TSTP Solution File: SET764^4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET764^4 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n025.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 17:45:39 EDT 2024
% Result : Theorem 0.39s 0.57s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.16 % Problem : SET764^4 : TPTP v8.2.0. Released v3.6.0.
% 0.13/0.17 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n025.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Tue May 28 10:29:39 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.24/0.52 %----Proving TH0
% 0.39/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.39/0.57 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.zWihtAk3HO/cvc5---1.0.5_843.smt2
% 0.39/0.57 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.zWihtAk3HO/cvc5---1.0.5_843.smt2
% 0.39/0.57 (assume a0 (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.39/0.57 (assume a1 (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.39/0.57 (assume a2 (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.39/0.57 (assume a3 (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.39/0.57 (assume a4 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.39/0.57 (assume a5 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.39/0.57 (assume a6 (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))))
% 0.39/0.57 (assume a7 (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.39/0.57 (assume a8 (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))
% 0.39/0.57 (assume a9 (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.39/0.57 (assume a10 (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))
% 0.39/0.57 (assume a11 (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))
% 0.39/0.57 (assume a12 (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))
% 0.39/0.57 (assume a13 (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))
% 0.39/0.57 (assume a14 (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))))))
% 0.39/0.57 (assume a15 (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X)))))
% 0.39/0.57 (assume a16 (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))))))
% 0.39/0.57 (assume a17 (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))))))
% 0.39/0.57 (assume a18 (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))))))
% 0.39/0.57 (assume a19 (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F)))))
% 0.39/0.57 (assume a20 (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X)))))))
% 0.39/0.57 (assume a21 (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y)))))))
% 0.39/0.57 (assume a22 (not (forall ((F (-> $$unsorted $$unsorted))) (= (@ (@ tptp.fun_inv_image F) tptp.emptyset) tptp.emptyset))))
% 0.39/0.57 (assume a23 true)
% 0.39/0.57 (step t1 (cl (not (= (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset)))) false)) (not (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset))))) false) :rule equiv_pos2)
% 0.39/0.57 (anchor :step t2 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t2.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t2 (cl (and (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y)))))) (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X)))))) (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))) (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X)))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) (= 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 (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$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_1029 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y))))))) (not (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X))))))) (not (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) (not (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) (not (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) (not (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) (not (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X))))) (not (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) (not (= tptp.misses (lambda ((X (-> $$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_1029 $$unsorted)) false) (lambda ((U $$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 $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$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)
% 0.39/0.57 (step t2.t3 (cl (not (= (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y)))))) (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y)))))))) (not (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y))))))) (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t4 (cl (= tptp.fun_increasing tptp.fun_increasing)) :rule refl)
% 0.39/0.57 (anchor :step t2.t5 :args ((F (-> $$unsorted $$unsorted)) (:= F F) (SMALLER (-> $$unsorted $$unsorted Bool)) (:= SMALLER SMALLER)))
% 0.39/0.57 (step t2.t5.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t5.t2 (cl (= SMALLER SMALLER)) :rule refl)
% 0.39/0.57 (step t2.t5.t3 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t5 (cl (= (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y))))) (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y))))))) :rule bind)
% 0.39/0.57 (step t2.t6 (cl (= (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y)))))) (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y)))))))) :rule cong :premises (t2.t4 t2.t5))
% 0.39/0.57 (step t2.t7 (cl (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y))))))) :rule resolution :premises (t2.t3 t2.t6 a21))
% 0.39/0.57 (step t2.t8 (cl (not (= (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X)))))) (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X)))))))) (not (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X))))))) (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t9 (cl (= tptp.fun_decreasing tptp.fun_decreasing)) :rule refl)
% 0.39/0.57 (anchor :step t2.t10 :args ((F (-> $$unsorted $$unsorted)) (:= F F) (SMALLER (-> $$unsorted $$unsorted Bool)) (:= SMALLER SMALLER)))
% 0.39/0.57 (step t2.t10.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t10.t2 (cl (= SMALLER SMALLER)) :rule refl)
% 0.39/0.57 (step t2.t10.t3 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t10 (cl (= (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X))))) (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X))))))) :rule bind)
% 0.39/0.57 (step t2.t11 (cl (= (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X)))))) (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X)))))))) :rule cong :premises (t2.t9 t2.t10))
% 0.39/0.57 (step t2.t12 (cl (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X))))))) :rule resolution :premises (t2.t8 t2.t11 a20))
% 0.39/0.57 (step t2.t13 (cl (not (= (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F)))) (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))))) (not (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F))))) (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t14 (cl (= tptp.fun_bijective tptp.fun_bijective)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t2.t15.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t15.t2 (cl (and (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))) (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X)))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) (= 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 (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$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_1029 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) (not (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) (not (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) (not (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X))))) (not (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) (not (= tptp.misses (lambda ((X (-> $$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_1029 $$unsorted)) false) (lambda ((U $$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 $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$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)
% 0.39/0.57 (step t2.t15.t3 (cl (not (= (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) (not (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X))))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t4 (cl (= tptp.fun_surjective tptp.fun_surjective)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t5 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t2.t15.t5.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t5.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t5.t2.t1 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t5.t2.t2 (cl (= (exists ((X $$unsorted)) (= Y (@ F X))) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t5.t2 (cl (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))) :rule bind)
% 0.39/0.57 (step t2.t15.t5 (cl (= (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X))))) (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule bind)
% 0.39/0.57 (step t2.t15.t6 (cl (= (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) :rule cong :premises (t2.t15.t4 t2.t15.t5))
% 0.39/0.57 (step t2.t15.t7 (cl (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule resolution :premises (t2.t15.t3 t2.t15.t6 a18))
% 0.39/0.57 (step t2.t15.t8 (cl (not (= (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))))) (not (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y)))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t9 (cl (= tptp.fun_injective tptp.fun_injective)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t10 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t2.t15.t10.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t15.t10.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t10 (cl (= (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y)))) (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) :rule bind)
% 0.39/0.57 (step t2.t15.t11 (cl (= (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))))) :rule cong :premises (t2.t15.t9 t2.t15.t10))
% 0.39/0.57 (step t2.t15.t12 (cl (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) :rule resolution :premises (t2.t15.t8 t2.t15.t11 a17))
% 0.39/0.57 (step t2.t15.t13 (cl (not (= (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))))) (not (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X))))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t14 (cl (= tptp.fun_inv_image tptp.fun_inv_image)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t15 :args ((F (-> $$unsorted $$unsorted)) (:= F F) (B (-> $$unsorted Bool)) (:= B B) (X $$unsorted) (:= X X)))
% 0.39/0.57 (step t2.t15.t15.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t15.t15.t2 (cl (= B B)) :rule refl)
% 0.39/0.57 (step t2.t15.t15.t3 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t15.t4 (cl (= (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))) (not (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X)))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t15.t5 (cl (= (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X))))) (forall ((Y $$unsorted)) (or (not (@ B Y)) (not (= Y (@ F X))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t15.t6 (cl (= (forall ((Y $$unsorted)) (or (not (@ B Y)) (not (= Y (@ F X))))) (or (not (@ B (@ F X))) (not (= (@ F X) (@ F X)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t15.t7 (cl (= (not (@ B (@ F X))) (not (@ B (@ F X))))) :rule refl)
% 0.39/0.57 (step t2.t15.t15.t8 (cl (= (= (@ F X) (@ F X)) true)) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t15.t9 (cl (= (not (= (@ F X) (@ F X))) (not true))) :rule cong :premises (t2.t15.t15.t8))
% 0.39/0.57 (step t2.t15.t15.t10 (cl (= (not true) false)) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t15.t11 (cl (= (not (= (@ F X) (@ F X))) false)) :rule trans :premises (t2.t15.t15.t9 t2.t15.t15.t10))
% 0.39/0.57 (step t2.t15.t15.t12 (cl (= (or (not (@ B (@ F X))) (not (= (@ F X) (@ F X)))) (or (not (@ B (@ F X))) false))) :rule cong :premises (t2.t15.t15.t7 t2.t15.t15.t11))
% 0.39/0.57 (step t2.t15.t15.t13 (cl (= (or (not (@ B (@ F X))) false) (not (@ B (@ F X))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t15.t14 (cl (= (or (not (@ B (@ F X))) (not (= (@ F X) (@ F X)))) (not (@ B (@ F X))))) :rule trans :premises (t2.t15.t15.t12 t2.t15.t15.t13))
% 0.39/0.57 (step t2.t15.t15.t15 (cl (= (forall ((Y $$unsorted)) (or (not (@ B Y)) (not (= Y (@ F X))))) (not (@ B (@ F X))))) :rule trans :premises (t2.t15.t15.t6 t2.t15.t15.t14))
% 0.39/0.57 (step t2.t15.t15.t16 (cl (= (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X))))) (not (@ B (@ F X))))) :rule trans :premises (t2.t15.t15.t5 t2.t15.t15.t15))
% 0.39/0.57 (step t2.t15.t15.t17 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X)))))) (not (not (@ B (@ F X)))))) :rule cong :premises (t2.t15.t15.t16))
% 0.39/0.57 (step t2.t15.t15.t18 (cl (= (not (not (@ B (@ F X)))) (@ B (@ F X)))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t15.t19 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X)))))) (@ B (@ F X)))) :rule trans :premises (t2.t15.t15.t17 t2.t15.t15.t18))
% 0.39/0.57 (step t2.t15.t15.t20 (cl (= (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))) (@ B (@ F X)))) :rule trans :premises (t2.t15.t15.t4 t2.t15.t15.t19))
% 0.39/0.57 (step t2.t15.t15 (cl (= (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X))))) (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule bind)
% 0.39/0.57 (step t2.t15.t16 (cl (= (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))))) :rule cong :premises (t2.t15.t14 t2.t15.t15))
% 0.39/0.57 (step t2.t15.t17 (cl (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule resolution :premises (t2.t15.t13 t2.t15.t16 a16))
% 0.39/0.57 (step t2.t15.t18 (cl (not (= (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))))) (not (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X))))))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t19 (cl (= tptp.fun_image tptp.fun_image)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t20 :args ((F (-> $$unsorted $$unsorted)) (:= F F) (A (-> $$unsorted Bool)) (:= A A) (Y $$unsorted) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t20.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t15.t20.t2 (cl (= A A)) :rule refl)
% 0.39/0.57 (step t2.t15.t20.t3 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t20.t4 (cl (= (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))) (not (forall ((X $$unsorted)) (not (and (@ A X) (= Y (@ F X)))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t20.t5 (cl (= (forall ((X $$unsorted)) (not (and (@ A X) (= Y (@ F X))))) (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t20.t6 (cl (= (not (forall ((X $$unsorted)) (not (and (@ A X) (= Y (@ F X)))))) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) :rule cong :premises (t2.t15.t20.t5))
% 0.39/0.57 (step t2.t15.t20.t7 (cl (= (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) :rule trans :premises (t2.t15.t20.t4 t2.t15.t20.t6))
% 0.39/0.57 (step t2.t15.t20 (cl (= (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X))))) (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) :rule bind)
% 0.39/0.57 (step t2.t15.t21 (cl (= (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))))) :rule cong :premises (t2.t15.t19 t2.t15.t20))
% 0.39/0.57 (step t2.t15.t22 (cl (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) :rule resolution :premises (t2.t15.t18 t2.t15.t21 a14))
% 0.39/0.57 (step t2.t15.t23 (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)
% 0.39/0.57 (step t2.t15.t24 (cl (= tptp.misses tptp.misses)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t25 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t25.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t25.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t25.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t25.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t25.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.t15.t25.t4))
% 0.39/0.57 (step t2.t15.t25.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.t15.t25.t3 t2.t15.t25.t5))
% 0.39/0.57 (step t2.t15.t25.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.t15.t25.t6))
% 0.39/0.57 (step t2.t15.t25.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)
% 0.39/0.57 (step t2.t15.t25.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.t15.t25.t7 t2.t15.t25.t8))
% 0.39/0.57 (step t2.t15.t25 (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)
% 0.39/0.57 (step t2.t15.t26 (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.t15.t24 t2.t15.t25))
% 0.39/0.57 (step t2.t15.t27 (cl (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule resolution :premises (t2.t15.t23 t2.t15.t26 a13))
% 0.39/0.57 (step t2.t15.t28 (cl (not (= (= tptp.meets (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t29 (cl (= tptp.meets tptp.meets)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t30 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t30.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t30.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t30.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t30.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t30.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t15.t30.t4))
% 0.39/0.57 (step t2.t15.t30.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t15.t30.t3 t2.t15.t30.t5))
% 0.39/0.57 (step t2.t15.t30 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule bind)
% 0.39/0.57 (step t2.t15.t31 (cl (= (= tptp.meets (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))))) :rule cong :premises (t2.t15.t29 t2.t15.t30))
% 0.39/0.57 (step t2.t15.t32 (cl (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule resolution :premises (t2.t15.t28 t2.t15.t31 a12))
% 0.39/0.57 (step t2.t15.t33 (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)
% 0.39/0.57 (step t2.t15.t34 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t35 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t35.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t35.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t35.t3 (cl (= (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t35 (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)
% 0.39/0.57 (step t2.t15.t36 (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.t15.t34 t2.t15.t35))
% 0.39/0.57 (step t2.t15.t37 (cl (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule resolution :premises (t2.t15.t33 t2.t15.t36 a11))
% 0.39/0.57 (step t2.t15.t38 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$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 (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t39 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t40 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t40.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t3 (cl (and (= tptp.complement (lambda ((X (-> $$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_1029 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$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_1029 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.39/0.57 (step t2.t15.t40.t4 (cl (not (= (= tptp.singleton (lambda ((X $$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 $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t40.t5 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t40.t6 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t15.t40.t6.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t6.t2 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t6.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t40.t6 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.39/0.57 (step t2.t15.t40.t7 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t15.t40.t5 t2.t15.t40.t6))
% 0.39/0.57 (step t2.t15.t40.t8 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t15.t40.t4 t2.t15.t40.t7 a4))
% 0.39/0.57 (step t2.t15.t40.t9 (cl (not (= (= tptp.unord_pair (lambda ((X $$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 $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t40.t10 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t40.t11 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t15.t40.t11.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t11.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t11.t3 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t11.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t40.t11.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t40.t11.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t15.t40.t11.t4 t2.t15.t40.t11.t5))
% 0.39/0.57 (step t2.t15.t40.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)
% 0.39/0.57 (step t2.t15.t40.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.t15.t40.t10 t2.t15.t40.t11))
% 0.39/0.57 (step t2.t15.t40.t13 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t15.t40.t9 t2.t15.t40.t12 a3))
% 0.39/0.57 (step t2.t15.t40.t14 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t40.t15 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t16 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t40.t17 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) :rule cong :premises (t2.t15.t40.t15 t2.t15.t40.t16))
% 0.39/0.57 (step t2.t15.t40.t18 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule resolution :premises (t2.t15.t40.t14 t2.t15.t40.t17 a2))
% 0.39/0.57 (step t2.t15.t40.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 $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$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.t15.t40.t3 a9 a8 a7 a6 a5 t2.t15.t40.t8 t2.t15.t40.t13 t2.t15.t40.t18 a1 a0))
% 0.39/0.57 (step t2.t15.t40.t20 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule and :premises (t2.t15.t40.t19))
% 0.39/0.57 (step t2.t15.t40.t21 (cl (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t2.t15.t40.t19))
% 0.39/0.57 (step t2.t15.t40.t22 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t23 (cl (= (@ tptp.intersection X) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X))) :rule cong :premises (t2.t15.t40.t21 t2.t15.t40.t22))
% 0.39/0.57 (step t2.t15.t40.t24 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t40.t25 (cl (= (@ (@ tptp.intersection X) Y) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) :rule cong :premises (t2.t15.t40.t23 t2.t15.t40.t24))
% 0.39/0.57 (step t2.t15.t40.t26 (cl (= (= tptp.emptyset (@ (@ tptp.intersection X) Y)) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) :rule cong :premises (t2.t15.t40.t20 t2.t15.t40.t25))
% 0.39/0.57 (step t2.t15.t40 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))))) :rule bind)
% 0.39/0.57 (step t2.t15.t41 (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_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))))) :rule cong :premises (t2.t15.t39 t2.t15.t40))
% 0.39/0.57 (step t2.t15.t42 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t43 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t43.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t43.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t43.t3 (cl (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule refl)
% 0.39/0.57 (step t2.t15.t43.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t43.t5 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t43.t6 (cl (= (@ (@ (lambda ((X (-> $$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.t15.t43.t4 t2.t15.t43.t5))
% 0.39/0.57 (step t2.t15.t43.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t43.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule trans :premises (t2.t15.t43.t6 t2.t15.t43.t7))
% 0.39/0.57 (step t2.t15.t43.t9 (cl (= (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) :rule cong :premises (t2.t15.t43.t3 t2.t15.t43.t8))
% 0.39/0.57 (step t2.t15.t43 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule bind)
% 0.39/0.57 (step t2.t15.t44 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$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 (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule cong :premises (t2.t15.t42 t2.t15.t43))
% 0.39/0.57 (step t2.t15.t45 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule trans :premises (t2.t15.t41 t2.t15.t44))
% 0.39/0.57 (step t2.t15.t46 (cl (not (= (= tptp.disjoint (lambda ((X (-> $$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 (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule equiv_pos2)
% 0.39/0.57 (anchor :step t2.t15.t47 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t15.t47.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t47.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t47.t3 (cl (= (= (@ (@ tptp.intersection X) Y) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t47 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset)) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule bind)
% 0.39/0.57 (step t2.t15.t48 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))))) :rule cong :premises (t2.t15.t42 t2.t15.t47))
% 0.39/0.57 (step t2.t15.t49 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule resolution :premises (t2.t15.t46 t2.t15.t48 a10))
% 0.39/0.57 (step t2.t15.t50 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule resolution :premises (t2.t15.t38 t2.t15.t45 t2.t15.t49))
% 0.39/0.57 (step t2.t15.t51 (cl (not (= (= tptp.singleton (lambda ((X $$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 $$unsorted)) (= X U)))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t52 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t53 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t15.t53.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t53.t2 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t15.t53.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t53 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.39/0.57 (step t2.t15.t54 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t15.t52 t2.t15.t53))
% 0.39/0.57 (step t2.t15.t55 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t15.t51 t2.t15.t54 a4))
% 0.39/0.57 (step t2.t15.t56 (cl (not (= (= tptp.unord_pair (lambda ((X $$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 $$unsorted)) (or (= X U) (= Y U))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t57 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.39/0.57 (anchor :step t2.t15.t58 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t15.t58.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t15.t58.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t15.t58.t3 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t15.t58.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t58.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t58.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t15.t58.t4 t2.t15.t58.t5))
% 0.39/0.57 (step t2.t15.t58 (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)
% 0.39/0.57 (step t2.t15.t59 (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.t15.t57 t2.t15.t58))
% 0.39/0.57 (step t2.t15.t60 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t15.t56 t2.t15.t59 a3))
% 0.39/0.57 (step t2.t15.t61 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t15.t62 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.39/0.57 (step t2.t15.t63 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule all_simplify)
% 0.39/0.57 (step t2.t15.t64 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) :rule cong :premises (t2.t15.t62 t2.t15.t63))
% 0.39/0.57 (step t2.t15.t65 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule resolution :premises (t2.t15.t61 t2.t15.t64 a2))
% 0.39/0.57 (step t2.t15.t66 (cl (and (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))) (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X)))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) (= 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 (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$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_1029 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t15.t2 t2.t15.t7 t2.t15.t12 t2.t15.t17 a15 t2.t15.t22 t2.t15.t27 t2.t15.t32 t2.t15.t37 t2.t15.t50 a9 a8 a7 a6 a5 t2.t15.t55 t2.t15.t60 t2.t15.t65 a1 a0))
% 0.39/0.57 (step t2.t15.t67 (cl (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) :rule and :premises (t2.t15.t66))
% 0.39/0.57 (step t2.t15.t68 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t15.t69 (cl (= (@ tptp.fun_injective F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F))) :rule cong :premises (t2.t15.t67 t2.t15.t68))
% 0.39/0.57 (step t2.t15.t70 (cl (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule and :premises (t2.t15.t66))
% 0.39/0.57 (step t2.t15.t71 (cl (= (@ tptp.fun_surjective F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F))) :rule cong :premises (t2.t15.t70 t2.t15.t68))
% 0.39/0.57 (step t2.t15.t72 (cl (= (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F)) (and (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F)))) :rule cong :premises (t2.t15.t69 t2.t15.t71))
% 0.39/0.57 (step t2.t15 (cl (= (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F))) (lambda ((F (-> $$unsorted $$unsorted))) (and (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F))))) :rule bind)
% 0.39/0.57 (step t2.t16 (cl (= (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F)))) (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F)))))) :rule cong :premises (t2.t14 t2.t15))
% 0.39/0.57 (step t2.t17 (cl (= tptp.fun_bijective tptp.fun_bijective)) :rule refl)
% 0.39/0.57 (anchor :step t2.t18 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t2.t18.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t18.t2 (cl (= (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))) :rule all_simplify)
% 0.39/0.57 (step t2.t18.t3 (cl (= (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t18.t4 (cl (= (and (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F)) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule cong :premises (t2.t18.t2 t2.t18.t3))
% 0.39/0.57 (step t2.t18 (cl (= (lambda ((F (-> $$unsorted $$unsorted))) (and (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F))) (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) :rule bind)
% 0.39/0.57 (step t2.t19 (cl (= (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))) F) (@ (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) F)))) (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))))) :rule cong :premises (t2.t17 t2.t18))
% 0.39/0.57 (step t2.t20 (cl (= (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F)))) (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))))) :rule trans :premises (t2.t16 t2.t19))
% 0.39/0.57 (step t2.t21 (cl (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) :rule resolution :premises (t2.t13 t2.t20 a19))
% 0.39/0.57 (step t2.t22 (cl (not (= (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) (not (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X))))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t23 (cl (= tptp.fun_surjective tptp.fun_surjective)) :rule refl)
% 0.39/0.57 (anchor :step t2.t24 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t2.t24.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (anchor :step t2.t24.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.39/0.57 (step t2.t24.t2.t1 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t24.t2.t2 (cl (= (exists ((X $$unsorted)) (= Y (@ F X))) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t24.t2 (cl (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))) :rule bind)
% 0.39/0.57 (step t2.t24 (cl (= (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X))))) (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule bind)
% 0.39/0.57 (step t2.t25 (cl (= (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))))) :rule cong :premises (t2.t23 t2.t24))
% 0.39/0.57 (step t2.t26 (cl (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) :rule resolution :premises (t2.t22 t2.t25 a18))
% 0.39/0.57 (step t2.t27 (cl (not (= (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))))) (not (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y)))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t28 (cl (= tptp.fun_injective tptp.fun_injective)) :rule refl)
% 0.39/0.57 (anchor :step t2.t29 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t2.t29.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t29.t2 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))) :rule all_simplify)
% 0.39/0.57 (step t2.t29 (cl (= (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y)))) (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) :rule bind)
% 0.39/0.57 (step t2.t30 (cl (= (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))))) :rule cong :premises (t2.t28 t2.t29))
% 0.39/0.57 (step t2.t31 (cl (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y)))))) :rule resolution :premises (t2.t27 t2.t30 a17))
% 0.39/0.57 (step t2.t32 (cl (not (= (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))))) (not (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X))))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t33 (cl (= tptp.fun_inv_image tptp.fun_inv_image)) :rule refl)
% 0.39/0.57 (anchor :step t2.t34 :args ((F (-> $$unsorted $$unsorted)) (:= F F) (B (-> $$unsorted Bool)) (:= B B) (X $$unsorted) (:= X X)))
% 0.39/0.57 (step t2.t34.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t34.t2 (cl (= B B)) :rule refl)
% 0.39/0.57 (step t2.t34.t3 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t34.t4 (cl (= (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))) (not (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X)))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t34.t5 (cl (= (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X))))) (forall ((Y $$unsorted)) (or (not (@ B Y)) (not (= Y (@ F X))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t34.t6 (cl (= (forall ((Y $$unsorted)) (or (not (@ B Y)) (not (= Y (@ F X))))) (or (not (@ B (@ F X))) (not (= (@ F X) (@ F X)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t34.t7 (cl (= (not (@ B (@ F X))) (not (@ B (@ F X))))) :rule refl)
% 0.39/0.57 (step t2.t34.t8 (cl (= (= (@ F X) (@ F X)) true)) :rule all_simplify)
% 0.39/0.57 (step t2.t34.t9 (cl (= (not (= (@ F X) (@ F X))) (not true))) :rule cong :premises (t2.t34.t8))
% 0.39/0.57 (step t2.t34.t10 (cl (= (not true) false)) :rule all_simplify)
% 0.39/0.57 (step t2.t34.t11 (cl (= (not (= (@ F X) (@ F X))) false)) :rule trans :premises (t2.t34.t9 t2.t34.t10))
% 0.39/0.57 (step t2.t34.t12 (cl (= (or (not (@ B (@ F X))) (not (= (@ F X) (@ F X)))) (or (not (@ B (@ F X))) false))) :rule cong :premises (t2.t34.t7 t2.t34.t11))
% 0.39/0.57 (step t2.t34.t13 (cl (= (or (not (@ B (@ F X))) false) (not (@ B (@ F X))))) :rule all_simplify)
% 0.39/0.57 (step t2.t34.t14 (cl (= (or (not (@ B (@ F X))) (not (= (@ F X) (@ F X)))) (not (@ B (@ F X))))) :rule trans :premises (t2.t34.t12 t2.t34.t13))
% 0.39/0.57 (step t2.t34.t15 (cl (= (forall ((Y $$unsorted)) (or (not (@ B Y)) (not (= Y (@ F X))))) (not (@ B (@ F X))))) :rule trans :premises (t2.t34.t6 t2.t34.t14))
% 0.39/0.57 (step t2.t34.t16 (cl (= (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X))))) (not (@ B (@ F X))))) :rule trans :premises (t2.t34.t5 t2.t34.t15))
% 0.39/0.57 (step t2.t34.t17 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X)))))) (not (not (@ B (@ F X)))))) :rule cong :premises (t2.t34.t16))
% 0.39/0.57 (step t2.t34.t18 (cl (= (not (not (@ B (@ F X)))) (@ B (@ F X)))) :rule all_simplify)
% 0.39/0.57 (step t2.t34.t19 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ B Y) (= Y (@ F X)))))) (@ B (@ F X)))) :rule trans :premises (t2.t34.t17 t2.t34.t18))
% 0.39/0.57 (step t2.t34.t20 (cl (= (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))) (@ B (@ F X)))) :rule trans :premises (t2.t34.t4 t2.t34.t19))
% 0.39/0.57 (step t2.t34 (cl (= (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X))))) (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule bind)
% 0.39/0.57 (step t2.t35 (cl (= (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))))) :rule cong :premises (t2.t33 t2.t34))
% 0.39/0.57 (step t2.t36 (cl (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule resolution :premises (t2.t32 t2.t35 a16))
% 0.39/0.57 (step t2.t37 (cl (not (= (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))))) (not (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X))))))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t38 (cl (= tptp.fun_image tptp.fun_image)) :rule refl)
% 0.39/0.57 (anchor :step t2.t39 :args ((F (-> $$unsorted $$unsorted)) (:= F F) (A (-> $$unsorted Bool)) (:= A A) (Y $$unsorted) (:= Y Y)))
% 0.39/0.57 (step t2.t39.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t39.t2 (cl (= A A)) :rule refl)
% 0.39/0.57 (step t2.t39.t3 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t39.t4 (cl (= (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))) (not (forall ((X $$unsorted)) (not (and (@ A X) (= Y (@ F X)))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t39.t5 (cl (= (forall ((X $$unsorted)) (not (and (@ A X) (= Y (@ F X))))) (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t39.t6 (cl (= (not (forall ((X $$unsorted)) (not (and (@ A X) (= Y (@ F X)))))) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) :rule cong :premises (t2.t39.t5))
% 0.39/0.57 (step t2.t39.t7 (cl (= (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) :rule trans :premises (t2.t39.t4 t2.t39.t6))
% 0.39/0.57 (step t2.t39 (cl (= (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X))))) (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) :rule bind)
% 0.39/0.57 (step t2.t40 (cl (= (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))))) :rule cong :premises (t2.t38 t2.t39))
% 0.39/0.57 (step t2.t41 (cl (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X))))))))) :rule resolution :premises (t2.t37 t2.t40 a14))
% 0.39/0.57 (step t2.t42 (cl (not (= (= tptp.misses (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t43 (cl (= tptp.misses tptp.misses)) :rule refl)
% 0.39/0.57 (anchor :step t2.t44 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t44.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t44.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t44.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t44.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t44.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t44.t4))
% 0.39/0.57 (step t2.t44.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t44.t3 t2.t44.t5))
% 0.39/0.57 (step t2.t44.t7 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t44.t6))
% 0.39/0.57 (step t2.t44.t8 (cl (= (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t44.t9 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule trans :premises (t2.t44.t7 t2.t44.t8))
% 0.39/0.57 (step t2.t44 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule bind)
% 0.39/0.57 (step t2.t45 (cl (= (= tptp.misses (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t43 t2.t44))
% 0.39/0.57 (step t2.t46 (cl (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule resolution :premises (t2.t42 t2.t45 a13))
% 0.39/0.57 (step t2.t47 (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)
% 0.39/0.57 (step t2.t48 (cl (= tptp.meets tptp.meets)) :rule refl)
% 0.39/0.57 (anchor :step t2.t49 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t49.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t49.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t49.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.39/0.57 (step t2.t49.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.39/0.57 (step t2.t49.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.t49.t4))
% 0.39/0.57 (step t2.t49.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.t49.t3 t2.t49.t5))
% 0.39/0.57 (step t2.t49 (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)
% 0.39/0.57 (step t2.t50 (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.t48 t2.t49))
% 0.39/0.57 (step t2.t51 (cl (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule resolution :premises (t2.t47 t2.t50 a12))
% 0.39/0.57 (step t2.t52 (cl (not (= (= tptp.subset (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t53 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.39/0.57 (anchor :step t2.t54 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t54.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t54.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t54.t3 (cl (= (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) :rule all_simplify)
% 0.39/0.57 (step t2.t54 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule bind)
% 0.39/0.57 (step t2.t55 (cl (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) :rule cong :premises (t2.t53 t2.t54))
% 0.39/0.57 (step t2.t56 (cl (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule resolution :premises (t2.t52 t2.t55 a11))
% 0.39/0.57 (step t2.t57 (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_1029 $$unsorted)) false) (lambda ((U $$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_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t58 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.39/0.57 (anchor :step t2.t59 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t59.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t59.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t59.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 $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$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 $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$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)
% 0.39/0.57 (step t2.t59.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)
% 0.39/0.57 (step t2.t59.t5 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.39/0.57 (anchor :step t2.t59.t6 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t59.t6.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t59.t6.t2 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t59.t6.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t59.t6 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.39/0.57 (step t2.t59.t7 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t59.t5 t2.t59.t6))
% 0.39/0.57 (step t2.t59.t8 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t59.t4 t2.t59.t7 a4))
% 0.39/0.57 (step t2.t59.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)
% 0.39/0.57 (step t2.t59.t10 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.39/0.57 (anchor :step t2.t59.t11 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t59.t11.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t59.t11.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t59.t11.t3 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t59.t11.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t59.t11.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.39/0.57 (step t2.t59.t11.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t59.t11.t4 t2.t59.t11.t5))
% 0.39/0.57 (step t2.t59.t11 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.39/0.57 (step t2.t59.t12 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t59.t10 t2.t59.t11))
% 0.39/0.57 (step t2.t59.t13 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t59.t9 t2.t59.t12 a3))
% 0.39/0.57 (step t2.t59.t14 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t59.t15 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.39/0.57 (step t2.t59.t16 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule all_simplify)
% 0.39/0.57 (step t2.t59.t17 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) :rule cong :premises (t2.t59.t15 t2.t59.t16))
% 0.39/0.57 (step t2.t59.t18 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule resolution :premises (t2.t59.t14 t2.t59.t17 a2))
% 0.39/0.57 (step t2.t59.t19 (cl (and (= tptp.complement (lambda ((X (-> $$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_1029 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t59.t3 a9 a8 a7 a6 a5 t2.t59.t8 t2.t59.t13 t2.t59.t18 a1 a0))
% 0.39/0.57 (step t2.t59.t20 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule and :premises (t2.t59.t19))
% 0.39/0.57 (step t2.t59.t21 (cl (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t2.t59.t19))
% 0.39/0.57 (step t2.t59.t22 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t59.t23 (cl (= (@ tptp.intersection X) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X))) :rule cong :premises (t2.t59.t21 t2.t59.t22))
% 0.39/0.57 (step t2.t59.t24 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t59.t25 (cl (= (@ (@ tptp.intersection X) Y) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) :rule cong :premises (t2.t59.t23 t2.t59.t24))
% 0.39/0.57 (step t2.t59.t26 (cl (= (= tptp.emptyset (@ (@ tptp.intersection X) Y)) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) :rule cong :premises (t2.t59.t20 t2.t59.t25))
% 0.39/0.57 (step t2.t59 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))))) :rule bind)
% 0.39/0.57 (step t2.t60 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))))) :rule cong :premises (t2.t58 t2.t59))
% 0.39/0.57 (step t2.t61 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.39/0.57 (anchor :step t2.t62 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t62.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t62.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t62.t3 (cl (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule refl)
% 0.39/0.57 (step t2.t62.t4 (cl (= (@ (lambda ((X (-> $$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)
% 0.39/0.57 (step t2.t62.t5 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t62.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y))) :rule cong :premises (t2.t62.t4 t2.t62.t5))
% 0.39/0.57 (step t2.t62.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.39/0.57 (step t2.t62.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.t62.t6 t2.t62.t7))
% 0.39/0.57 (step t2.t62.t9 (cl (= (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) :rule cong :premises (t2.t62.t3 t2.t62.t8))
% 0.39/0.57 (step t2.t62 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule bind)
% 0.39/0.57 (step t2.t63 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((X (-> $$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_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule cong :premises (t2.t61 t2.t62))
% 0.39/0.57 (step t2.t64 (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_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule trans :premises (t2.t60 t2.t63))
% 0.39/0.57 (step t2.t65 (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)
% 0.39/0.57 (anchor :step t2.t66 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.39/0.57 (step t2.t66.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t66.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t66.t3 (cl (= (= (@ (@ tptp.intersection X) Y) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) :rule all_simplify)
% 0.39/0.57 (step t2.t66 (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)
% 0.39/0.57 (step t2.t67 (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.t61 t2.t66))
% 0.39/0.57 (step t2.t68 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule resolution :premises (t2.t65 t2.t67 a10))
% 0.39/0.57 (step t2.t69 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule resolution :premises (t2.t57 t2.t64 t2.t68))
% 0.39/0.57 (step t2.t70 (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)
% 0.39/0.57 (step t2.t71 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.39/0.57 (anchor :step t2.t72 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t72.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t72.t2 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t72.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t72 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.39/0.57 (step t2.t73 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t71 t2.t72))
% 0.39/0.57 (step t2.t74 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t70 t2.t73 a4))
% 0.39/0.57 (step t2.t75 (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)
% 0.39/0.57 (step t2.t76 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.39/0.57 (anchor :step t2.t77 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.39/0.57 (step t2.t77.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t2.t77.t2 (cl (= Y Y)) :rule refl)
% 0.39/0.57 (step t2.t77.t3 (cl (= U U)) :rule refl)
% 0.39/0.57 (step t2.t77.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.39/0.57 (step t2.t77.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.39/0.57 (step t2.t77.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t77.t4 t2.t77.t5))
% 0.39/0.57 (step t2.t77 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.39/0.57 (step t2.t78 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t76 t2.t77))
% 0.39/0.57 (step t2.t79 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t75 t2.t78 a3))
% 0.39/0.57 (step t2.t80 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule equiv_pos2)
% 0.39/0.57 (step t2.t81 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.39/0.57 (step t2.t82 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule all_simplify)
% 0.39/0.57 (step t2.t83 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) :rule cong :premises (t2.t81 t2.t82))
% 0.39/0.57 (step t2.t84 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule resolution :premises (t2.t80 t2.t83 a2))
% 0.39/0.57 (step t2.t85 (cl (and (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F X)) (@ F Y)))))) (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ SMALLER X) Y)) (@ (@ SMALLER (@ F Y)) (@ F X)))))) (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))))) (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X)))))))) (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ F X) (@ F Y))) (= X Y))))) (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X)))) (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X)))) (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (not (forall ((X $$unsorted)) (or (not (@ A X)) (not (= Y (@ F X)))))))) (= tptp.misses (lambda ((X (-> $$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_1029 $$unsorted)) false) (lambda ((U $$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 $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$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.t2 t2.t7 t2.t12 t2.t21 t2.t26 t2.t31 t2.t36 a15 t2.t41 t2.t46 t2.t51 t2.t56 t2.t69 a9 a8 a7 a6 a5 t2.t74 t2.t79 t2.t84 a1 a0))
% 0.39/0.57 (step t2.t86 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule and :premises (t2.t85))
% 0.39/0.57 (step t2.t87 (cl (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule and :premises (t2.t85))
% 0.39/0.57 (step t2.t88 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t2.t89 (cl (= (@ tptp.fun_inv_image F) (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F))) :rule cong :premises (t2.t87 t2.t88))
% 0.39/0.57 (step t2.t90 (cl (= (@ (@ tptp.fun_inv_image F) tptp.emptyset) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) :rule cong :premises (t2.t89 t2.t86))
% 0.39/0.57 (step t2.t91 (cl (= (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset)) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))))) :rule cong :premises (t2.t86 t2.t90))
% 0.39/0.57 (step t2 (cl (= (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset))) (forall ((F (-> $$unsorted $$unsorted))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))))) :rule bind)
% 0.39/0.57 (step t3 (cl (= (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset)))) (not (forall ((F (-> $$unsorted $$unsorted))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))))))) :rule cong :premises (t2))
% 0.39/0.57 (anchor :step t4 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t4.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t4.t2 (cl (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule refl)
% 0.39/0.57 (step t4.t3 (cl (= (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))))) :rule all_simplify)
% 0.39/0.57 (step t4.t4 (cl (= (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)) (@ (lambda ((B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) :rule cong :premises (t4.t3 t4.t2))
% 0.39/0.57 (step t4.t5 (cl (= (@ (lambda ((B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)) (lambda ((X $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ F X))))) :rule all_simplify)
% 0.39/0.57 (anchor :step t4.t6 :args ((X $$unsorted) (:= X X)))
% 0.39/0.57 (step t4.t6.t1 (cl (= X X)) :rule refl)
% 0.39/0.57 (step t4.t6.t2 (cl (= (@ (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ F X)) false)) :rule all_simplify)
% 0.39/0.57 (step t4.t6 (cl (= (lambda ((X $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ F X))) (lambda ((X $$unsorted)) false))) :rule bind)
% 0.39/0.57 (step t4.t7 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule all_simplify)
% 0.39/0.57 (step t4.t8 (cl (= (lambda ((X $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ F X))) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule trans :premises (t4.t6 t4.t7))
% 0.39/0.57 (step t4.t9 (cl (= (@ (lambda ((B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule trans :premises (t4.t5 t4.t8))
% 0.39/0.57 (step t4.t10 (cl (= (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) :rule trans :premises (t4.t4 t4.t9))
% 0.39/0.57 (step t4.t11 (cl (= (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) :rule cong :premises (t4.t2 t4.t10))
% 0.39/0.57 (step t4.t12 (cl (= (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)) true)) :rule all_simplify)
% 0.39/0.57 (step t4.t13 (cl (= (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))) true)) :rule trans :premises (t4.t11 t4.t12))
% 0.39/0.57 (step t4 (cl (= (forall ((F (-> $$unsorted $$unsorted))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) (forall ((F (-> $$unsorted $$unsorted))) true))) :rule bind)
% 0.39/0.57 (step t5 (cl (= (forall ((F (-> $$unsorted $$unsorted))) true) true)) :rule all_simplify)
% 0.39/0.57 (step t6 (cl (= (forall ((F (-> $$unsorted $$unsorted))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false)))) true)) :rule trans :premises (t4 t5))
% 0.39/0.57 (step t7 (cl (= (not (forall ((F (-> $$unsorted $$unsorted))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))))) (not true))) :rule cong :premises (t6))
% 0.39/0.57 (step t8 (cl (= (not true) false)) :rule all_simplify)
% 0.39/0.57 (step t9 (cl (= (not (forall ((F (-> $$unsorted $$unsorted))) (= (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false) (@ (@ (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (@ B (@ F X))) F) (lambda ((BOUND_VARIABLE_1029 $$unsorted)) false))))) false)) :rule trans :premises (t7 t8))
% 0.39/0.57 (step t10 (cl (= (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset)))) false)) :rule trans :premises (t3 t9))
% 0.39/0.57 (step t11 (cl (not (= (not (forall ((F (-> $$unsorted $$unsorted))) (= (@ (@ tptp.fun_inv_image F) tptp.emptyset) tptp.emptyset))) (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset)))))) (not (not (forall ((F (-> $$unsorted $$unsorted))) (= (@ (@ tptp.fun_inv_image F) tptp.emptyset) tptp.emptyset)))) (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset))))) :rule equiv_pos2)
% 0.39/0.57 (anchor :step t12 :args ((F (-> $$unsorted $$unsorted)) (:= F F)))
% 0.39/0.57 (step t12.t1 (cl (= F F)) :rule refl)
% 0.39/0.57 (step t12.t2 (cl (= (= (@ (@ tptp.fun_inv_image F) tptp.emptyset) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset)))) :rule all_simplify)
% 0.39/0.57 (step t12 (cl (= (forall ((F (-> $$unsorted $$unsorted))) (= (@ (@ tptp.fun_inv_image F) tptp.emptyset) tptp.emptyset)) (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset))))) :rule bind)
% 0.39/0.57 (step t13 (cl (= (not (forall ((F (-> $$unsorted $$unsorted))) (= (@ (@ tptp.fun_inv_image F) tptp.emptyset) tptp.emptyset))) (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset)))))) :rule cong :premises (t12))
% 0.39/0.57 (step t14 (cl (not (forall ((F (-> $$unsorted $$unsorted))) (= tptp.emptyset (@ (@ tptp.fun_inv_image F) tptp.emptyset))))) :rule resolution :premises (t11 t13 a22))
% 0.39/0.57 (step t15 (cl false) :rule resolution :premises (t1 t10 t14))
% 0.39/0.57 (step t16 (cl (not false)) :rule false)
% 0.39/0.57 (step t17 (cl) :rule resolution :premises (t15 t16))
% 0.39/0.57
% 0.39/0.57 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.zWihtAk3HO/cvc5---1.0.5_843.smt2
% 0.39/0.57 % cvc5---1.0.5 exiting
% 0.39/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------