%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV435^3 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 09:01:32 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV435^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n015.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % 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 20:18:04 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.37/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-sort tptp.individuals 0) % 0.37/0.59 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.a (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.icl_true (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.icl_false (-> $$unsorted Bool)) % 0.37/0.59 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.59 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.37/0.59 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.59 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.59 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.37/0.59 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.59 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.59 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.59 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.59 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.59 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.59 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.icl_atom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) _let_2) _let_1))))) % 0.37/0.59 (define tptp.icl_princ () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.37/0.59 (define tptp.icl_and () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.37/0.59 (define tptp.icl_or () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor _let_3) _let_2) _let_1)))))) % 0.37/0.59 (define tptp.icl_impl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.37/0.59 (define tptp.icl_says () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "S" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mor _let_3) _let_2)) _let_1)))))) % 0.37/0.59 (define tptp.iclval () (let ((_let_1 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_1) (_ tptp.mvalid _let_1)))) % 0.37/0.59 (define @t1 () (= tptp.icl_true tptp.mtrue)) % 0.37/0.59 (define @t2 () (= tptp.icl_false tptp.mfalse)) % 0.37/0.59 (define @t3 () (_ tptp.icl_princ tptp.a)) % 0.37/0.59 (define @t4 () (= @t3 tptp.icl_true)) % 0.37/0.59 (define @t5 () (not (_ tptp.iclval (_ (_ tptp.icl_says @t3) tptp.icl_false)))) % 0.37/0.59 (define @t6 () (@var "X" $$unsorted)) % 0.37/0.59 (define @t7 () (@list @t6)) % 0.37/0.59 (define @t8 () (lambda @t7 false)) % 0.37/0.59 (define @t9 () (lambda @t7 true)) % 0.37/0.59 (define @t10 () (@var "U" $$unsorted)) % 0.37/0.59 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.59 (define @t12 () (_ @t11 @t10)) % 0.37/0.59 (define @t13 () (lambda (@list @t11 @t10) (not @t12))) % 0.37/0.59 (define @t14 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.59 (define @t15 () (_ @t14 @t10)) % 0.37/0.59 (define @t16 () (@list @t11 @t14 @t10)) % 0.37/0.59 (define @t17 () (lambda @t16 (or @t12 @t15))) % 0.37/0.59 (define @t18 () (lambda @t16 (and @t12 @t15))) % 0.37/0.59 (define @t19 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.59 (define @t20 () (@var "V" (-> $$unsorted Bool))) % 0.37/0.59 (define @t21 () (@var "U" (-> $$unsorted Bool))) % 0.37/0.59 (define @t22 () (@list @t21 @t20 @t19)) % 0.37/0.59 (define @t23 () (lambda @t22 (_ (_ (_ tptp.mor (_ tptp.mnot @t21)) @t20) @t19))) % 0.37/0.59 (define @t24 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t21) @t20)) (_ (_ tptp.mimpl @t20) @t21)) @t19))) % 0.37/0.59 (define @t25 () (@var "Y" $$unsorted)) % 0.37/0.59 (define @t26 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.59 (define @t27 () (_ @t26 @t25)) % 0.37/0.59 (define @t28 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.59 (define @t29 () (_ (_ @t28 @t6) @t25)) % 0.37/0.59 (define @t30 () (@list @t25)) % 0.37/0.59 (define @t31 () (forall @t30 (=> @t29 @t27))) % 0.37/0.59 (define @t32 () (@list @t28 @t26 @t6)) % 0.37/0.59 (define @t33 () (lambda @t32 @t31)) % 0.37/0.59 (define @t34 () (lambda @t32 (exists @t30 (and @t29 @t27)))) % 0.37/0.59 (define @t35 () (@var "W" $$unsorted)) % 0.37/0.59 (define @t36 () (@var "X" tptp.individuals)) % 0.37/0.59 (define @t37 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.37/0.59 (define @t38 () (_ (_ @t37 @t36) @t35)) % 0.37/0.59 (define @t39 () (@list @t36)) % 0.37/0.59 (define @t40 () (@list @t37 @t35)) % 0.37/0.59 (define @t41 () (lambda @t40 (forall @t39 @t38))) % 0.37/0.59 (define @t42 () (lambda @t40 (exists @t39 @t38))) % 0.37/0.59 (define @t43 () (_ @t26 @t35)) % 0.37/0.59 (define @t44 () (@list @t35)) % 0.37/0.59 (define @t45 () (forall @t44 @t43)) % 0.37/0.59 (define @t46 () (@list @t26)) % 0.37/0.59 (define @t47 () (lambda @t46 @t45)) % 0.37/0.59 (define @t48 () (lambda @t46 (exists @t44 @t43))) % 0.37/0.59 (define @t49 () (not @t43)) % 0.37/0.59 (define @t50 () (lambda @t46 (exists @t44 @t49))) % 0.37/0.59 (define @t51 () (lambda @t46 (forall @t44 @t49))) % 0.37/0.59 (define @t52 () (_ tptp.mbox tptp.rel)) % 0.37/0.59 (define @t53 () (@list @t26 @t19)) % 0.37/0.59 (define @t54 () (lambda @t53 (_ (_ @t52 @t26) @t19))) % 0.37/0.59 (define @t55 () (lambda @t53 (_ @t26 @t19))) % 0.37/0.59 (define @t56 () (@var "B" (-> $$unsorted Bool))) % 0.37/0.59 (define @t57 () (@var "A" (-> $$unsorted Bool))) % 0.37/0.59 (define @t58 () (@list @t57 @t56 @t19)) % 0.37/0.59 (define @t59 () (lambda @t58 (_ (_ (_ tptp.mand @t57) @t56) @t19))) % 0.37/0.59 (define @t60 () (_ tptp.mor @t57)) % 0.37/0.59 (define @t61 () (lambda @t58 (_ (_ @t60 @t56) @t19))) % 0.37/0.59 (define @t62 () (lambda @t58 (_ (_ @t52 (_ (_ tptp.mimpl @t57) @t56)) @t19))) % 0.37/0.59 (define @t63 () (@var "S" (-> $$unsorted Bool))) % 0.37/0.59 (define @t64 () (@list @t57 @t63 @t19)) % 0.37/0.59 (define @t65 () (lambda @t64 (_ (_ @t52 (_ @t60 @t63)) @t19))) % 0.37/0.59 (define @t66 () (@list @t11)) % 0.37/0.59 (define @t67 () (lambda @t66 (_ tptp.mvalid @t11))) % 0.37/0.59 (define @t68 () (tptp.a @t25)) % 0.37/0.59 (define @t69 () (not (tptp.rel @t35 @t25))) % 0.37/0.59 (define @t70 () (or @t69 @t68)) % 0.37/0.59 (define @t71 () (@var "BOUND_VARIABLE_8052" $$unsorted)) % 0.37/0.59 (define @t72 () (lambda (@list @t71) false)) % 0.37/0.59 (define @t73 () (_ @t72 @t25)) % 0.37/0.59 (define @t74 () (or @t69 @t68 @t73)) % 0.37/0.59 (define @t75 () (@list @t35 @t25)) % 0.37/0.59 (define @t76 () (forall @t75 @t74)) % 0.37/0.59 (define @t77 () (@list @t6)) % 0.37/0.59 (define @t78 () (tptp.icl_false @t25)) % 0.37/0.59 (define @t79 () (or @t69 @t68 @t78)) % 0.37/0.59 (define @t80 () (forall @t75 @t79)) % 0.37/0.59 (define @t81 () (forall @t30 @t79)) % 0.37/0.59 (define @t82 () (not (tptp.rel @t19 @t25))) % 0.37/0.59 (define @t83 () (@list @t19)) % 0.37/0.59 (define @t84 () (lambda @t83 (forall @t30 (or @t82 @t68 @t78)))) % 0.37/0.59 (define @t85 () (_ @t84 @t35)) % 0.37/0.59 (define @t86 () (forall @t44 @t85)) % 0.37/0.59 (define @t87 () (forall @t44 (_ @t11 @t35))) % 0.37/0.59 (define @t88 () (lambda @t66 @t87)) % 0.37/0.59 (define @t89 () (_ @t63 @t25)) % 0.37/0.59 (define @t90 () (@list @t63 @t19)) % 0.37/0.59 (define @t91 () (_ tptp.a @t25)) % 0.37/0.59 (define @t92 () (or @t82 @t91 @t89)) % 0.37/0.59 (define @t93 () (_ tptp.a @t19)) % 0.37/0.59 (define @t94 () (lambda @t83 @t93)) % 0.37/0.59 (define @t95 () (_ @t94 @t25)) % 0.37/0.59 (define @t96 () (or @t82 @t95 @t89)) % 0.37/0.59 (define @t97 () (forall @t30 @t96)) % 0.37/0.59 (define @t98 () (lambda @t90 @t97)) % 0.37/0.59 (define @t99 () (_ @t57 @t25)) % 0.37/0.59 (define @t100 () (forall @t30 (or @t82 @t99 @t89))) % 0.37/0.59 (define @t101 () (lambda @t64 @t100)) % 0.37/0.59 (define @t102 () (_ @t55 tptp.a)) % 0.37/0.59 (define @t103 () (not (tptp.rel @t6 @t25))) % 0.37/0.59 (define @t104 () (_ @t63 @t25)) % 0.37/0.59 (define @t105 () (_ @t57 @t25)) % 0.37/0.59 (define @t106 () (or @t103 @t105 @t104)) % 0.37/0.59 (define @t107 () (or @t105 @t104)) % 0.37/0.59 (define @t108 () (_ @t57 @t10)) % 0.37/0.59 (define @t109 () (lambda (@list @t10) (or @t108 (_ @t63 @t10)))) % 0.37/0.59 (define @t110 () (_ @t109 @t25)) % 0.37/0.59 (define @t111 () (or @t103 @t110)) % 0.37/0.59 (define @t112 () (forall @t30 @t111)) % 0.37/0.59 (define @t113 () (lambda @t7 @t112)) % 0.37/0.59 (define @t114 () (_ @t26 @t25)) % 0.37/0.59 (define @t115 () (lambda (@list @t26 @t6) (forall @t30 (or @t103 @t114)))) % 0.37/0.59 (define @t116 () (lambda (@list @t14 @t10) (or @t108 @t15))) % 0.37/0.59 (define @t117 () (_ @t28 @t6 @t25)) % 0.37/0.59 (define @t118 () (not @t29)) % 0.37/0.59 (define @t119 () (or @t118 @t27)) % 0.37/0.59 (define @t120 () (_ @t26 @t35)) % 0.37/0.59 (define @t121 () (forall @t75 @t70)) % 0.37/0.59 (define @t122 () (@quantifiers_skolemize @t121 1)) % 0.37/0.59 (define @t123 () (tptp.a @t122)) % 0.37/0.59 (define @t124 () (or (not (tptp.rel (@quantifiers_skolemize @t121 0) @t122)) @t123)) % 0.37/0.59 (define @t125 () (@var "BOUND_VARIABLE_8073" $$unsorted)) % 0.37/0.59 (define @t126 () (lambda (@list @t125) true)) % 0.37/0.59 (define @t127 () (@purify @t126)) % 0.37/0.59 (define @t128 () (@purify @t94)) % 0.37/0.59 (define @t129 () (tptp.a @t19)) % 0.37/0.59 (define @t130 () (forall @t83 (= @t93 true))) % 0.37/0.59 (define @t131 () (= @t128 @t127)) % 0.37/0.59 (define @t132 () (=> @t131 @t130)) % 0.37/0.59 (define @t133 () (forall @t83 @t129)) % 0.37/0.59 (assume @p1 @t1) % 0.37/0.59 (assume @p2 @t2) % 0.37/0.59 (assume @p3 @t4) % 0.37/0.59 (assume @p4 @t5) % 0.37/0.59 (assume @p5 true) % 0.37/0.59 (step @p6 (= tptp.mfalse @t8) :rule refl :args (@t8)) % 0.37/0.59 (step @p7 (= tptp.mtrue @t9) :rule refl :args (@t9)) % 0.37/0.59 (step @p8 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.37/0.59 (step @p9 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.37/0.59 (step @p10 (= tptp.mand @t18) :rule refl :args (@t18)) % 0.37/0.59 (step @p11 (= tptp.mimpl @t23) :rule refl :args (@t23)) % 0.37/0.59 (step @p12 (= tptp.miff @t24) :rule refl :args (@t24)) % 0.37/0.59 (step @p13 (= tptp.mbox @t33) :rule refl :args (@t33)) % 0.37/0.59 (step @p14 (= tptp.mdia @t34) :rule refl :args (@t34)) % 0.37/0.59 (step @p15 (= tptp.mall @t41) :rule refl :args (@t41)) % 0.37/0.59 (step @p16 (= tptp.mexists @t42) :rule refl :args (@t42)) % 0.37/0.59 (step @p17 (= tptp.mvalid @t47) :rule refl :args (@t47)) % 0.37/0.59 (step @p18 (= tptp.msatisfiable @t48) :rule refl :args (@t48)) % 0.37/0.59 (step @p19 (= tptp.mcountersatisfiable @t50) :rule refl :args (@t50)) % 0.37/0.59 (step @p20 (= tptp.minvalid @t51) :rule refl :args (@t51)) % 0.37/0.59 (step @p21 (= tptp.icl_atom @t54) :rule refl :args (@t54)) % 0.37/0.59 (step @p22 (= tptp.icl_princ @t55) :rule refl :args (@t55)) % 0.37/0.59 (step @p23 (= tptp.icl_and @t59) :rule refl :args (@t59)) % 0.37/0.59 (step @p24 (= tptp.icl_or @t61) :rule refl :args (@t61)) % 0.37/0.59 (step @p25 (= tptp.icl_impl @t62) :rule refl :args (@t62)) % 0.37/0.59 (step @p26 (= tptp.icl_says @t65) :rule refl :args (@t65)) % 0.37/0.59 (step @p27 (= tptp.iclval @t67) :rule refl :args (@t67)) % 0.37/0.59 (step @p28 :rule aci_norm :args ((= (or @t69 @t68 false) @t70))) % 0.37/0.59 (step @p29 :rule beta-reduce :args ((= @t73 false))) % 0.37/0.59 (step @p30 :rule refl :args (@t68)) % 0.37/0.59 (step @p31 :rule refl :args (@t69)) % 0.37/0.59 (step @p32 :rule nary_cong :premises (@p31 @p30 @p29) :args (@t74)) % 0.37/0.59 (step @p33 :rule trans :premises (@p32 @p28)) % 0.37/0.59 (step @p34 :rule cong :premises (@p33) :args (@t76)) % 0.37/0.59 (step @p35 :rule cong :premises (@p34) :args ((not @t76))) % 0.37/0.59 (step @p36 :rule refl :args (@t25)) % 0.37/0.59 (step @p37 :rule refl :args (@t72)) % 0.37/0.59 (step @p38 :rule symm :premises (@p37)) % 0.37/0.59 (step @p39 :rule alpha_equiv :args (@t8 @t77 (@list @t71))) % 0.37/0.59 (step @p40 :rule trans :premises (@p39 @p38)) % 0.37/0.59 (step @p41 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(step @p103 :rule aci_norm :args ((= (or @t103 @t107) @t106))) % 0.37/0.59 (step @p104 :rule beta-reduce :args ((= @t110 @t107))) % 0.37/0.59 (step @p105 :rule refl :args (@t103)) % 0.37/0.59 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t111)) % 0.37/0.59 (step @p107 :rule trans :premises (@p106 @p103)) % 0.37/0.59 (step @p108 :rule cong :premises (@p107) :args (@t112)) % 0.37/0.59 (step @p109 :rule trans :premises (@p108 @p102)) % 0.37/0.59 (step @p110 :rule cong :premises (@p109) :args (@t113)) % 0.37/0.59 (step @p111 :rule beta-reduce :args ((= (_ @t115 @t109) @t113))) % 0.37/0.59 (step @p112 :rule trans :premises (@p111 @p110)) % 0.37/0.59 (step @p113 :rule beta-reduce :args ((= (_ @t116 @t63) @t109))) % 0.37/0.59 (step @p114 :rule refl :args (@t63)) % 0.37/0.59 (step @p115 :rule beta-reduce :args ((= (_ @t17 @t57) @t116))) % 0.37/0.59 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 0.37/0.59 (step @p117 :rule trans :premises (@p116 @p113)) % 0.37/0.59 (step @p118 :rule beta-reduce :args ((= (_ (lambda @t32 (forall @t30 (or (not @t117) @t114))) tptp.rel) @t115))) % 0.37/0.59 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.37/0.59 (step @p120 :rule trans :premises (@p119 @p112)) % 0.37/0.59 (step @p121 :rule ho_cong :premises (@p120 @p89)) % 0.37/0.59 (step @p122 :rule trans :premises (@p121 @p88)) % 0.37/0.59 (step @p123 :rule refl :args (@t57)) % 0.37/0.59 (step @p124 :rule ho_cong :premises (@p9 @p123)) % 0.37/0.59 (step @p125 :rule ho_cong :premises (@p124 @p114)) % 0.37/0.59 (step @p126 :rule refl :args (tptp.rel)) % 0.37/0.59 (step @p127 :rule refl :args (@t114)) % 0.37/0.59 (step @p128 :rule refl :args (@t27)) % 0.37/0.59 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t27 @t114))) % 0.37/0.59 (step @p130 :rule symm :premises (@p129)) % 0.37/0.59 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.37/0.59 (step @p132 :rule refl :args (@t117)) % 0.37/0.59 (step @p133 :rule refl :args (@t29)) % 0.37/0.59 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t29 @t117))) % 0.37/0.59 (step @p135 :rule symm :premises (@p134)) % 0.37/0.59 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.37/0.59 (step @p137 :rule cong :premises (@p136) :args (@t118)) % 0.37/0.59 (step @p138 :rule nary_cong :premises (@p137 @p131) :args (@t119)) % 0.37/0.59 (step @p139 :rule cong :premises (@p138) :args ((forall @t30 @t119))) % 0.37/0.59 (step @p140 :rule bool-impl-elim :args (@t29 @t27)) % 0.37/0.59 (step @p141 :rule cong :premises (@p140) :args (@t31)) % 0.37/0.59 (step @p142 :rule trans :premises (@p141 @p139)) % 0.37/0.59 (step @p143 :rule cong :premises (@p142) :args (@t33)) % 0.37/0.59 (step @p144 :rule trans :premises (@p13 @p143)) % 0.37/0.59 (step @p145 :rule ho_cong :premises (@p144 @p126)) % 0.37/0.59 (step @p146 :rule ho_cong :premises (@p145 @p125)) % 0.37/0.59 (step @p147 :rule ho_cong :premises (@p146 @p89)) % 0.37/0.59 (step @p148 :rule trans :premises (@p147 @p122)) % 0.37/0.59 (step @p149 :rule cong :premises (@p148) :args (@t65)) % 0.37/0.59 (step @p150 :rule trans :premises (@p26 @p149)) % 0.37/0.59 (step @p151 :rule ho_cong :premises (@p150 @p87)) % 0.37/0.59 (step @p152 :rule ho_cong :premises (@p151 @p41)) % 0.37/0.59 (step @p153 :rule beta-reduce :args ((= (_ (lambda @t46 (forall @t44 @t120)) @t11) @t87))) % 0.37/0.59 (step @p154 :rule refl :args (@t11)) % 0.37/0.59 (step @p155 :rule refl :args (@t120)) % 0.37/0.59 (step @p156 :rule refl :args (@t43)) % 0.37/0.59 (step @p157 :rule cong :premises (@p156 @p155) :args ((= @t43 @t120))) % 0.37/0.59 (step @p158 :rule symm :premises (@p157)) % 0.37/0.59 (step @p159 :rule eq_resolve :premises (@p156 @p158)) % 0.37/0.59 (step @p160 :rule cong :premises (@p159) :args (@t45)) % 0.37/0.59 (step @p161 :rule cong :premises (@p160) :args (@t47)) % 0.37/0.59 (step @p162 :rule trans :premises (@p17 @p161)) % 0.37/0.59 (step @p163 :rule ho_cong :premises (@p162 @p154)) % 0.37/0.59 (step @p164 :rule trans :premises (@p163 @p153)) % 0.37/0.59 (step @p165 :rule cong :premises (@p164) :args (@t67)) % 0.37/0.59 (step @p166 :rule trans :premises (@p27 @p165)) % 0.37/0.59 (step @p167 :rule ho_cong :premises (@p166 @p152)) % 0.37/0.59 (step @p168 :rule cong :premises (@p167) :args (@t5)) % 0.37/0.59 (step @p169 :rule trans :premises (@p168 @p85)) % 0.37/0.59 (step @p170 :rule trans :premises (@p169 @p50)) % 0.37/0.59 (step @p171 :rule eq_resolve :premises (@p4 @p170)) % 0.37/0.59 (step @p172 :rule skolemize :premises (@p171)) % 0.37/0.59 (step @p173 :rule cnf_or_neg :args (@t124 1)) % 0.37/0.59 (step @p174 :rule chain_m_resolution :premises (@p173 @p172) :args ((not @t123) (@list true) (@list @t124))) % 0.37/0.59 (step @p175 :rule eq-symm :args (@t127 @t128)) % 0.37/0.59 (step @p176 :rule eq-refl :args (@t94)) % 0.37/0.59 (step @p177 :rule skolem_intro :args (@t128)) % 0.37/0.59 (step @p178 :rule refl :args (@t94)) % 0.37/0.59 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t94 @t128))) % 0.37/0.59 (step @p180 :rule trans :premises (@p179 @p176)) % 0.37/0.59 (step @p181 :rule true_elim :premises (@p180)) % 0.37/0.59 (step @p182 :rule eq-refl :args (@t126)) % 0.37/0.59 (step @p183 :rule refl :args (@t126)) % 0.37/0.59 (step @p184 :rule symm :premises (@p183)) % 0.37/0.59 (step @p185 :rule refl :args (@t126)) % 0.37/0.59 (step @p186 :rule cong :premises (@p185 @p184) :args ((= @t126 @t126))) % 0.37/0.59 (step @p187 :rule trans :premises (@p186 @p182)) % 0.37/0.59 (step @p188 :rule skolem_intro :args (@t127)) % 0.37/0.59 (step @p189 :rule cong :premises (@p185 @p188) :args ((= @t126 @t127))) % 0.37/0.59 (step @p190 :rule trans :premises (@p189 @p187)) % 0.37/0.59 (step @p191 :rule true_elim :premises (@p190)) % 0.37/0.59 (step @p192 :rule cong :premises (@p191 @p181) :args ((= @t126 @t94))) % 0.37/0.59 (step @p193 :rule trans :premises (@p192 @p175)) % 0.37/0.59 (step @p194 :rule symm :premises (@p183)) % 0.37/0.59 (step @p195 :rule alpha_equiv :args (@t9 @t77 (@list @t125))) % 0.37/0.59 (step @p196 :rule trans :premises (@p195 @p194)) % 0.37/0.59 (step @p197 :rule refl :args (tptp.icl_true)) % 0.37/0.59 (step @p198 :rule cong :premises (@p197 @p196) :args ((= tptp.icl_true @t9))) % 0.37/0.59 (step @p199 :rule cong :premises (@p197 @p7) :args (@t1)) % 0.37/0.59 (step @p200 :rule trans :premises (@p199 @p198)) % 0.37/0.59 (step @p201 :rule eq_resolve :premises (@p1 @p200)) % 0.37/0.59 (step @p202 :rule cong :premises (@p201 @p178) :args ((= tptp.icl_true @t94))) % 0.37/0.59 (step @p203 :rule eq-symm :args (@t94 tptp.icl_true)) % 0.37/0.59 (step @p204 :rule cong :premises (@p76 @p197) :args ((= @t102 tptp.icl_true))) % 0.37/0.59 (step @p205 :rule trans :premises (@p204 @p203)) % 0.37/0.59 (step @p206 :rule cong :premises (@p87 @p197) :args (@t4)) % 0.37/0.59 (step @p207 :rule trans :premises (@p206 @p205)) % 0.37/0.59 (step @p208 :rule trans :premises (@p207 @p202 @p193)) % 0.37/0.59 (step @p209 :rule eq_resolve :premises (@p3 @p208)) % 0.37/0.59 (step @p210 :rule refl :args (@t129)) % 0.37/0.59 (step @p211 :rule refl :args (@t93)) % 0.37/0.59 (step @p212 :rule cong :premises (@p211 @p210) :args ((= @t93 @t129))) % 0.37/0.59 (step @p213 :rule symm :premises (@p212)) % 0.37/0.59 (step @p214 :rule eq_resolve :premises (@p211 @p213)) % 0.37/0.59 (step @p215 :rule cong :premises (@p214) :args ((forall @t83 @t93))) % 0.37/0.59 (step @p216 :rule bool-eq-true :args (@t93)) % 0.37/0.59 (step @p217 :rule cong :premises (@p216) :args (@t130)) % 0.37/0.59 (step @p218 :rule trans :premises (@p217 @p215)) % 0.37/0.59 (step @p219 :rule refl :args (@t131)) % 0.37/0.59 (step @p220 :rule cong :premises (@p219 @p218) :args (@t132)) % 0.37/0.59 ; WARNING: add trust step for TRUST % 0.37/0.59 ; trust TRUST THEORY_LEMMA % 0.37/0.59 (step @p221 :rule trust :premises () :args (@t132)) % 0.37/0.59 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 0.37/0.59 (step @p223 :rule implies_elim :premises (@p222)) % 0.37/0.59 (step @p224 :rule chain_m_resolution :premises (@p223 @p209) :args (@t133 (@list false) (@list @t131))) % 0.37/0.59 (assume-push @p232 @t133) % 0.37/0.59 (step @p226 :rule instantiate :premises (@p224) :args ((@list @t122))) % 0.37/0.59 (step-pop @p233 :rule scope :premises (@p226)) % 0.37/0.59 (step @p227 :rule process_scope :premises (@p233) :args (@t123)) % 0.37/0.59 (step @p229 :rule implies_elim :premises (@p227)) % 0.37/0.59 (step @p230 :rule reordering :premises (@p229) :args ((or @t123 (not @t133)))) % 0.37/0.59 (step @p231 false :rule chain_m_resolution :premises (@p230 @p224 @p174) :args (false (@list false true) (@list @t133 @t123))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------