tptp.is_rel_on)) :rule refl)
% 0.42/0.60 (anchor :step t2.t64 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (A (-> $$unsorted Bool)) (:= A A) (B (-> $$unsorted Bool)) (:= B B)))
% 0.42/0.60 (step t2.t64.t1 (cl (= R R)) :rule refl)
% 0.42/0.60 (step t2.t64.t2 (cl (= A A)) :rule refl)
% 0.42/0.60 (step t2.t64.t3 (cl (= B B)) :rule refl)
% 0.42/0.60 (step t2.t64.t4 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t64 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y))))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule bind)
% 0.42/0.60 (step t2.t65 (cl (= (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))))) :rule cong :premises (t2.t63 t2.t64))
% 0.42/0.60 (step t2.t66 (cl (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y))))))) :rule resolution :premises (t2.t62 t2.t65 a18))
% 0.42/0.60 (step t2.t67 (cl (not (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) (not (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t68 (cl (= tptp.sub_rel tptp.sub_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t69 :args ((R1 (-> $$unsorted $$unsorted Bool)) (:= R1 R1) (R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2)))
% 0.42/0.60 (step t2.t69.t1 (cl (= R1 R1)) :rule refl)
% 0.42/0.60 (step t2.t69.t2 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (step t2.t69.t3 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) :rule all_simplify)
% 0.42/0.60 (step t2.t69 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule bind)
% 0.42/0.60 (step t2.t70 (cl (= (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))))) :rule cong :premises (t2.t68 t2.t69))
% 0.42/0.60 (step t2.t71 (cl (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule resolution :premises (t2.t67 t2.t70 a17))
% 0.42/0.60 (step t2.t72 (cl (not (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) (not (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t73 (cl (= tptp.pair_rel tptp.pair_rel)) :rule refl)
% 0.42/0.60 (anchor :step t2.t74 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t2.t74.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t74.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t74.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t74.t4 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t2.t74.t5 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t74.t6 (cl (= (= V Y) (= Y V))) :rule all_simplify)
% 0.42/0.60 (step t2.t74.t7 (cl (= (or (= U X) (= V Y)) (or (= X U) (= Y V)))) :rule cong :premises (t2.t74.t5 t2.t74.t6))
% 0.42/0.60 (step t2.t74 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule bind)
% 0.42/0.60 (step t2.t75 (cl (= (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))))) :rule cong :premises (t2.t73 t2.t74))
% 0.42/0.60 (step t2.t76 (cl (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule resolution :premises (t2.t72 t2.t75 a15))
% 0.42/0.60 (step t2.t77 (cl (not (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) (not (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t78 (cl (= tptp.misses tptp.misses)) :rule refl)
% 0.42/0.60 (anchor :step t2.t79 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t79.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t79.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t79.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t79.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t79.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t79.t4))
% 0.42/0.60 (step t2.t79.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t79.t3 t2.t79.t5))
% 0.42/0.60 (step t2.t79.t7 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t79.t6))
% 0.42/0.60 (step t2.t79.t8 (cl (= (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t79.t9 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule trans :premises (t2.t79.t7 t2.t79.t8))
% 0.42/0.60 (step t2.t79 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t80 (cl (= (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t78 t2.t79))
% 0.42/0.60 (step t2.t81 (cl (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule resolution :premises (t2.t77 t2.t80 a13))
% 0.42/0.60 (step t2.t82 (cl (not (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) (not (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t83 (cl (= tptp.meets tptp.meets)) :rule refl)
% 0.42/0.60 (anchor :step t2.t84 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t84.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t84.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t84.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.42/0.60 (step t2.t84.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.42/0.60 (step t2.t84.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t84.t4))
% 0.42/0.60 (step t2.t84.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t84.t3 t2.t84.t5))
% 0.42/0.60 (step t2.t84 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule bind)
% 0.42/0.60 (step t2.t85 (cl (= (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) :rule cong :premises (t2.t83 t2.t84))
% 0.42/0.60 (step t2.t86 (cl (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule resolution :premises (t2.t82 t2.t85 a12))
% 0.42/0.60 (step t2.t87 (cl (not (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) (not (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t88 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.42/0.60 (anchor :step t2.t89 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t89.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t89.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t89.t3 (cl (= (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t89 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule bind)
% 0.42/0.60 (step t2.t90 (cl (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) :rule cong :premises (t2.t88 t2.t89))
% 0.42/0.60 (step t2.t91 (cl (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule resolution :premises (t2.t87 t2.t90 a11))
% 0.42/0.60 (step t2.t92 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t93 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t94 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t94.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t94.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t94.t3 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U)))))) (not (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U)))))) (not (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.42/0.60 (step t2.t94.t4 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t94.t5 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t94.t6 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t94.t6.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t94.t6.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t94.t6.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t94.t6 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t94.t7 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t94.t5 t2.t94.t6))
% 0.42/0.60 (step t2.t94.t8 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t94.t4 t2.t94.t7 a4))
% 0.42/0.60 (step t2.t94.t9 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t94.t10 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t94.t11 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t94.t11.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t94.t11.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t94.t11.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t94.t11.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t94.t11.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t94.t11.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t94.t11.t4 t2.t94.t11.t5))
% 0.42/0.60 (step t2.t94.t11 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t94.t12 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t94.t10 t2.t94.t11))
% 0.42/0.60 (step t2.t94.t13 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t94.t9 t2.t94.t12 a3))
% 0.42/0.60 (step t2.t94.t14 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t94.t15 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t94.t16 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t94.t17 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t94.t15 t2.t94.t16))
% 0.42/0.60 (step t2.t94.t18 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t94.t14 t2.t94.t17 a2))
% 0.42/0.60 (step t2.t94.t19 (cl (and (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t94.t3 a9 a8 a7 a6 a5 t2.t94.t8 t2.t94.t13 t2.t94.t18 a1 a0))
% 0.42/0.60 (step t2.t94.t20 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule and :premises (t2.t94.t19))
% 0.42/0.60 (step t2.t94.t21 (cl (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t2.t94.t19))
% 0.42/0.60 (step t2.t94.t22 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t94.t23 (cl (= (@ tptp.intersection X) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X))) :rule cong :premises (t2.t94.t21 t2.t94.t22))
% 0.42/0.60 (step t2.t94.t24 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t94.t25 (cl (= (@ (@ tptp.intersection X) Y) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) :rule cong :premises (t2.t94.t23 t2.t94.t24))
% 0.42/0.60 (step t2.t94.t26 (cl (= (= tptp.emptyset (@ (@ tptp.intersection X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) :rule cong :premises (t2.t94.t20 t2.t94.t25))
% 0.42/0.60 (step t2.t94 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t95 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))))) :rule cong :premises (t2.t93 t2.t94))
% 0.42/0.60 (step t2.t96 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.42/0.60 (anchor :step t2.t97 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t97.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t97.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t97.t3 (cl (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule refl)
% 0.42/0.60 (step t2.t97.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t97.t5 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t97.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y))) :rule cong :premises (t2.t97.t4 t2.t97.t5))
% 0.42/0.60 (step t2.t97.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.42/0.60 (step t2.t97.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule trans :premises (t2.t97.t6 t2.t97.t7))
% 0.42/0.60 (step t2.t97.t9 (cl (= (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) :rule cong :premises (t2.t97.t3 t2.t97.t8))
% 0.42/0.60 (step t2.t97 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule bind)
% 0.42/0.60 (step t2.t98 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule cong :premises (t2.t96 t2.t97))
% 0.42/0.60 (step t2.t99 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule trans :premises (t2.t95 t2.t98))
% 0.42/0.60 (step t2.t100 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) (not (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule equiv_pos2)
% 0.42/0.60 (anchor :step t2.t101 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.42/0.60 (step t2.t101.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t101.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t101.t3 (cl (= (= (@ (@ tptp.intersection X) Y) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) :rule all_simplify)
% 0.42/0.60 (step t2.t101 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule bind)
% 0.42/0.60 (step t2.t102 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) :rule cong :premises (t2.t96 t2.t101))
% 0.42/0.60 (step t2.t103 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule resolution :premises (t2.t100 t2.t102 a10))
% 0.42/0.60 (step t2.t104 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule resolution :premises (t2.t92 t2.t99 t2.t103))
% 0.42/0.60 (step t2.t105 (cl (not (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) (not (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t106 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.42/0.60 (anchor :step t2.t107 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t107.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t107.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t107.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t107 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.42/0.60 (step t2.t108 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t106 t2.t107))
% 0.42/0.60 (step t2.t109 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t105 t2.t108 a4))
% 0.42/0.60 (step t2.t110 (cl (not (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) (not (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t111 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.42/0.60 (anchor :step t2.t112 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.42/0.60 (step t2.t112.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t112.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t112.t3 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t2.t112.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.42/0.60 (step t2.t112.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.42/0.60 (step t2.t112.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t112.t4 t2.t112.t5))
% 0.42/0.60 (step t2.t112 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.42/0.60 (step t2.t113 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t111 t2.t112))
% 0.42/0.60 (step t2.t114 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t110 t2.t113 a3))
% 0.42/0.60 (step t2.t115 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule equiv_pos2)
% 0.42/0.60 (step t2.t116 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.42/0.60 (step t2.t117 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule all_simplify)
% 0.42/0.60 (step t2.t118 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)))) :rule cong :premises (t2.t116 t2.t117))
% 0.42/0.60 (step t2.t119 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false))) :rule resolution :premises (t2.t115 t2.t118 a2))
% 0.42/0.60 (step t2.t120 (cl (and (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (and (@ (@ R Y) Y) (not (forall ((W $$unsorted)) (not (@ X W)))))))))))) (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (or (not (@ X Z)) (not (forall ((Y $$unsorted)) (or (not (@ X Y)) (not (forall ((W $$unsorted)) (or (not (@ (@ R Y) W)) (not (@ X W)))))))))))) (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))) (not (forall ((X $$unsorted)) (not (@ (@ R X) X))))))) (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))) (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (not (forall ((X $$unsorted)) (or (not (@ S1 X)) (not (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))) (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))) (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (forall ((X $$unsorted)) (@ (@ R X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z)))))) (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ (@ R Y) Z)) (@ (@ R X) Z))))) (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ (@ R Y) X))))) (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))) (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))) (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (not (@ (@ R2 Y) Z))))))) (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))) (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))) (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R X) Y)) (and (@ A X) (@ B Y)))))) (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y))))) (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))) (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V)))) (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))) (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))) (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))) (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_3193 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t3 t2.t8 t2.t13 t2.t22 a31 t2.t27 a29 t2.t32 t2.t37 t2.t46 t2.t51 t2.t56 a23 a22 t2.t61 a20 a19 t2.t66 t2.t71 a16 t2.t76 a14 t2.t81 t2.t86 t2.t91 t2.t104 a9 a8 a7 a6 a5 t2.t109 t2.t114 t2.t119 a1 a0))
% 0.42/0.60 (step t2.t121 (cl (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule and :premises (t2.t120))
% 0.42/0.60 (step t2.t122 (cl (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule and :premises (t2.t120))
% 0.42/0.60 (step t2.t123 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t2.t124 (cl (= (@ tptp.pair_rel X) (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X))) :rule cong :premises (t2.t122 t2.t123))
% 0.42/0.60 (step t2.t125 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t2.t126 (cl (= (@ (@ tptp.pair_rel X) Y) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y))) :rule cong :premises (t2.t124 t2.t125))
% 0.42/0.60 (step t2.t127 (cl (= (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)))) :rule cong :premises (t2.t121 t2.t126))
% 0.42/0.60 (step t2.t128 (cl (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))))) :rule and :premises (t2.t120))
% 0.42/0.60 (step t2.t129 (cl (= (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule refl)
% 0.42/0.60 (step t2.t130 (cl (= (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) :rule cong :premises (t2.t128 t2.t129))
% 0.42/0.60 (step t2.t131 (cl (= (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) :rule cong :premises (t2.t130 t2.t129))
% 0.42/0.60 (step t2.t132 (cl (= (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))) :rule cong :premises (t2.t127 t2.t131))
% 0.42/0.60 (step t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))))) :rule bind)
% 0.42/0.60 (step t3 (cl (= (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))))) :rule cong :premises (t2))
% 0.42/0.60 (anchor :step t4 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t4.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t4.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t4.t3 (cl (= (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))))) :rule refl)
% 0.42/0.60 (step t4.t4 (cl (= (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) (lambda ((Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t5 :args ((Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t4.t5.t1 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t4.t5.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t4.t5.t3 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t4.t5.t4 (cl (= (= X U) (= U X))) :rule all_simplify)
% 0.42/0.60 (step t4.t5.t5 (cl (= (= Y V) (= Y V))) :rule refl)
% 0.42/0.60 (step t4.t5.t6 (cl (= (or (= X U) (= Y V)) (or (= U X) (= Y V)))) :rule cong :premises (t4.t5.t4 t4.t5.t5))
% 0.42/0.60 (step t4.t5 (cl (= (lambda ((Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) (lambda ((Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= Y V))))) :rule bind)
% 0.42/0.60 (step t4.t6 (cl (= (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) (lambda ((Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= Y V))))) :rule trans :premises (t4.t4 t4.t5))
% 0.42/0.60 (step t4.t7 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t4.t8 (cl (= (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y) (@ (lambda ((Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= Y V))) Y))) :rule cong :premises (t4.t6 t4.t7))
% 0.42/0.60 (step t4.t9 (cl (= (@ (lambda ((Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= Y V))) Y) (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= Y V))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t10 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t4.t10.t1 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t4.t10.t2 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t4.t10.t3 (cl (= (= U X) (= U X))) :rule refl)
% 0.42/0.60 (step t4.t10.t4 (cl (= (= Y V) (= V Y))) :rule all_simplify)
% 0.42/0.60 (step t4.t10.t5 (cl (= (or (= U X) (= Y V)) (or (= U X) (= V Y)))) :rule cong :premises (t4.t10.t3 t4.t10.t4))
% 0.42/0.60 (step t4.t10 (cl (= (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= Y V))) (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))))) :rule bind)
% 0.42/0.60 (step t4.t11 (cl (= (@ (lambda ((Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= Y V))) Y) (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))))) :rule trans :premises (t4.t9 t4.t10))
% 0.42/0.60 (step t4.t12 (cl (= (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y) (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))))) :rule trans :premises (t4.t8 t4.t11))
% 0.42/0.60 (step t4.t13 (cl (= (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))))) :rule cong :premises (t4.t3 t4.t12))
% 0.42/0.60 (step t4.t14 (cl (= (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y)) (@ (@ R2 X) Y)))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t15 :args ((R2 (-> $$unsorted $$unsorted Bool)) (:= R2 R2)))
% 0.42/0.60 (step t4.t15.t1 (cl (= R2 R2)) :rule refl)
% 0.42/0.60 (anchor :step t4.t15.t2 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t4.t15.t2.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t4.t15.t2.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t4.t15.t2.t3 (cl (= (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) (lambda ((V $$unsorted)) (or (= X X) (= V Y))))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t2.t4 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t4.t15.t2.t5 (cl (= (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y) (@ (lambda ((V $$unsorted)) (or (= X X) (= V Y))) Y))) :rule cong :premises (t4.t15.t2.t3 t4.t15.t2.t4))
% 0.42/0.60 (step t4.t15.t2.t6 (cl (= (@ (lambda ((V $$unsorted)) (or (= X X) (= V Y))) Y) (or (= X X) (= Y Y)))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t2.t7 (cl (= (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y) (or (= X X) (= Y Y)))) :rule trans :premises (t4.t15.t2.t5 t4.t15.t2.t6))
% 0.42/0.60 (step t4.t15.t2.t8 (cl (= (not (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y)) (not (or (= X X) (= Y Y))))) :rule cong :premises (t4.t15.t2.t7))
% 0.42/0.60 (step t4.t15.t2.t9 (cl (= (@ (@ R2 X) Y) (@ (@ R2 X) Y))) :rule refl)
% 0.42/0.60 (step t4.t15.t2.t10 (cl (= (or (not (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y)) (@ (@ R2 X) Y)) (or (not (or (= X X) (= Y Y))) (@ (@ R2 X) Y)))) :rule cong :premises (t4.t15.t2.t8 t4.t15.t2.t9))
% 0.42/0.60 (step t4.t15.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y)) (@ (@ R2 X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (or (= X X) (= Y Y))) (@ (@ R2 X) Y))))) :rule bind)
% 0.42/0.60 (step t4.t15.t3 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (or (= X X) (= Y Y))) (@ (@ R2 X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (and (not (= X X)) (not (= Y Y))) (@ (@ R2 X) Y))))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t4 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (and (not (= X X)) (not (= Y Y))) (@ (@ R2 X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (and (or (not (= X X)) (@ (@ R2 X) Y)) (or (not (= Y Y)) (@ (@ R2 X) Y)))))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t5 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (and (or (not (= X X)) (@ (@ R2 X) Y)) (or (not (= Y Y)) (@ (@ R2 X) Y)))) (and (forall ((BOUND_VARIABLE_1381 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (or (not (= BOUND_VARIABLE_1381 X)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))) (forall ((BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (= BOUND_VARIABLE_1394 Y)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394)))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t15.t6 :args ((BOUND_VARIABLE_1381 $$unsorted) (:= BOUND_VARIABLE_1381 BOUND_VARIABLE_1381) (BOUND_VARIABLE_1383 $$unsorted) (:= BOUND_VARIABLE_1383 BOUND_VARIABLE_1383)))
% 0.42/0.60 (step t4.t15.t6.t1 (cl (= BOUND_VARIABLE_1381 BOUND_VARIABLE_1381)) :rule refl)
% 0.42/0.60 (step t4.t15.t6.t2 (cl (= BOUND_VARIABLE_1383 BOUND_VARIABLE_1383)) :rule refl)
% 0.42/0.60 (step t4.t15.t6.t3 (cl (= (= BOUND_VARIABLE_1381 X) (= X BOUND_VARIABLE_1381))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t6.t4 (cl (= (not (= BOUND_VARIABLE_1381 X)) (not (= X BOUND_VARIABLE_1381)))) :rule cong :premises (t4.t15.t6.t3))
% 0.42/0.60 (step t4.t15.t6.t5 (cl (= (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))) :rule refl)
% 0.42/0.60 (step t4.t15.t6.t6 (cl (= (or (not (= BOUND_VARIABLE_1381 X)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383)) (or (not (= X BOUND_VARIABLE_1381)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383)))) :rule cong :premises (t4.t15.t6.t4 t4.t15.t6.t5))
% 0.42/0.60 (step t4.t15.t6 (cl (= (forall ((BOUND_VARIABLE_1381 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (or (not (= BOUND_VARIABLE_1381 X)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))) (forall ((BOUND_VARIABLE_1381 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (or (not (= X BOUND_VARIABLE_1381)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))))) :rule bind)
% 0.42/0.60 (step t4.t15.t7 (cl (= (forall ((BOUND_VARIABLE_1381 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (or (not (= X BOUND_VARIABLE_1381)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))) (forall ((BOUND_VARIABLE_1383 $$unsorted)) (or (not (= X X)) (@ (@ R2 X) BOUND_VARIABLE_1383))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t15.t8 :args ((BOUND_VARIABLE_1383 $$unsorted) (:= BOUND_VARIABLE_1383 BOUND_VARIABLE_1383)))
% 0.42/0.60 (step t4.t15.t8.t1 (cl (= BOUND_VARIABLE_1383 BOUND_VARIABLE_1383)) :rule refl)
% 0.42/0.60 (step t4.t15.t8.t2 (cl (= (= X X) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t8.t3 (cl (= (not (= X X)) (not true))) :rule cong :premises (t4.t15.t8.t2))
% 0.42/0.60 (step t4.t15.t8.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t8.t5 (cl (= (not (= X X)) false)) :rule trans :premises (t4.t15.t8.t3 t4.t15.t8.t4))
% 0.42/0.60 (step t4.t15.t8.t6 (cl (= (@ (@ R2 X) BOUND_VARIABLE_1383) (@ (@ R2 X) BOUND_VARIABLE_1383))) :rule refl)
% 0.42/0.60 (step t4.t15.t8.t7 (cl (= (or (not (= X X)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (or false (@ (@ R2 X) BOUND_VARIABLE_1383)))) :rule cong :premises (t4.t15.t8.t5 t4.t15.t8.t6))
% 0.42/0.60 (step t4.t15.t8.t8 (cl (= (or false (@ (@ R2 X) BOUND_VARIABLE_1383)) (@ (@ R2 X) BOUND_VARIABLE_1383))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t8.t9 (cl (= (or (not (= X X)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (@ (@ R2 X) BOUND_VARIABLE_1383))) :rule trans :premises (t4.t15.t8.t7 t4.t15.t8.t8))
% 0.42/0.60 (step t4.t15.t8 (cl (= (forall ((BOUND_VARIABLE_1383 $$unsorted)) (or (not (= X X)) (@ (@ R2 X) BOUND_VARIABLE_1383))) (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)))) :rule bind)
% 0.42/0.60 (step t4.t15.t9 (cl (= (forall ((BOUND_VARIABLE_1381 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (or (not (= X BOUND_VARIABLE_1381)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))) (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)))) :rule trans :premises (t4.t15.t7 t4.t15.t8))
% 0.42/0.60 (step t4.t15.t10 (cl (= (forall ((BOUND_VARIABLE_1381 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (or (not (= BOUND_VARIABLE_1381 X)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))) (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)))) :rule trans :premises (t4.t15.t6 t4.t15.t9))
% 0.42/0.60 (anchor :step t4.t15.t11 :args ((BOUND_VARIABLE_1392 $$unsorted) (:= BOUND_VARIABLE_1392 BOUND_VARIABLE_1392) (BOUND_VARIABLE_1394 $$unsorted) (:= BOUND_VARIABLE_1394 BOUND_VARIABLE_1394)))
% 0.42/0.60 (step t4.t15.t11.t1 (cl (= BOUND_VARIABLE_1392 BOUND_VARIABLE_1392)) :rule refl)
% 0.42/0.60 (step t4.t15.t11.t2 (cl (= BOUND_VARIABLE_1394 BOUND_VARIABLE_1394)) :rule refl)
% 0.42/0.60 (step t4.t15.t11.t3 (cl (= (= BOUND_VARIABLE_1394 Y) (= Y BOUND_VARIABLE_1394))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t11.t4 (cl (= (not (= BOUND_VARIABLE_1394 Y)) (not (= Y BOUND_VARIABLE_1394)))) :rule cong :premises (t4.t15.t11.t3))
% 0.42/0.60 (step t4.t15.t11.t5 (cl (= (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394))) :rule refl)
% 0.42/0.60 (step t4.t15.t11.t6 (cl (= (or (not (= BOUND_VARIABLE_1394 Y)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394)) (or (not (= Y BOUND_VARIABLE_1394)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394)))) :rule cong :premises (t4.t15.t11.t4 t4.t15.t11.t5))
% 0.42/0.60 (step t4.t15.t11 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (= BOUND_VARIABLE_1394 Y)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394))) (forall ((BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (= Y BOUND_VARIABLE_1394)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394))))) :rule bind)
% 0.42/0.60 (step t4.t15.t12 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (= Y BOUND_VARIABLE_1394)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394))) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (or (not (= Y Y)) (@ (@ R2 BOUND_VARIABLE_1392) Y))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t15.t13 :args ((BOUND_VARIABLE_1392 $$unsorted) (:= BOUND_VARIABLE_1392 BOUND_VARIABLE_1392)))
% 0.42/0.60 (step t4.t15.t13.t1 (cl (= BOUND_VARIABLE_1392 BOUND_VARIABLE_1392)) :rule refl)
% 0.42/0.60 (step t4.t15.t13.t2 (cl (= (= Y Y) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t13.t3 (cl (= (not (= Y Y)) (not true))) :rule cong :premises (t4.t15.t13.t2))
% 0.42/0.60 (step t4.t15.t13.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t13.t5 (cl (= (not (= Y Y)) false)) :rule trans :premises (t4.t15.t13.t3 t4.t15.t13.t4))
% 0.42/0.60 (step t4.t15.t13.t6 (cl (= (@ (@ R2 BOUND_VARIABLE_1392) Y) (@ (@ R2 BOUND_VARIABLE_1392) Y))) :rule refl)
% 0.42/0.60 (step t4.t15.t13.t7 (cl (= (or (not (= Y Y)) (@ (@ R2 BOUND_VARIABLE_1392) Y)) (or false (@ (@ R2 BOUND_VARIABLE_1392) Y)))) :rule cong :premises (t4.t15.t13.t5 t4.t15.t13.t6))
% 0.42/0.60 (step t4.t15.t13.t8 (cl (= (or false (@ (@ R2 BOUND_VARIABLE_1392) Y)) (@ (@ R2 BOUND_VARIABLE_1392) Y))) :rule all_simplify)
% 0.42/0.60 (step t4.t15.t13.t9 (cl (= (or (not (= Y Y)) (@ (@ R2 BOUND_VARIABLE_1392) Y)) (@ (@ R2 BOUND_VARIABLE_1392) Y))) :rule trans :premises (t4.t15.t13.t7 t4.t15.t13.t8))
% 0.42/0.60 (step t4.t15.t13 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted)) (or (not (= Y Y)) (@ (@ R2 BOUND_VARIABLE_1392) Y))) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))) :rule bind)
% 0.42/0.60 (step t4.t15.t14 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (= Y BOUND_VARIABLE_1394)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394))) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))) :rule trans :premises (t4.t15.t12 t4.t15.t13))
% 0.42/0.60 (step t4.t15.t15 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (= BOUND_VARIABLE_1394 Y)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394))) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))) :rule trans :premises (t4.t15.t11 t4.t15.t14))
% 0.42/0.60 (step t4.t15.t16 (cl (= (and (forall ((BOUND_VARIABLE_1381 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (or (not (= BOUND_VARIABLE_1381 X)) (@ (@ R2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1383))) (forall ((BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (= BOUND_VARIABLE_1394 Y)) (@ (@ R2 BOUND_VARIABLE_1392) BOUND_VARIABLE_1394)))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y))))) :rule cong :premises (t4.t15.t10 t4.t15.t15))
% 0.42/0.60 (step t4.t15.t17 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (and (or (not (= X X)) (@ (@ R2 X) Y)) (or (not (= Y Y)) (@ (@ R2 X) Y)))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y))))) :rule trans :premises (t4.t15.t5 t4.t15.t16))
% 0.42/0.60 (step t4.t15.t18 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (and (not (= X X)) (not (= Y Y))) (@ (@ R2 X) Y))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y))))) :rule trans :premises (t4.t15.t4 t4.t15.t17))
% 0.42/0.60 (step t4.t15.t19 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (or (= X X) (= Y Y))) (@ (@ R2 X) Y))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y))))) :rule trans :premises (t4.t15.t3 t4.t15.t18))
% 0.42/0.60 (step t4.t15.t20 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y)) (@ (@ R2 X) Y))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y))))) :rule trans :premises (t4.t15.t2 t4.t15.t19))
% 0.42/0.60 (step t4.t15 (cl (= (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y))) X) Y)) (@ (@ R2 X) Y)))) (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))))) :rule bind)
% 0.42/0.60 (step t4.t16 (cl (= (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (lambda ((U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))) (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))))) :rule trans :premises (t4.t14 t4.t15))
% 0.42/0.60 (step t4.t17 (cl (= (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))))) :rule trans :premises (t4.t13 t4.t16))
% 0.42/0.60 (step t4.t18 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) U) (@ Y V))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t19 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t4.t19.t1 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t4.t19.t2 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t4.t19.t3 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t4.t19.t4 (cl (= (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) U) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t19.t5 (cl (= (@ Y V) (@ Y V))) :rule refl)
% 0.42/0.60 (step t4.t19.t6 (cl (= (and (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) U) (@ Y V)) (and true (@ Y V)))) :rule cong :premises (t4.t19.t4 t4.t19.t5))
% 0.42/0.60 (step t4.t19.t7 (cl (= (and true (@ Y V)) (@ Y V))) :rule all_simplify)
% 0.42/0.60 (step t4.t19.t8 (cl (= (and (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) U) (@ Y V)) (@ Y V))) :rule trans :premises (t4.t19.t6 t4.t19.t7))
% 0.42/0.60 (step t4.t19 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) U) (@ Y V))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (@ Y V)))) :rule bind)
% 0.42/0.60 (step t4.t20 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (@ Y V)))) :rule trans :premises (t4.t18 t4.t19))
% 0.42/0.60 (step t4.t21 (cl (= (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule refl)
% 0.42/0.60 (step t4.t22 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (@ Y V)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) :rule cong :premises (t4.t20 t4.t21))
% 0.42/0.60 (step t4.t23 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (@ Y V)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((U $$unsorted) (V $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) V)))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t24 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 0.42/0.60 (step t4.t24.t1 (cl (= U U)) :rule refl)
% 0.42/0.60 (step t4.t24.t2 (cl (= V V)) :rule refl)
% 0.42/0.60 (step t4.t24.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) V) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t24 (cl (= (lambda ((U $$unsorted) (V $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) V)) (lambda ((U $$unsorted) (V $$unsorted)) true))) :rule bind)
% 0.42/0.60 (step t4.t25 (cl (= (lambda ((U $$unsorted) (V $$unsorted)) true) (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true))) :rule all_simplify)
% 0.42/0.60 (step t4.t26 (cl (= (lambda ((U $$unsorted) (V $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) V)) (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true))) :rule trans :premises (t4.t24 t4.t25))
% 0.42/0.60 (step t4.t27 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (@ Y V)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true))) :rule trans :premises (t4.t23 t4.t26))
% 0.42/0.60 (step t4.t28 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true))) :rule trans :premises (t4.t22 t4.t27))
% 0.42/0.60 (step t4.t29 (cl (= (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) (@ (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))) (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true)))) :rule cong :premises (t4.t17 t4.t28))
% 0.42/0.60 (step t4.t30 (cl (= (@ (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))) (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true)) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) Y))))) :rule all_simplify)
% 0.42/0.60 (anchor :step t4.t31 :args ((BOUND_VARIABLE_1383 $$unsorted) (:= BOUND_VARIABLE_1383 BOUND_VARIABLE_1383)))
% 0.42/0.60 (step t4.t31.t1 (cl (= BOUND_VARIABLE_1383 BOUND_VARIABLE_1383)) :rule refl)
% 0.42/0.60 (step t4.t31.t2 (cl (= (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) (lambda ((BOUND_VARIABLE_1461 $$unsorted)) true))) :rule all_simplify)
% 0.42/0.60 (step t4.t31.t3 (cl (= (lambda ((BOUND_VARIABLE_1461 $$unsorted)) true) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule all_simplify)
% 0.42/0.60 (step t4.t31.t4 (cl (= (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule trans :premises (t4.t31.t2 t4.t31.t3))
% 0.42/0.60 (step t4.t31.t5 (cl (= BOUND_VARIABLE_1383 BOUND_VARIABLE_1383)) :rule refl)
% 0.42/0.60 (step t4.t31.t6 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) BOUND_VARIABLE_1383) (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) BOUND_VARIABLE_1383))) :rule cong :premises (t4.t31.t4 t4.t31.t5))
% 0.42/0.60 (step t4.t31.t7 (cl (= (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) BOUND_VARIABLE_1383) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t31.t8 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) BOUND_VARIABLE_1383) true)) :rule trans :premises (t4.t31.t6 t4.t31.t7))
% 0.42/0.60 (step t4.t31 (cl (= (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1383 $$unsorted)) true))) :rule bind)
% 0.42/0.60 (step t4.t32 (cl (= (forall ((BOUND_VARIABLE_1383 $$unsorted)) true) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t33 (cl (= (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) BOUND_VARIABLE_1383)) true)) :rule trans :premises (t4.t31 t4.t32))
% 0.42/0.60 (anchor :step t4.t34 :args ((BOUND_VARIABLE_1392 $$unsorted) (:= BOUND_VARIABLE_1392 BOUND_VARIABLE_1392)))
% 0.42/0.60 (step t4.t34.t1 (cl (= BOUND_VARIABLE_1392 BOUND_VARIABLE_1392)) :rule refl)
% 0.42/0.60 (step t4.t34.t2 (cl (= (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) (lambda ((BOUND_VARIABLE_1461 $$unsorted)) true))) :rule all_simplify)
% 0.42/0.60 (step t4.t34.t3 (cl (= (lambda ((BOUND_VARIABLE_1461 $$unsorted)) true) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule all_simplify)
% 0.42/0.60 (step t4.t34.t4 (cl (= (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule trans :premises (t4.t34.t2 t4.t34.t3))
% 0.42/0.60 (step t4.t34.t5 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) Y) (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) Y))) :rule cong :premises (t4.t34.t4 t4.t7))
% 0.42/0.60 (step t4.t34.t6 (cl (= (@ (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t34.t7 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) Y) true)) :rule trans :premises (t4.t34.t5 t4.t34.t6))
% 0.42/0.60 (step t4.t34 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) Y)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) true))) :rule bind)
% 0.42/0.60 (step t4.t35 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted)) true) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t36 (cl (= (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) Y)) true)) :rule trans :premises (t4.t34 t4.t35))
% 0.42/0.60 (step t4.t37 (cl (= (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) Y))) (and true true))) :rule cong :premises (t4.t33 t4.t36))
% 0.42/0.60 (step t4.t38 (cl (= (and true true) true)) :rule all_simplify)
% 0.42/0.60 (step t4.t39 (cl (= (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true) BOUND_VARIABLE_1392) Y))) true)) :rule trans :premises (t4.t37 t4.t38))
% 0.42/0.60 (step t4.t40 (cl (= (@ (lambda ((R2 (-> $$unsorted $$unsorted Bool))) (and (forall ((BOUND_VARIABLE_1383 $$unsorted)) (@ (@ R2 X) BOUND_VARIABLE_1383)) (forall ((BOUND_VARIABLE_1392 $$unsorted)) (@ (@ R2 BOUND_VARIABLE_1392) Y)))) (lambda ((BOUND_VARIABLE_1459 $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) true)) true)) :rule trans :premises (t4.t30 t4.t39))
% 0.42/0.60 (step t4.t41 (cl (= (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) true)) :rule trans :premises (t4.t29 t4.t40))
% 0.42/0.60 (step t4 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) (forall ((X $$unsorted) (Y $$unsorted)) true))) :rule bind)
% 0.42/0.60 (step t5 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) true) true)) :rule all_simplify)
% 0.42/0.60 (step t6 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) true)) :rule trans :premises (t4 t5))
% 0.42/0.60 (step t7 (cl (= (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))) (not true))) :rule cong :premises (t6))
% 0.42/0.60 (step t8 (cl (= (not true) false)) :rule all_simplify)
% 0.42/0.60 (step t9 (cl (= (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ R1 X) Y)) (@ (@ R2 X) Y)))) (@ (@ (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= X U) (= Y V))) X) Y)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V))) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))) false)) :rule trans :premises (t7 t8))
% 0.42/0.60 (step t10 (cl (= (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))) false)) :rule trans :premises (t3 t9))
% 0.42/0.60 (step t11 (cl (not (= (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (lambda ((X $$unsorted)) true))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))))) (not (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (lambda ((X $$unsorted)) true)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))))) :rule equiv_pos2)
% 0.42/0.60 (anchor :step t12 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.42/0.60 (step t12.t1 (cl (= X X)) :rule refl)
% 0.42/0.60 (step t12.t2 (cl (= Y Y)) :rule refl)
% 0.42/0.60 (step t12.t3 (cl (= (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)))) :rule refl)
% 0.42/0.60 (step t12.t4 (cl (= tptp.cartesian_product tptp.cartesian_product)) :rule refl)
% 0.42/0.60 (step t12.t5 (cl (= (lambda ((X $$unsorted)) true) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule all_simplify)
% 0.42/0.60 (step t12.t6 (cl (= (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) :rule cong :premises (t12.t4 t12.t5))
% 0.42/0.60 (step t12.t7 (cl (= (lambda ((X $$unsorted)) true) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))) :rule all_simplify)
% 0.42/0.60 (step t12.t8 (cl (= (@ (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (lambda ((X $$unsorted)) true)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))) :rule cong :premises (t12.t6 t12.t7))
% 0.42/0.60 (step t12.t9 (cl (= (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (lambda ((X $$unsorted)) true))) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))) :rule cong :premises (t12.t3 t12.t8))
% 0.42/0.60 (step t12 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (lambda ((X $$unsorted)) true)))) (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))))) :rule bind)
% 0.42/0.60 (step t13 (cl (= (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((X $$unsorted)) true)) (lambda ((X $$unsorted)) true))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true))))))) :rule cong :premises (t12))
% 0.42/0.60 (step t14 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.sub_rel (@ (@ tptp.pair_rel X) Y)) (@ (@ tptp.cartesian_product (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_1435 $$unsorted)) true)))))) :rule resolution :premises (t11 t13 a35))
% 0.42/0.60 (step t15 (cl false) :rule resolution :premises (t1 t10 t14))
% 0.42/0.60 (step t16 (cl (not false)) :rule false)
% 0.42/0.60 (step t17 (cl) :rule resolution :premises (t15 t16))
% 0.42/0.60
% 0.42/0.60 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.upLVOam16P/cvc5---1.0.5_32389.smt2
% 0.42/0.60 % cvc5---1.0.5 exiting
% 0.42/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------