%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV435^4 : 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 : n028.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 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV435^4 : TPTP v9.2.1. Released v3.6.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n028.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 20:18:06 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.39/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-sort tptp.individuals 0) % 0.39/0.60 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.a (-> $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.icl_true (-> $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.icl_false (-> $$unsorted Bool)) % 0.39/0.60 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.39/0.60 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mand () (let ((_let_1 (@var "U" $$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))))))) % 0.39/0.60 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.39/0.60 (define tptp.mdia () (let ((_let_1 (@var "Y" $$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))))))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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))))) % 0.39/0.60 (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))))) % 0.39/0.60 (define tptp.icl_and () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.icl_or () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.icl_impl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.39/0.60 (define tptp.icl_says () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.iclval () (let ((_let_1 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_1) (_ tptp.mvalid _let_1)))) % 0.39/0.60 (define @t1 () (= tptp.icl_true tptp.mtrue)) % 0.39/0.60 (define @t2 () (= tptp.icl_false tptp.mfalse)) % 0.39/0.60 (define @t3 () (@var "A" (-> $$unsorted Bool))) % 0.39/0.60 (define @t4 () (_ tptp.mbox tptp.rel)) % 0.39/0.60 (define @t5 () (@var "B" (-> $$unsorted Bool))) % 0.39/0.60 (define @t6 () (_ @t4 @t5)) % 0.39/0.60 (define @t7 () (_ tptp.icl_princ tptp.a)) % 0.39/0.60 (define @t8 () (= @t7 tptp.icl_true)) % 0.39/0.60 (define @t9 () (not (_ tptp.iclval (_ (_ tptp.icl_says @t7) tptp.icl_false)))) % 0.39/0.60 (define @t10 () (@var "X" $$unsorted)) % 0.39/0.60 (define @t11 () (@list @t10)) % 0.39/0.60 (define @t12 () (lambda @t11 false)) % 0.39/0.60 (define @t13 () (lambda @t11 true)) % 0.39/0.60 (define @t14 () (@var "U" $$unsorted)) % 0.39/0.60 (define @t15 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.60 (define @t16 () (_ @t15 @t14)) % 0.39/0.60 (define @t17 () (lambda (@list @t15 @t14) (not @t16))) % 0.39/0.60 (define @t18 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.60 (define @t19 () (_ @t18 @t14)) % 0.39/0.60 (define @t20 () (@list @t15 @t18 @t14)) % 0.39/0.60 (define @t21 () (lambda @t20 (or @t16 @t19))) % 0.39/0.60 (define @t22 () (lambda @t20 (and @t16 @t19))) % 0.39/0.60 (define @t23 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.60 (define @t24 () (@var "V" (-> $$unsorted Bool))) % 0.39/0.60 (define @t25 () (@var "U" (-> $$unsorted Bool))) % 0.39/0.60 (define @t26 () (@list @t25 @t24 @t23)) % 0.39/0.60 (define @t27 () (lambda @t26 (_ (_ (_ tptp.mor (_ tptp.mnot @t25)) @t24) @t23))) % 0.39/0.60 (define @t28 () (lambda @t26 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t25) @t24)) (_ (_ tptp.mimpl @t24) @t25)) @t23))) % 0.39/0.60 (define @t29 () (@var "Y" $$unsorted)) % 0.39/0.60 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.60 (define @t31 () (_ @t30 @t29)) % 0.39/0.60 (define @t32 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.39/0.60 (define @t33 () (_ (_ @t32 @t10) @t29)) % 0.39/0.60 (define @t34 () (@list @t29)) % 0.39/0.60 (define @t35 () (forall @t34 (=> @t33 @t31))) % 0.39/0.60 (define @t36 () (@list @t32 @t30 @t10)) % 0.39/0.60 (define @t37 () (lambda @t36 @t35)) % 0.39/0.60 (define @t38 () (lambda @t36 (exists @t34 (and @t33 @t31)))) % 0.39/0.60 (define @t39 () (@var "W" $$unsorted)) % 0.39/0.60 (define @t40 () (@var "X" tptp.individuals)) % 0.39/0.60 (define @t41 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.39/0.60 (define @t42 () (_ (_ @t41 @t40) @t39)) % 0.39/0.60 (define @t43 () (@list @t40)) % 0.39/0.60 (define @t44 () (@list @t41 @t39)) % 0.39/0.60 (define @t45 () (lambda @t44 (forall @t43 @t42))) % 0.39/0.60 (define @t46 () (lambda @t44 (exists @t43 @t42))) % 0.39/0.60 (define @t47 () (_ @t30 @t39)) % 0.39/0.60 (define @t48 () (@list @t39)) % 0.39/0.60 (define @t49 () (forall @t48 @t47)) % 0.39/0.60 (define @t50 () (@list @t30)) % 0.39/0.60 (define @t51 () (lambda @t50 @t49)) % 0.39/0.60 (define @t52 () (lambda @t50 (exists @t48 @t47))) % 0.39/0.60 (define @t53 () (not @t47)) % 0.39/0.60 (define @t54 () (lambda @t50 (exists @t48 @t53))) % 0.39/0.60 (define @t55 () (lambda @t50 (forall @t48 @t53))) % 0.39/0.60 (define @t56 () (@list @t30 @t23)) % 0.39/0.60 (define @t57 () (lambda @t56 (_ (_ @t4 @t30) @t23))) % 0.39/0.60 (define @t58 () (lambda @t56 (_ @t30 @t23))) % 0.39/0.60 (define @t59 () (@list @t3 @t5 @t23)) % 0.39/0.60 (define @t60 () (lambda @t59 (_ (_ (_ tptp.mand @t3) @t5) @t23))) % 0.39/0.60 (define @t61 () (_ tptp.mor @t3)) % 0.39/0.60 (define @t62 () (lambda @t59 (_ (_ @t61 @t5) @t23))) % 0.39/0.60 (define @t63 () (lambda @t59 (_ (_ @t4 (_ (_ tptp.mimpl @t3) @t5)) @t23))) % 0.39/0.60 (define @t64 () (@var "S" (-> $$unsorted Bool))) % 0.39/0.60 (define @t65 () (@list @t3 @t64 @t23)) % 0.39/0.60 (define @t66 () (lambda @t65 (_ (_ @t4 (_ @t61 @t64)) @t23))) % 0.39/0.60 (define @t67 () (@list @t15)) % 0.39/0.60 (define @t68 () (lambda @t67 (_ tptp.mvalid @t15))) % 0.39/0.60 (define @t69 () (tptp.a @t29)) % 0.39/0.60 (define @t70 () (not (tptp.rel @t39 @t29))) % 0.39/0.60 (define @t71 () (or @t70 @t69)) % 0.39/0.60 (define @t72 () (@var "BOUND_VARIABLE_8195" $$unsorted)) % 0.39/0.60 (define @t73 () (lambda (@list @t72) false)) % 0.39/0.60 (define @t74 () (_ @t73 @t29)) % 0.39/0.60 (define @t75 () (or @t70 @t69 @t74)) % 0.39/0.60 (define @t76 () (@list @t39 @t29)) % 0.39/0.60 (define @t77 () (forall @t76 @t75)) % 0.39/0.60 (define @t78 () (@list @t10)) % 0.39/0.60 (define @t79 () (tptp.icl_false @t29)) % 0.39/0.60 (define @t80 () (or @t70 @t69 @t79)) % 0.39/0.60 (define @t81 () (forall @t76 @t80)) % 0.39/0.60 (define @t82 () (forall @t34 @t80)) % 0.39/0.60 (define @t83 () (not (tptp.rel @t23 @t29))) % 0.39/0.60 (define @t84 () (@list @t23)) % 0.39/0.60 (define @t85 () (lambda @t84 (forall @t34 (or @t83 @t69 @t79)))) % 0.39/0.60 (define @t86 () (_ @t85 @t39)) % 0.39/0.60 (define @t87 () (forall @t48 @t86)) % 0.39/0.60 (define @t88 () (forall @t48 (_ @t15 @t39))) % 0.39/0.60 (define @t89 () (lambda @t67 @t88)) % 0.39/0.60 (define @t90 () (_ @t64 @t29)) % 0.39/0.60 (define @t91 () (@list @t64 @t23)) % 0.39/0.60 (define @t92 () (_ tptp.a @t29)) % 0.39/0.60 (define @t93 () (or @t83 @t92 @t90)) % 0.39/0.60 (define @t94 () (_ tptp.a @t23)) % 0.39/0.60 (define @t95 () (lambda @t84 @t94)) % 0.39/0.60 (define @t96 () (_ @t95 @t29)) % 0.39/0.60 (define @t97 () (or @t83 @t96 @t90)) % 0.39/0.60 (define @t98 () (forall @t34 @t97)) % 0.39/0.60 (define @t99 () (lambda @t91 @t98)) % 0.39/0.60 (define @t100 () (_ @t3 @t29)) % 0.39/0.60 (define @t101 () (forall @t34 (or @t83 @t100 @t90))) % 0.39/0.60 (define @t102 () (lambda @t65 @t101)) % 0.39/0.60 (define @t103 () (_ @t58 tptp.a)) % 0.39/0.60 (define @t104 () (not (tptp.rel @t10 @t29))) % 0.39/0.60 (define @t105 () (_ @t64 @t29)) % 0.39/0.60 (define @t106 () (_ @t3 @t29)) % 0.39/0.60 (define @t107 () (or @t104 @t106 @t105)) % 0.39/0.60 (define @t108 () (or @t106 @t105)) % 0.39/0.60 (define @t109 () (_ @t3 @t14)) % 0.39/0.60 (define @t110 () (lambda (@list @t14) (or @t109 (_ @t64 @t14)))) % 0.39/0.60 (define @t111 () (_ @t110 @t29)) % 0.39/0.60 (define @t112 () (or @t104 @t111)) % 0.39/0.60 (define @t113 () (forall @t34 @t112)) % 0.39/0.60 (define @t114 () (lambda @t11 @t113)) % 0.39/0.60 (define @t115 () (_ @t30 @t29)) % 0.39/0.60 (define @t116 () (lambda (@list @t30 @t10) (forall @t34 (or @t104 @t115)))) % 0.39/0.60 (define @t117 () (lambda (@list @t18 @t14) (or @t109 @t19))) % 0.39/0.60 (define @t118 () (_ @t32 @t10 @t29)) % 0.39/0.60 (define @t119 () (not @t33)) % 0.39/0.60 (define @t120 () (or @t119 @t31)) % 0.39/0.60 (define @t121 () (_ @t30 @t39)) % 0.39/0.60 (define @t122 () (forall @t76 @t71)) % 0.39/0.60 (define @t123 () (@quantifiers_skolemize @t122 1)) % 0.39/0.60 (define @t124 () (tptp.a @t123)) % 0.39/0.60 (define @t125 () (or (not (tptp.rel (@quantifiers_skolemize @t122 0) @t123)) @t124)) % 0.39/0.60 (define @t126 () (@var "BOUND_VARIABLE_8218" $$unsorted)) % 0.39/0.60 (define @t127 () (lambda (@list @t126) true)) % 0.39/0.60 (define @t128 () (@purify @t127)) % 0.39/0.60 (define @t129 () (@purify @t95)) % 0.39/0.60 (define @t130 () (tptp.a @t23)) % 0.39/0.60 (define @t131 () (forall @t84 (= @t94 true))) % 0.39/0.60 (define @t132 () (= @t129 @t128)) % 0.39/0.60 (define @t133 () (=> @t132 @t131)) % 0.39/0.60 (define @t134 () (forall @t84 @t130)) % 0.39/0.60 (assume @p1 @t1) % 0.39/0.60 (assume @p2 @t2) % 0.39/0.60 (assume @p3 (forall (@list @t3) (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t4 @t3)) @t3)))) % 0.39/0.60 (assume @p4 (forall (@list @t5) (_ tptp.mvalid (_ (_ tptp.mimpl @t6) (_ @t4 @t6))))) % 0.39/0.60 (assume @p5 @t8) % 0.39/0.60 (assume @p6 @t9) % 0.39/0.60 (assume @p7 true) % 0.39/0.60 (step @p8 (= tptp.mfalse @t12) :rule refl :args (@t12)) % 0.39/0.60 (step @p9 (= tptp.mtrue @t13) :rule refl :args (@t13)) % 0.39/0.60 (step @p10 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.39/0.60 (step @p11 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.39/0.60 (step @p12 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.39/0.60 (step @p13 (= tptp.mimpl @t27) :rule refl :args (@t27)) % 0.39/0.60 (step @p14 (= tptp.miff @t28) :rule refl :args (@t28)) % 0.39/0.60 (step @p15 (= tptp.mbox @t37) :rule refl :args (@t37)) % 0.39/0.60 (step @p16 (= tptp.mdia @t38) :rule refl :args (@t38)) % 0.39/0.60 (step @p17 (= tptp.mall @t45) :rule refl :args (@t45)) % 0.39/0.60 (step @p18 (= tptp.mexists @t46) :rule refl :args (@t46)) % 0.39/0.60 (step @p19 (= tptp.mvalid @t51) :rule refl :args (@t51)) % 0.39/0.60 (step @p20 (= tptp.msatisfiable @t52) :rule refl :args (@t52)) % 0.39/0.60 (step @p21 (= tptp.mcountersatisfiable @t54) :rule refl :args (@t54)) % 0.39/0.60 (step @p22 (= tptp.minvalid @t55) :rule refl :args (@t55)) % 0.39/0.60 (step @p23 (= tptp.icl_atom @t57) :rule refl :args (@t57)) % 0.39/0.60 (step @p24 (= tptp.icl_princ @t58) :rule refl :args (@t58)) % 0.39/0.60 (step @p25 (= tptp.icl_and @t60) :rule refl :args (@t60)) % 0.39/0.60 (step @p26 (= tptp.icl_or @t62) :rule refl :args (@t62)) % 0.39/0.60 (step @p27 (= tptp.icl_impl @t63) :rule refl :args (@t63)) % 0.39/0.60 (step @p28 (= tptp.icl_says @t66) :rule refl :args (@t66)) % 0.39/0.60 (step @p29 (= tptp.iclval @t68) :rule refl :args (@t68)) % 0.39/0.60 (step @p30 :rule aci_norm :args ((= (or @t70 @t69 false) @t71))) % 0.39/0.60 (step @p31 :rule beta-reduce :args ((= @t74 false))) % 0.39/0.60 (step @p32 :rule refl :args (@t69)) % 0.39/0.60 (step @p33 :rule refl :args (@t70)) % 0.39/0.60 (step @p34 :rule nary_cong :premises (@p33 @p32 @p31) :args (@t75)) % 0.39/0.60 (step @p35 :rule trans :premises (@p34 @p30)) % 0.39/0.60 (step @p36 :rule cong :premises (@p35) :args (@t77)) % 0.39/0.60 (step @p37 :rule cong :premises (@p36) :args ((not @t77))) % 0.39/0.60 (step @p38 :rule refl :args (@t29)) % 0.39/0.60 (step @p39 :rule refl :args (@t73)) % 0.39/0.60 (step @p40 :rule symm :premises (@p39)) % 0.39/0.60 (step @p41 :rule alpha_equiv :args (@t12 @t78 (@list @t72))) % 0.39/0.60 (step @p42 :rule trans :premises (@p41 @p40)) % 0.39/0.60 (step @p43 :rule refl :args (tptp.icl_false)) % 0.39/0.60 (step @p44 :rule cong :premises (@p43 @p42) :args ((= tptp.icl_false @t12))) % 0.39/0.60 (step @p45 :rule cong :premises (@p43 @p8) :args (@t2)) % 0.39/0.60 (step @p46 :rule trans :premises (@p45 @p44)) % 0.39/0.60 (step @p47 :rule eq_resolve :premises (@p2 @p46)) % 0.39/0.60 (step @p48 :rule ho_cong :premises (@p47 @p38)) % 0.39/0.60 (step @p49 :rule nary_cong :premises (@p33 @p32 @p48) :args (@t80)) % 0.39/0.60 (step @p50 :rule cong :premises (@p49) :args (@t81)) % 0.39/0.60 (step @p51 :rule cong :premises (@p50) :args ((not @t81))) % 0.39/0.60 (step @p52 :rule trans :premises (@p51 @p37)) % 0.39/0.60 (step @p53 :rule quant-merge-prenex :args ((= (forall @t48 @t82) @t81))) % 0.39/0.60 (step @p54 :rule beta-reduce :args ((= @t86 @t82))) % 0.39/0.60 (step @p55 :rule cong :premises (@p54) :args (@t87)) % 0.39/0.60 (step @p56 :rule trans :premises (@p55 @p53)) % 0.39/0.60 (step @p57 :rule beta-reduce :args ((= (_ @t89 @t85) @t87))) % 0.39/0.60 (step @p58 :rule trans :premises (@p57 @p56)) % 0.39/0.60 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t91 (forall @t34 (or @t83 @t69 @t90))) tptp.icl_false) @t85))) % 0.39/0.60 (step @p60 :rule refl :args (@t90)) % 0.39/0.60 (step @p61 :rule refl :args (@t69)) % 0.39/0.60 (step @p62 :rule refl :args (@t92)) % 0.39/0.60 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t92 @t69))) % 0.39/0.60 (step @p64 :rule symm :premises (@p63)) % 0.39/0.60 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.39/0.60 (step @p66 :rule refl :args (@t83)) % 0.39/0.60 (step @p67 :rule nary_cong :premises (@p66 @p65 @p60) :args (@t93)) % 0.39/0.60 (step @p68 :rule cong :premises (@p67) :args ((forall @t34 @t93))) % 0.39/0.60 (step @p69 :rule refl :args (@t90)) % 0.39/0.60 (step @p70 :rule beta-reduce :args ((= @t96 @t92))) % 0.39/0.60 (step @p71 :rule refl :args (@t83)) % 0.39/0.60 (step @p72 :rule nary_cong :premises (@p71 @p70 @p69) :args (@t97)) % 0.39/0.60 (step @p73 :rule cong :premises (@p72) :args (@t98)) % 0.39/0.60 (step @p74 :rule trans :premises (@p73 @p68)) % 0.39/0.60 (step @p75 :rule cong :premises (@p74) :args (@t99)) % 0.39/0.60 (step @p76 :rule beta-reduce :args ((= (_ @t102 @t95) @t99))) % 0.39/0.60 (step @p77 :rule trans :premises (@p76 @p75)) % 0.39/0.60 (step @p78 :rule beta-reduce :args ((= @t103 @t95))) % 0.39/0.60 (step @p79 :rule refl :args (@t102)) % 0.39/0.60 (step @p80 :rule ho_cong :premises (@p79 @p78)) % 0.39/0.60 (step @p81 :rule trans :premises (@p80 @p77)) % 0.39/0.60 (step @p82 :rule ho_cong :premises (@p81 @p43)) % 0.39/0.60 (step @p83 :rule trans :premises (@p82 @p59)) % 0.39/0.60 (step @p84 :rule refl :args (@t89)) % 0.39/0.60 (step @p85 :rule ho_cong :premises (@p84 @p83)) % 0.39/0.60 (step @p86 :rule trans :premises (@p85 @p58)) % 0.39/0.60 (step @p87 :rule cong :premises (@p86) :args ((not (_ @t89 (_ (_ @t102 @t103) tptp.icl_false))))) % 0.39/0.60 (step @p88 :rule refl :args (tptp.a)) % 0.39/0.60 (step @p89 :rule ho_cong :premises (@p24 @p88)) % 0.39/0.60 (step @p90 :rule beta-reduce :args ((= (_ (lambda @t11 (forall @t34 (or @t104 @t100 @t90))) @t23) @t101))) % 0.39/0.60 (step @p91 :rule refl :args (@t23)) % 0.39/0.60 (step @p92 :rule refl :args (@t90)) % 0.39/0.60 (step @p93 :rule refl :args (@t105)) % 0.39/0.60 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t105 @t90))) % 0.39/0.60 (step @p95 :rule symm :premises (@p94)) % 0.39/0.60 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.39/0.60 (step @p97 :rule refl :args (@t100)) % 0.39/0.60 (step @p98 :rule refl :args (@t106)) % 0.39/0.60 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t106 @t100))) % 0.39/0.60 (step @p100 :rule symm :premises (@p99)) % 0.39/0.60 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.39/0.60 (step @p102 :rule refl :args (@t104)) % 0.39/0.60 (step @p103 :rule nary_cong :premises (@p102 @p101 @p96) :args (@t107)) % 0.39/0.60 (step @p104 :rule cong :premises (@p103) :args ((forall @t34 @t107))) % 0.39/0.60 (step @p105 :rule aci_norm :args ((= (or @t104 @t108) @t107))) % 0.39/0.60 (step @p106 :rule beta-reduce :args ((= @t111 @t108))) % 0.39/0.60 (step @p107 :rule refl :args (@t104)) % 0.39/0.60 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t112)) % 0.39/0.60 (step @p109 :rule trans :premises (@p108 @p105)) % 0.39/0.60 (step @p110 :rule cong :premises (@p109) :args (@t113)) % 0.39/0.60 (step @p111 :rule trans :premises (@p110 @p104)) % 0.39/0.60 (step @p112 :rule cong :premises (@p111) :args (@t114)) % 0.39/0.60 (step @p113 :rule beta-reduce :args ((= (_ @t116 @t110) @t114))) % 0.39/0.60 (step @p114 :rule trans :premises (@p113 @p112)) % 0.39/0.60 (step @p115 :rule beta-reduce :args ((= (_ @t117 @t64) @t110))) % 0.39/0.60 (step @p116 :rule refl :args (@t64)) % 0.39/0.60 (step @p117 :rule beta-reduce :args ((= (_ @t21 @t3) @t117))) % 0.39/0.60 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.39/0.60 (step @p119 :rule trans :premises (@p118 @p115)) % 0.39/0.60 (step @p120 :rule beta-reduce :args ((= (_ (lambda @t36 (forall @t34 (or (not @t118) @t115))) tptp.rel) @t116))) % 0.39/0.60 (step @p121 :rule ho_cong :premises (@p120 @p119)) % 0.39/0.60 (step @p122 :rule trans :premises (@p121 @p114)) % 0.39/0.60 (step @p123 :rule ho_cong :premises (@p122 @p91)) % 0.39/0.60 (step @p124 :rule trans :premises (@p123 @p90)) % 0.39/0.60 (step @p125 :rule refl :args (@t3)) % 0.39/0.60 (step @p126 :rule ho_cong :premises (@p11 @p125)) % 0.39/0.60 (step @p127 :rule ho_cong :premises (@p126 @p116)) % 0.39/0.60 (step @p128 :rule refl :args (tptp.rel)) % 0.39/0.60 (step @p129 :rule refl :args (@t115)) % 0.39/0.60 (step @p130 :rule refl :args (@t31)) % 0.39/0.60 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t31 @t115))) % 0.39/0.60 (step @p132 :rule symm :premises (@p131)) % 0.39/0.60 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.39/0.60 (step @p134 :rule refl :args (@t118)) % 0.39/0.60 (step @p135 :rule refl :args (@t33)) % 0.39/0.60 (step @p136 :rule cong :premises (@p135 @p134) :args ((= @t33 @t118))) % 0.39/0.60 (step @p137 :rule symm :premises (@p136)) % 0.39/0.60 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 0.39/0.60 (step @p139 :rule cong :premises (@p138) :args (@t119)) % 0.39/0.60 (step @p140 :rule nary_cong :premises (@p139 @p133) :args (@t120)) % 0.39/0.60 (step @p141 :rule cong :premises (@p140) :args ((forall @t34 @t120))) % 0.39/0.60 (step @p142 :rule bool-impl-elim :args (@t33 @t31)) % 0.39/0.60 (step @p143 :rule cong :premises (@p142) :args (@t35)) % 0.39/0.60 (step @p144 :rule trans :premises (@p143 @p141)) % 0.39/0.60 (step @p145 :rule cong :premises (@p144) :args (@t37)) % 0.39/0.60 (step @p146 :rule trans :premises (@p15 @p145)) % 0.39/0.60 (step @p147 :rule ho_cong :premises (@p146 @p128)) % 0.39/0.60 (step @p148 :rule ho_cong :premises (@p147 @p127)) % 0.39/0.60 (step @p149 :rule ho_cong :premises (@p148 @p91)) % 0.39/0.60 (step @p150 :rule trans :premises (@p149 @p124)) % 0.39/0.60 (step @p151 :rule cong :premises (@p150) :args (@t66)) % 0.39/0.60 (step @p152 :rule trans :premises (@p28 @p151)) % 0.39/0.60 (step @p153 :rule ho_cong :premises (@p152 @p89)) % 0.39/0.60 (step @p154 :rule ho_cong :premises (@p153 @p43)) % 0.39/0.60 (step @p155 :rule beta-reduce :args ((= (_ (lambda @t50 (forall @t48 @t121)) @t15) @t88))) % 0.39/0.60 (step @p156 :rule refl :args (@t15)) % 0.39/0.60 (step @p157 :rule refl :args (@t121)) % 0.39/0.60 (step @p158 :rule refl :args (@t47)) % 0.39/0.60 (step @p159 :rule cong :premises (@p158 @p157) :args ((= @t47 @t121))) % 0.39/0.60 (step @p160 :rule symm :premises (@p159)) % 0.39/0.60 (step @p161 :rule eq_resolve :premises (@p158 @p160)) % 0.39/0.60 (step @p162 :rule cong :premises (@p161) :args (@t49)) % 0.39/0.60 (step @p163 :rule cong :premises (@p162) :args (@t51)) % 0.39/0.60 (step @p164 :rule trans :premises (@p19 @p163)) % 0.39/0.60 (step @p165 :rule ho_cong :premises (@p164 @p156)) % 0.39/0.60 (step @p166 :rule trans :premises (@p165 @p155)) % 0.39/0.60 (step @p167 :rule cong :premises (@p166) :args (@t68)) % 0.39/0.60 (step @p168 :rule trans :premises (@p29 @p167)) % 0.39/0.60 (step @p169 :rule ho_cong :premises (@p168 @p154)) % 0.39/0.60 (step @p170 :rule cong :premises (@p169) :args (@t9)) % 0.39/0.60 (step @p171 :rule trans :premises (@p170 @p87)) % 0.39/0.60 (step @p172 :rule trans :premises (@p171 @p52)) % 0.39/0.60 (step @p173 :rule eq_resolve :premises (@p6 @p172)) % 0.39/0.60 (step @p174 :rule skolemize :premises (@p173)) % 0.39/0.60 (step @p175 :rule cnf_or_neg :args (@t125 1)) % 0.39/0.60 (step @p176 :rule chain_m_resolution :premises (@p175 @p174) :args ((not @t124) (@list true) (@list @t125))) % 0.39/0.60 (step @p177 :rule eq-symm :args (@t128 @t129)) % 0.39/0.60 (step @p178 :rule eq-refl :args (@t95)) % 0.39/0.60 (step @p179 :rule skolem_intro :args (@t129)) % 0.39/0.60 (step @p180 :rule refl :args (@t95)) % 0.39/0.60 (step @p181 :rule cong :premises (@p180 @p179) :args ((= @t95 @t129))) % 0.39/0.60 (step @p182 :rule trans :premises (@p181 @p178)) % 0.39/0.60 (step @p183 :rule true_elim :premises (@p182)) % 0.39/0.60 (step @p184 :rule eq-refl :args (@t127)) % 0.39/0.60 (step @p185 :rule refl :args (@t127)) % 0.39/0.60 (step @p186 :rule symm :premises (@p185)) % 0.39/0.60 (step @p187 :rule refl :args (@t127)) % 0.39/0.60 (step @p188 :rule cong :premises (@p187 @p186) :args ((= @t127 @t127))) % 0.39/0.60 (step @p189 :rule trans :premises (@p188 @p184)) % 0.39/0.60 (step @p190 :rule skolem_intro :args (@t128)) % 0.39/0.60 (step @p191 :rule cong :premises (@p187 @p190) :args ((= @t127 @t128))) % 0.39/0.60 (step @p192 :rule trans :premises (@p191 @p189)) % 0.39/0.60 (step @p193 :rule true_elim :premises (@p192)) % 0.39/0.60 (step @p194 :rule cong :premises (@p193 @p183) :args ((= @t127 @t95))) % 0.39/0.60 (step @p195 :rule trans :premises (@p194 @p177)) % 0.39/0.60 (step @p196 :rule symm :premises (@p185)) % 0.39/0.60 (step @p197 :rule alpha_equiv :args (@t13 @t78 (@list @t126))) % 0.39/0.60 (step @p198 :rule trans :premises (@p197 @p196)) % 0.39/0.60 (step @p199 :rule refl :args (tptp.icl_true)) % 0.39/0.60 (step @p200 :rule cong :premises (@p199 @p198) :args ((= tptp.icl_true @t13))) % 0.39/0.60 (step @p201 :rule cong :premises (@p199 @p9) :args (@t1)) % 0.39/0.60 (step @p202 :rule trans :premises (@p201 @p200)) % 0.39/0.60 (step @p203 :rule eq_resolve :premises (@p1 @p202)) % 0.39/0.60 (step @p204 :rule cong :premises (@p203 @p180) :args ((= tptp.icl_true @t95))) % 0.39/0.60 (step @p205 :rule eq-symm :args (@t95 tptp.icl_true)) % 0.39/0.60 (step @p206 :rule cong :premises (@p78 @p199) :args ((= @t103 tptp.icl_true))) % 0.39/0.60 (step @p207 :rule trans :premises (@p206 @p205)) % 0.39/0.60 (step @p208 :rule cong :premises (@p89 @p199) :args (@t8)) % 0.39/0.60 (step @p209 :rule trans :premises (@p208 @p207)) % 0.39/0.60 (step @p210 :rule trans :premises (@p209 @p204 @p195)) % 0.39/0.60 (step @p211 :rule eq_resolve :premises (@p5 @p210)) % 0.39/0.60 (step @p212 :rule refl :args (@t130)) % 0.39/0.60 (step @p213 :rule refl :args (@t94)) % 0.39/0.60 (step @p214 :rule cong :premises (@p213 @p212) :args ((= @t94 @t130))) % 0.39/0.60 (step @p215 :rule symm :premises (@p214)) % 0.39/0.60 (step @p216 :rule eq_resolve :premises (@p213 @p215)) % 0.39/0.60 (step @p217 :rule cong :premises (@p216) :args ((forall @t84 @t94))) % 0.39/0.60 (step @p218 :rule bool-eq-true :args (@t94)) % 0.39/0.60 (step @p219 :rule cong :premises (@p218) :args (@t131)) % 0.39/0.60 (step @p220 :rule trans :premises (@p219 @p217)) % 0.39/0.60 (step @p221 :rule refl :args (@t132)) % 0.39/0.60 (step @p222 :rule cong :premises (@p221 @p220) :args (@t133)) % 0.39/0.60 ; WARNING: add trust step for TRUST % 0.39/0.60 ; trust TRUST THEORY_LEMMA % 0.39/0.60 (step @p223 :rule trust :premises () :args (@t133)) % 0.39/0.60 (step @p224 :rule eq_resolve :premises (@p223 @p222)) % 0.39/0.60 (step @p225 :rule implies_elim :premises (@p224)) % 0.39/0.60 (step @p226 :rule chain_m_resolution :premises (@p225 @p211) :args (@t134 (@list false) (@list @t132))) % 0.39/0.60 (assume-push @p234 @t134) % 0.39/0.60 (step @p228 :rule instantiate :premises (@p226) :args ((@list @t123))) % 0.39/0.60 (step-pop @p235 :rule scope :premises (@p228)) % 0.39/0.60 (step @p229 :rule process_scope :premises (@p235) :args (@t124)) % 0.39/0.60 (step @p231 :rule implies_elim :premises (@p229)) % 0.39/0.60 (step @p232 :rule reordering :premises (@p231) :args ((or @t124 (not @t134)))) % 0.39/0.60 (step @p233 false :rule chain_m_resolution :premises (@p232 @p226 @p176) :args (false (@list false true) (@list @t134 @t124))) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------