TSTP Solution File: SET086^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET086^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n019.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 17:44:06 EDT 2024
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET086^1 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue May 28 08:15:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.54 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.wupSJ2gB5F/cvc5---1.0.5_32096.smt2
% 0.21/0.54 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.wupSJ2gB5F/cvc5---1.0.5_32096.smt2
% 0.21/0.54 (assume a0 (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.21/0.54 (assume a1 (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.21/0.54 (assume a2 (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.21/0.54 (assume a3 (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.21/0.54 (assume a4 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.21/0.54 (assume a5 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.21/0.54 (assume a6 (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (and (@ X U) (not (@ Y U))) (and (not (@ X U)) (@ Y U))))))
% 0.21/0.54 (assume a7 (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.21/0.54 (assume a8 (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))
% 0.21/0.54 (assume a9 (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.21/0.54 (assume a10 (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))
% 0.21/0.54 (assume a11 (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))
% 0.21/0.54 (assume a12 (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))
% 0.21/0.54 (assume a13 (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))
% 0.21/0.54 (assume a14 (not (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ tptp.singleton X) Y)))))
% 0.21/0.54 (assume a15 true)
% 0.21/0.54 (step t1 (cl (not (= (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y)))))) false)) (not (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y))))))) false) :rule equiv_pos2)
% 0.21/0.54 (anchor :step t2 :args ((X $$unsorted) (:= X X)))
% 0.21/0.54 (step t2.t1 (cl (= X X)) :rule refl)
% 0.21/0.54 (anchor :step t2.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.21/0.54 (step t2.t2.t1 (cl (= Y Y)) :rule refl)
% 0.21/0.54 (step t2.t2.t2 (cl (and (= tptp.misses (lambda ((X (-> $$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_1375 $$unsorted)) false) (lambda ((U $$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 $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$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.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 (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1375 $$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_1375 $$unsorted)) false))) (not (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X)))) (not (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule and_neg)
% 0.21/0.54 (step t2.t2.t3 (cl (not (= (= tptp.misses (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule equiv_pos2)
% 0.21/0.54 (step t2.t2.t4 (cl (= tptp.misses tptp.misses)) :rule refl)
% 0.21/0.54 (anchor :step t2.t2.t5 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.21/0.54 (step t2.t2.t5.t1 (cl (= X X)) :rule refl)
% 0.21/0.54 (step t2.t2.t5.t2 (cl (= Y Y)) :rule refl)
% 0.21/0.54 (step t2.t2.t5.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.21/0.54 (step t2.t2.t5.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.21/0.54 (step t2.t2.t5.t5 (cl (= (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule cong :premises (t2.t2.t5.t4))
% 0.21/0.54 (step t2.t2.t5.t6 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule trans :premises (t2.t2.t5.t3 t2.t2.t5.t5))
% 0.37/0.54 (step t2.t2.t5.t7 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t2.t5.t6))
% 0.37/0.54 (step t2.t2.t5.t8 (cl (= (not (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t5.t9 (cl (= (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule trans :premises (t2.t2.t5.t7 t2.t2.t5.t8))
% 0.37/0.54 (step t2.t2.t5 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule bind)
% 0.37/0.54 (step t2.t2.t6 (cl (= (= tptp.misses (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule cong :premises (t2.t2.t4 t2.t2.t5))
% 0.37/0.54 (step t2.t2.t7 (cl (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U))))))) :rule resolution :premises (t2.t2.t3 t2.t2.t6 a13))
% 0.37/0.54 (step t2.t2.t8 (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)
% 0.37/0.54 (step t2.t2.t9 (cl (= tptp.meets tptp.meets)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t10 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.37/0.54 (step t2.t2.t10.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t10.t2 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t10.t3 (cl (= (exists ((U $$unsorted)) (and (@ X U) (@ Y U))) (not (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U))))))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t10.t4 (cl (= (forall ((U $$unsorted)) (not (and (@ X U) (@ Y U)))) (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t10.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.t2.t10.t4))
% 0.37/0.54 (step t2.t2.t10.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.t2.t10.t3 t2.t2.t10.t5))
% 0.37/0.54 (step t2.t2.t10 (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)
% 0.37/0.54 (step t2.t2.t11 (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.t2.t9 t2.t2.t10))
% 0.37/0.54 (step t2.t2.t12 (cl (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (forall ((U $$unsorted)) (or (not (@ X U)) (not (@ Y U)))))))) :rule resolution :premises (t2.t2.t8 t2.t2.t11 a12))
% 0.37/0.54 (step t2.t2.t13 (cl (not (= (= tptp.subset (lambda ((X (-> $$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 $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule equiv_pos2)
% 0.37/0.54 (step t2.t2.t14 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t15 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.37/0.54 (step t2.t2.t15.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t15.t2 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t15.t3 (cl (= (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t15 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U)))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule bind)
% 0.37/0.54 (step t2.t2.t16 (cl (= (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))) (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U))))))) :rule cong :premises (t2.t2.t14 t2.t2.t15))
% 0.37/0.54 (step t2.t2.t17 (cl (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (or (not (@ X U)) (@ Y U)))))) :rule resolution :premises (t2.t2.t13 t2.t2.t16 a11))
% 0.37/0.54 (step t2.t2.t18 (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_1375 $$unsorted)) false) (lambda ((U $$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_1375 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule equiv_pos2)
% 0.37/0.54 (step t2.t2.t19 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t20 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.37/0.54 (step t2.t2.t20.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t2 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.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 $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$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 $$unsorted)) (or (= X U) (= Y U))))) (not (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$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)
% 0.37/0.54 (step t2.t2.t20.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)
% 0.37/0.54 (step t2.t2.t20.t5 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t20.t6 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.37/0.54 (step t2.t2.t20.t6.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t6.t2 (cl (= U U)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t6.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t20.t6 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.37/0.54 (step t2.t2.t20.t7 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t2.t20.t5 t2.t2.t20.t6))
% 0.37/0.54 (step t2.t2.t20.t8 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t2.t20.t4 t2.t2.t20.t7 a4))
% 0.37/0.54 (step t2.t2.t20.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)
% 0.37/0.54 (step t2.t2.t20.t10 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t20.t11 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.37/0.54 (step t2.t2.t20.t11.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t11.t2 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t11.t3 (cl (= U U)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t11.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t20.t11.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t20.t11.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t2.t20.t11.t4 t2.t2.t20.t11.t5))
% 0.37/0.54 (step t2.t2.t20.t11 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.37/0.54 (step t2.t2.t20.t12 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t2.t20.t10 t2.t2.t20.t11))
% 0.37/0.54 (step t2.t2.t20.t13 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t2.t20.t9 t2.t2.t20.t12 a3))
% 0.37/0.54 (step t2.t2.t20.t14 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule equiv_pos2)
% 0.37/0.54 (step t2.t2.t20.t15 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t16 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t20.t17 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false)))) :rule cong :premises (t2.t2.t20.t15 t2.t2.t20.t16))
% 0.37/0.54 (step t2.t2.t20.t18 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule resolution :premises (t2.t2.t20.t14 t2.t2.t20.t17 a2))
% 0.37/0.54 (step t2.t2.t20.t19 (cl (and (= tptp.complement (lambda ((X (-> $$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_1375 $$unsorted)) false)) (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))) (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) :rule resolution :premises (t2.t2.t20.t3 a9 a8 a7 a6 a5 t2.t2.t20.t8 t2.t2.t20.t13 t2.t2.t20.t18 a1 a0))
% 0.37/0.54 (step t2.t2.t20.t20 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule and :premises (t2.t2.t20.t19))
% 0.37/0.54 (step t2.t2.t20.t21 (cl (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t2.t2.t20.t19))
% 0.37/0.54 (step t2.t2.t20.t22 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t23 (cl (= (@ tptp.intersection X) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X))) :rule cong :premises (t2.t2.t20.t21 t2.t2.t20.t22))
% 0.37/0.54 (step t2.t2.t20.t24 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t20.t25 (cl (= (@ (@ tptp.intersection X) Y) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) :rule cong :premises (t2.t2.t20.t23 t2.t2.t20.t24))
% 0.37/0.54 (step t2.t2.t20.t26 (cl (= (= tptp.emptyset (@ (@ tptp.intersection X) Y)) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))) :rule cong :premises (t2.t2.t20.t20 t2.t2.t20.t25))
% 0.37/0.54 (step t2.t2.t20 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))))) :rule bind)
% 0.37/0.54 (step t2.t2.t21 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)))))) :rule cong :premises (t2.t2.t19 t2.t2.t20))
% 0.37/0.54 (step t2.t2.t22 (cl (= tptp.disjoint tptp.disjoint)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t23 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.37/0.54 (step t2.t2.t23.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t23.t2 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t23.t3 (cl (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule refl)
% 0.37/0.54 (step t2.t2.t23.t4 (cl (= (@ (lambda ((X (-> $$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)
% 0.37/0.54 (step t2.t2.t23.t5 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t23.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y))) :rule cong :premises (t2.t2.t23.t4 t2.t2.t23.t5))
% 0.37/0.54 (step t2.t2.t23.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) Y) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t23.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.t2.t23.t6 t2.t2.t23.t7))
% 0.37/0.54 (step t2.t2.t23.t9 (cl (= (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y)) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))) :rule cong :premises (t2.t2.t23.t3 t2.t2.t23.t8))
% 0.37/0.54 (step t2.t2.t23 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) X) Y))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule bind)
% 0.37/0.54 (step t2.t2.t24 (cl (= (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (@ (@ (lambda ((X (-> $$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_1375 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule cong :premises (t2.t2.t22 t2.t2.t23))
% 0.37/0.54 (step t2.t2.t25 (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_1375 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) :rule trans :premises (t2.t2.t21 t2.t2.t24))
% 0.37/0.54 (step t2.t2.t26 (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)
% 0.37/0.54 (anchor :step t2.t2.t27 :args ((X (-> $$unsorted Bool)) (:= X X) (Y (-> $$unsorted Bool)) (:= Y Y)))
% 0.37/0.54 (step t2.t2.t27.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t27.t2 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t27.t3 (cl (= (= (@ (@ tptp.intersection X) Y) tptp.emptyset) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t27 (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)
% 0.37/0.54 (step t2.t2.t28 (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.t2.t22 t2.t2.t27))
% 0.37/0.54 (step t2.t2.t29 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y))))) :rule resolution :premises (t2.t2.t26 t2.t2.t28 a10))
% 0.37/0.54 (step t2.t2.t30 (cl (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false) (lambda ((U $$unsorted)) (and (@ X U) (@ Y U))))))) :rule resolution :premises (t2.t2.t18 t2.t2.t25 t2.t2.t29))
% 0.37/0.54 (step t2.t2.t31 (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)
% 0.37/0.54 (step t2.t2.t32 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t33 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U)))
% 0.37/0.54 (step t2.t2.t33.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t33.t2 (cl (= U U)) :rule refl)
% 0.37/0.54 (step t2.t2.t33.t3 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t33 (cl (= (lambda ((X $$unsorted) (U $$unsorted)) (= U X)) (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule bind)
% 0.37/0.54 (step t2.t2.t34 (cl (= (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))) (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U))))) :rule cong :premises (t2.t2.t32 t2.t2.t33))
% 0.37/0.54 (step t2.t2.t35 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule resolution :premises (t2.t2.t31 t2.t2.t34 a4))
% 0.37/0.54 (step t2.t2.t36 (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)
% 0.37/0.54 (step t2.t2.t37 (cl (= tptp.unord_pair tptp.unord_pair)) :rule refl)
% 0.37/0.54 (anchor :step t2.t2.t38 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.37/0.54 (step t2.t2.t38.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t38.t2 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t38.t3 (cl (= U U)) :rule refl)
% 0.37/0.54 (step t2.t2.t38.t4 (cl (= (= U X) (= X U))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t38.t5 (cl (= (= U Y) (= Y U))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t38.t6 (cl (= (or (= U X) (= U Y)) (or (= X U) (= Y U)))) :rule cong :premises (t2.t2.t38.t4 t2.t2.t38.t5))
% 0.37/0.54 (step t2.t2.t38 (cl (= (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y))) (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule bind)
% 0.37/0.54 (step t2.t2.t39 (cl (= (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))) (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U)))))) :rule cong :premises (t2.t2.t37 t2.t2.t38))
% 0.37/0.54 (step t2.t2.t40 (cl (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= X U) (= Y U))))) :rule resolution :premises (t2.t2.t36 t2.t2.t39 a3))
% 0.37/0.54 (step t2.t2.t41 (cl (not (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false)))) (not (= tptp.emptyset (lambda ((X $$unsorted)) false))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule equiv_pos2)
% 0.37/0.54 (step t2.t2.t42 (cl (= tptp.emptyset tptp.emptyset)) :rule refl)
% 0.37/0.54 (step t2.t2.t43 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule all_simplify)
% 0.37/0.54 (step t2.t2.t44 (cl (= (= tptp.emptyset (lambda ((X $$unsorted)) false)) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false)))) :rule cong :premises (t2.t2.t42 t2.t2.t43))
% 0.37/0.54 (step t2.t2.t45 (cl (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$unsorted)) false))) :rule resolution :premises (t2.t2.t41 t2.t2.t44 a2))
% 0.37/0.54 (step t2.t2.t46 (cl (and (= tptp.misses (lambda ((X (-> $$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_1375 $$unsorted)) false) (lambda ((U $$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 $$unsorted)) (or (= X U) (= Y U)))) (= tptp.emptyset (lambda ((BOUND_VARIABLE_1375 $$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 t2.t2.t7 t2.t2.t12 t2.t2.t17 t2.t2.t30 a9 a8 a7 a6 a5 t2.t2.t35 t2.t2.t40 t2.t2.t45 a1 a0))
% 0.37/0.54 (step t2.t2.t47 (cl (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= X U)))) :rule and :premises (t2.t2.t46))
% 0.37/0.54 (step t2.t2.t48 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t2.t2.t49 (cl (= (@ tptp.singleton X) (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X))) :rule cong :premises (t2.t2.t47 t2.t2.t48))
% 0.37/0.54 (step t2.t2.t50 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t2.t2.t51 (cl (= (@ (@ tptp.singleton X) Y) (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y))) :rule cong :premises (t2.t2.t49 t2.t2.t50))
% 0.37/0.54 (step t2.t2.t52 (cl (= (not (@ (@ tptp.singleton X) Y)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)))) :rule cong :premises (t2.t2.t51))
% 0.37/0.54 (step t2.t2 (cl (= (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y))) (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y))))) :rule bind)
% 0.37/0.54 (step t2.t3 (cl (= (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y)))) (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)))))) :rule cong :premises (t2.t2))
% 0.37/0.54 (step t2 (cl (= (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y))))) (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y))))))) :rule bind)
% 0.37/0.54 (step t3 (cl (= (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y)))))) (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)))))))) :rule cong :premises (t2))
% 0.37/0.54 (anchor :step t4 :args ((X $$unsorted) (:= X X)))
% 0.37/0.54 (step t4.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (anchor :step t4.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.37/0.54 (step t4.t2.t1 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t4.t2.t2 (cl (= (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) (lambda ((U $$unsorted)) (= X U)))) :rule all_simplify)
% 0.37/0.54 (anchor :step t4.t2.t3 :args ((U $$unsorted) (:= U U)))
% 0.37/0.54 (step t4.t2.t3.t1 (cl (= U U)) :rule refl)
% 0.37/0.54 (step t4.t2.t3.t2 (cl (= (= X U) (= U X))) :rule all_simplify)
% 0.37/0.54 (step t4.t2.t3 (cl (= (lambda ((U $$unsorted)) (= X U)) (lambda ((U $$unsorted)) (= U X)))) :rule bind)
% 0.37/0.54 (step t4.t2.t4 (cl (= (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) (lambda ((U $$unsorted)) (= U X)))) :rule trans :premises (t4.t2.t2 t4.t2.t3))
% 0.37/0.54 (step t4.t2.t5 (cl (= Y Y)) :rule refl)
% 0.37/0.54 (step t4.t2.t6 (cl (= (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y) (@ (lambda ((U $$unsorted)) (= U X)) Y))) :rule cong :premises (t4.t2.t4 t4.t2.t5))
% 0.37/0.54 (step t4.t2.t7 (cl (= (@ (lambda ((U $$unsorted)) (= U X)) Y) (= Y X))) :rule all_simplify)
% 0.37/0.54 (step t4.t2.t8 (cl (= (= Y X) (= X Y))) :rule all_simplify)
% 0.37/0.54 (step t4.t2.t9 (cl (= (@ (lambda ((U $$unsorted)) (= U X)) Y) (= X Y))) :rule trans :premises (t4.t2.t7 t4.t2.t8))
% 0.37/0.54 (step t4.t2.t10 (cl (= (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y) (= X Y))) :rule trans :premises (t4.t2.t6 t4.t2.t9))
% 0.37/0.54 (step t4.t2.t11 (cl (= (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)) (not (= X Y)))) :rule cong :premises (t4.t2.t10))
% 0.37/0.54 (step t4.t2 (cl (= (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y))) (forall ((Y $$unsorted)) (not (= X Y))))) :rule bind)
% 0.37/0.54 (step t4.t3 (cl (= (forall ((Y $$unsorted)) (not (= X Y))) (not (= X X)))) :rule all_simplify)
% 0.37/0.54 (step t4.t4 (cl (= (= X X) true)) :rule all_simplify)
% 0.37/0.54 (step t4.t5 (cl (= (not (= X X)) (not true))) :rule cong :premises (t4.t4))
% 0.37/0.54 (step t4.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.37/0.54 (step t4.t7 (cl (= (not (= X X)) false)) :rule trans :premises (t4.t5 t4.t6))
% 0.37/0.54 (step t4.t8 (cl (= (forall ((Y $$unsorted)) (not (= X Y))) false)) :rule trans :premises (t4.t3 t4.t7))
% 0.37/0.54 (step t4.t9 (cl (= (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y))) false)) :rule trans :premises (t4.t2 t4.t8))
% 0.37/0.54 (step t4.t10 (cl (= (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)))) (not false))) :rule cong :premises (t4.t9))
% 0.37/0.54 (step t4.t11 (cl (= (not false) true)) :rule all_simplify)
% 0.37/0.54 (step t4.t12 (cl (= (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)))) true)) :rule trans :premises (t4.t10 t4.t11))
% 0.37/0.54 (step t4 (cl (= (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y))))) (forall ((X $$unsorted)) true))) :rule bind)
% 0.37/0.54 (step t5 (cl (= (forall ((X $$unsorted)) true) true)) :rule all_simplify)
% 0.37/0.54 (step t6 (cl (= (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y))))) true)) :rule trans :premises (t4 t5))
% 0.37/0.54 (step t7 (cl (= (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)))))) (not true))) :rule cong :premises (t6))
% 0.37/0.54 (step t8 (cl (= (not true) false)) :rule all_simplify)
% 0.37/0.54 (step t9 (cl (= (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ (lambda ((X $$unsorted) (U $$unsorted)) (= X U)) X) Y)))))) false)) :rule trans :premises (t7 t8))
% 0.37/0.54 (step t10 (cl (= (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y)))))) false)) :rule trans :premises (t3 t9))
% 0.37/0.54 (step t11 (cl (not (= (not (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ tptp.singleton X) Y)))) (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y)))))))) (not (not (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ tptp.singleton X) Y))))) (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y))))))) :rule equiv_pos2)
% 0.37/0.54 (anchor :step t12 :args ((X $$unsorted) (:= X X)))
% 0.37/0.54 (step t12.t1 (cl (= X X)) :rule refl)
% 0.37/0.54 (step t12.t2 (cl (= (exists ((Y $$unsorted)) (@ (@ tptp.singleton X) Y)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y)))))) :rule all_simplify)
% 0.37/0.54 (step t12 (cl (= (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ tptp.singleton X) Y))) (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y))))))) :rule bind)
% 0.37/0.54 (step t13 (cl (= (not (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ tptp.singleton X) Y)))) (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y)))))))) :rule cong :premises (t12))
% 0.37/0.54 (step t14 (cl (not (forall ((X $$unsorted)) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.singleton X) Y))))))) :rule resolution :premises (t11 t13 a14))
% 0.37/0.54 (step t15 (cl false) :rule resolution :premises (t1 t10 t14))
% 0.37/0.54 (step t16 (cl (not false)) :rule false)
% 0.37/0.54 (step t17 (cl) :rule resolution :premises (t15 t16))
% 0.37/0.54
% 0.37/0.54 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.wupSJ2gB5F/cvc5---1.0.5_32096.smt2
% 0.37/0.54 % cvc5---1.0.5 exiting
% 0.37/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------