%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL592^1 : TPTP v9.3.1. 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 : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:07 AM UTC 2026 % Result : Theorem 0.21s 0.52s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL592^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n013.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 17:34:35 UTC 2026 % 0.10/0.36 % CPUTime : % 0.15/0.44 %----Proving TH0 % 0.21/0.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.21/0.52 % SZS status Theorem % 0.21/0.52 % SZS output start Proof % 0.21/0.52 ( % 0.21/0.52 (declare-sort $$unsorted 0) % 0.21/0.52 (declare-sort tptp.individuals 0) % 0.21/0.52 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.21/0.52 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.21/0.52 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.21/0.52 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.21/0.52 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.21/0.52 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.52 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.21/0.52 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.21/0.52 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.21/0.52 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.52 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.52 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.52 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.52 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.52 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.52 (define @t1 () (@var "B" (-> $$unsorted Bool))) % 0.21/0.52 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.21/0.52 (define @t3 () (_ tptp.mbox @t2)) % 0.21/0.52 (define @t4 () (@var "A" (-> $$unsorted Bool))) % 0.21/0.52 (define @t5 () (@list @t2 @t4 @t1)) % 0.21/0.52 (define @t6 () (forall @t5 (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t3 (_ (_ tptp.mimpl @t4) @t1))) (_ (_ tptp.mimpl (_ @t3 @t4)) (_ @t3 @t1)))))) % 0.21/0.52 (define @t7 () (not @t6)) % 0.21/0.52 (define @t8 () (@var "X" $$unsorted)) % 0.21/0.52 (define @t9 () (@list @t8)) % 0.21/0.52 (define @t10 () (lambda @t9 false)) % 0.21/0.52 (define @t11 () (lambda @t9 true)) % 0.21/0.52 (define @t12 () (@var "U" $$unsorted)) % 0.21/0.52 (define @t13 () (@var "X" (-> $$unsorted Bool))) % 0.21/0.52 (define @t14 () (_ @t13 @t12)) % 0.21/0.52 (define @t15 () (lambda (@list @t13 @t12) (not @t14))) % 0.21/0.52 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.21/0.52 (define @t17 () (_ @t16 @t12)) % 0.21/0.52 (define @t18 () (@list @t13 @t16 @t12)) % 0.21/0.52 (define @t19 () (lambda @t18 (or @t14 @t17))) % 0.21/0.52 (define @t20 () (lambda @t18 (and @t14 @t17))) % 0.21/0.52 (define @t21 () (@var "__flatten_var_0" $$unsorted)) % 0.21/0.52 (define @t22 () (@var "V" (-> $$unsorted Bool))) % 0.21/0.52 (define @t23 () (@var "U" (-> $$unsorted Bool))) % 0.21/0.52 (define @t24 () (@list @t23 @t22 @t21)) % 0.21/0.52 (define @t25 () (lambda @t24 (_ (_ (_ tptp.mor (_ tptp.mnot @t23)) @t22) @t21))) % 0.21/0.52 (define @t26 () (lambda @t24 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t23) @t22)) (_ (_ tptp.mimpl @t22) @t23)) @t21))) % 0.21/0.52 (define @t27 () (@var "Y" $$unsorted)) % 0.21/0.52 (define @t28 () (@var "P" (-> $$unsorted Bool))) % 0.21/0.52 (define @t29 () (_ @t28 @t27)) % 0.21/0.52 (define @t30 () (_ (_ @t2 @t8) @t27)) % 0.21/0.52 (define @t31 () (@list @t27)) % 0.21/0.52 (define @t32 () (forall @t31 (=> @t30 @t29))) % 0.21/0.52 (define @t33 () (@list @t2 @t28 @t8)) % 0.21/0.52 (define @t34 () (lambda @t33 @t32)) % 0.21/0.52 (define @t35 () (lambda @t33 (exists @t31 (and @t30 @t29)))) % 0.21/0.52 (define @t36 () (@var "W" $$unsorted)) % 0.21/0.52 (define @t37 () (@var "X" tptp.individuals)) % 0.21/0.52 (define @t38 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.21/0.52 (define @t39 () (_ (_ @t38 @t37) @t36)) % 0.21/0.52 (define @t40 () (@list @t37)) % 0.21/0.52 (define @t41 () (@list @t38 @t36)) % 0.21/0.52 (define @t42 () (lambda @t41 (forall @t40 @t39))) % 0.21/0.52 (define @t43 () (lambda @t41 (exists @t40 @t39))) % 0.21/0.52 (define @t44 () (_ @t28 @t36)) % 0.21/0.52 (define @t45 () (@list @t36)) % 0.21/0.52 (define @t46 () (forall @t45 @t44)) % 0.21/0.52 (define @t47 () (@list @t28)) % 0.21/0.52 (define @t48 () (lambda @t47 @t46)) % 0.21/0.52 (define @t49 () (lambda @t47 (exists @t45 @t44))) % 0.21/0.52 (define @t50 () (not @t44)) % 0.21/0.52 (define @t51 () (lambda @t47 (exists @t45 @t50))) % 0.21/0.52 (define @t52 () (lambda @t47 (forall @t45 @t50))) % 0.21/0.52 (define @t53 () (@var "BOUND_VARIABLE_7870" $$unsorted)) % 0.21/0.52 (define @t54 () (_ @t1 @t53)) % 0.21/0.52 (define @t55 () (not (_ @t2 @t36 @t53))) % 0.21/0.52 (define @t56 () (_ @t4 @t27)) % 0.21/0.52 (define @t57 () (not (_ @t2 @t36 @t27))) % 0.21/0.52 (define @t58 () (not (forall @t31 (or @t57 @t56)))) % 0.21/0.52 (define @t59 () (_ @t1 @t27)) % 0.21/0.52 (define @t60 () (not @t56)) % 0.21/0.52 (define @t61 () (not (forall @t31 (or @t57 @t60 @t59)))) % 0.21/0.52 (define @t62 () (or @t61 @t58 @t55 @t54)) % 0.21/0.52 (define @t63 () (forall (@list @t2 @t4 @t1 @t36 @t53) @t62)) % 0.21/0.52 (define @t64 () (@list @t36 @t53)) % 0.21/0.52 (define @t65 () (or @t55 @t54)) % 0.21/0.52 (define @t66 () (or @t61 @t58 @t65)) % 0.21/0.52 (define @t67 () (forall @t64 @t66)) % 0.21/0.52 (define @t68 () (@list @t53)) % 0.21/0.52 (define @t69 () (forall @t68 @t66)) % 0.21/0.52 (define @t70 () (forall @t68 @t65)) % 0.21/0.52 (define @t71 () (or @t61 @t58 @t70)) % 0.21/0.52 (define @t72 () (or @t61 @t58 (forall @t31 (or @t57 @t59)))) % 0.21/0.52 (define @t73 () (not (_ @t2 @t21 @t27))) % 0.21/0.52 (define @t74 () (forall @t31 (or @t73 @t59))) % 0.21/0.52 (define @t75 () (forall @t31 (or @t73 @t56))) % 0.21/0.52 (define @t76 () (not @t75)) % 0.21/0.52 (define @t77 () (forall @t31 (or @t73 @t60 @t59))) % 0.21/0.52 (define @t78 () (not @t77)) % 0.21/0.52 (define @t79 () (or @t78 @t76 @t74)) % 0.21/0.52 (define @t80 () (@list @t21)) % 0.21/0.52 (define @t81 () (lambda @t80 @t79)) % 0.21/0.52 (define @t82 () (_ @t81 @t36)) % 0.21/0.52 (define @t83 () (forall @t45 @t82)) % 0.21/0.52 (define @t84 () (_ @t28 @t36)) % 0.21/0.52 (define @t85 () (lambda @t47 (forall @t45 @t84))) % 0.21/0.52 (define @t86 () (or @t76 @t74)) % 0.21/0.52 (define @t87 () (lambda @t80 @t86)) % 0.21/0.52 (define @t88 () (_ @t87 @t21)) % 0.21/0.52 (define @t89 () (or @t78 @t88)) % 0.21/0.52 (define @t90 () (lambda @t80 @t89)) % 0.21/0.52 (define @t91 () (_ @t22 @t21)) % 0.21/0.52 (define @t92 () (@list @t22 @t21)) % 0.21/0.52 (define @t93 () (_ @t2 @t8 @t27)) % 0.21/0.52 (define @t94 () (not @t93)) % 0.21/0.52 (define @t95 () (lambda @t9 (forall @t31 (or @t94 @t59)))) % 0.21/0.52 (define @t96 () (_ @t95 @t21)) % 0.21/0.52 (define @t97 () (or @t76 @t96)) % 0.21/0.52 (define @t98 () (lambda @t80 @t97)) % 0.21/0.52 (define @t99 () (_ @t28 @t27)) % 0.21/0.52 (define @t100 () (forall @t31 (or @t94 @t99))) % 0.21/0.52 (define @t101 () (lambda (@list @t28 @t8) @t100)) % 0.21/0.52 (define @t102 () (_ (lambda @t33 @t100) @t2)) % 0.21/0.52 (define @t103 () (lambda @t9 (forall @t31 (or @t94 @t56)))) % 0.21/0.52 (define @t104 () (_ @t103 @t21)) % 0.21/0.52 (define @t105 () (not @t104)) % 0.21/0.52 (define @t106 () (or @t105 @t91)) % 0.21/0.52 (define @t107 () (lambda @t92 @t106)) % 0.21/0.52 (define @t108 () (or (not (_ @t23 @t21)) @t91)) % 0.21/0.52 (define @t109 () (lambda @t24 @t108)) % 0.21/0.52 (define @t110 () (lambda @t9 (forall @t31 (or @t94 @t60 @t59)))) % 0.21/0.52 (define @t111 () (_ @t110 @t21)) % 0.21/0.52 (define @t112 () (not @t111)) % 0.21/0.52 (define @t113 () (or @t112 @t91)) % 0.21/0.52 (define @t114 () (lambda @t92 @t113)) % 0.21/0.52 (define @t115 () (_ @t1 @t27)) % 0.21/0.52 (define @t116 () (_ @t4 @t27)) % 0.21/0.52 (define @t117 () (not @t116)) % 0.21/0.52 (define @t118 () (or @t94 @t117 @t115)) % 0.21/0.52 (define @t119 () (or @t117 @t115)) % 0.21/0.52 (define @t120 () (not (_ @t4 @t21))) % 0.21/0.52 (define @t121 () (lambda @t80 (or @t120 (_ @t1 @t21)))) % 0.21/0.52 (define @t122 () (_ @t121 @t27)) % 0.21/0.52 (define @t123 () (or @t94 @t122)) % 0.21/0.52 (define @t124 () (forall @t31 @t123)) % 0.21/0.52 (define @t125 () (lambda @t9 @t124)) % 0.21/0.52 (define @t126 () (lambda @t92 (or @t120 @t91))) % 0.21/0.52 (define @t127 () (_ @t109 @t4)) % 0.21/0.52 (define @t128 () (forall @t5 (_ @t85 (_ (_ @t109 (_ @t102 (_ @t127 @t1))) (_ (_ @t109 (_ @t102 @t4)) (_ @t102 @t1)))))) % 0.21/0.52 (define @t129 () (not @t30)) % 0.21/0.52 (define @t130 () (or @t129 @t29)) % 0.21/0.52 (define @t131 () (not (_ @t23 @t12))) % 0.21/0.52 (define @t132 () (@list @t12)) % 0.21/0.52 (define @t133 () (lambda @t132 (or @t131 (_ @t22 @t12)))) % 0.21/0.52 (define @t134 () (@list @t16 @t12)) % 0.21/0.52 (define @t135 () (lambda @t132 @t131)) % 0.21/0.52 (define @t136 () (_ @t135 @t12)) % 0.21/0.52 (define @t137 () (or @t136 @t17)) % 0.21/0.52 (define @t138 () (lambda @t134 @t137)) % 0.21/0.52 (define @t139 () (@quantifiers_skolemize @t63 4)) % 0.21/0.52 (define @t140 () (@quantifiers_skolemize @t63 3)) % 0.21/0.52 (define @t141 () (@quantifiers_skolemize @t63 0)) % 0.21/0.52 (define @t142 () (_ @t141 @t140 @t139)) % 0.21/0.52 (define @t143 () (@quantifiers_skolemize @t63 2)) % 0.21/0.52 (define @t144 () (_ @t143 @t139)) % 0.21/0.52 (define @t145 () (not @t142)) % 0.21/0.52 (define @t146 () (@quantifiers_skolemize @t63 1)) % 0.21/0.52 (define @t147 () (_ @t146 @t27)) % 0.21/0.52 (define @t148 () (not (_ @t141 @t140 @t27))) % 0.21/0.52 (define @t149 () (forall @t31 (or @t148 @t147))) % 0.21/0.52 (define @t150 () (not @t149)) % 0.21/0.52 (define @t151 () (forall @t31 (or @t148 (not @t147) (_ @t143 @t27)))) % 0.21/0.52 (define @t152 () (not @t151)) % 0.21/0.52 (define @t153 () (or @t152 @t150 @t145 @t144)) % 0.21/0.52 (define @t154 () (@list true)) % 0.21/0.52 (define @t155 () (@list @t153)) % 0.21/0.52 (define @t156 () (@list @t139)) % 0.21/0.52 (define @t157 () (_ @t146 @t139)) % 0.21/0.52 (define @t158 () (not @t157)) % 0.21/0.52 (define @t159 () (or @t145 @t158 @t144)) % 0.21/0.52 (define @t160 () (or @t145 @t157)) % 0.21/0.52 (assume @p1 @t7) % 0.21/0.52 (assume @p2 true) % 0.21/0.52 (step @p3 (= tptp.mfalse @t10) :rule refl :args (@t10)) % 0.21/0.52 (step @p4 (= tptp.mtrue @t11) :rule refl :args (@t11)) % 0.21/0.52 (step @p5 (= tptp.mnot @t15) :rule refl :args (@t15)) % 0.21/0.52 (step @p6 (= tptp.mor @t19) :rule refl :args (@t19)) % 0.21/0.52 (step @p7 (= tptp.mand @t20) :rule refl :args (@t20)) % 0.21/0.52 (step @p8 (= tptp.mimpl @t25) :rule refl :args (@t25)) % 0.21/0.52 (step @p9 (= tptp.miff @t26) :rule refl :args (@t26)) % 0.21/0.52 (step @p10 (= tptp.mbox @t34) :rule refl :args (@t34)) % 0.21/0.52 (step @p11 (= tptp.mdia @t35) :rule refl :args (@t35)) % 0.21/0.52 (step @p12 (= tptp.mall @t42) :rule refl :args (@t42)) % 0.21/0.52 (step @p13 (= tptp.mexists @t43) :rule refl :args (@t43)) % 0.21/0.52 (step @p14 (= tptp.mvalid @t48) :rule refl :args (@t48)) % 0.21/0.52 (step @p15 (= tptp.msatisfiable @t49) :rule refl :args (@t49)) % 0.21/0.52 (step @p16 (= tptp.mcountersatisfiable @t51) :rule refl :args (@t51)) % 0.21/0.52 (step @p17 (= tptp.minvalid @t52) :rule refl :args (@t52)) % 0.21/0.52 (step @p18 :rule quant-merge-prenex :args ((= (forall @t5 (forall @t64 @t62)) @t63))) % 0.21/0.52 (step @p19 :rule aci_norm :args ((= @t66 @t62))) % 0.21/0.52 (step @p20 :rule cong :premises (@p19) :args (@t67)) % 0.21/0.52 (step @p21 :rule quant-merge-prenex :args ((= (forall @t45 @t69) @t67))) % 0.21/0.52 (step @p22 :rule alpha_equiv :args (@t70 (@list @t53) (@list @t27))) % 0.21/0.52 (step @p23 :rule refl :args (@t58)) % 0.21/0.52 (step @p24 :rule refl :args (@t61)) % 0.21/0.52 (step @p25 :rule nary_cong :premises (@p24 @p23 @p22) :args (@t71)) % 0.21/0.52 (step @p26 :rule quant-miniscope-or :args ((= @t69 @t71))) % 0.21/0.52 (step @p27 :rule trans :premises (@p26 @p25)) % 0.21/0.52 (step @p28 :rule symm :premises (@p27)) % 0.21/0.52 (step @p29 :rule cong :premises (@p28) :args ((forall @t45 @t72))) % 0.21/0.52 (step @p30 :rule trans :premises (@p29 @p21)) % 0.21/0.52 (step @p31 :rule trans :premises (@p30 @p20)) % 0.21/0.52 (step @p32 :rule beta-reduce :args ((= @t82 @t72))) % 0.21/0.52 (step @p33 :rule cong :premises (@p32) :args (@t83)) % 0.21/0.52 (step @p34 :rule trans :premises (@p33 @p31)) % 0.21/0.52 (step @p35 :rule beta-reduce :args ((= (_ @t85 @t81) @t83))) % 0.21/0.52 (step @p36 :rule trans :premises (@p35 @p34)) % 0.21/0.52 (step @p37 :rule aci_norm :args ((= (or @t78 @t86) @t79))) % 0.21/0.52 (step @p38 :rule beta-reduce :args ((= @t88 @t86))) % 0.21/0.52 (step @p39 :rule refl :args (@t78)) % 0.21/0.52 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t89)) % 0.21/0.52 (step @p41 :rule trans :premises (@p40 @p37)) % 0.21/0.52 (step @p42 :rule cong :premises (@p41) :args (@t90)) % 0.21/0.52 (step @p43 :rule beta-reduce :args ((= (_ (lambda @t92 (or @t78 @t91)) @t87) @t90))) % 0.21/0.52 (step @p44 :rule trans :premises (@p43 @p42)) % 0.21/0.52 (step @p45 :rule beta-reduce :args ((= @t96 @t74))) % 0.21/0.52 (step @p46 :rule refl :args (@t76)) % 0.21/0.52 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t97)) % 0.21/0.52 (step @p48 :rule cong :premises (@p47) :args (@t98)) % 0.21/0.52 (step @p49 :rule beta-reduce :args ((= (_ (lambda @t92 (or @t76 @t91)) @t95) @t98))) % 0.21/0.52 (step @p50 :rule trans :premises (@p49 @p48)) % 0.21/0.52 (step @p51 :rule beta-reduce :args ((= (_ @t101 @t1) @t95))) % 0.21/0.52 (step @p52 :rule refl :args (@t1)) % 0.21/0.52 (step @p53 :rule beta-reduce :args ((= @t102 @t101))) % 0.21/0.52 (step @p54 :rule ho_cong :premises (@p53 @p52)) % 0.21/0.52 (step @p55 :rule trans :premises (@p54 @p51)) % 0.21/0.52 (step @p56 :rule refl :args (@t91)) % 0.21/0.52 (step @p57 :rule beta-reduce :args ((= @t104 @t75))) % 0.21/0.52 (step @p58 :rule cong :premises (@p57) :args (@t105)) % 0.21/0.52 (step @p59 :rule nary_cong :premises (@p58 @p56) :args (@t106)) % 0.21/0.52 (step @p60 :rule cong :premises (@p59) :args (@t107)) % 0.21/0.52 (step @p61 :rule beta-reduce :args ((= (_ @t109 @t103) @t107))) % 0.21/0.52 (step @p62 :rule trans :premises (@p61 @p60)) % 0.21/0.52 (step @p63 :rule beta-reduce :args ((= (_ @t101 @t4) @t103))) % 0.21/0.52 (step @p64 :rule refl :args (@t4)) % 0.21/0.52 (step @p65 :rule ho_cong :premises (@p53 @p64)) % 0.21/0.52 (step @p66 :rule trans :premises (@p65 @p63)) % 0.21/0.52 (step @p67 :rule refl :args (@t109)) % 0.21/0.52 (step @p68 :rule ho_cong :premises (@p67 @p66)) % 0.21/0.52 (step @p69 :rule trans :premises (@p68 @p62)) % 0.21/0.52 (step @p70 :rule ho_cong :premises (@p69 @p55)) % 0.21/0.52 (step @p71 :rule trans :premises (@p70 @p50)) % 0.21/0.52 (step @p72 :rule beta-reduce :args ((= @t111 @t77))) % 0.21/0.52 (step @p73 :rule cong :premises (@p72) :args (@t112)) % 0.21/0.52 (step @p74 :rule nary_cong :premises (@p73 @p56) :args (@t113)) % 0.21/0.52 (step @p75 :rule cong :premises (@p74) :args (@t114)) % 0.21/0.52 (step @p76 :rule beta-reduce :args ((= (_ @t109 @t110) @t114))) % 0.21/0.52 (step @p77 :rule trans :premises (@p76 @p75)) % 0.21/0.52 (step @p78 :rule refl :args (@t59)) % 0.21/0.52 (step @p79 :rule refl :args (@t115)) % 0.21/0.52 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t115 @t59))) % 0.21/0.52 (step @p81 :rule symm :premises (@p80)) % 0.21/0.52 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.21/0.52 (step @p83 :rule refl :args (@t56)) % 0.21/0.52 (step @p84 :rule refl :args (@t116)) % 0.21/0.52 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t116 @t56))) % 0.21/0.52 (step @p86 :rule symm :premises (@p85)) % 0.21/0.52 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.21/0.52 (step @p88 :rule cong :premises (@p87) :args (@t117)) % 0.21/0.52 (step @p89 :rule refl :args (@t94)) % 0.21/0.52 (step @p90 :rule nary_cong :premises (@p89 @p88 @p82) :args (@t118)) % 0.21/0.52 (step @p91 :rule cong :premises (@p90) :args ((forall @t31 @t118))) % 0.21/0.52 (step @p92 :rule aci_norm :args ((= (or @t94 @t119) @t118))) % 0.21/0.52 (step @p93 :rule beta-reduce :args ((= @t122 @t119))) % 0.21/0.52 (step @p94 :rule refl :args (@t94)) % 0.21/0.52 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t123)) % 0.21/0.52 (step @p96 :rule trans :premises (@p95 @p92)) % 0.21/0.52 (step @p97 :rule cong :premises (@p96) :args (@t124)) % 0.21/0.52 (step @p98 :rule trans :premises (@p97 @p91)) % 0.21/0.52 (step @p99 :rule cong :premises (@p98) :args (@t125)) % 0.21/0.52 (step @p100 :rule beta-reduce :args ((= (_ @t101 @t121) @t125))) % 0.21/0.52 (step @p101 :rule trans :premises (@p100 @p99)) % 0.21/0.52 (step @p102 :rule beta-reduce :args ((= (_ @t126 @t1) @t121))) % 0.21/0.52 (step @p103 :rule beta-reduce :args ((= @t127 @t126))) % 0.21/0.52 (step @p104 :rule ho_cong :premises (@p103 @p52)) % 0.21/0.52 (step @p105 :rule trans :premises (@p104 @p102)) % 0.21/0.52 (step @p106 :rule ho_cong :premises (@p53 @p105)) % 0.21/0.52 (step @p107 :rule trans :premises (@p106 @p101)) % 0.21/0.52 (step @p108 :rule ho_cong :premises (@p67 @p107)) % 0.21/0.52 (step @p109 :rule trans :premises (@p108 @p77)) % 0.21/0.52 (step @p110 :rule ho_cong :premises (@p109 @p71)) % 0.21/0.52 (step @p111 :rule trans :premises (@p110 @p44)) % 0.21/0.52 (step @p112 :rule refl :args (@t85)) % 0.21/0.52 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.21/0.52 (step @p114 :rule trans :premises (@p113 @p36)) % 0.21/0.52 (step @p115 :rule cong :premises (@p114) :args (@t128)) % 0.21/0.52 (step @p116 :rule trans :premises (@p115 @p18)) % 0.21/0.52 (step @p117 :rule cong :premises (@p116) :args ((not @t128))) % 0.21/0.52 (step @p118 :rule refl :args (@t2)) % 0.21/0.52 (step @p119 :rule refl :args (@t99)) % 0.21/0.52 (step @p120 :rule refl :args (@t29)) % 0.21/0.52 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t29 @t99))) % 0.21/0.52 (step @p122 :rule symm :premises (@p121)) % 0.21/0.52 (step @p123 :rule eq_resolve :premises (@p120 @p122)) % 0.21/0.52 (step @p124 :rule refl :args (@t93)) % 0.21/0.52 (step @p125 :rule refl :args (@t30)) % 0.21/0.52 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t30 @t93))) % 0.21/0.52 (step @p127 :rule symm :premises (@p126)) % 0.21/0.52 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 0.21/0.52 (step @p129 :rule cong :premises (@p128) :args (@t129)) % 0.21/0.52 (step @p130 :rule nary_cong :premises (@p129 @p123) :args (@t130)) % 0.21/0.52 (step @p131 :rule cong :premises (@p130) :args ((forall @t31 @t130))) % 0.21/0.52 (step @p132 :rule bool-impl-elim :args (@t30 @t29)) % 0.21/0.52 (step @p133 :rule cong :premises (@p132) :args (@t32)) % 0.21/0.52 (step @p134 :rule trans :premises (@p133 @p131)) % 0.21/0.52 (step @p135 :rule cong :premises (@p134) :args (@t34)) % 0.21/0.52 (step @p136 :rule trans :premises (@p10 @p135)) % 0.21/0.52 (step @p137 :rule ho_cong :premises (@p136 @p118)) % 0.21/0.52 (step @p138 :rule ho_cong :premises (@p137 @p52)) % 0.21/0.52 (step @p139 :rule ho_cong :premises (@p137 @p64)) % 0.21/0.52 (step @p140 :rule beta-reduce :args ((= (_ @t133 @t21) @t108))) % 0.21/0.52 (step @p141 :rule refl :args (@t21)) % 0.21/0.52 (step @p142 :rule beta-reduce :args ((= (_ (lambda @t134 (or @t131 @t17)) @t22) @t133))) % 0.21/0.52 (step @p143 :rule refl :args (@t22)) % 0.21/0.52 (step @p144 :rule refl :args (@t17)) % 0.21/0.52 (step @p145 :rule beta-reduce :args ((= @t136 @t131))) % 0.21/0.52 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t137)) % 0.21/0.52 (step @p147 :rule cong :premises (@p146) :args (@t138)) % 0.21/0.52 (step @p148 :rule beta-reduce :args ((= (_ @t19 @t135) @t138))) % 0.21/0.52 (step @p149 :rule trans :premises (@p148 @p147)) % 0.21/0.52 (step @p150 :rule beta-reduce :args ((= (_ @t15 @t23) @t135))) % 0.21/0.52 (step @p151 :rule refl :args (@t19)) % 0.21/0.52 (step @p152 :rule ho_cong :premises (@p151 @p150)) % 0.21/0.52 (step @p153 :rule trans :premises (@p152 @p149)) % 0.21/0.52 (step @p154 :rule ho_cong :premises (@p153 @p143)) % 0.21/0.52 (step @p155 :rule trans :premises (@p154 @p142)) % 0.21/0.52 (step @p156 :rule ho_cong :premises (@p155 @p141)) % 0.21/0.52 (step @p157 :rule trans :premises (@p156 @p140)) % 0.21/0.52 (step @p158 :rule refl :args (@t23)) % 0.21/0.52 (step @p159 :rule ho_cong :premises (@p5 @p158)) % 0.21/0.52 (step @p160 :rule ho_cong :premises (@p6 @p159)) % 0.21/0.52 (step @p161 :rule ho_cong :premises (@p160 @p143)) % 0.21/0.52 (step @p162 :rule ho_cong :premises (@p161 @p141)) % 0.21/0.52 (step @p163 :rule trans :premises (@p162 @p157)) % 0.21/0.52 (step @p164 :rule cong :premises (@p163) :args (@t25)) % 0.21/0.52 (step @p165 :rule trans :premises (@p8 @p164)) % 0.21/0.52 (step @p166 :rule ho_cong :premises (@p165 @p139)) % 0.21/0.52 (step @p167 :rule ho_cong :premises (@p166 @p138)) % 0.21/0.52 (step @p168 :rule ho_cong :premises (@p165 @p64)) % 0.21/0.52 (step @p169 :rule ho_cong :premises (@p168 @p52)) % 0.21/0.52 (step @p170 :rule ho_cong :premises (@p137 @p169)) % 0.21/0.52 (step @p171 :rule ho_cong :premises (@p165 @p170)) % 0.21/0.52 (step @p172 :rule ho_cong :premises (@p171 @p167)) % 0.21/0.52 (step @p173 :rule refl :args (@t84)) % 0.21/0.52 (step @p174 :rule refl :args (@t44)) % 0.21/0.52 (step @p175 :rule cong :premises (@p174 @p173) :args ((= @t44 @t84))) % 0.21/0.52 (step @p176 :rule symm :premises (@p175)) % 0.21/0.52 (step @p177 :rule eq_resolve :premises (@p174 @p176)) % 0.21/0.52 (step @p178 :rule cong :premises (@p177) :args (@t46)) % 0.21/0.52 (step @p179 :rule cong :premises (@p178) :args (@t48)) % 0.21/0.52 (step @p180 :rule trans :premises (@p14 @p179)) % 0.21/0.53 (step @p181 :rule ho_cong :premises (@p180 @p172)) % 0.21/0.53 (step @p182 :rule cong :premises (@p181) :args (@t6)) % 0.21/0.53 (step @p183 :rule cong :premises (@p182) :args (@t7)) % 0.21/0.53 (step @p184 :rule trans :premises (@p183 @p117)) % 0.21/0.53 (step @p185 :rule eq_resolve :premises (@p1 @p184)) % 0.21/0.53 (step @p186 :rule skolemize :premises (@p185)) % 0.21/0.53 (step @p187 :rule bool-double-not-elim :args (@t142)) % 0.21/0.53 (step @p188 :rule refl :args (@t153)) % 0.21/0.53 (step @p189 :rule nary_cong :premises (@p188 @p187) :args ((or @t153 (not @t145)))) % 0.21/0.53 (step @p190 :rule cnf_or_neg :args (@t153 2)) % 0.21/0.53 (step @p191 :rule eq_resolve :premises (@p190 @p189)) % 0.21/0.53 (step @p192 :rule reordering :premises (@p191) :args ((or @t142 @t153))) % 0.21/0.53 (step @p193 :rule chain_m_resolution :premises (@p192 @p186) :args (@t142 @t154 @t155)) % 0.21/0.53 (step @p194 :rule bool-double-not-elim :args (@t149)) % 0.21/0.53 (step @p195 :rule nary_cong :premises (@p188 @p194) :args ((or @t153 (not @t150)))) % 0.21/0.53 (step @p196 :rule cnf_or_neg :args (@t153 1)) % 0.21/0.53 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 0.21/0.53 (step @p198 :rule reordering :premises (@p197) :args ((or @t149 @t153))) % 0.21/0.53 (step @p199 :rule chain_m_resolution :premises (@p198 @p186) :args (@t149 @t154 @t155)) % 0.21/0.53 (step @p200 :rule instantiate :premises (@p199) :args (@t156)) % 0.21/0.53 (step @p201 :rule bool-double-not-elim :args (@t151)) % 0.21/0.53 (step @p202 :rule nary_cong :premises (@p188 @p201) :args ((or @t153 (not @t152)))) % 0.21/0.53 (step @p203 :rule cnf_or_neg :args (@t153 0)) % 0.21/0.53 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.21/0.53 (step @p205 :rule reordering :premises (@p204) :args ((or @t151 @t153))) % 0.21/0.53 (step @p206 :rule chain_m_resolution :premises (@p205 @p186) :args (@t151 @t154 @t155)) % 0.21/0.53 (step @p207 :rule instantiate :premises (@p206) :args (@t156)) % 0.21/0.53 (step @p208 :rule cnf_or_neg :args (@t153 3)) % 0.21/0.53 (step @p209 :rule chain_m_resolution :premises (@p208 @p186) :args ((not @t144) @t154 @t155)) % 0.21/0.53 (step @p210 :rule cnf_or_pos :args (@t159)) % 0.21/0.53 (step @p211 :rule reordering :premises (@p210) :args ((or @t145 @t144 @t158 (not @t159)))) % 0.21/0.53 (step @p212 :rule chain_m_resolution :premises (@p211 @p193 @p209 @p207) :args (@t158 (@list false true false) (@list @t142 @t144 @t159))) % 0.21/0.53 (step @p213 :rule cnf_or_pos :args (@t160)) % 0.21/0.53 (step @p214 :rule reordering :premises (@p213) :args ((or @t145 @t157 (not @t160)))) % 0.21/0.53 (step @p215 false :rule chain_m_resolution :premises (@p214 @p212 @p200 @p193) :args (false (@list true false false) (@list @t157 @t160 @t142))) % 0.21/0.53 ) % 0.21/0.53 % SZS output end Proof % 0.21/0.53 % cvc5 exiting %------------------------------------------------------------------------------