%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL597^1 : TPTP v9.3.1. 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 : n031.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 11:23:08 AM UTC 2026 % Result : Theorem 0.25s 0.52s % Output : Proof 0.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL597^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.11/0.35 % Computer : n031.cluster.edu % 0.11/0.35 % Model : x86_64 x86_64 % 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.35 % Memory : 8046.5625MB % 0.11/0.35 % OS : Linux 6.8.0-71-generic % 0.11/0.35 % CPULimit : 300 % 0.11/0.35 % WCLimit : 300 % 0.11/0.35 % DateTime : Sat Sep 5 02:10:09 UTC 2026 % 0.11/0.36 % CPUTime : % 0.14/0.42 %----Proving TH0 % 0.25/0.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.25/0.52 % SZS status Theorem % 0.25/0.52 % SZS output start Proof % 0.25/0.52 ( % 0.25/0.52 (declare-sort $$unsorted 0) % 0.25/0.52 (declare-sort tptp.individuals 0) % 0.25/0.52 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.25/0.52 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.25/0.52 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.25/0.52 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.25/0.52 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.25/0.52 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.25/0.52 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.25/0.52 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.25/0.52 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.25/0.52 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.25/0.52 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.25/0.52 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.25/0.52 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.25/0.52 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.25/0.52 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.25/0.52 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.25/0.52 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.25/0.52 (define @t3 () (_ tptp.mbox @t2)) % 0.25/0.52 (define @t4 () (_ @t3 @t1)) % 0.25/0.52 (define @t5 () (@list @t1)) % 0.25/0.52 (define @t6 () (forall @t5 (_ tptp.mvalid (_ (_ tptp.mimpl @t4) (_ @t3 @t4))))) % 0.25/0.52 (define @t7 () (@list @t2)) % 0.25/0.52 (define @t8 () (exists @t7 @t6)) % 0.25/0.52 (define @t9 () (not @t8)) % 0.25/0.52 (define @t10 () (@var "X" $$unsorted)) % 0.25/0.52 (define @t11 () (@list @t10)) % 0.25/0.52 (define @t12 () (lambda @t11 false)) % 0.25/0.52 (define @t13 () (lambda @t11 true)) % 0.25/0.52 (define @t14 () (@var "U" $$unsorted)) % 0.25/0.52 (define @t15 () (@var "X" (-> $$unsorted Bool))) % 0.25/0.52 (define @t16 () (_ @t15 @t14)) % 0.25/0.52 (define @t17 () (lambda (@list @t15 @t14) (not @t16))) % 0.25/0.52 (define @t18 () (@var "Y" (-> $$unsorted Bool))) % 0.25/0.52 (define @t19 () (_ @t18 @t14)) % 0.25/0.52 (define @t20 () (@list @t15 @t18 @t14)) % 0.25/0.52 (define @t21 () (lambda @t20 (or @t16 @t19))) % 0.25/0.52 (define @t22 () (lambda @t20 (and @t16 @t19))) % 0.25/0.52 (define @t23 () (@var "__flatten_var_0" $$unsorted)) % 0.25/0.52 (define @t24 () (@var "V" (-> $$unsorted Bool))) % 0.25/0.52 (define @t25 () (@var "U" (-> $$unsorted Bool))) % 0.25/0.52 (define @t26 () (@list @t25 @t24 @t23)) % 0.25/0.52 (define @t27 () (lambda @t26 (_ (_ (_ tptp.mor (_ tptp.mnot @t25)) @t24) @t23))) % 0.25/0.52 (define @t28 () (lambda @t26 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t25) @t24)) (_ (_ tptp.mimpl @t24) @t25)) @t23))) % 0.25/0.52 (define @t29 () (@var "Y" $$unsorted)) % 0.25/0.52 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.25/0.52 (define @t31 () (_ @t30 @t29)) % 0.25/0.52 (define @t32 () (_ (_ @t2 @t10) @t29)) % 0.25/0.52 (define @t33 () (@list @t29)) % 0.25/0.52 (define @t34 () (forall @t33 (=> @t32 @t31))) % 0.25/0.52 (define @t35 () (@list @t2 @t30 @t10)) % 0.25/0.52 (define @t36 () (lambda @t35 @t34)) % 0.25/0.52 (define @t37 () (lambda @t35 (exists @t33 (and @t32 @t31)))) % 0.25/0.52 (define @t38 () (@var "W" $$unsorted)) % 0.25/0.52 (define @t39 () (@var "X" tptp.individuals)) % 0.25/0.52 (define @t40 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.25/0.52 (define @t41 () (_ (_ @t40 @t39) @t38)) % 0.25/0.52 (define @t42 () (@list @t39)) % 0.25/0.52 (define @t43 () (@list @t40 @t38)) % 0.25/0.52 (define @t44 () (lambda @t43 (forall @t42 @t41))) % 0.25/0.52 (define @t45 () (lambda @t43 (exists @t42 @t41))) % 0.25/0.52 (define @t46 () (_ @t30 @t38)) % 0.25/0.52 (define @t47 () (@list @t38)) % 0.25/0.52 (define @t48 () (forall @t47 @t46)) % 0.25/0.52 (define @t49 () (@list @t30)) % 0.25/0.52 (define @t50 () (lambda @t49 @t48)) % 0.25/0.52 (define @t51 () (lambda @t49 (exists @t47 @t46))) % 0.25/0.52 (define @t52 () (not @t46)) % 0.25/0.52 (define @t53 () (lambda @t49 (exists @t47 @t52))) % 0.25/0.52 (define @t54 () (lambda @t49 (forall @t47 @t52))) % 0.25/0.52 (define @t55 () (@var "BOUND_VARIABLE_7846" $$unsorted)) % 0.25/0.52 (define @t56 () (_ @t1 @t55)) % 0.25/0.52 (define @t57 () (@var "BOUND_VARIABLE_7844" $$unsorted)) % 0.25/0.52 (define @t58 () (not (_ @t2 @t57 @t55))) % 0.25/0.52 (define @t59 () (not (_ @t2 @t38 @t57))) % 0.25/0.52 (define @t60 () (_ @t1 @t29)) % 0.25/0.52 (define @t61 () (not (_ @t2 @t38 @t29))) % 0.25/0.52 (define @t62 () (not (forall @t33 (or @t61 @t60)))) % 0.25/0.52 (define @t63 () (or @t62 @t59 @t58 @t56)) % 0.25/0.52 (define @t64 () (@list @t1 @t38 @t57 @t55)) % 0.25/0.52 (define @t65 () (forall @t64 @t63)) % 0.25/0.52 (define @t66 () (forall @t7 (not @t65))) % 0.25/0.52 (define @t67 () (@list @t38 @t57 @t55)) % 0.25/0.52 (define @t68 () (or @t59 @t58 @t56)) % 0.25/0.52 (define @t69 () (or @t62 @t68)) % 0.25/0.52 (define @t70 () (forall @t67 @t69)) % 0.25/0.52 (define @t71 () (@list @t57 @t55)) % 0.25/0.52 (define @t72 () (forall @t71 @t69)) % 0.25/0.52 (define @t73 () (forall @t71 @t68)) % 0.25/0.52 (define @t74 () (@var "BOUND_VARIABLE_7811" $$unsorted)) % 0.25/0.52 (define @t75 () (or @t62 @t73)) % 0.25/0.52 (define @t76 () (_ @t1 @t74)) % 0.25/0.52 (define @t77 () (not (_ @t2 @t29 @t74))) % 0.25/0.52 (define @t78 () (@list @t29 @t74)) % 0.25/0.52 (define @t79 () (or @t62 (forall @t78 (or @t61 @t77 @t76)))) % 0.25/0.52 (define @t80 () (not (_ @t2 @t23 @t29))) % 0.25/0.52 (define @t81 () (forall @t78 (or @t80 @t77 @t76))) % 0.25/0.52 (define @t82 () (forall @t33 (or @t80 @t60))) % 0.25/0.52 (define @t83 () (not @t82)) % 0.25/0.52 (define @t84 () (@list @t23)) % 0.25/0.52 (define @t85 () (lambda @t84 (or @t83 @t81))) % 0.25/0.52 (define @t86 () (_ @t85 @t38)) % 0.25/0.52 (define @t87 () (forall @t47 @t86)) % 0.25/0.52 (define @t88 () (_ @t30 @t38)) % 0.25/0.52 (define @t89 () (lambda @t49 (forall @t47 @t88))) % 0.25/0.52 (define @t90 () (_ @t2 @t10 @t29)) % 0.25/0.52 (define @t91 () (not @t90)) % 0.25/0.52 (define @t92 () (or @t91 @t77 @t76)) % 0.25/0.52 (define @t93 () (lambda @t11 (forall @t78 @t92))) % 0.25/0.52 (define @t94 () (_ @t93 @t23)) % 0.25/0.52 (define @t95 () (or @t83 @t94)) % 0.25/0.52 (define @t96 () (lambda @t84 @t95)) % 0.25/0.52 (define @t97 () (_ @t24 @t23)) % 0.25/0.52 (define @t98 () (@list @t24 @t23)) % 0.25/0.52 (define @t99 () (or @t77 @t76)) % 0.25/0.52 (define @t100 () (or @t91 @t99)) % 0.25/0.52 (define @t101 () (forall @t78 @t100)) % 0.25/0.52 (define @t102 () (@list @t74)) % 0.25/0.52 (define @t103 () (forall @t102 @t100)) % 0.25/0.52 (define @t104 () (forall @t102 @t99)) % 0.25/0.52 (define @t105 () (@var "BOUND_VARIABLE_7795" $$unsorted)) % 0.25/0.52 (define @t106 () (@list @t105)) % 0.25/0.52 (define @t107 () (or @t91 @t104)) % 0.25/0.52 (define @t108 () (_ @t1 @t105)) % 0.25/0.52 (define @t109 () (@list @t105)) % 0.25/0.52 (define @t110 () (forall @t109 (or (not (_ @t2 @t29 @t105)) @t108))) % 0.25/0.52 (define @t111 () (forall @t33 (or @t91 @t60))) % 0.25/0.52 (define @t112 () (lambda @t11 @t111)) % 0.25/0.52 (define @t113 () (or @t91 (_ @t112 @t29))) % 0.25/0.52 (define @t114 () (forall @t33 @t113)) % 0.25/0.52 (define @t115 () (lambda @t11 @t114)) % 0.25/0.52 (define @t116 () (_ @t30 @t29)) % 0.25/0.52 (define @t117 () (forall @t33 (or @t91 @t116))) % 0.25/0.52 (define @t118 () (lambda (@list @t30 @t10) @t117)) % 0.25/0.52 (define @t119 () (_ (lambda @t35 @t117) @t2)) % 0.25/0.52 (define @t120 () (_ @t112 @t23)) % 0.25/0.52 (define @t121 () (not @t120)) % 0.25/0.52 (define @t122 () (or @t121 @t97)) % 0.25/0.52 (define @t123 () (lambda @t98 @t122)) % 0.25/0.52 (define @t124 () (or (not (_ @t25 @t23)) @t97)) % 0.25/0.52 (define @t125 () (lambda @t26 @t124)) % 0.25/0.52 (define @t126 () (_ @t119 @t1)) % 0.25/0.52 (define @t127 () (forall @t5 (_ @t89 (_ (_ @t125 @t126) (_ @t119 @t126))))) % 0.25/0.52 (define @t128 () (exists @t7 @t127)) % 0.25/0.52 (define @t129 () (not @t32)) % 0.25/0.52 (define @t130 () (or @t129 @t31)) % 0.25/0.52 (define @t131 () (not (_ @t25 @t14))) % 0.25/0.52 (define @t132 () (@list @t14)) % 0.25/0.52 (define @t133 () (lambda @t132 (or @t131 (_ @t24 @t14)))) % 0.25/0.52 (define @t134 () (@list @t18 @t14)) % 0.25/0.52 (define @t135 () (lambda @t132 @t131)) % 0.25/0.52 (define @t136 () (_ @t135 @t14)) % 0.25/0.52 (define @t137 () (or @t136 @t19)) % 0.25/0.52 (define @t138 () (lambda @t134 @t137)) % 0.25/0.52 (define @t139 () (not (forall @t33 @t60))) % 0.25/0.52 (define @t140 () (or @t139 @t56)) % 0.25/0.52 (define @t141 () (forall (@list @t1 @t55) @t140)) % 0.25/0.52 (define @t142 () (lambda (@list (@var "BOUND_VARIABLE_15002" $$unsorted) (@var "BOUND_VARIABLE_15003" $$unsorted)) true)) % 0.25/0.52 (define @t143 () (_ @t142 @t57 @t55)) % 0.25/0.52 (define @t144 () (not @t143)) % 0.25/0.52 (define @t145 () (_ @t142 @t38 @t57)) % 0.25/0.52 (define @t146 () (not @t145)) % 0.25/0.52 (define @t147 () (_ @t142 @t38 @t29)) % 0.25/0.52 (define @t148 () (not @t147)) % 0.25/0.52 (define @t149 () (or @t148 @t60)) % 0.25/0.52 (define @t150 () (forall @t33 @t149)) % 0.25/0.52 (define @t151 () (not @t150)) % 0.25/0.52 (define @t152 () (or @t151 @t146 @t144 @t56)) % 0.25/0.52 (define @t153 () (forall @t64 @t152)) % 0.25/0.52 (define @t154 () (not @t153)) % 0.25/0.52 (define @t155 () (@quantifiers_skolemize @t141 0)) % 0.25/0.52 (define @t156 () (forall @t33 (_ @t155 @t29))) % 0.25/0.52 (define @t157 () (@quantifiers_skolemize @t141 1)) % 0.25/0.52 (define @t158 () (_ @t155 @t157)) % 0.25/0.52 (define @t159 () (not @t156)) % 0.25/0.52 (define @t160 () (or @t159 @t158)) % 0.25/0.52 (define @t161 () (@list true)) % 0.25/0.52 (define @t162 () (@list @t160)) % 0.25/0.52 (assume @p1 @t9) % 0.25/0.52 (assume @p2 true) % 0.25/0.52 (step @p3 (= tptp.mfalse @t12) :rule refl :args (@t12)) % 0.25/0.52 (step @p4 (= tptp.mtrue @t13) :rule refl :args (@t13)) % 0.25/0.52 (step @p5 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.25/0.52 (step @p6 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.25/0.52 (step @p7 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.25/0.52 (step @p8 (= tptp.mimpl @t27) :rule refl :args (@t27)) % 0.25/0.52 (step @p9 (= tptp.miff @t28) :rule refl :args (@t28)) % 0.25/0.52 (step @p10 (= tptp.mbox @t36) :rule refl :args (@t36)) % 0.25/0.52 (step @p11 (= tptp.mdia @t37) :rule refl :args (@t37)) % 0.25/0.52 (step @p12 (= tptp.mall @t44) :rule refl :args (@t44)) % 0.25/0.52 (step @p13 (= tptp.mexists @t45) :rule refl :args (@t45)) % 0.25/0.52 (step @p14 (= tptp.mvalid @t50) :rule refl :args (@t50)) % 0.25/0.52 (step @p15 (= tptp.msatisfiable @t51) :rule refl :args (@t51)) % 0.25/0.52 (step @p16 (= tptp.mcountersatisfiable @t53) :rule refl :args (@t53)) % 0.25/0.52 (step @p17 (= tptp.minvalid @t54) :rule refl :args (@t54)) % 0.25/0.52 (step @p18 :rule bool-double-not-elim :args (@t66)) % 0.25/0.52 (step @p19 :rule exists-elim :args ((= (exists @t7 @t65) (not @t66)))) % 0.25/0.52 (step @p20 :rule quant-merge-prenex :args ((= (forall @t5 (forall @t67 @t63)) @t65))) % 0.25/0.52 (step @p21 :rule aci_norm :args ((= @t69 @t63))) % 0.25/0.52 (step @p22 :rule cong :premises (@p21) :args (@t70)) % 0.25/0.52 (step @p23 :rule quant-merge-prenex :args ((= (forall @t47 @t72) @t70))) % 0.25/0.52 (step @p24 :rule alpha_equiv :args (@t73 (@list @t57 @t55) (@list @t29 @t74))) % 0.25/0.52 (step @p25 :rule refl :args (@t62)) % 0.25/0.52 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t75)) % 0.25/0.52 (step @p27 :rule quant-miniscope-or :args ((= @t72 @t75))) % 0.25/0.52 (step @p28 :rule trans :premises (@p27 @p26)) % 0.25/0.52 (step @p29 :rule symm :premises (@p28)) % 0.25/0.52 (step @p30 :rule cong :premises (@p29) :args ((forall @t47 @t79))) % 0.25/0.52 (step @p31 :rule trans :premises (@p30 @p23)) % 0.25/0.52 (step @p32 :rule trans :premises (@p31 @p22)) % 0.25/0.52 (step @p33 :rule beta-reduce :args ((= @t86 @t79))) % 0.25/0.52 (step @p34 :rule cong :premises (@p33) :args (@t87)) % 0.25/0.52 (step @p35 :rule trans :premises (@p34 @p32)) % 0.25/0.52 (step @p36 :rule beta-reduce :args ((= (_ @t89 @t85) @t87))) % 0.25/0.52 (step @p37 :rule trans :premises (@p36 @p35)) % 0.25/0.52 (step @p38 :rule beta-reduce :args ((= @t94 @t81))) % 0.25/0.52 (step @p39 :rule refl :args (@t83)) % 0.25/0.52 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t95)) % 0.25/0.52 (step @p41 :rule cong :premises (@p40) :args (@t96)) % 0.25/0.52 (step @p42 :rule beta-reduce :args ((= (_ (lambda @t98 (or @t83 @t97)) @t93) @t96))) % 0.25/0.52 (step @p43 :rule trans :premises (@p42 @p41)) % 0.25/0.52 (step @p44 :rule aci_norm :args ((= @t100 @t92))) % 0.25/0.52 (step @p45 :rule cong :premises (@p44) :args (@t101)) % 0.25/0.52 (step @p46 :rule quant-merge-prenex :args ((= (forall @t33 @t103) @t101))) % 0.25/0.52 (step @p47 :rule alpha_equiv :args (@t104 (@list @t74) @t106)) % 0.25/0.52 (step @p48 :rule refl :args (@t91)) % 0.25/0.52 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t107)) % 0.25/0.52 (step @p50 :rule quant-miniscope-or :args ((= @t103 @t107))) % 0.25/0.52 (step @p51 :rule trans :premises (@p50 @p49)) % 0.25/0.52 (step @p52 :rule symm :premises (@p51)) % 0.25/0.52 (step @p53 :rule cong :premises (@p52) :args ((forall @t33 (or @t91 @t110)))) % 0.25/0.52 (step @p54 :rule trans :premises (@p53 @p46)) % 0.25/0.52 (step @p55 :rule trans :premises (@p54 @p45)) % 0.25/0.52 (step @p56 :rule beta-reduce :args ((= (_ (lambda @t11 (forall @t109 (or (not (_ @t2 @t10 @t105)) @t108))) @t29) @t110))) % 0.25/0.52 (step @p57 :rule refl :args (@t29)) % 0.25/0.52 (step @p58 :rule alpha_equiv :args (@t111 (@list @t29) @t106)) % 0.25/0.52 (step @p59 :rule cong :premises (@p58) :args (@t112)) % 0.25/0.52 (step @p60 :rule ho_cong :premises (@p59 @p57)) % 0.25/0.52 (step @p61 :rule trans 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@t82))) % 0.25/0.52 (step @p78 :rule cong :premises (@p77) :args (@t121)) % 0.25/0.52 (step @p79 :rule nary_cong :premises (@p78 @p76) :args (@t122)) % 0.25/0.52 (step @p80 :rule cong :premises (@p79) :args (@t123)) % 0.25/0.52 (step @p81 :rule beta-reduce :args ((= (_ @t125 @t112) @t123))) % 0.25/0.52 (step @p82 :rule trans :premises (@p81 @p80)) % 0.25/0.52 (step @p83 :rule refl :args (@t125)) % 0.25/0.52 (step @p84 :rule ho_cong :premises (@p83 @p73)) % 0.25/0.52 (step @p85 :rule trans :premises (@p84 @p82)) % 0.25/0.52 (step @p86 :rule ho_cong :premises (@p85 @p75)) % 0.25/0.52 (step @p87 :rule trans :premises (@p86 @p43)) % 0.25/0.52 (step @p88 :rule refl :args (@t89)) % 0.25/0.52 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.25/0.52 (step @p90 :rule trans :premises (@p89 @p37)) % 0.25/0.52 (step @p91 :rule cong :premises (@p90) :args (@t127)) % 0.25/0.52 (step @p92 :rule trans :premises (@p91 @p20)) % 0.25/0.52 (step @p93 :rule cong :premises (@p92) :args (@t128)) % 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:rule cong :premises (@p109) :args ((forall @t33 @t130))) % 0.25/0.52 (step @p111 :rule bool-impl-elim :args (@t32 @t31)) % 0.25/0.52 (step @p112 :rule cong :premises (@p111) :args (@t34)) % 0.25/0.52 (step @p113 :rule trans :premises (@p112 @p110)) % 0.25/0.52 (step @p114 :rule cong :premises (@p113) :args (@t36)) % 0.25/0.52 (step @p115 :rule trans :premises (@p10 @p114)) % 0.25/0.52 (step @p116 :rule ho_cong :premises (@p115 @p97)) % 0.25/0.52 (step @p117 :rule ho_cong :premises (@p116 @p70)) % 0.25/0.52 (step @p118 :rule ho_cong :premises (@p116 @p117)) % 0.25/0.52 (step @p119 :rule beta-reduce :args ((= (_ @t133 @t23) @t124))) % 0.25/0.52 (step @p120 :rule refl :args (@t23)) % 0.25/0.52 (step @p121 :rule beta-reduce :args ((= (_ (lambda @t134 (or @t131 @t19)) @t24) @t133))) % 0.25/0.52 (step @p122 :rule refl :args (@t24)) % 0.25/0.52 (step @p123 :rule refl :args (@t19)) % 0.25/0.52 (step @p124 :rule beta-reduce :args ((= @t136 @t131))) % 0.25/0.52 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t137)) % 0.25/0.52 (step @p126 :rule cong :premises (@p125) :args (@t138)) % 0.25/0.52 (step @p127 :rule beta-reduce :args ((= (_ @t21 @t135) @t138))) % 0.25/0.52 (step @p128 :rule trans :premises (@p127 @p126)) % 0.25/0.52 (step @p129 :rule beta-reduce :args ((= (_ @t17 @t25) @t135))) % 0.25/0.52 (step @p130 :rule refl :args (@t21)) % 0.25/0.52 (step @p131 :rule ho_cong :premises (@p130 @p129)) % 0.25/0.52 (step @p132 :rule trans :premises (@p131 @p128)) % 0.25/0.52 (step @p133 :rule ho_cong :premises (@p132 @p122)) % 0.25/0.52 (step @p134 :rule trans :premises (@p133 @p121)) % 0.25/0.52 (step @p135 :rule ho_cong :premises (@p134 @p120)) % 0.25/0.52 (step @p136 :rule trans :premises (@p135 @p119)) % 0.25/0.52 (step @p137 :rule refl :args (@t25)) % 0.25/0.52 (step @p138 :rule ho_cong :premises (@p5 @p137)) % 0.25/0.52 (step @p139 :rule ho_cong :premises (@p6 @p138)) % 0.25/0.52 (step @p140 :rule ho_cong :premises (@p139 @p122)) % 0.25/0.52 (step @p141 :rule ho_cong :premises (@p140 @p120)) % 0.25/0.52 (step @p142 :rule trans :premises (@p141 @p136)) % 0.25/0.52 (step @p143 :rule cong :premises (@p142) :args (@t27)) % 0.25/0.52 (step @p144 :rule trans :premises (@p8 @p143)) % 0.25/0.52 (step @p145 :rule ho_cong :premises (@p144 @p117)) % 0.25/0.52 (step @p146 :rule ho_cong :premises (@p145 @p118)) % 0.25/0.52 (step @p147 :rule refl :args (@t88)) % 0.25/0.52 (step @p148 :rule refl :args (@t46)) % 0.25/0.52 (step @p149 :rule cong :premises (@p148 @p147) :args ((= @t46 @t88))) % 0.25/0.52 (step @p150 :rule symm :premises (@p149)) % 0.25/0.52 (step @p151 :rule eq_resolve :premises (@p148 @p150)) % 0.25/0.52 (step @p152 :rule cong :premises (@p151) :args (@t48)) % 0.25/0.52 (step @p153 :rule cong :premises (@p152) :args (@t50)) % 0.25/0.52 (step @p154 :rule trans :premises (@p14 @p153)) % 0.25/0.52 (step @p155 :rule ho_cong :premises (@p154 @p146)) % 0.25/0.52 (step @p156 :rule cong :premises (@p155) :args (@t6)) % 0.25/0.52 (step @p157 :rule cong :premises (@p156) :args (@t8)) % 0.25/0.52 (step @p158 :rule cong :premises (@p157) :args (@t9)) % 0.25/0.52 (step @p159 :rule trans :premises (@p158 @p96)) % 0.25/0.52 (step @p160 :rule eq_resolve :premises (@p1 @p159)) % 0.25/0.52 (step @p161 :rule quant-unused-vars :args ((= (forall @t64 @t140) @t141))) % 0.25/0.52 (step @p162 :rule aci_norm :args ((= (or @t139 false false @t56) @t140))) % 0.25/0.52 (step @p163 :rule refl :args (@t56)) % 0.25/0.52 (step @p164 :rule evaluate :args ((not true))) % 0.25/0.52 (step @p165 :rule beta-reduce :args ((= @t143 true))) % 0.25/0.52 (step @p166 :rule cong :premises (@p165) :args (@t144)) % 0.25/0.52 (step @p167 :rule trans :premises (@p166 @p164)) % 0.25/0.52 (step @p168 :rule beta-reduce :args ((= @t145 true))) % 0.25/0.52 (step @p169 :rule cong :premises (@p168) :args (@t146)) % 0.25/0.52 (step @p170 :rule trans :premises (@p169 @p164)) % 0.25/0.52 (step @p171 :rule aci_norm :args ((= (or false @t60) @t60))) % 0.25/0.52 (step @p172 :rule refl :args (@t60)) % 0.25/0.52 (step @p173 :rule beta-reduce :args ((= @t147 true))) % 0.25/0.52 (step @p174 :rule cong :premises (@p173) :args (@t148)) % 0.25/0.52 (step @p175 :rule trans :premises (@p174 @p164)) % 0.25/0.52 (step @p176 :rule nary_cong :premises (@p175 @p172) :args (@t149)) % 0.25/0.52 (step @p177 :rule trans :premises (@p176 @p171)) % 0.25/0.52 (step @p178 :rule cong :premises (@p177) :args (@t150)) % 0.25/0.52 (step @p179 :rule cong :premises (@p178) :args (@t151)) % 0.25/0.52 (step @p180 :rule nary_cong :premises (@p179 @p170 @p167 @p163) :args (@t152)) % 0.25/0.52 (step @p181 :rule trans :premises (@p180 @p162)) % 0.25/0.52 (step @p182 :rule cong :premises (@p181) :args (@t153)) % 0.25/0.52 (step @p183 :rule trans :premises (@p182 @p161)) % 0.25/0.52 (step @p184 :rule cong :premises (@p183) :args (@t154)) % 0.25/0.52 (step @p185 :rule refl :args (@t66)) % 0.25/0.52 (step @p186 :rule cong :premises (@p185 @p184) :args ((=> @t66 @t154))) % 0.25/0.52 (assume-push @p210 @t66) % 0.25/0.52 (step @p188 :rule instantiate :premises (@p160) :args ((@list @t142))) % 0.25/0.52 (step-pop @p211 :rule scope :premises (@p188)) % 0.25/0.52 (step @p189 :rule process_scope :premises (@p211) :args (@t154)) % 0.25/0.52 (step @p191 :rule eq_resolve :premises (@p189 @p186)) % 0.25/0.52 (step @p192 :rule implies_elim :premises (@p191)) % 0.25/0.52 (step @p193 :rule chain_m_resolution :premises (@p192 @p160) :args ((not @t141) (@list false) (@list @t66))) % 0.25/0.52 (step @p194 :rule skolemize :premises (@p193)) % 0.25/0.52 (step @p195 :rule bool-double-not-elim :args (@t156)) % 0.25/0.52 (step @p196 :rule refl :args (@t160)) % 0.25/0.52 (step @p197 :rule nary_cong :premises (@p196 @p195) :args ((or @t160 (not @t159)))) % 0.25/0.52 (step @p198 :rule cnf_or_neg :args (@t160 0)) % 0.25/0.52 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 0.25/0.52 (step @p200 :rule reordering :premises (@p199) :args ((or @t156 @t160))) % 0.25/0.52 (step @p201 :rule chain_m_resolution :premises (@p200 @p194) :args (@t156 @t161 @t162)) % 0.25/0.52 (step @p202 :rule cnf_or_neg :args (@t160 1)) % 0.25/0.52 (step @p203 :rule chain_m_resolution :premises (@p202 @p194) :args ((not @t158) @t161 @t162)) % 0.25/0.52 (assume-push @p212 @t156) % 0.25/0.52 (step @p205 :rule instantiate :premises (@p201) :args ((@list @t157))) % 0.25/0.52 (step-pop @p213 :rule scope :premises (@p205)) % 0.25/0.52 (step @p206 :rule process_scope :premises (@p213) :args (@t158)) % 0.25/0.52 (step @p208 :rule implies_elim :premises (@p206)) % 0.25/0.52 (step @p209 false :rule chain_m_resolution :premises (@p208 @p203 @p201) :args (false (@list true false) (@list @t158 @t156))) % 0.25/0.52 ) % 0.25/0.52 % SZS output end Proof % 0.25/0.52 % cvc5 exiting %------------------------------------------------------------------------------