%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO886^8 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 09:13:41 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO886^8 : TPTP v9.2.1. Released v3.6.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.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 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 01:07:16 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-sort tptp.individuals 0) % 0.38/0.57 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.38/0.57 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.38/0.57 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.57 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.57 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.57 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.57 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.38/0.57 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.38/0.57 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.38/0.57 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.57 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.57 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.57 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.57 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.57 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.57 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.57 (define @t2 () (@var "X" tptp.individuals)) % 0.38/0.57 (define @t3 () (@var "A" (-> tptp.individuals $$unsorted Bool))) % 0.38/0.57 (define @t4 () (_ @t3 @t2)) % 0.38/0.57 (define @t5 () (@list @t2 @t1)) % 0.38/0.57 (define @t6 () (lambda @t5 (_ @t4 @t1))) % 0.38/0.57 (define @t7 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.57 (define @t8 () (_ tptp.mbox @t7)) % 0.38/0.57 (define @t9 () (lambda @t5 (_ (_ @t8 @t4) @t1))) % 0.38/0.57 (define @t10 () (@list @t7 @t3)) % 0.38/0.57 (define @t11 () (forall @t10 (_ tptp.mvalid (_ (_ tptp.mimpl (_ tptp.mall @t9)) (_ @t8 (_ tptp.mall @t6)))))) % 0.38/0.57 (define @t12 () (not @t11)) % 0.38/0.57 (define @t13 () (@var "X" $$unsorted)) % 0.38/0.57 (define @t14 () (@list @t13)) % 0.38/0.57 (define @t15 () (lambda @t14 false)) % 0.38/0.57 (define @t16 () (lambda @t14 true)) % 0.38/0.57 (define @t17 () (@var "U" $$unsorted)) % 0.38/0.57 (define @t18 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.57 (define @t19 () (_ @t18 @t17)) % 0.38/0.57 (define @t20 () (lambda (@list @t18 @t17) (not @t19))) % 0.38/0.57 (define @t21 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.57 (define @t22 () (_ @t21 @t17)) % 0.38/0.57 (define @t23 () (@list @t18 @t21 @t17)) % 0.38/0.57 (define @t24 () (lambda @t23 (or @t19 @t22))) % 0.38/0.57 (define @t25 () (lambda @t23 (and @t19 @t22))) % 0.38/0.57 (define @t26 () (@var "V" (-> $$unsorted Bool))) % 0.38/0.57 (define @t27 () (@var "U" (-> $$unsorted Bool))) % 0.38/0.57 (define @t28 () (@list @t27 @t26 @t1)) % 0.38/0.57 (define @t29 () (lambda @t28 (_ (_ (_ tptp.mor (_ tptp.mnot @t27)) @t26) @t1))) % 0.38/0.57 (define @t30 () (lambda @t28 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t27) @t26)) (_ (_ tptp.mimpl @t26) @t27)) @t1))) % 0.38/0.57 (define @t31 () (@var "Y" $$unsorted)) % 0.38/0.57 (define @t32 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.57 (define @t33 () (_ @t32 @t31)) % 0.38/0.57 (define @t34 () (_ (_ @t7 @t13) @t31)) % 0.38/0.57 (define @t35 () (@list @t31)) % 0.38/0.57 (define @t36 () (forall @t35 (=> @t34 @t33))) % 0.38/0.57 (define @t37 () (@list @t7 @t32 @t13)) % 0.38/0.57 (define @t38 () (lambda @t37 @t36)) % 0.38/0.57 (define @t39 () (lambda @t37 (exists @t35 (and @t34 @t33)))) % 0.38/0.57 (define @t40 () (@var "W" $$unsorted)) % 0.38/0.57 (define @t41 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.38/0.57 (define @t42 () (_ (_ @t41 @t2) @t40)) % 0.38/0.57 (define @t43 () (@list @t2)) % 0.38/0.57 (define @t44 () (forall @t43 @t42)) % 0.38/0.57 (define @t45 () (@list @t41 @t40)) % 0.38/0.57 (define @t46 () (lambda @t45 @t44)) % 0.38/0.57 (define @t47 () (lambda @t45 (exists @t43 @t42))) % 0.38/0.57 (define @t48 () (_ @t32 @t40)) % 0.38/0.57 (define @t49 () (@list @t40)) % 0.38/0.57 (define @t50 () (forall @t49 @t48)) % 0.38/0.57 (define @t51 () (@list @t32)) % 0.38/0.57 (define @t52 () (lambda @t51 @t50)) % 0.38/0.57 (define @t53 () (lambda @t51 (exists @t49 @t48))) % 0.38/0.57 (define @t54 () (not @t48)) % 0.38/0.57 (define @t55 () (lambda @t51 (exists @t49 @t54))) % 0.38/0.57 (define @t56 () (lambda @t51 (forall @t49 @t54))) % 0.38/0.57 (define @t57 () (@var "BOUND_VARIABLE_7863" $$unsorted)) % 0.38/0.57 (define @t58 () (@var "BOUND_VARIABLE_7865" tptp.individuals)) % 0.38/0.57 (define @t59 () (_ @t3 @t58 @t57)) % 0.38/0.57 (define @t60 () (not (_ @t7 @t40 @t57))) % 0.38/0.57 (define @t61 () (_ @t3 @t2 @t31)) % 0.38/0.57 (define @t62 () (not (_ @t7 @t40 @t31))) % 0.38/0.57 (define @t63 () (or @t62 @t61)) % 0.38/0.57 (define @t64 () (@list @t2 @t31)) % 0.38/0.57 (define @t65 () (forall @t64 @t63)) % 0.38/0.57 (define @t66 () (not @t65)) % 0.38/0.57 (define @t67 () (or @t66 @t60 @t59)) % 0.38/0.57 (define @t68 () (forall (@list @t7 @t3 @t40 @t57 @t58) @t67)) % 0.38/0.57 (define @t69 () (@list @t40 @t57 @t58)) % 0.38/0.57 (define @t70 () (or @t60 @t59)) % 0.38/0.57 (define @t71 () (or @t66 @t70)) % 0.38/0.57 (define @t72 () (forall @t69 @t71)) % 0.38/0.57 (define @t73 () (@list @t57 @t58)) % 0.38/0.57 (define @t74 () (forall @t73 @t71)) % 0.38/0.57 (define @t75 () (forall @t73 @t70)) % 0.38/0.57 (define @t76 () (@var "BOUND_VARIABLE_7839" tptp.individuals)) % 0.38/0.57 (define @t77 () (or @t66 @t75)) % 0.38/0.57 (define @t78 () (_ @t3 @t76 @t31)) % 0.38/0.57 (define @t79 () (@list @t31 @t76)) % 0.38/0.57 (define @t80 () (or @t66 (forall @t79 (or @t62 @t78)))) % 0.38/0.57 (define @t81 () (not (_ @t7 @t1 @t31))) % 0.38/0.57 (define @t82 () (forall @t79 (or @t81 @t78))) % 0.38/0.57 (define @t83 () (or @t81 @t61)) % 0.38/0.57 (define @t84 () (forall @t64 @t83)) % 0.38/0.57 (define @t85 () (not @t84)) % 0.38/0.57 (define @t86 () (@list @t1)) % 0.38/0.57 (define @t87 () (lambda @t86 (or @t85 @t82))) % 0.38/0.57 (define @t88 () (_ @t87 @t40)) % 0.38/0.57 (define @t89 () (forall @t49 @t88)) % 0.38/0.57 (define @t90 () (_ @t32 @t40)) % 0.38/0.57 (define @t91 () (lambda @t51 (forall @t49 @t90))) % 0.38/0.57 (define @t92 () (_ @t7 @t13 @t31)) % 0.38/0.57 (define @t93 () (not @t92)) % 0.38/0.57 (define @t94 () (or @t93 @t78)) % 0.38/0.57 (define @t95 () (forall @t79 @t94)) % 0.38/0.57 (define @t96 () (lambda @t14 @t95)) % 0.38/0.57 (define @t97 () (_ @t96 @t1)) % 0.38/0.57 (define @t98 () (or @t85 @t97)) % 0.38/0.57 (define @t99 () (lambda @t86 @t98)) % 0.38/0.57 (define @t100 () (_ @t26 @t1)) % 0.38/0.57 (define @t101 () (@list @t26 @t1)) % 0.38/0.57 (define @t102 () (@list @t76)) % 0.38/0.57 (define @t103 () (forall @t102 @t94)) % 0.38/0.57 (define @t104 () (forall @t102 @t78)) % 0.38/0.57 (define @t105 () (or @t93 @t104)) % 0.38/0.57 (define @t106 () (forall @t43 @t61)) % 0.38/0.57 (define @t107 () (_ @t3 @t2 @t40)) % 0.38/0.57 (define @t108 () (lambda @t49 (forall @t43 @t107))) % 0.38/0.57 (define @t109 () (_ @t108 @t31)) % 0.38/0.57 (define @t110 () (or @t93 @t109)) % 0.38/0.57 (define @t111 () (forall @t35 @t110)) % 0.38/0.57 (define @t112 () (lambda @t14 @t111)) % 0.38/0.57 (define @t113 () (_ @t32 @t31)) % 0.38/0.57 (define @t114 () (forall @t35 (or @t93 @t113))) % 0.38/0.57 (define @t115 () (lambda (@list @t32 @t13) @t114)) % 0.38/0.57 (define @t116 () (_ @t4 @t40)) % 0.38/0.57 (define @t117 () (_ @t6 @t2 @t40)) % 0.38/0.57 (define @t118 () (forall @t43 @t117)) % 0.38/0.57 (define @t119 () (lambda @t49 @t118)) % 0.38/0.57 (define @t120 () (_ @t41 @t2 @t40)) % 0.38/0.57 (define @t121 () (lambda @t45 (forall @t43 @t120))) % 0.38/0.57 (define @t122 () (_ @t121 @t6)) % 0.38/0.57 (define @t123 () (_ (lambda @t37 @t114) @t7)) % 0.38/0.57 (define @t124 () (lambda @t49 @t65)) % 0.38/0.57 (define @t125 () (_ @t124 @t1)) % 0.38/0.57 (define @t126 () (not @t125)) % 0.38/0.57 (define @t127 () (or @t126 @t100)) % 0.38/0.57 (define @t128 () (lambda @t101 @t127)) % 0.38/0.57 (define @t129 () (or (not (_ @t27 @t1)) @t100)) % 0.38/0.57 (define @t130 () (lambda @t28 @t129)) % 0.38/0.57 (define @t131 () (forall @t35 @t63)) % 0.38/0.57 (define @t132 () (forall @t35 @t83)) % 0.38/0.57 (define @t133 () (lambda @t5 @t132)) % 0.38/0.57 (define @t134 () (_ @t133 @t2 @t40)) % 0.38/0.57 (define @t135 () (forall @t43 @t134)) % 0.38/0.57 (define @t136 () (lambda @t49 @t135)) % 0.38/0.57 (define @t137 () (_ @t4 @t31)) % 0.38/0.57 (define @t138 () (or @t93 @t137)) % 0.38/0.57 (define @t139 () (_ @t4 @t31)) % 0.38/0.57 (define @t140 () (or @t93 @t139)) % 0.38/0.57 (define @t141 () (forall @t35 @t140)) % 0.38/0.57 (define @t142 () (lambda @t14 @t141)) % 0.38/0.57 (define @t143 () (lambda @t5 (_ (_ @t123 @t4) @t1))) % 0.38/0.57 (define @t144 () (forall @t10 (_ @t91 (_ (_ @t130 (_ @t121 @t143)) (_ @t123 @t122))))) % 0.38/0.57 (define @t145 () (not @t34)) % 0.38/0.57 (define @t146 () (or @t145 @t33)) % 0.38/0.57 (define @t147 () (not (_ @t27 @t17))) % 0.38/0.57 (define @t148 () (@list @t17)) % 0.38/0.57 (define @t149 () (lambda @t148 (or @t147 (_ @t26 @t17)))) % 0.38/0.57 (define @t150 () (@list @t21 @t17)) % 0.38/0.57 (define @t151 () (lambda @t148 @t147)) % 0.38/0.57 (define @t152 () (_ @t151 @t17)) % 0.38/0.57 (define @t153 () (or @t152 @t22)) % 0.38/0.57 (define @t154 () (lambda @t150 @t153)) % 0.38/0.57 (define @t155 () (@quantifiers_skolemize @t68 1)) % 0.38/0.57 (define @t156 () (@quantifiers_skolemize @t68 2)) % 0.38/0.57 (define @t157 () (@quantifiers_skolemize @t68 0)) % 0.38/0.57 (define @t158 () (forall @t64 (or (not (_ @t157 @t156 @t31)) (_ @t155 @t2 @t31)))) % 0.38/0.57 (define @t159 () (@quantifiers_skolemize @t68 3)) % 0.38/0.57 (define @t160 () (@quantifiers_skolemize @t68 4)) % 0.38/0.57 (define @t161 () (_ @t155 @t160 @t159)) % 0.38/0.57 (define @t162 () (_ @t157 @t156 @t159)) % 0.38/0.57 (define @t163 () (not @t162)) % 0.38/0.57 (define @t164 () (not @t158)) % 0.38/0.57 (define @t165 () (or @t164 @t163 @t161)) % 0.38/0.57 (define @t166 () (@list true)) % 0.38/0.57 (define @t167 () (@list @t165)) % 0.38/0.57 (define @t168 () (or @t163 @t161)) % 0.38/0.57 (define @t169 () (not @t168)) % 0.38/0.57 (assume @p1 @t12) % 0.38/0.57 (assume @p2 true) % 0.38/0.57 (step @p3 (= tptp.mfalse @t15) :rule refl :args (@t15)) % 0.38/0.57 (step @p4 (= tptp.mtrue @t16) :rule refl :args (@t16)) % 0.38/0.57 (step @p5 (= tptp.mnot @t20) :rule refl :args (@t20)) % 0.38/0.57 (step @p6 (= tptp.mor @t24) :rule refl :args (@t24)) % 0.38/0.57 (step @p7 (= tptp.mand @t25) :rule refl :args (@t25)) % 0.38/0.57 (step @p8 (= tptp.mimpl @t29) :rule refl :args (@t29)) % 0.38/0.57 (step @p9 (= tptp.miff @t30) :rule refl :args (@t30)) % 0.38/0.57 (step @p10 (= tptp.mbox @t38) :rule refl :args (@t38)) % 0.38/0.57 (step @p11 (= tptp.mdia @t39) :rule refl :args (@t39)) % 0.38/0.57 (step @p12 (= tptp.mall @t46) :rule refl :args (@t46)) % 0.38/0.57 (step @p13 (= tptp.mexists @t47) :rule refl :args (@t47)) % 0.38/0.57 (step @p14 (= tptp.mvalid @t52) :rule refl :args (@t52)) % 0.38/0.57 (step @p15 (= tptp.msatisfiable @t53) :rule refl :args (@t53)) % 0.38/0.57 (step @p16 (= tptp.mcountersatisfiable @t55) :rule refl :args (@t55)) % 0.38/0.57 (step @p17 (= tptp.minvalid @t56) :rule refl :args (@t56)) % 0.38/0.57 (step @p18 :rule quant-merge-prenex :args ((= (forall @t10 (forall @t69 @t67)) @t68))) % 0.38/0.57 (step @p19 :rule aci_norm :args ((= @t71 @t67))) % 0.38/0.57 (step @p20 :rule cong :premises (@p19) :args (@t72)) % 0.38/0.57 (step @p21 :rule quant-merge-prenex :args ((= (forall @t49 @t74) @t72))) % 0.38/0.57 (step @p22 :rule alpha_equiv :args (@t75 (@list @t57 @t58) (@list @t31 @t76))) % 0.38/0.57 (step @p23 :rule refl :args (@t66)) % 0.38/0.57 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t77)) % 0.38/0.57 (step @p25 :rule quant-miniscope-or :args ((= @t74 @t77))) % 0.38/0.57 (step @p26 :rule trans :premises (@p25 @p24)) % 0.38/0.57 (step @p27 :rule symm :premises (@p26)) % 0.38/0.57 (step @p28 :rule cong :premises (@p27) :args ((forall @t49 @t80))) % 0.38/0.57 (step @p29 :rule trans :premises (@p28 @p21)) % 0.38/0.57 (step @p30 :rule trans :premises (@p29 @p20)) % 0.38/0.57 (step @p31 :rule beta-reduce :args ((= @t88 @t80))) % 0.38/0.57 (step @p32 :rule cong :premises (@p31) :args (@t89)) % 0.38/0.57 (step @p33 :rule trans :premises (@p32 @p30)) % 0.38/0.57 (step @p34 :rule beta-reduce :args ((= (_ @t91 @t87) @t89))) % 0.38/0.57 (step @p35 :rule trans :premises (@p34 @p33)) % 0.38/0.57 (step @p36 :rule beta-reduce :args ((= @t97 @t82))) % 0.38/0.57 (step @p37 :rule refl :args (@t85)) % 0.38/0.57 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t98)) % 0.38/0.57 (step @p39 :rule cong :premises (@p38) :args (@t99)) % 0.38/0.57 (step @p40 :rule beta-reduce :args ((= (_ (lambda @t101 (or @t85 @t100)) @t96) @t99))) % 0.38/0.57 (step @p41 :rule trans :premises (@p40 @p39)) % 0.38/0.57 (step @p42 :rule quant-merge-prenex :args ((= (forall @t35 @t103) @t95))) % 0.38/0.57 (step @p43 :rule alpha_equiv :args (@t104 (@list @t76) (@list @t2))) % 0.38/0.57 (step @p44 :rule refl :args (@t93)) % 0.38/0.57 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t105)) % 0.38/0.57 (step @p46 :rule quant-miniscope-or :args ((= @t103 @t105))) % 0.38/0.57 (step @p47 :rule trans :premises (@p46 @p45)) % 0.38/0.57 (step @p48 :rule symm :premises (@p47)) % 0.38/0.57 (step @p49 :rule cong :premises (@p48) :args ((forall @t35 (or @t93 @t106)))) % 0.38/0.57 (step @p50 :rule trans :premises (@p49 @p42)) % 0.38/0.57 (step @p51 :rule beta-reduce :args ((= @t109 @t106))) % 0.38/0.57 (step @p52 :rule refl :args (@t93)) % 0.38/0.57 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t110)) % 0.38/0.57 (step @p54 :rule cong :premises (@p53) :args (@t111)) % 0.38/0.57 (step @p55 :rule trans :premises (@p54 @p50)) % 0.38/0.57 (step @p56 :rule cong :premises (@p55) :args (@t112)) % 0.38/0.57 (step @p57 :rule beta-reduce :args ((= (_ @t115 @t108) @t112))) % 0.38/0.57 (step @p58 :rule trans :premises (@p57 @p56)) % 0.38/0.57 (step @p59 :rule refl :args (@t107)) % 0.38/0.57 (step @p60 :rule refl :args (@t116)) % 0.38/0.57 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t116 @t107))) % 0.38/0.57 (step @p62 :rule symm :premises (@p61)) % 0.38/0.57 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.38/0.57 (step @p64 :rule cong :premises (@p63) :args ((forall @t43 @t116))) % 0.38/0.57 (step @p65 :rule beta-reduce :args ((= @t117 @t116))) % 0.38/0.57 (step @p66 :rule cong :premises (@p65) :args (@t118)) % 0.38/0.57 (step @p67 :rule trans :premises (@p66 @p64)) % 0.38/0.57 (step @p68 :rule cong :premises (@p67) :args (@t119)) % 0.38/0.57 (step @p69 :rule beta-reduce :args ((= @t122 @t119))) % 0.38/0.57 (step @p70 :rule trans :premises (@p69 @p68)) % 0.38/0.57 (step @p71 :rule beta-reduce :args ((= @t123 @t115))) % 0.38/0.57 (step @p72 :rule ho_cong :premises (@p71 @p70)) % 0.38/0.57 (step @p73 :rule trans :premises (@p72 @p58)) % 0.38/0.57 (step @p74 :rule refl :args (@t100)) % 0.38/0.57 (step @p75 :rule beta-reduce :args ((= @t125 @t84))) % 0.38/0.57 (step @p76 :rule cong :premises (@p75) :args (@t126)) % 0.38/0.57 (step @p77 :rule nary_cong :premises (@p76 @p74) :args (@t127)) % 0.38/0.57 (step @p78 :rule cong :premises (@p77) :args (@t128)) % 0.38/0.57 (step @p79 :rule beta-reduce :args ((= (_ @t130 @t124) @t128))) % 0.38/0.57 (step @p80 :rule trans :premises (@p79 @p78)) % 0.38/0.57 (step @p81 :rule quant-merge-prenex :args ((= (forall @t43 @t131) @t65))) % 0.38/0.57 (step @p82 :rule beta-reduce :args ((= @t134 @t131))) % 0.38/0.57 (step @p83 :rule cong :premises (@p82) :args (@t135)) % 0.38/0.57 (step @p84 :rule trans :premises (@p83 @p81)) % 0.38/0.57 (step @p85 :rule cong :premises (@p84) :args (@t136)) % 0.38/0.57 (step @p86 :rule beta-reduce :args ((= (_ @t121 @t133) @t136))) % 0.38/0.57 (step @p87 :rule trans :premises (@p86 @p85)) % 0.38/0.57 (step @p88 :rule beta-reduce :args ((= (_ (lambda @t14 (forall @t35 (or @t93 @t61))) @t1) @t132))) % 0.38/0.57 (step @p89 :rule refl :args (@t1)) % 0.38/0.57 (step @p90 :rule refl :args (@t61)) % 0.38/0.57 (step @p91 :rule refl :args (@t137)) % 0.38/0.57 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t137 @t61))) % 0.38/0.57 (step @p93 :rule symm :premises (@p92)) % 0.38/0.57 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 0.38/0.57 (step @p95 :rule nary_cong :premises (@p44 @p94) :args (@t138)) % 0.38/0.57 (step @p96 :rule cong :premises (@p95) :args ((forall @t35 @t138))) % 0.38/0.57 (step @p97 :rule refl :args (@t139)) % 0.38/0.57 (step @p98 :rule nary_cong :premises (@p52 @p97) :args (@t140)) % 0.38/0.57 (step @p99 :rule cong :premises (@p98) :args (@t141)) % 0.38/0.57 (step @p100 :rule trans :premises (@p99 @p96)) % 0.38/0.57 (step @p101 :rule cong :premises (@p100) :args (@t142)) % 0.38/0.57 (step @p102 :rule beta-reduce :args ((= (_ @t115 @t4) @t142))) % 0.38/0.57 (step @p103 :rule trans :premises (@p102 @p101)) % 0.38/0.57 (step @p104 :rule refl :args (@t4)) % 0.38/0.57 (step @p105 :rule ho_cong :premises (@p71 @p104)) % 0.38/0.57 (step @p106 :rule trans :premises (@p105 @p103)) % 0.38/0.57 (step @p107 :rule ho_cong :premises (@p106 @p89)) % 0.38/0.57 (step @p108 :rule trans :premises (@p107 @p88)) % 0.38/0.57 (step @p109 :rule cong :premises (@p108) :args (@t143)) % 0.38/0.57 (step @p110 :rule refl :args (@t121)) % 0.38/0.57 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 0.38/0.57 (step @p112 :rule trans :premises (@p111 @p87)) % 0.38/0.57 (step @p113 :rule refl :args (@t130)) % 0.38/0.57 (step @p114 :rule ho_cong :premises (@p113 @p112)) % 0.38/0.57 (step @p115 :rule trans :premises (@p114 @p80)) % 0.38/0.57 (step @p116 :rule ho_cong :premises (@p115 @p73)) % 0.38/0.57 (step @p117 :rule trans :premises (@p116 @p41)) % 0.38/0.57 (step @p118 :rule refl :args (@t91)) % 0.38/0.57 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.38/0.57 (step @p120 :rule trans :premises (@p119 @p35)) % 0.38/0.57 (step @p121 :rule cong :premises (@p120) :args (@t144)) % 0.38/0.57 (step @p122 :rule trans :premises (@p121 @p18)) % 0.38/0.57 (step @p123 :rule cong :premises (@p122) :args ((not @t144))) % 0.38/0.57 (step @p124 :rule refl :args (@t6)) % 0.38/0.57 (step @p125 :rule refl :args (@t120)) % 0.38/0.57 (step @p126 :rule refl :args (@t42)) % 0.38/0.57 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t42 @t120))) % 0.38/0.57 (step @p128 :rule symm :premises (@p127)) % 0.38/0.57 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.38/0.57 (step @p130 :rule cong :premises (@p129) :args (@t44)) % 0.38/0.57 (step @p131 :rule cong :premises (@p130) :args (@t46)) % 0.38/0.57 (step @p132 :rule trans :premises (@p12 @p131)) % 0.38/0.57 (step @p133 :rule ho_cong :premises (@p132 @p124)) % 0.38/0.57 (step @p134 :rule refl :args (@t7)) % 0.38/0.57 (step @p135 :rule refl :args (@t113)) % 0.38/0.57 (step @p136 :rule refl :args (@t33)) % 0.38/0.57 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t33 @t113))) % 0.38/0.57 (step @p138 :rule symm :premises (@p137)) % 0.38/0.57 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.38/0.57 (step @p140 :rule refl :args (@t92)) % 0.38/0.57 (step @p141 :rule refl :args (@t34)) % 0.38/0.57 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t34 @t92))) % 0.38/0.57 (step @p143 :rule symm :premises (@p142)) % 0.38/0.57 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.38/0.57 (step @p145 :rule cong :premises (@p144) :args (@t145)) % 0.38/0.57 (step @p146 :rule nary_cong :premises (@p145 @p139) :args (@t146)) % 0.38/0.57 (step @p147 :rule cong :premises (@p146) :args ((forall @t35 @t146))) % 0.38/0.57 (step @p148 :rule bool-impl-elim :args (@t34 @t33)) % 0.38/0.57 (step @p149 :rule cong :premises (@p148) :args (@t36)) % 0.38/0.57 (step @p150 :rule trans :premises (@p149 @p147)) % 0.38/0.57 (step @p151 :rule cong :premises (@p150) :args (@t38)) % 0.38/0.57 (step @p152 :rule trans :premises (@p10 @p151)) % 0.38/0.57 (step @p153 :rule ho_cong :premises (@p152 @p134)) % 0.38/0.57 (step @p154 :rule ho_cong :premises (@p153 @p133)) % 0.38/0.57 (step @p155 :rule ho_cong :premises (@p153 @p104)) % 0.38/0.57 (step @p156 :rule ho_cong :premises (@p155 @p89)) % 0.38/0.57 (step @p157 :rule cong :premises (@p156) :args (@t9)) % 0.38/0.57 (step @p158 :rule ho_cong :premises (@p132 @p157)) % 0.38/0.57 (step @p159 :rule beta-reduce :args ((= (_ @t149 @t1) @t129))) % 0.38/0.57 (step @p160 :rule beta-reduce :args ((= (_ (lambda @t150 (or @t147 @t22)) @t26) @t149))) % 0.38/0.57 (step @p161 :rule refl :args (@t26)) % 0.38/0.57 (step @p162 :rule refl :args (@t22)) % 0.38/0.57 (step @p163 :rule beta-reduce :args ((= @t152 @t147))) % 0.38/0.57 (step @p164 :rule nary_cong :premises (@p163 @p162) :args (@t153)) % 0.38/0.57 (step @p165 :rule cong :premises (@p164) :args (@t154)) % 0.38/0.57 (step @p166 :rule beta-reduce :args ((= (_ @t24 @t151) @t154))) % 0.38/0.57 (step @p167 :rule trans :premises (@p166 @p165)) % 0.38/0.57 (step @p168 :rule beta-reduce :args ((= (_ @t20 @t27) @t151))) % 0.38/0.57 (step @p169 :rule refl :args (@t24)) % 0.38/0.57 (step @p170 :rule ho_cong :premises (@p169 @p168)) % 0.38/0.57 (step @p171 :rule trans :premises (@p170 @p167)) % 0.38/0.57 (step @p172 :rule ho_cong :premises (@p171 @p161)) % 0.38/0.57 (step @p173 :rule trans :premises (@p172 @p160)) % 0.38/0.57 (step @p174 :rule ho_cong :premises (@p173 @p89)) % 0.38/0.57 (step @p175 :rule trans :premises (@p174 @p159)) % 0.38/0.57 (step @p176 :rule refl :args (@t27)) % 0.38/0.57 (step @p177 :rule ho_cong :premises (@p5 @p176)) % 0.38/0.57 (step @p178 :rule ho_cong :premises (@p6 @p177)) % 0.38/0.57 (step @p179 :rule ho_cong :premises (@p178 @p161)) % 0.38/0.57 (step @p180 :rule ho_cong :premises (@p179 @p89)) % 0.38/0.57 (step @p181 :rule trans :premises (@p180 @p175)) % 0.38/0.57 (step @p182 :rule cong :premises (@p181) :args (@t29)) % 0.38/0.57 (step @p183 :rule trans :premises (@p8 @p182)) % 0.38/0.57 (step @p184 :rule ho_cong :premises (@p183 @p158)) % 0.38/0.57 (step @p185 :rule ho_cong :premises (@p184 @p154)) % 0.38/0.57 (step @p186 :rule refl :args (@t90)) % 0.38/0.57 (step @p187 :rule refl :args (@t48)) % 0.38/0.57 (step @p188 :rule cong :premises (@p187 @p186) :args ((= @t48 @t90))) % 0.38/0.57 (step @p189 :rule symm :premises (@p188)) % 0.38/0.57 (step @p190 :rule eq_resolve :premises (@p187 @p189)) % 0.38/0.57 (step @p191 :rule cong :premises (@p190) :args (@t50)) % 0.38/0.57 (step @p192 :rule cong :premises (@p191) :args (@t52)) % 0.38/0.57 (step @p193 :rule trans :premises (@p14 @p192)) % 0.38/0.57 (step @p194 :rule ho_cong :premises (@p193 @p185)) % 0.38/0.57 (step @p195 :rule cong :premises (@p194) :args (@t11)) % 0.38/0.57 (step @p196 :rule cong :premises (@p195) :args (@t12)) % 0.38/0.57 (step @p197 :rule trans :premises (@p196 @p123)) % 0.38/0.57 (step @p198 :rule eq_resolve :premises (@p1 @p197)) % 0.38/0.57 (step @p199 :rule skolemize :premises (@p198)) % 0.38/0.57 (step @p200 :rule bool-double-not-elim :args (@t158)) % 0.38/0.57 (step @p201 :rule refl :args (@t165)) % 0.38/0.57 (step @p202 :rule nary_cong :premises (@p201 @p200) :args ((or @t165 (not @t164)))) % 0.38/0.57 (step @p203 :rule cnf_or_neg :args (@t165 0)) % 0.38/0.57 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.38/0.57 (step @p205 :rule reordering :premises (@p204) :args ((or @t158 @t165))) % 0.38/0.57 (step @p206 :rule chain_m_resolution :premises (@p205 @p199) :args (@t158 @t166 @t167)) % 0.38/0.57 (step @p207 :rule cnf_or_neg :args (@t165 2)) % 0.38/0.57 (step @p208 :rule chain_m_resolution :premises (@p207 @p199) :args ((not @t161) @t166 @t167)) % 0.38/0.57 (step @p209 :rule bool-double-not-elim :args (@t162)) % 0.38/0.57 (step @p210 :rule nary_cong :premises (@p201 @p209) :args ((or @t165 (not @t163)))) % 0.38/0.57 (step @p211 :rule cnf_or_neg :args (@t165 1)) % 0.38/0.57 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 0.38/0.57 (step @p213 :rule reordering :premises (@p212) :args ((or @t162 @t165))) % 0.38/0.57 (step @p214 :rule chain_m_resolution :premises (@p213 @p199) :args (@t162 @t166 @t167)) % 0.38/0.57 (step @p215 :rule cnf_or_pos :args (@t168)) % 0.38/0.57 (step @p216 :rule reordering :premises (@p215) :args ((or @t163 @t161 @t169))) % 0.38/0.57 (step @p217 :rule chain_m_resolution :premises (@p216 @p214 @p208) :args (@t169 (@list false true) (@list @t162 @t161))) % 0.38/0.57 (assume-push @p224 @t158) % 0.38/0.57 (step @p219 :rule instantiate :premises (@p206) :args ((@list @t160 @t159))) % 0.38/0.57 (step-pop @p225 :rule scope :premises (@p219)) % 0.38/0.57 (step @p220 :rule process_scope :premises (@p225) :args (@t168)) % 0.38/0.57 (step @p222 :rule implies_elim :premises (@p220)) % 0.38/0.57 (step @p223 false :rule chain_m_resolution :premises (@p222 @p217 @p206) :args (false (@list true false) (@list @t168 @t158))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------