TSTP Solution File: SYO007^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYO007^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n009.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 18:29:38 EDT 2024
% Result : Theorem 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO007^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n009.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 : Tue May 28 07:21:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 0.20/0.51 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.51 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.OBYaFzH1hY/cvc5---1.0.5_28030.smt2
% 0.20/0.51 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.OBYaFzH1hY/cvc5---1.0.5_28030.smt2
% 0.20/0.51 (assume a0 (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (=> (@ Q U) (@ Q V))))))
% 0.20/0.51 (assume a1 (not (forall ((A Bool) (B Bool)) (=> (= A B) (@ (@ tptp.leibeq A) B)))))
% 0.20/0.51 (assume a2 true)
% 0.20/0.51 (step t1 (cl (not (= (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A))) false)) (not (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A)))) false) :rule equiv_pos2)
% 0.20/0.51 (anchor :step t2 :args ((A Bool) (:= A A)))
% 0.20/0.51 (step t2.t1 (cl (= A A)) :rule refl)
% 0.20/0.51 (step t2.t2 (cl (not (= (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (=> (@ Q U) (@ Q V))))) (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V))))))) (not (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (=> (@ Q U) (@ Q V)))))) (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))))) :rule equiv_pos2)
% 0.20/0.51 (step t2.t3 (cl (= tptp.leibeq tptp.leibeq)) :rule refl)
% 0.20/0.51 (anchor :step t2.t4 :args ((U Bool) (:= U U) (V Bool) (:= V V)))
% 0.20/0.51 (step t2.t4.t1 (cl (= U U)) :rule refl)
% 0.20/0.51 (step t2.t4.t2 (cl (= V V)) :rule refl)
% 0.20/0.51 (step t2.t4.t3 (cl (= (forall ((Q (-> Bool Bool))) (=> (@ Q U) (@ Q V))) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V))))) :rule all_simplify)
% 0.20/0.51 (step t2.t4 (cl (= (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (=> (@ Q U) (@ Q V)))) (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))))) :rule bind)
% 0.20/0.51 (step t2.t5 (cl (= (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (=> (@ Q U) (@ Q V))))) (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V))))))) :rule cong :premises (t2.t3 t2.t4))
% 0.20/0.51 (step t2.t6 (cl (= tptp.leibeq (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))))) :rule resolution :premises (t2.t2 t2.t5 a0))
% 0.20/0.51 (step t2.t7 (cl (= A A)) :rule refl)
% 0.20/0.51 (step t2.t8 (cl (= (@ tptp.leibeq A) (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A))) :rule cong :premises (t2.t6 t2.t7))
% 0.20/0.51 (step t2.t9 (cl (= (@ (@ tptp.leibeq A) A) (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A))) :rule cong :premises (t2.t8 t2.t7))
% 0.20/0.51 (step t2 (cl (= (forall ((A Bool)) (@ (@ tptp.leibeq A) A)) (forall ((A Bool)) (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A)))) :rule bind)
% 0.20/0.51 (step t3 (cl (= (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A))) (not (forall ((A Bool)) (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A))))) :rule cong :premises (t2))
% 0.20/0.51 (anchor :step t4 :args ((A Bool) (:= A A)))
% 0.20/0.51 (step t4.t1 (cl (= A A)) :rule refl)
% 0.20/0.51 (step t4.t2 (cl (= (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) (lambda ((V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q A)) (@ Q V)))))) :rule all_simplify)
% 0.20/0.51 (step t4.t3 (cl (= A A)) :rule refl)
% 0.20/0.51 (step t4.t4 (cl (= (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A) (@ (lambda ((V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q A)) (@ Q V)))) A))) :rule cong :premises (t4.t2 t4.t3))
% 0.20/0.51 (step t4.t5 (cl (= (@ (lambda ((V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q A)) (@ Q V)))) A) (forall ((Q (-> Bool Bool))) (or (not (@ Q A)) (@ Q A))))) :rule all_simplify)
% 0.20/0.51 (step t4.t6 (cl (= (forall ((Q (-> Bool Bool))) (or (not (@ Q A)) (@ Q A))) (forall ((Q (-> Bool Bool))) true))) :rule all_simplify)
% 0.20/0.51 (step t4.t7 (cl (= (forall ((Q (-> Bool Bool))) true) true)) :rule all_simplify)
% 0.20/0.51 (step t4.t8 (cl (= (forall ((Q (-> Bool Bool))) (or (not (@ Q A)) (@ Q A))) true)) :rule trans :premises (t4.t6 t4.t7))
% 0.20/0.51 (step t4.t9 (cl (= (@ (lambda ((V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q A)) (@ Q V)))) A) true)) :rule trans :premises (t4.t5 t4.t8))
% 0.20/0.52 (step t4.t10 (cl (= (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A) true)) :rule trans :premises (t4.t4 t4.t9))
% 0.20/0.52 (step t4 (cl (= (forall ((A Bool)) (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A)) (forall ((A Bool)) true))) :rule bind)
% 0.20/0.52 (step t5 (cl (= (forall ((A Bool)) true) true)) :rule all_simplify)
% 0.20/0.52 (step t6 (cl (= (forall ((A Bool)) (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A)) true)) :rule trans :premises (t4 t5))
% 0.20/0.52 (step t7 (cl (= (not (forall ((A Bool)) (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A))) (not true))) :rule cong :premises (t6))
% 0.20/0.52 (step t8 (cl (= (not true) false)) :rule all_simplify)
% 0.20/0.52 (step t9 (cl (= (not (forall ((A Bool)) (@ (@ (lambda ((U Bool) (V Bool)) (forall ((Q (-> Bool Bool))) (or (not (@ Q U)) (@ Q V)))) A) A))) false)) :rule trans :premises (t7 t8))
% 0.20/0.52 (step t10 (cl (= (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A))) false)) :rule trans :premises (t3 t9))
% 0.20/0.52 (step t11 (cl (not (= (not (forall ((A Bool) (B Bool)) (=> (= A B) (@ (@ tptp.leibeq A) B)))) (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A))))) (not (not (forall ((A Bool) (B Bool)) (=> (= A B) (@ (@ tptp.leibeq A) B))))) (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A)))) :rule equiv_pos2)
% 0.20/0.52 (step t12 (cl (= (forall ((A Bool) (B Bool)) (=> (= A B) (@ (@ tptp.leibeq A) B))) (forall ((A Bool) (B Bool)) (or (= (not A) B) (@ (@ tptp.leibeq A) B))))) :rule all_simplify)
% 0.20/0.52 (anchor :step t13 :args ((A Bool) (:= A A) (B Bool) (:= B B)))
% 0.20/0.52 (step t13.t1 (cl (= A A)) :rule refl)
% 0.20/0.52 (step t13.t2 (cl (= B B)) :rule refl)
% 0.20/0.52 (step t13.t3 (cl (= (= (not A) B) (= B (not A)))) :rule all_simplify)
% 0.20/0.52 (step t13.t4 (cl (= (@ (@ tptp.leibeq A) B) (@ (@ tptp.leibeq A) B))) :rule refl)
% 0.20/0.52 (step t13.t5 (cl (= (or (= (not A) B) (@ (@ tptp.leibeq A) B)) (or (= B (not A)) (@ (@ tptp.leibeq A) B)))) :rule cong :premises (t13.t3 t13.t4))
% 0.20/0.52 (step t13 (cl (= (forall ((A Bool) (B Bool)) (or (= (not A) B) (@ (@ tptp.leibeq A) B))) (forall ((A Bool) (B Bool)) (or (= B (not A)) (@ (@ tptp.leibeq A) B))))) :rule bind)
% 0.20/0.52 (step t14 (cl (= (forall ((A Bool) (B Bool)) (or (= B (not A)) (@ (@ tptp.leibeq A) B))) (forall ((A Bool)) (or (= A (not A)) (@ (@ tptp.leibeq A) A))))) :rule all_simplify)
% 0.20/0.52 (anchor :step t15 :args ((A Bool) (:= A A)))
% 0.20/0.52 (step t15.t1 (cl (= A A)) :rule refl)
% 0.20/0.52 (step t15.t2 (cl (= (= A (not A)) false)) :rule all_simplify)
% 0.20/0.52 (step t15.t3 (cl (= (@ (@ tptp.leibeq A) A) (@ (@ tptp.leibeq A) A))) :rule refl)
% 0.20/0.52 (step t15.t4 (cl (= (or (= A (not A)) (@ (@ tptp.leibeq A) A)) (or false (@ (@ tptp.leibeq A) A)))) :rule cong :premises (t15.t2 t15.t3))
% 0.20/0.52 (step t15.t5 (cl (= (or false (@ (@ tptp.leibeq A) A)) (@ (@ tptp.leibeq A) A))) :rule all_simplify)
% 0.20/0.52 (step t15.t6 (cl (= (or (= A (not A)) (@ (@ tptp.leibeq A) A)) (@ (@ tptp.leibeq A) A))) :rule trans :premises (t15.t4 t15.t5))
% 0.20/0.52 (step t15 (cl (= (forall ((A Bool)) (or (= A (not A)) (@ (@ tptp.leibeq A) A))) (forall ((A Bool)) (@ (@ tptp.leibeq A) A)))) :rule bind)
% 0.20/0.52 (step t16 (cl (= (forall ((A Bool) (B Bool)) (or (= B (not A)) (@ (@ tptp.leibeq A) B))) (forall ((A Bool)) (@ (@ tptp.leibeq A) A)))) :rule trans :premises (t14 t15))
% 0.20/0.52 (step t17 (cl (= (forall ((A Bool) (B Bool)) (or (= (not A) B) (@ (@ tptp.leibeq A) B))) (forall ((A Bool)) (@ (@ tptp.leibeq A) A)))) :rule trans :premises (t13 t16))
% 0.20/0.52 (step t18 (cl (= (forall ((A Bool) (B Bool)) (=> (= A B) (@ (@ tptp.leibeq A) B))) (forall ((A Bool)) (@ (@ tptp.leibeq A) A)))) :rule trans :premises (t12 t17))
% 0.20/0.52 (step t19 (cl (= (not (forall ((A Bool) (B Bool)) (=> (= A B) (@ (@ tptp.leibeq A) B)))) (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A))))) :rule cong :premises (t18))
% 0.20/0.52 (step t20 (cl (not (forall ((A Bool)) (@ (@ tptp.leibeq A) A)))) :rule resolution :premises (t11 t19 a1))
% 0.20/0.52 (step t21 (cl false) :rule resolution :premises (t1 t10 t20))
% 0.20/0.52 (step t22 (cl (not false)) :rule false)
% 0.20/0.52 (step t23 (cl) :rule resolution :premises (t21 t22))
% 0.20/0.52
% 0.20/0.52 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.OBYaFzH1hY/cvc5---1.0.5_28030.smt2
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------