%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n006.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 Jun 3 09:07:17 AM UTC 2026 % Result : Theorem 0.39s 0.59s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n006.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 23:04:04 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.39/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.59 % SZS status Theorem % 0.39/0.59 % SZS output start Proof % 0.39/0.59 ( % 0.39/0.59 (declare-sort $$unsorted 0) % 0.39/0.59 (declare-sort tptp.d_unsorted 0) % 0.39/0.59 (declare-sort tptp.mu 0) % 0.39/0.59 (declare-sort tptp.d_mu 0) % 0.39/0.59 (declare-const tptp.meq_prop (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mnot (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mor (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mand (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mimplies (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mimplied (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mvalid (-> (-> $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.minvalid (-> (-> $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mcountersatisfiable (-> (-> $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mxor (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.msatisfiable (-> (-> $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mequiv (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.meq_ind (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mtransitive (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mweakly_directed (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.d_mu_0 tptp.d_mu) % 0.39/0.59 (declare-const tptp.mtrue (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.d2mu (-> tptp.d_mu tptp.mu)) % 0.39/0.59 (declare-const tptp.mexists_ind (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.d2unsorted (-> tptp.d_unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.mweakly_connected (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.d_unsorted_0 tptp.d_unsorted) % 0.39/0.59 (declare-const tptp.mexists_prop (-> (-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mweakly_dense (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mfunctional (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mpartially_functional (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.meuclidean (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mserial (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.msymmetric (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mreflexive (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.39/0.59 (declare-const tptp.mdia (-> (-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mbox (-> (-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mforall_prop (-> (-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.mforall_ind (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 0.39/0.59 (define @t1 () (_ tptp.d2unsorted tptp.d_unsorted_0)) % 0.39/0.59 (define @t2 () (_ tptp.d2mu tptp.d_mu_0)) % 0.39/0.59 (define @t3 () (@var "W" $$unsorted)) % 0.39/0.59 (define @t4 () (@var "Phi" (-> $$unsorted Bool))) % 0.39/0.59 (define @t5 () (_ @t4 @t3)) % 0.39/0.59 (define @t6 () (@list @t3)) % 0.39/0.59 (define @t7 () (forall @t6 @t5)) % 0.39/0.59 (define @t8 () (@list @t4)) % 0.39/0.59 (define @t9 () (not @t5)) % 0.39/0.59 (define @t10 () (forall @t6 @t9)) % 0.39/0.59 (define @t11 () (@var "V" $$unsorted)) % 0.39/0.59 (define @t12 () (@var "U" $$unsorted)) % 0.39/0.59 (define @t13 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.39/0.59 (define @t14 () (_ @t13 @t12)) % 0.39/0.59 (define @t15 () (@var "T" $$unsorted)) % 0.39/0.59 (define @t16 () (_ @t13 @t15)) % 0.39/0.59 (define @t17 () (@list @t11)) % 0.39/0.59 (define @t18 () (@var "S" $$unsorted)) % 0.39/0.59 (define @t19 () (_ @t13 @t18)) % 0.39/0.59 (define @t20 () (_ @t19 @t12)) % 0.39/0.59 (define @t21 () (not @t20)) % 0.39/0.59 (define @t22 () (not (_ @t19 @t15))) % 0.39/0.59 (define @t23 () (@list @t18 @t15 @t12)) % 0.39/0.59 (define @t24 () (@list @t13)) % 0.39/0.59 (define @t25 () (= @t15 @t12)) % 0.39/0.59 (define @t26 () (_ @t16 @t12)) % 0.39/0.59 (define @t27 () (@var "Bound_variable_953" $$unsorted)) % 0.39/0.59 (define @t28 () (@list @t18 @t15)) % 0.39/0.59 (define @t29 () (@list @t12)) % 0.39/0.59 (define @t30 () (@list @t15)) % 0.39/0.59 (define @t31 () (@list @t18)) % 0.39/0.59 (define @t32 () (_ @t4 @t11)) % 0.39/0.59 (define @t33 () (@var "Flatten_var_0" $$unsorted)) % 0.39/0.59 (define @t34 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.59 (define @t35 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.39/0.59 (define @t36 () (_ @t35 @t34)) % 0.39/0.59 (define @t37 () (@list @t34)) % 0.39/0.59 (define @t38 () (@var "X" tptp.mu)) % 0.39/0.59 (define @t39 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.39/0.59 (define @t40 () (_ @t39 @t38)) % 0.39/0.59 (define @t41 () (@list @t38)) % 0.39/0.59 (define @t42 () (_ @t4 @t33)) % 0.39/0.59 (define @t43 () (@var "Psi" (-> $$unsorted Bool))) % 0.39/0.59 (define @t44 () (_ @t43 @t33)) % 0.39/0.59 (define @t45 () (not @t44)) % 0.39/0.59 (define @t46 () (or @t45 @t42)) % 0.39/0.59 (define @t47 () (not @t42)) % 0.39/0.59 (define @t48 () (or @t47 @t44)) % 0.39/0.59 (define @t49 () (not @t48)) % 0.39/0.59 (define @t50 () (or @t49 (not @t46))) % 0.39/0.59 (define @t51 () (@list @t4 @t43 @t33)) % 0.39/0.59 (define @t52 () (not @t50)) % 0.39/0.59 (define @t53 () (lambda @t51 @t52)) % 0.39/0.59 (define @t54 () (lambda @t51 @t48)) % 0.39/0.59 (define @t55 () (lambda @t51 (not (or @t47 @t45)))) % 0.39/0.59 (define @t56 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.59 (define @t57 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.59 (define @t58 () (@var "DM2" tptp.d_mu)) % 0.39/0.59 (define @t59 () (@var "DM1" tptp.d_mu)) % 0.39/0.59 (define @t60 () (@var "DM" tptp.d_mu)) % 0.39/0.59 (define @t61 () (@list @t60)) % 0.39/0.59 (define @t62 () (@var "M" tptp.mu)) % 0.39/0.59 (define @t63 () (@var "DU2" tptp.d_unsorted)) % 0.39/0.59 (define @t64 () (@var "DU1" tptp.d_unsorted)) % 0.39/0.59 (define @t65 () (@var "DU" tptp.d_unsorted)) % 0.39/0.59 (define @t66 () (@list @t65)) % 0.39/0.59 (define @t67 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.59 (define @t68 () (@list @t4 @t43 @t67)) % 0.39/0.59 (define @t69 () (lambda @t68 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t4) @t43)) (_ (_ tptp.mimplies @t43) @t4)) @t67))) % 0.39/0.59 (define @t70 () (= tptp.mequiv @t69)) % 0.39/0.59 (define @t71 () (not @t70)) % 0.39/0.59 (define @t72 () (@purify @t53)) % 0.39/0.59 (define @t73 () (_ @t4 @t67)) % 0.39/0.59 (define @t74 () (_ @t43 @t67)) % 0.39/0.59 (define @t75 () (not (or (not (or (not @t73) @t74)) (not (or (not @t74) @t73))))) % 0.39/0.59 (define @t76 () (lambda @t68 @t75)) % 0.39/0.59 (define @t77 () (@purify @t76)) % 0.39/0.59 (define @t78 () (= @t53 @t76)) % 0.39/0.59 (define @t79 () (@list @t33)) % 0.39/0.59 (define @t80 () (lambda @t79 @t46)) % 0.39/0.59 (define @t81 () (_ @t80 @t33)) % 0.39/0.59 (define @t82 () (not @t81)) % 0.39/0.59 (define @t83 () (or @t49 @t82)) % 0.39/0.59 (define @t84 () (not @t83)) % 0.39/0.59 (define @t85 () (lambda @t79 @t84)) % 0.39/0.59 (define @t86 () (@var "BOUND_VARIABLE_7997" (-> $$unsorted Bool))) % 0.39/0.59 (define @t87 () (not (_ @t86 @t33))) % 0.39/0.59 (define @t88 () (@list @t86 @t33)) % 0.39/0.59 (define @t89 () (@var "BOUND_VARIABLE_8016" (-> $$unsorted Bool))) % 0.39/0.59 (define @t90 () (_ @t89 @t33)) % 0.39/0.59 (define @t91 () (lambda (@list @t89 @t33) (or @t45 @t90))) % 0.39/0.59 (define @t92 () (@list @t43)) % 0.39/0.59 (define @t93 () (lambda @t79 @t48)) % 0.39/0.59 (define @t94 () (_ @t93 @t33)) % 0.39/0.59 (define @t95 () (not @t94)) % 0.39/0.59 (define @t96 () (or @t95 @t87)) % 0.39/0.59 (define @t97 () (not @t96)) % 0.39/0.59 (define @t98 () (lambda @t88 @t97)) % 0.39/0.59 (define @t99 () (lambda (@list @t43 @t33) @t48)) % 0.39/0.59 (define @t100 () (_ @t54 @t4)) % 0.39/0.59 (define @t101 () (lambda @t68 (_ (_ (_ @t55 (_ @t100 @t43)) (_ (_ @t54 @t43) @t4)) @t67))) % 0.39/0.59 (define @t102 () (= @t53 @t101)) % 0.39/0.59 (define @t103 () (= @t77 @t72)) % 0.39/0.59 (define @t104 () (@const 0 $$unsorted)) % 0.39/0.59 (define @t105 () (@const 1 (-> $$unsorted Bool))) % 0.39/0.59 (define @t106 () (_ @t105 @t104)) % 0.39/0.59 (define @t107 () (@const 2 (-> $$unsorted Bool))) % 0.39/0.59 (define @t108 () (_ @t107 @t104)) % 0.39/0.59 (define @t109 () (_ @t105 @t104)) % 0.39/0.59 (define @t110 () (_ @t107 @t104)) % 0.39/0.59 (define @t111 () (not @t110)) % 0.39/0.59 (define @t112 () (or @t111 @t109)) % 0.39/0.59 (define @t113 () (not @t112)) % 0.39/0.59 (define @t114 () (not @t109)) % 0.39/0.59 (define @t115 () (or @t114 @t110)) % 0.39/0.59 (define @t116 () (not @t115)) % 0.39/0.59 (define @t117 () (or @t116 @t113)) % 0.39/0.59 (define @t118 () (not @t117)) % 0.39/0.59 (define @t119 () (= (_ @t53 @t105 @t107 @t104) @t118)) % 0.39/0.59 (define @t120 () (_ @t72 @t105 @t107 @t104)) % 0.39/0.59 (define @t121 () (_ @t76 @t105 @t107 @t104)) % 0.39/0.59 (define @t122 () (_ @t77 @t105 @t107 @t104)) % 0.39/0.59 (define @t123 () (= @t122 @t120)) % 0.39/0.59 (define @t124 () (not @t123)) % 0.39/0.59 (define @t125 () (or @t103 @t124)) % 0.39/0.59 (assume @p1 (and (forall @t29 (exists @t66 (= @t12 (_ tptp.d2unsorted @t65)))) (forall @t66 (= @t65 tptp.d_unsorted_0)) (forall (@list @t64 @t63) (=> (= (_ tptp.d2unsorted @t64) (_ tptp.d2unsorted @t63)) (= @t64 @t63))) (forall (@list @t62) (exists @t61 (= @t62 (_ tptp.d2mu @t60)))) (forall @t61 (= @t60 tptp.d_mu_0)) (forall (@list @t59 @t58) (=> (= (_ tptp.d2mu @t59) (_ tptp.d2mu @t58)) (= @t59 @t58))) (= tptp.meq_prop (lambda (@list @t57 @t56 @t3) (= (_ @t57 @t3) (_ @t56 @t3)))) (= tptp.mnot (lambda (@list @t4 @t3) @t9)) (= tptp.mor (lambda (@list @t4 @t43 @t3) (or @t5 (_ @t43 @t3)))) (= tptp.mand @t55) (= tptp.mimplies @t54) (= tptp.mimplied (lambda @t51 @t46)) (= tptp.mequiv @t53) (= tptp.mxor (lambda @t51 @t50)) (= tptp.mforall_ind (lambda (@list @t39 @t3) (forall @t41 (_ @t40 @t3)))) (= tptp.mforall_prop (lambda (@list @t35 @t3) (forall @t37 (_ @t36 @t3)))) (= tptp.mexists_ind (lambda (@list @t39 @t33) (not (forall @t41 (not (_ @t40 @t33)))))) (= tptp.mexists_prop (lambda (@list @t35 @t33) (not (forall @t37 (not (_ @t36 @t33)))))) (= tptp.mbox (lambda (@list @t13 @t4 @t3) (forall @t17 (or (not (_ (_ @t13 @t3) @t11)) @t32)))) (= tptp.mdia (lambda (@list @t13 @t4 @t33) (not (forall @t17 (or (not (_ (_ @t13 @t33) @t11)) (not @t32)))))) (= tptp.mreflexive (lambda @t24 (forall @t31 (_ @t19 @t18)))) (= tptp.msymmetric (lambda @t24 (forall @t28 (or @t22 (_ @t16 @t18))))) (= tptp.mserial (lambda @t24 (forall @t31 (not (forall @t30 @t22))))) (= tptp.mtransitive (lambda @t24 (forall @t23 (or @t22 (not @t26) @t20)))) (= tptp.meuclidean (lambda @t24 (forall @t23 (or @t22 @t21 @t26)))) (= tptp.mpartially_functional (lambda @t24 (forall @t23 (or @t22 @t21 @t25)))) (= tptp.mfunctional (lambda @t24 (forall @t31 (not (forall @t30 (or @t22 (not (forall @t29 (or @t21 @t25))))))))) (= tptp.mweakly_dense (lambda @t24 (forall @t28 (or @t22 (not (forall (@list @t27) (or (not (_ @t19 @t27)) (not (_ (_ @t13 @t27) @t15))))))))) (= tptp.mweakly_connected (lambda @t24 (forall @t23 (or @t22 @t21 @t26 @t25 (_ @t14 @t15))))) (= tptp.mweakly_directed (lambda @t24 (forall @t23 (or @t22 @t21 (not (forall @t17 (or (not (_ @t16 @t11)) (not (_ @t14 @t11))))))))) (= tptp.mvalid (lambda @t8 @t7)) (= tptp.minvalid (lambda @t8 @t10)) (= tptp.msatisfiable (lambda @t8 (not @t10))) (= tptp.mcountersatisfiable (lambda @t8 (not @t7))) (_ (_ (_ tptp.meq_ind @t2) @t2) @t1) (_ tptp.mtrue @t1) (not (_ tptp.mfalse @t1)))) % 0.39/0.59 (assume @p2 @t71) % 0.39/0.59 (assume @p3 true) % 0.39/0.59 (step @p4 :rule eq-symm :args (@t72 @t77)) % 0.39/0.59 (step @p5 :rule eq-refl :args (@t76)) % 0.39/0.59 (step @p6 :rule skolem_intro :args (@t77)) % 0.39/0.59 (step @p7 :rule refl :args (@t76)) % 0.39/0.59 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t76 @t77))) % 0.39/0.59 (step @p9 :rule trans :premises (@p8 @p5)) % 0.39/0.59 (step @p10 :rule true_elim :premises (@p9)) % 0.39/0.59 (step @p11 :rule eq-refl :args (@t53)) % 0.39/0.59 (step @p12 :rule skolem_intro :args (@t72)) % 0.39/0.59 (step @p13 :rule refl :args (@t53)) % 0.39/0.59 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t53 @t72))) % 0.39/0.59 (step @p15 :rule trans :premises (@p14 @p11)) % 0.39/0.59 (step @p16 :rule true_elim :premises (@p15)) % 0.39/0.59 (step @p17 :rule cong :premises (@p16 @p10) :args (@t78)) % 0.39/0.59 (step @p18 :rule trans :premises (@p17 @p4)) % 0.39/0.59 (step @p19 :rule cong :premises (@p18) :args ((not @t78))) % 0.39/0.59 (step @p20 :rule beta-reduce :args ((= (_ (lambda @t79 @t52) @t67) @t75))) % 0.39/0.59 (step @p21 :rule refl :args (@t67)) % 0.39/0.59 (step @p22 :rule beta-reduce :args ((= @t81 @t46))) % 0.39/0.59 (step @p23 :rule cong :premises (@p22) :args (@t82)) % 0.39/0.59 (step @p24 :rule refl :args (@t49)) % 0.39/0.59 (step @p25 :rule nary_cong :premises (@p24 @p23) :args (@t83)) % 0.39/0.59 (step @p26 :rule cong :premises (@p25) :args (@t84)) % 0.39/0.59 (step @p27 :rule cong :premises (@p26) :args (@t85)) % 0.39/0.59 (step @p28 :rule beta-reduce :args ((= (_ (lambda @t88 (not (or @t49 @t87))) @t80) @t85))) % 0.39/0.59 (step @p29 :rule trans :premises (@p28 @p27)) % 0.39/0.59 (step @p30 :rule beta-reduce :args ((= (_ @t91 @t4) @t80))) % 0.39/0.59 (step @p31 :rule refl :args (@t4)) % 0.39/0.59 (step @p32 :rule beta-reduce :args ((= (_ (lambda (@list @t4 @t89 @t33) (or @t47 @t90)) @t43) @t91))) % 0.39/0.59 (step @p33 :rule refl :args (@t43)) % 0.39/0.59 (step @p34 :rule alpha_equiv :args (@t54 @t92 (@list @t89))) % 0.39/0.59 (step @p35 :rule ho_cong :premises (@p34 @p33)) % 0.39/0.59 (step @p36 :rule trans :premises (@p35 @p32)) % 0.39/0.59 (step @p37 :rule ho_cong :premises (@p36 @p31)) % 0.39/0.59 (step @p38 :rule trans :premises (@p37 @p30)) % 0.39/0.59 (step @p39 :rule refl :args (@t87)) % 0.39/0.59 (step @p40 :rule beta-reduce :args ((= @t94 @t48))) % 0.39/0.59 (step @p41 :rule cong :premises (@p40) :args (@t95)) % 0.39/0.59 (step @p42 :rule nary_cong :premises (@p41 @p39) :args (@t96)) % 0.39/0.59 (step @p43 :rule cong :premises (@p42) :args (@t97)) % 0.39/0.59 (step @p44 :rule cong :premises (@p43) :args (@t98)) % 0.39/0.59 (step @p45 :rule beta-reduce :args ((= (_ (lambda (@list @t4 @t86 @t33) (not (or @t47 @t87))) @t93) @t98))) % 0.39/0.59 (step @p46 :rule trans :premises (@p45 @p44)) % 0.39/0.59 (step @p47 :rule refl :args (@t93)) % 0.39/0.59 (step @p48 :rule alpha_equiv :args (@t55 @t92 (@list @t86))) % 0.39/0.59 (step @p49 :rule ho_cong :premises (@p48 @p47)) % 0.39/0.59 (step @p50 :rule trans :premises (@p49 @p46)) % 0.39/0.59 (step @p51 :rule beta-reduce :args ((= (_ @t99 @t43) @t93))) % 0.39/0.59 (step @p52 :rule refl :args (@t43)) % 0.39/0.59 (step @p53 :rule beta-reduce :args ((= @t100 @t99))) % 0.39/0.59 (step @p54 :rule ho_cong :premises (@p53 @p52)) % 0.39/0.59 (step @p55 :rule trans :premises (@p54 @p51)) % 0.39/0.59 (step @p56 :rule refl :args (@t55)) % 0.39/0.59 (step @p57 :rule ho_cong :premises (@p56 @p55)) % 0.39/0.59 (step @p58 :rule trans :premises (@p57 @p50)) % 0.39/0.59 (step @p59 :rule ho_cong :premises (@p58 @p38)) % 0.39/0.59 (step @p60 :rule trans :premises (@p59 @p29)) % 0.39/0.59 (step @p61 :rule ho_cong :premises (@p60 @p21)) % 0.39/0.59 (step @p62 :rule trans :premises (@p61 @p20)) % 0.39/0.59 (step @p63 :rule cong :premises (@p62) :args (@t101)) % 0.39/0.59 (step @p64 :rule cong :premises (@p13 @p63) :args (@t102)) % 0.39/0.59 (step @p65 :rule cong :premises (@p64) :args ((not @t102))) % 0.39/0.59 (step @p66 :rule and_elim :premises (@p1) :args (10)) % 0.39/0.59 (step @p67 :rule ho_cong :premises (@p66 @p52)) % 0.39/0.59 (step @p68 :rule ho_cong :premises (@p67 @p31)) % 0.39/0.59 (step @p69 :rule ho_cong :premises (@p66 @p31)) % 0.39/0.59 (step @p70 :rule ho_cong :premises (@p69 @p52)) % 0.39/0.59 (step @p71 :rule and_elim :premises (@p1) :args (9)) % 0.39/0.59 (step @p72 :rule ho_cong :premises (@p71 @p70)) % 0.39/0.59 (step @p73 :rule ho_cong :premises (@p72 @p68)) % 0.39/0.59 (step @p74 :rule ho_cong :premises (@p73 @p21)) % 0.39/0.59 (step @p75 :rule cong :premises (@p74) :args (@t69)) % 0.39/0.59 (step @p76 :rule and_elim :premises (@p1) :args (12)) % 0.39/0.59 (step @p77 :rule cong :premises (@p76 @p75) :args (@t70)) % 0.39/0.59 (step @p78 :rule cong :premises (@p77) :args (@t71)) % 0.39/0.59 (step @p79 :rule trans :premises (@p78 @p65)) % 0.39/0.59 (step @p80 :rule trans :premises (@p79 @p19)) % 0.39/0.59 (step @p81 :rule eq_resolve :premises (@p2 @p80)) % 0.39/0.59 (step @p82 :rule aci_norm :args ((= (or @t103 false) @t103))) % 0.39/0.59 (step @p83 :rule evaluate :args ((not true))) % 0.39/0.59 (step @p84 :rule eq-refl :args ((not (or (not (or (not @t106) @t108)) (not (or (not @t108) @t106)))))) % 0.39/0.59 (step @p85 :rule refl :args (@t106)) % 0.39/0.59 (step @p86 :rule refl :args (@t109)) % 0.39/0.59 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t109 @t106))) % 0.39/0.59 (step @p88 :rule symm :premises (@p87)) % 0.39/0.59 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.39/0.59 (step @p90 :rule refl :args (@t108)) % 0.39/0.59 (step @p91 :rule refl :args (@t110)) % 0.39/0.59 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t110 @t108))) % 0.39/0.59 (step @p93 :rule symm :premises (@p92)) % 0.39/0.59 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 0.39/0.59 (step @p95 :rule cong :premises (@p94) :args (@t111)) % 0.39/0.59 (step @p96 :rule nary_cong :premises (@p95 @p89) :args (@t112)) % 0.39/0.59 (step @p97 :rule cong :premises (@p96) :args (@t113)) % 0.39/0.59 (step @p98 :rule cong :premises (@p89) :args (@t114)) % 0.39/0.59 (step @p99 :rule nary_cong :premises (@p98 @p94) :args (@t115)) % 0.39/0.59 (step @p100 :rule cong :premises (@p99) :args (@t116)) % 0.39/0.59 (step @p101 :rule nary_cong :premises (@p100 @p97) :args (@t117)) % 0.39/0.59 (step @p102 :rule cong :premises (@p101) :args (@t118)) % 0.39/0.59 (step @p103 :rule eq-refl :args (@t118)) % 0.39/0.59 (step @p104 :rule refl :args (@t118)) % 0.39/0.59 (step @p105 :rule beta-reduce :args (@t119)) % 0.39/0.59 (step @p106 :rule cong :premises (@p105 @p104) :args (@t119)) % 0.39/0.59 (step @p107 :rule trans :premises (@p106 @p103)) % 0.39/0.59 (step @p108 :rule refl :args (@t104)) % 0.39/0.59 (step @p109 :rule refl :args (@t107)) % 0.39/0.59 (step @p110 :rule refl :args (@t105)) % 0.39/0.59 (step @p111 :rule ho_cong :premises (@p12 @p110 @p109 @p108)) % 0.39/0.59 (step @p112 :rule cong :premises (@p111 @p104) :args ((= @t120 @t118))) % 0.39/0.59 (step @p113 :rule trans :premises (@p112 @p107)) % 0.39/0.59 (step @p114 :rule true_elim :premises (@p113)) % 0.39/0.59 (step @p115 :rule trans :premises (@p114 @p102)) % 0.39/0.59 (step @p116 :rule beta-reduce :args ((= @t121 @t118))) % 0.39/0.59 (step @p117 :rule cong :premises (@p104 @p116) :args ((= @t118 @t121))) % 0.39/0.59 (step @p118 :rule trans :premises (@p117 @p103)) % 0.39/0.59 (step @p119 :rule eq-symm :args (@t121 @t118)) % 0.39/0.59 (step @p120 :rule trans :premises (@p119 @p118)) % 0.39/0.59 (step @p121 :rule ho_cong :premises (@p6 @p110 @p109 @p108)) % 0.39/0.59 (step @p122 :rule cong :premises (@p121 @p104) :args ((= @t122 @t118))) % 0.39/0.59 (step @p123 :rule trans :premises (@p122 @p120)) % 0.39/0.59 (step @p124 :rule true_elim :premises (@p123)) % 0.39/0.59 (step @p125 :rule trans :premises (@p124 @p102)) % 0.39/0.59 (step @p126 :rule cong :premises (@p125 @p115) :args (@t123)) % 0.39/0.59 (step @p127 :rule trans :premises (@p126 @p84)) % 0.39/0.59 (step @p128 :rule cong :premises (@p127) :args (@t124)) % 0.39/0.59 (step @p129 :rule trans :premises (@p128 @p83)) % 0.39/0.59 (step @p130 :rule refl :args (@t103)) % 0.39/0.59 (step @p131 :rule nary_cong :premises (@p130 @p129) :args (@t125)) % 0.39/0.59 (step @p132 :rule trans :premises (@p131 @p82)) % 0.39/0.59 ; WARNING: add trust step for TRUST % 0.39/0.59 ; trust TRUST THEORY_LEMMA % 0.39/0.59 (step @p133 :rule trust :premises () :args (@t125)) % 0.39/0.59 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.39/0.59 (step @p135 false :rule chain_m_resolution :premises (@p134 @p81) :args (false (@list true) (@list @t103))) % 0.39/0.59 ) % 0.39/0.59 % SZS output end Proof % 0.39/0.59 % cvc5 exiting %------------------------------------------------------------------------------