TSTP Solution File: SEU561^2 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU561^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n004.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 17:54:07 EDT 2024
% Result : Theorem 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU561^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 27 08:41:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.53 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.SXDA5Gxbkz/cvc5---1.0.5_12144.smt2
% 0.22/0.53 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.SXDA5Gxbkz/cvc5---1.0.5_12144.smt2
% 0.22/0.53 (assume a0 (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))))
% 0.22/0.53 (assume a1 (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))))
% 0.22/0.53 (assume a2 (not (=> tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))))))
% 0.22/0.53 (assume a3 true)
% 0.22/0.53 (step t1 (cl (not (= (not (forall ((B $$unsorted)) (@ (@ tptp.subset B) B))) false)) (not (not (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)))) false) :rule equiv_pos2)
% 0.22/0.53 (anchor :step t2 :args ((B $$unsorted) (:= B B)))
% 0.22/0.53 (step t2.t1 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t2 (cl (and (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) (not (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B))))) (not (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))))) :rule and_neg)
% 0.22/0.53 (step t2.t3 (cl (not (= (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B)))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))))) (not (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B))))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B))))) :rule equiv_pos2)
% 0.22/0.53 (step t2.t4 (cl (= tptp.subsetI1 tptp.subsetI1)) :rule refl)
% 0.22/0.53 (anchor :step t2.t5 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 0.22/0.53 (step t2.t5.t1 (cl (= A A)) :rule refl)
% 0.22/0.53 (step t2.t5.t2 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t5.t3 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule refl)
% 0.22/0.53 (step t2.t5.t4 (cl (not (= (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))))) (not (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B)))))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule equiv_pos2)
% 0.22/0.53 (step t2.t5.t5 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.22/0.53 (anchor :step t2.t5.t6 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 0.22/0.53 (step t2.t5.t6.t1 (cl (= A A)) :rule refl)
% 0.22/0.53 (step t2.t5.t6.t2 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t5.t6.t3 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))) :rule all_simplify)
% 0.22/0.53 (step t2.t5.t6 (cl (= (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B)))) (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule bind)
% 0.22/0.53 (step t2.t5.t7 (cl (= (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))))) :rule cong :premises (t2.t5.t5 t2.t5.t6))
% 0.22/0.53 (step t2.t5.t8 (cl (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule resolution :premises (t2.t5.t4 t2.t5.t7 a0))
% 0.22/0.53 (step t2.t5.t9 (cl (= A A)) :rule refl)
% 0.22/0.53 (step t2.t5.t10 (cl (= (@ tptp.subset A) (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A))) :rule cong :premises (t2.t5.t8 t2.t5.t9))
% 0.22/0.53 (step t2.t5.t11 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t5.t12 (cl (= (@ (@ tptp.subset A) B) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B))) :rule cong :premises (t2.t5.t10 t2.t5.t11))
% 0.22/0.53 (step t2.t5.t13 (cl (= (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B)))) :rule cong :premises (t2.t5.t3 t2.t5.t12))
% 0.22/0.53 (step t2.t5 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B))))) :rule bind)
% 0.22/0.53 (step t2.t6 (cl (= (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B)))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B)))))) :rule cong :premises (t2.t4 t2.t5))
% 0.22/0.53 (step t2.t7 (cl (= tptp.subsetI1 tptp.subsetI1)) :rule refl)
% 0.22/0.53 (anchor :step t2.t8 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 0.22/0.53 (step t2.t8.t1 (cl (= A A)) :rule refl)
% 0.22/0.53 (step t2.t8.t2 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t8.t3 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule refl)
% 0.22/0.53 (step t2.t8.t4 (cl (= (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule all_simplify)
% 0.22/0.53 (step t2.t8.t5 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t8.t6 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B) (@ (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B))) :rule cong :premises (t2.t8.t4 t2.t8.t5))
% 0.22/0.53 (step t2.t8.t7 (cl (= (@ (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))) :rule all_simplify)
% 0.22/0.53 (step t2.t8.t8 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))) :rule trans :premises (t2.t8.t6 t2.t8.t7))
% 0.22/0.53 (step t2.t8.t9 (cl (= (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule cong :premises (t2.t8.t3 t2.t8.t8))
% 0.22/0.53 (step t2.t8 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))))) :rule bind)
% 0.22/0.53 (step t2.t9 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))) (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (or (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))))) :rule all_simplify)
% 0.22/0.53 (anchor :step t2.t10 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (BOUND_VARIABLE_669 $$unsorted) (:= BOUND_VARIABLE_669 BOUND_VARIABLE_669)))
% 0.22/0.53 (step t2.t10.t1 (cl (= A A)) :rule refl)
% 0.22/0.53 (step t2.t10.t2 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t10.t3 (cl (= BOUND_VARIABLE_669 BOUND_VARIABLE_669)) :rule refl)
% 0.22/0.53 (step t2.t10.t4 (cl (= (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (or (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B))) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))) :rule all_simplify)
% 0.22/0.53 (step t2.t10 (cl (= (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (or (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))) (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B))))) :rule bind)
% 0.22/0.53 (step t2.t11 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))) (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B))))) :rule trans :premises (t2.t9 t2.t10))
% 0.22/0.53 (step t2.t12 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B))) (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B))))) :rule trans :premises (t2.t8 t2.t11))
% 0.22/0.53 (step t2.t13 (cl (= (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) A) B)))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))))) :rule cong :premises (t2.t7 t2.t12))
% 0.22/0.53 (step t2.t14 (cl (= (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B)))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))))) :rule trans :premises (t2.t6 t2.t13))
% 0.22/0.53 (step t2.t15 (cl (not (= (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B)))))) (not (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B))))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B))))) :rule equiv_pos2)
% 0.22/0.53 (anchor :step t2.t16 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 0.22/0.53 (step t2.t16.t1 (cl (= A A)) :rule refl)
% 0.22/0.53 (step t2.t16.t2 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t16.t3 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))) :rule all_simplify)
% 0.22/0.53 (step t2.t16.t4 (cl (= (@ (@ tptp.subset A) B) (@ (@ tptp.subset A) B))) :rule refl)
% 0.22/0.53 (step t2.t16.t5 (cl (= (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)) (=> (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))) :rule cong :premises (t2.t16.t3 t2.t16.t4))
% 0.22/0.53 (step t2.t16 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B))))) :rule bind)
% 0.22/0.53 (step t2.t17 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B))))) :rule all_simplify)
% 0.22/0.53 (step t2.t18 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B))))) :rule trans :premises (t2.t16 t2.t17))
% 0.22/0.53 (step t2.t19 (cl (= (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (@ (@ tptp.subset A) B)))) (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B)))))) :rule cong :premises (t2.t7 t2.t18))
% 0.22/0.53 (step t2.t20 (cl (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (@ (@ tptp.subset A) B))))) :rule resolution :premises (t2.t15 t2.t19 a1))
% 0.22/0.53 (step t2.t21 (cl (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B))))) :rule resolution :premises (t2.t3 t2.t14 t2.t20))
% 0.22/0.53 (step t2.t22 (cl (not (= (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))))) (not (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B)))))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule equiv_pos2)
% 0.22/0.53 (step t2.t23 (cl (= tptp.subset tptp.subset)) :rule refl)
% 0.22/0.53 (anchor :step t2.t24 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 0.22/0.53 (step t2.t24.t1 (cl (= A A)) :rule refl)
% 0.22/0.53 (step t2.t24.t2 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t24.t3 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))) :rule all_simplify)
% 0.22/0.53 (step t2.t24 (cl (= (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B)))) (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule bind)
% 0.22/0.53 (step t2.t25 (cl (= (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xx) B))))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))))) :rule cong :premises (t2.t23 t2.t24))
% 0.22/0.53 (step t2.t26 (cl (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule resolution :premises (t2.t22 t2.t25 a0))
% 0.22/0.53 (step t2.t27 (cl (and (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_669) A)) (@ (@ tptp.in BOUND_VARIABLE_669) B)))) (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B))))))) :rule resolution :premises (t2.t2 t2.t21 t2.t26))
% 0.22/0.53 (step t2.t28 (cl (= tptp.subset (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))))) :rule and :premises (t2.t27))
% 0.22/0.53 (step t2.t29 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t2.t30 (cl (= (@ tptp.subset B) (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B))) :rule cong :premises (t2.t28 t2.t29))
% 0.22/0.53 (step t2.t31 (cl (= (@ (@ tptp.subset B) B) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B))) :rule cong :premises (t2.t30 t2.t29))
% 0.22/0.53 (step t2 (cl (= (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)) (forall ((B $$unsorted)) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B)))) :rule bind)
% 0.22/0.53 (step t3 (cl (= (not (forall ((B $$unsorted)) (@ (@ tptp.subset B) B))) (not (forall ((B $$unsorted)) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B))))) :rule cong :premises (t2))
% 0.22/0.53 (anchor :step t4 :args ((B $$unsorted) (:= B B)))
% 0.22/0.53 (step t4.t1 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t4.t2 (cl (= (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B)))))) :rule all_simplify)
% 0.22/0.53 (step t4.t3 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t4.t4 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B) (@ (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B)))) B))) :rule cong :premises (t4.t2 t4.t3))
% 0.22/0.53 (step t4.t5 (cl (= (@ (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B)))) B) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B))))) :rule all_simplify)
% 0.22/0.53 (step t4.t6 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B))) (forall ((Xx $$unsorted)) true))) :rule all_simplify)
% 0.22/0.53 (step t4.t7 (cl (= (forall ((Xx $$unsorted)) true) true)) :rule all_simplify)
% 0.22/0.53 (step t4.t8 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B))) true)) :rule trans :premises (t4.t6 t4.t7))
% 0.22/0.53 (step t4.t9 (cl (= (@ (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (@ (@ tptp.in Xx) B)))) B) true)) :rule trans :premises (t4.t5 t4.t8))
% 0.22/0.53 (step t4.t10 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B) true)) :rule trans :premises (t4.t4 t4.t9))
% 0.22/0.53 (step t4 (cl (= (forall ((B $$unsorted)) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B)) (forall ((B $$unsorted)) true))) :rule bind)
% 0.22/0.53 (step t5 (cl (= (forall ((B $$unsorted)) true) true)) :rule all_simplify)
% 0.22/0.53 (step t6 (cl (= (forall ((B $$unsorted)) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B)) true)) :rule trans :premises (t4 t5))
% 0.22/0.53 (step t7 (cl (= (not (forall ((B $$unsorted)) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B))) (not true))) :rule cong :premises (t6))
% 0.22/0.53 (step t8 (cl (= (not true) false)) :rule all_simplify)
% 0.22/0.53 (step t9 (cl (= (not (forall ((B $$unsorted)) (@ (@ (lambda ((A $$unsorted) (B $$unsorted)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in Xx) B)))) B) B))) false)) :rule trans :premises (t7 t8))
% 0.22/0.53 (step t10 (cl (= (not (forall ((B $$unsorted)) (@ (@ tptp.subset B) B))) false)) :rule trans :premises (t3 t9))
% 0.22/0.53 (step t11 (cl (not (= (not (=> tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))))) (not (=> tptp.subsetI1 (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)))))) (not (not (=> tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B)))))) (not (=> tptp.subsetI1 (forall ((B $$unsorted)) (@ (@ tptp.subset B) B))))) :rule equiv_pos2)
% 0.22/0.53 (step t12 (cl (= tptp.subsetI1 tptp.subsetI1)) :rule refl)
% 0.22/0.53 (step t13 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (= A B)) (@ (@ tptp.subset A) B))))) :rule all_simplify)
% 0.22/0.53 (step t14 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (= A B)) (@ (@ tptp.subset A) B))) (forall ((B $$unsorted)) (or (not (= B B)) (@ (@ tptp.subset B) B))))) :rule all_simplify)
% 0.22/0.53 (anchor :step t15 :args ((B $$unsorted) (:= B B)))
% 0.22/0.53 (step t15.t1 (cl (= B B)) :rule refl)
% 0.22/0.53 (step t15.t2 (cl (= (= B B) true)) :rule all_simplify)
% 0.22/0.53 (step t15.t3 (cl (= (not (= B B)) (not true))) :rule cong :premises (t15.t2))
% 0.22/0.53 (step t15.t4 (cl (= (not (= B B)) false)) :rule trans :premises (t15.t3 t8))
% 0.22/0.53 (step t15.t5 (cl (= (@ (@ tptp.subset B) B) (@ (@ tptp.subset B) B))) :rule refl)
% 0.22/0.53 (step t15.t6 (cl (= (or (not (= B B)) (@ (@ tptp.subset B) B)) (or false (@ (@ tptp.subset B) B)))) :rule cong :premises (t15.t4 t15.t5))
% 0.22/0.53 (step t15.t7 (cl (= (or false (@ (@ tptp.subset B) B)) (@ (@ tptp.subset B) B))) :rule all_simplify)
% 0.22/0.53 (step t15.t8 (cl (= (or (not (= B B)) (@ (@ tptp.subset B) B)) (@ (@ tptp.subset B) B))) :rule trans :premises (t15.t6 t15.t7))
% 0.22/0.53 (step t15 (cl (= (forall ((B $$unsorted)) (or (not (= B B)) (@ (@ tptp.subset B) B))) (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)))) :rule bind)
% 0.22/0.53 (step t16 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (= A B)) (@ (@ tptp.subset A) B))) (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)))) :rule trans :premises (t14 t15))
% 0.22/0.53 (step t17 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))) (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)))) :rule trans :premises (t13 t16))
% 0.22/0.53 (step t18 (cl (= (=> tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B)))) (=> tptp.subsetI1 (forall ((B $$unsorted)) (@ (@ tptp.subset B) B))))) :rule cong :premises (t12 t17))
% 0.22/0.53 (step t19 (cl (= (not (=> tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))))) (not (=> tptp.subsetI1 (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)))))) :rule cong :premises (t18))
% 0.22/0.53 (step t20 (cl (not (=> tptp.subsetI1 (forall ((B $$unsorted)) (@ (@ tptp.subset B) B))))) :rule resolution :premises (t11 t19 a2))
% 0.22/0.53 (step t21 (cl (not (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)))) :rule not_implies2 :premises (t20))
% 0.22/0.53 (step t22 (cl false) :rule resolution :premises (t1 t10 t21))
% 0.22/0.53 (step t23 (cl (not false)) :rule false)
% 0.22/0.53 (step t24 (cl) :rule resolution :premises (t22 t23))
% 0.22/0.53
% 0.22/0.53 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.SXDA5Gxbkz/cvc5---1.0.5_12144.smt2
% 0.22/0.53 % cvc5---1.0.5 exiting
% 0.22/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------