%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL589^1 : 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 : n008.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 0.19s 0.53s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL589^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.37 % Computer : n008.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Sat Sep 5 08:18:08 UTC 2026 % 0.09/0.38 % CPUTime : % 0.09/0.44 %----Proving TH0 % 0.19/0.53 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.19/0.53 % SZS status Theorem % 0.19/0.53 % SZS output start Proof % 0.19/0.53 ( % 0.19/0.53 (declare-sort $$unsorted 0) % 0.19/0.53 (declare-sort tptp.individuals 0) % 0.19/0.53 (declare-const tptp.a (-> $$unsorted Bool)) % 0.19/0.53 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.19/0.53 (declare-const tptp.b (-> $$unsorted Bool)) % 0.19/0.53 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.19/0.53 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.19/0.53 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.19/0.53 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.19/0.53 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.53 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.19/0.53 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.19/0.53 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.19/0.53 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.53 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.53 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.53 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.53 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.53 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.53 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.53 (define @t1 () (_ tptp.mbox tptp.r)) % 0.19/0.53 (define @t2 () (_ @t1 tptp.b)) % 0.19/0.53 (define @t3 () (not (_ tptp.mvalid (_ (_ tptp.mimpl (_ (_ tptp.mimpl (_ (_ tptp.mdia tptp.r) tptp.a)) @t2)) (_ (_ tptp.mimpl (_ @t1 tptp.a)) @t2))))) % 0.19/0.53 (define @t4 () (@var "X" $$unsorted)) % 0.19/0.53 (define @t5 () (@list @t4)) % 0.19/0.53 (define @t6 () (lambda @t5 false)) % 0.19/0.53 (define @t7 () (lambda @t5 true)) % 0.19/0.53 (define @t8 () (@var "U" $$unsorted)) % 0.19/0.53 (define @t9 () (@var "X" (-> $$unsorted Bool))) % 0.19/0.53 (define @t10 () (_ @t9 @t8)) % 0.19/0.53 (define @t11 () (lambda (@list @t9 @t8) (not @t10))) % 0.19/0.53 (define @t12 () (@var "Y" (-> $$unsorted Bool))) % 0.19/0.53 (define @t13 () (_ @t12 @t8)) % 0.19/0.53 (define @t14 () (@list @t9 @t12 @t8)) % 0.19/0.53 (define @t15 () (lambda @t14 (or @t10 @t13))) % 0.19/0.53 (define @t16 () (lambda @t14 (and @t10 @t13))) % 0.19/0.53 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.19/0.53 (define @t18 () (@var "V" (-> $$unsorted Bool))) % 0.19/0.53 (define @t19 () (@var "U" (-> $$unsorted Bool))) % 0.19/0.53 (define @t20 () (@list @t19 @t18 @t17)) % 0.19/0.53 (define @t21 () (lambda @t20 (_ (_ (_ tptp.mor (_ tptp.mnot @t19)) @t18) @t17))) % 0.19/0.53 (define @t22 () (lambda @t20 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t19) @t18)) (_ (_ tptp.mimpl @t18) @t19)) @t17))) % 0.19/0.53 (define @t23 () (@var "Y" $$unsorted)) % 0.19/0.53 (define @t24 () (@var "P" (-> $$unsorted Bool))) % 0.19/0.53 (define @t25 () (_ @t24 @t23)) % 0.19/0.53 (define @t26 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.19/0.53 (define @t27 () (_ (_ @t26 @t4) @t23)) % 0.19/0.53 (define @t28 () (@list @t23)) % 0.19/0.53 (define @t29 () (forall @t28 (=> @t27 @t25))) % 0.19/0.53 (define @t30 () (@list @t26 @t24 @t4)) % 0.19/0.53 (define @t31 () (lambda @t30 @t29)) % 0.19/0.53 (define @t32 () (and @t27 @t25)) % 0.19/0.53 (define @t33 () (exists @t28 @t32)) % 0.19/0.53 (define @t34 () (lambda @t30 @t33)) % 0.19/0.53 (define @t35 () (@var "W" $$unsorted)) % 0.19/0.53 (define @t36 () (@var "X" tptp.individuals)) % 0.19/0.53 (define @t37 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.19/0.53 (define @t38 () (_ (_ @t37 @t36) @t35)) % 0.19/0.53 (define @t39 () (@list @t36)) % 0.19/0.53 (define @t40 () (@list @t37 @t35)) % 0.19/0.53 (define @t41 () (lambda @t40 (forall @t39 @t38))) % 0.19/0.53 (define @t42 () (lambda @t40 (exists @t39 @t38))) % 0.19/0.53 (define @t43 () (_ @t24 @t35)) % 0.19/0.53 (define @t44 () (@list @t35)) % 0.19/0.53 (define @t45 () (forall @t44 @t43)) % 0.19/0.53 (define @t46 () (@list @t24)) % 0.19/0.53 (define @t47 () (lambda @t46 @t45)) % 0.19/0.53 (define @t48 () (lambda @t46 (exists @t44 @t43))) % 0.19/0.53 (define @t49 () (not @t43)) % 0.19/0.53 (define @t50 () (lambda @t46 (exists @t44 @t49))) % 0.19/0.53 (define @t51 () (lambda @t46 (forall @t44 @t49))) % 0.19/0.53 (define @t52 () (@var "BOUND_VARIABLE_7884" $$unsorted)) % 0.19/0.53 (define @t53 () (tptp.b @t52)) % 0.19/0.53 (define @t54 () (not (tptp.r @t35 @t52))) % 0.19/0.53 (define @t55 () (tptp.a @t23)) % 0.19/0.53 (define @t56 () (not (tptp.r @t35 @t23))) % 0.19/0.53 (define @t57 () (not (forall @t28 (or @t56 @t55)))) % 0.19/0.53 (define @t58 () (tptp.b @t23)) % 0.19/0.53 (define @t59 () (forall @t28 (or @t56 @t58))) % 0.19/0.53 (define @t60 () (not @t55)) % 0.19/0.53 (define @t61 () (forall @t28 (or @t56 @t60))) % 0.19/0.53 (define @t62 () (and (not @t61) (not @t59))) % 0.19/0.53 (define @t63 () (or @t62 @t57 @t54 @t53)) % 0.19/0.53 (define @t64 () (or @t54 @t53)) % 0.19/0.53 (define @t65 () (or @t62 @t57 @t64)) % 0.19/0.53 (define @t66 () (@list @t35 @t52)) % 0.19/0.53 (define @t67 () (forall @t66 @t65)) % 0.19/0.53 (define @t68 () (@list @t52)) % 0.19/0.53 (define @t69 () (forall @t68 @t65)) % 0.19/0.53 (define @t70 () (forall @t68 @t64)) % 0.19/0.53 (define @t71 () (or @t62 @t57 @t70)) % 0.19/0.53 (define @t72 () (or (not (or @t61 @t59)) @t57 @t59)) % 0.19/0.53 (define @t73 () (not (tptp.r @t17 @t23))) % 0.19/0.53 (define @t74 () (forall @t28 (or @t73 @t58))) % 0.19/0.53 (define @t75 () (forall @t28 (or @t73 @t55))) % 0.19/0.53 (define @t76 () (not @t75)) % 0.19/0.53 (define @t77 () (forall @t28 (or @t73 @t60))) % 0.19/0.53 (define @t78 () (or @t77 @t74)) % 0.19/0.53 (define @t79 () (not @t78)) % 0.19/0.53 (define @t80 () (or @t79 @t76 @t74)) % 0.19/0.53 (define @t81 () (@list @t17)) % 0.19/0.53 (define @t82 () (lambda @t81 @t80)) % 0.19/0.53 (define @t83 () (_ @t82 @t35)) % 0.19/0.53 (define @t84 () (forall @t44 @t83)) % 0.19/0.53 (define @t85 () (_ @t24 @t35)) % 0.19/0.53 (define @t86 () (lambda @t46 (forall @t44 @t85))) % 0.19/0.53 (define @t87 () (or @t76 @t74)) % 0.19/0.53 (define @t88 () (lambda @t81 @t87)) % 0.19/0.53 (define @t89 () (_ @t88 @t17)) % 0.19/0.53 (define @t90 () (or @t79 @t89)) % 0.19/0.53 (define @t91 () (lambda @t81 @t90)) % 0.19/0.53 (define @t92 () (_ @t18 @t17)) % 0.19/0.53 (define @t93 () (@list @t18 @t17)) % 0.19/0.53 (define @t94 () (not (tptp.r @t4 @t23))) % 0.19/0.53 (define @t95 () (lambda @t5 (forall @t28 (or @t94 @t58)))) % 0.19/0.53 (define @t96 () (_ @t95 @t17)) % 0.19/0.53 (define @t97 () (or @t76 @t96)) % 0.19/0.53 (define @t98 () (lambda @t81 @t97)) % 0.19/0.53 (define @t99 () (_ @t24 @t23)) % 0.19/0.53 (define @t100 () (@list @t24 @t4)) % 0.19/0.53 (define @t101 () (lambda @t100 (forall @t28 (or @t94 @t99)))) % 0.19/0.53 (define @t102 () (_ @t26 @t4 @t23)) % 0.19/0.53 (define @t103 () (not @t102)) % 0.19/0.53 (define @t104 () (_ (lambda @t30 (forall @t28 (or @t103 @t99))) tptp.r)) % 0.19/0.53 (define @t105 () (lambda @t5 (forall @t28 (or @t94 @t55)))) % 0.19/0.53 (define @t106 () (_ @t105 @t17)) % 0.19/0.53 (define @t107 () (not @t106)) % 0.19/0.53 (define @t108 () (or @t107 @t92)) % 0.19/0.53 (define @t109 () (lambda @t93 @t108)) % 0.19/0.53 (define @t110 () (or (not (_ @t19 @t17)) @t92)) % 0.19/0.53 (define @t111 () (lambda @t20 @t110)) % 0.19/0.53 (define @t112 () (lambda @t81 @t78)) % 0.19/0.53 (define @t113 () (_ @t112 @t17)) % 0.19/0.53 (define @t114 () (not @t113)) % 0.19/0.53 (define @t115 () (or @t114 @t92)) % 0.19/0.53 (define @t116 () (lambda @t93 @t115)) % 0.19/0.53 (define @t117 () (or @t77 @t96)) % 0.19/0.53 (define @t118 () (lambda @t81 @t117)) % 0.19/0.53 (define @t119 () (lambda @t5 (not (forall @t28 (or @t94 @t60))))) % 0.19/0.53 (define @t120 () (_ @t119 @t17)) % 0.19/0.53 (define @t121 () (not @t120)) % 0.19/0.53 (define @t122 () (or @t121 @t92)) % 0.19/0.53 (define @t123 () (lambda @t93 @t122)) % 0.19/0.53 (define @t124 () (not @t99)) % 0.19/0.53 (define @t125 () (lambda @t100 (not (forall @t28 (or @t94 @t124))))) % 0.19/0.53 (define @t126 () (_ (lambda @t30 (not (forall @t28 (or @t103 @t124)))) tptp.r)) % 0.19/0.53 (define @t127 () (_ @t104 tptp.b)) % 0.19/0.53 (define @t128 () (not @t27)) % 0.19/0.53 (define @t129 () (or @t128 @t25)) % 0.19/0.53 (define @t130 () (not (_ @t19 @t8))) % 0.19/0.53 (define @t131 () (@list @t8)) % 0.19/0.53 (define @t132 () (lambda @t131 (or @t130 (_ @t18 @t8)))) % 0.19/0.53 (define @t133 () (@list @t12 @t8)) % 0.19/0.53 (define @t134 () (lambda @t131 @t130)) % 0.19/0.53 (define @t135 () (_ @t134 @t8)) % 0.19/0.53 (define @t136 () (or @t135 @t13)) % 0.19/0.53 (define @t137 () (lambda @t133 @t136)) % 0.19/0.53 (define @t138 () (not @t25)) % 0.19/0.53 (define @t139 () (or @t128 @t138)) % 0.19/0.53 (define @t140 () (forall @t28 (not @t32))) % 0.19/0.53 (define @t141 () (not @t140)) % 0.19/0.53 (define @t142 () (forall @t66 @t63)) % 0.19/0.53 (define @t143 () (@quantifiers_skolemize @t142 1)) % 0.19/0.53 (define @t144 () (tptp.b @t143)) % 0.19/0.53 (define @t145 () (@quantifiers_skolemize @t142 0)) % 0.19/0.53 (define @t146 () (tptp.r @t145 @t143)) % 0.19/0.53 (define @t147 () (not @t146)) % 0.19/0.53 (define @t148 () (not (tptp.r @t145 @t23))) % 0.19/0.53 (define @t149 () (forall @t28 (or @t148 @t55))) % 0.19/0.53 (define @t150 () (not @t149)) % 0.19/0.53 (define @t151 () (forall @t28 (or @t148 @t58))) % 0.19/0.53 (define @t152 () (not @t151)) % 0.19/0.53 (define @t153 () (forall @t28 (or @t148 @t60))) % 0.19/0.53 (define @t154 () (not @t153)) % 0.19/0.53 (define @t155 () (and @t154 @t152)) % 0.19/0.53 (define @t156 () (or @t155 @t150 @t147 @t144)) % 0.19/0.53 (define @t157 () (@list true)) % 0.19/0.53 (define @t158 () (@list @t156)) % 0.19/0.53 (define @t159 () (@list @t143)) % 0.19/0.53 (define @t160 () (tptp.a @t143)) % 0.19/0.53 (define @t161 () (or @t147 @t160)) % 0.19/0.53 (define @t162 () (@list false false)) % 0.19/0.53 (define @t163 () (not @t160)) % 0.19/0.53 (define @t164 () (or @t147 @t163)) % 0.19/0.53 (define @t165 () (not @t164)) % 0.19/0.53 (define @t166 () (or @t147 @t144)) % 0.19/0.53 (define @t167 () (not @t166)) % 0.19/0.53 (assume @p1 @t3) % 0.19/0.53 (assume @p2 true) % 0.19/0.53 (step @p3 (= tptp.mfalse @t6) :rule refl :args (@t6)) % 0.19/0.53 (step @p4 (= tptp.mtrue @t7) :rule refl :args (@t7)) % 0.19/0.53 (step @p5 (= tptp.mnot @t11) :rule refl :args (@t11)) % 0.19/0.53 (step @p6 (= tptp.mor @t15) :rule refl :args (@t15)) % 0.19/0.53 (step @p7 (= tptp.mand @t16) :rule refl :args (@t16)) % 0.19/0.53 (step @p8 (= tptp.mimpl @t21) :rule refl :args (@t21)) % 0.19/0.53 (step @p9 (= tptp.miff @t22) :rule refl :args (@t22)) % 0.19/0.53 (step @p10 (= tptp.mbox @t31) :rule refl :args (@t31)) % 0.19/0.53 (step @p11 (= tptp.mdia @t34) :rule refl :args (@t34)) % 0.19/0.53 (step @p12 (= tptp.mall @t41) :rule refl :args (@t41)) % 0.19/0.53 (step @p13 (= tptp.mexists @t42) :rule refl :args (@t42)) % 0.19/0.53 (step @p14 (= tptp.mvalid @t47) :rule refl :args (@t47)) % 0.19/0.53 (step @p15 (= tptp.msatisfiable @t48) :rule refl :args (@t48)) % 0.19/0.53 (step @p16 (= tptp.mcountersatisfiable @t50) :rule refl :args (@t50)) % 0.19/0.53 (step @p17 (= tptp.minvalid @t51) :rule refl :args (@t51)) % 0.19/0.53 (step @p18 :rule aci_norm :args ((= @t65 @t63))) % 0.19/0.53 (step @p19 :rule cong :premises (@p18) :args (@t67)) % 0.19/0.53 (step @p20 :rule quant-merge-prenex :args ((= (forall @t44 @t69) @t67))) % 0.19/0.53 (step @p21 :rule alpha_equiv :args (@t70 (@list @t52) (@list @t23))) % 0.19/0.53 (step @p22 :rule refl :args (@t57)) % 0.19/0.53 (step @p23 :rule refl :args (@t62)) % 0.19/0.53 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t71)) % 0.19/0.53 (step @p25 :rule quant-miniscope-or :args ((= @t69 @t71))) % 0.19/0.53 (step @p26 :rule trans :premises (@p25 @p24)) % 0.19/0.53 (step @p27 :rule symm :premises (@p26)) % 0.19/0.53 (step @p28 :rule cong :premises (@p27) :args ((forall @t44 (or @t62 @t57 @t59)))) % 0.19/0.53 (step @p29 :rule trans :premises (@p28 @p20)) % 0.19/0.53 (step @p30 :rule trans :premises (@p29 @p19)) % 0.19/0.53 (step @p31 :rule refl :args (@t59)) % 0.19/0.53 (step @p32 :rule bool-or-de-morgan :args (@t61 @t59 false)) % 0.19/0.53 (step @p33 :rule nary_cong :premises (@p32 @p22 @p31) :args (@t72)) % 0.19/0.53 (step @p34 :rule cong :premises (@p33) :args ((forall @t44 @t72))) % 0.19/0.53 (step @p35 :rule trans :premises (@p34 @p30)) % 0.19/0.53 (step @p36 :rule beta-reduce :args ((= @t83 @t72))) % 0.19/0.53 (step @p37 :rule cong :premises (@p36) :args (@t84)) % 0.19/0.53 (step @p38 :rule trans :premises (@p37 @p35)) % 0.19/0.53 (step @p39 :rule beta-reduce :args ((= (_ @t86 @t82) @t84))) % 0.19/0.53 (step @p40 :rule trans :premises (@p39 @p38)) % 0.19/0.53 (step @p41 :rule aci_norm :args ((= (or @t79 @t87) @t80))) % 0.19/0.53 (step @p42 :rule beta-reduce :args ((= @t89 @t87))) % 0.19/0.53 (step @p43 :rule refl :args (@t79)) % 0.19/0.53 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t90)) % 0.19/0.53 (step @p45 :rule trans :premises (@p44 @p41)) % 0.19/0.53 (step @p46 :rule cong :premises (@p45) :args (@t91)) % 0.19/0.53 (step @p47 :rule beta-reduce :args ((= (_ (lambda @t93 (or @t79 @t92)) @t88) @t91))) % 0.19/0.53 (step @p48 :rule trans :premises (@p47 @p46)) % 0.19/0.53 (step @p49 :rule beta-reduce :args ((= @t96 @t74))) % 0.19/0.53 (step @p50 :rule refl :args (@t76)) % 0.19/0.53 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t97)) % 0.19/0.53 (step @p52 :rule cong :premises (@p51) :args (@t98)) % 0.19/0.53 (step @p53 :rule beta-reduce :args ((= (_ (lambda @t93 (or @t76 @t92)) @t95) @t98))) % 0.19/0.53 (step @p54 :rule trans :premises (@p53 @p52)) % 0.19/0.53 (step @p55 :rule beta-reduce :args ((= (_ @t101 tptp.b) @t95))) % 0.19/0.53 (step @p56 :rule refl :args (tptp.b)) % 0.19/0.53 (step @p57 :rule beta-reduce :args ((= @t104 @t101))) % 0.19/0.53 (step @p58 :rule ho_cong :premises (@p57 @p56)) % 0.19/0.53 (step @p59 :rule trans :premises (@p58 @p55)) % 0.19/0.53 (step @p60 :rule refl :args (@t92)) % 0.19/0.53 (step @p61 :rule beta-reduce :args ((= @t106 @t75))) % 0.19/0.53 (step @p62 :rule cong :premises (@p61) :args (@t107)) % 0.19/0.53 (step @p63 :rule nary_cong :premises (@p62 @p60) :args (@t108)) % 0.19/0.53 (step @p64 :rule cong :premises (@p63) :args (@t109)) % 0.19/0.53 (step @p65 :rule beta-reduce :args ((= (_ @t111 @t105) @t109))) % 0.19/0.53 (step @p66 :rule trans :premises (@p65 @p64)) % 0.19/0.53 (step @p67 :rule beta-reduce :args ((= (_ @t101 tptp.a) @t105))) % 0.19/0.53 (step @p68 :rule refl :args (tptp.a)) % 0.19/0.53 (step @p69 :rule ho_cong :premises (@p57 @p68)) % 0.19/0.53 (step @p70 :rule trans :premises (@p69 @p67)) % 0.19/0.53 (step @p71 :rule refl :args (@t111)) % 0.19/0.53 (step @p72 :rule ho_cong :premises (@p71 @p70)) % 0.19/0.53 (step @p73 :rule trans :premises (@p72 @p66)) % 0.19/0.53 (step @p74 :rule ho_cong :premises (@p73 @p59)) % 0.19/0.53 (step @p75 :rule trans :premises (@p74 @p54)) % 0.19/0.53 (step @p76 :rule beta-reduce :args ((= @t113 @t78))) % 0.19/0.53 (step @p77 :rule cong :premises (@p76) :args (@t114)) % 0.19/0.53 (step @p78 :rule nary_cong :premises (@p77 @p60) :args (@t115)) % 0.19/0.53 (step @p79 :rule cong :premises (@p78) :args (@t116)) % 0.19/0.53 (step @p80 :rule beta-reduce :args ((= (_ @t111 @t112) @t116))) % 0.19/0.53 (step @p81 :rule trans :premises (@p80 @p79)) % 0.19/0.53 (step @p82 :rule refl :args (@t77)) % 0.19/0.53 (step @p83 :rule nary_cong :premises (@p82 @p49) :args (@t117)) % 0.19/0.53 (step @p84 :rule cong :premises (@p83) :args (@t118)) % 0.19/0.53 (step @p85 :rule beta-reduce :args ((= (_ (lambda @t93 (or @t77 @t92)) @t95) @t118))) % 0.19/0.53 (step @p86 :rule trans :premises (@p85 @p84)) % 0.19/0.53 (step @p87 :rule bool-double-not-elim :args (@t77)) % 0.19/0.53 (step @p88 :rule beta-reduce :args ((= @t120 (not @t77)))) % 0.19/0.53 (step @p89 :rule cong :premises (@p88) :args (@t121)) % 0.19/0.53 (step @p90 :rule trans :premises (@p89 @p87)) % 0.19/0.53 (step @p91 :rule nary_cong :premises (@p90 @p60) :args (@t122)) % 0.19/0.53 (step @p92 :rule cong :premises (@p91) :args (@t123)) % 0.19/0.53 (step @p93 :rule beta-reduce :args ((= (_ @t111 @t119) @t123))) % 0.19/0.53 (step @p94 :rule trans :premises (@p93 @p92)) % 0.19/0.53 (step @p95 :rule beta-reduce :args ((= (_ @t125 tptp.a) @t119))) % 0.19/0.53 (step @p96 :rule beta-reduce :args ((= @t126 @t125))) % 0.19/0.53 (step @p97 :rule ho_cong :premises (@p96 @p68)) % 0.19/0.53 (step @p98 :rule trans :premises (@p97 @p95)) % 0.19/0.53 (step @p99 :rule ho_cong :premises (@p71 @p98)) % 0.19/0.53 (step @p100 :rule trans :premises (@p99 @p94)) % 0.19/0.53 (step @p101 :rule ho_cong :premises (@p100 @p59)) % 0.19/0.53 (step @p102 :rule trans :premises (@p101 @p86)) % 0.19/0.53 (step @p103 :rule ho_cong :premises (@p71 @p102)) % 0.19/0.53 (step @p104 :rule trans :premises (@p103 @p81)) % 0.19/0.53 (step @p105 :rule ho_cong :premises (@p104 @p75)) % 0.19/0.53 (step @p106 :rule trans :premises (@p105 @p48)) % 0.19/0.53 (step @p107 :rule refl :args (@t86)) % 0.19/0.53 (step @p108 :rule ho_cong :premises (@p107 @p106)) % 0.19/0.53 (step @p109 :rule trans :premises (@p108 @p40)) % 0.19/0.53 (step @p110 :rule cong :premises (@p109) :args ((not (_ @t86 (_ (_ @t111 (_ (_ @t111 (_ @t126 tptp.a)) @t127)) (_ (_ @t111 (_ @t104 tptp.a)) @t127)))))) % 0.19/0.53 (step @p111 :rule refl :args (tptp.r)) % 0.19/0.53 (step @p112 :rule refl :args (@t99)) % 0.19/0.53 (step @p113 :rule refl :args (@t25)) % 0.19/0.53 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t25 @t99))) % 0.19/0.53 (step @p115 :rule symm :premises (@p114)) % 0.19/0.53 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 0.19/0.53 (step @p117 :rule refl :args (@t102)) % 0.19/0.53 (step @p118 :rule refl :args (@t27)) % 0.19/0.53 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t27 @t102))) % 0.19/0.53 (step @p120 :rule symm :premises (@p119)) % 0.19/0.53 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 0.19/0.53 (step @p122 :rule cong :premises (@p121) :args (@t128)) % 0.19/0.53 (step @p123 :rule nary_cong :premises (@p122 @p116) :args (@t129)) % 0.19/0.53 (step @p124 :rule cong :premises (@p123) :args ((forall @t28 @t129))) % 0.19/0.53 (step @p125 :rule bool-impl-elim :args (@t27 @t25)) % 0.19/0.53 (step @p126 :rule cong :premises (@p125) :args (@t29)) % 0.19/0.53 (step @p127 :rule trans :premises (@p126 @p124)) % 0.19/0.53 (step @p128 :rule cong :premises (@p127) :args (@t31)) % 0.19/0.53 (step @p129 :rule trans :premises (@p10 @p128)) % 0.19/0.53 (step @p130 :rule ho_cong :premises (@p129 @p111)) % 0.19/0.53 (step @p131 :rule ho_cong :premises (@p130 @p56)) % 0.19/0.53 (step @p132 :rule ho_cong :premises (@p130 @p68)) % 0.19/0.53 (step @p133 :rule beta-reduce :args ((= (_ @t132 @t17) @t110))) % 0.19/0.53 (step @p134 :rule refl :args (@t17)) % 0.19/0.53 (step @p135 :rule beta-reduce :args ((= (_ (lambda @t133 (or @t130 @t13)) @t18) @t132))) % 0.19/0.53 (step @p136 :rule refl :args (@t18)) % 0.19/0.53 (step @p137 :rule refl :args (@t13)) % 0.19/0.53 (step @p138 :rule beta-reduce :args ((= @t135 @t130))) % 0.19/0.53 (step @p139 :rule nary_cong :premises (@p138 @p137) :args (@t136)) % 0.19/0.53 (step @p140 :rule cong :premises (@p139) :args (@t137)) % 0.19/0.53 (step @p141 :rule beta-reduce :args ((= (_ @t15 @t134) @t137))) % 0.19/0.53 (step @p142 :rule trans :premises (@p141 @p140)) % 0.19/0.53 (step @p143 :rule beta-reduce :args ((= (_ @t11 @t19) @t134))) % 0.19/0.53 (step @p144 :rule refl :args (@t15)) % 0.19/0.53 (step @p145 :rule ho_cong :premises (@p144 @p143)) % 0.19/0.53 (step @p146 :rule trans :premises (@p145 @p142)) % 0.19/0.53 (step @p147 :rule ho_cong :premises (@p146 @p136)) % 0.19/0.53 (step @p148 :rule trans :premises (@p147 @p135)) % 0.19/0.53 (step @p149 :rule ho_cong :premises (@p148 @p134)) % 0.19/0.53 (step @p150 :rule trans :premises (@p149 @p133)) % 0.19/0.53 (step @p151 :rule refl :args (@t19)) % 0.19/0.53 (step @p152 :rule ho_cong :premises (@p5 @p151)) % 0.19/0.53 (step @p153 :rule ho_cong :premises (@p6 @p152)) % 0.19/0.53 (step @p154 :rule ho_cong :premises (@p153 @p136)) % 0.19/0.53 (step @p155 :rule ho_cong :premises (@p154 @p134)) % 0.19/0.53 (step @p156 :rule trans :premises (@p155 @p150)) % 0.19/0.53 (step @p157 :rule cong :premises (@p156) :args (@t21)) % 0.19/0.53 (step @p158 :rule trans :premises (@p8 @p157)) % 0.19/0.53 (step @p159 :rule ho_cong :premises (@p158 @p132)) % 0.19/0.53 (step @p160 :rule ho_cong :premises (@p159 @p131)) % 0.19/0.53 (step @p161 :rule cong :premises (@p116) :args (@t138)) % 0.19/0.53 (step @p162 :rule nary_cong :premises (@p122 @p161) :args (@t139)) % 0.19/0.53 (step @p163 :rule cong :premises (@p162) :args ((forall @t28 @t139))) % 0.19/0.53 (step @p164 :rule bool-and-de-morgan :args (@t27 @t25 true)) % 0.19/0.53 (step @p165 :rule cong :premises (@p164) :args (@t140)) % 0.19/0.53 (step @p166 :rule trans :premises (@p165 @p163)) % 0.19/0.53 (step @p167 :rule cong :premises (@p166) :args (@t141)) % 0.19/0.53 (step @p168 :rule exists-elim :args ((= @t33 @t141))) % 0.19/0.53 (step @p169 :rule trans :premises (@p168 @p167)) % 0.19/0.53 (step @p170 :rule cong :premises (@p169) :args (@t34)) % 0.19/0.53 (step @p171 :rule trans :premises (@p11 @p170)) % 0.19/0.53 (step @p172 :rule ho_cong :premises (@p171 @p111)) % 0.19/0.53 (step @p173 :rule ho_cong :premises (@p172 @p68)) % 0.19/0.53 (step @p174 :rule ho_cong :premises (@p158 @p173)) % 0.19/0.53 (step @p175 :rule ho_cong :premises (@p174 @p131)) % 0.19/0.53 (step @p176 :rule ho_cong :premises (@p158 @p175)) % 0.19/0.53 (step @p177 :rule ho_cong :premises (@p176 @p160)) % 0.19/0.53 (step @p178 :rule refl :args (@t85)) % 0.19/0.53 (step @p179 :rule refl :args (@t43)) % 0.19/0.53 (step @p180 :rule cong :premises (@p179 @p178) :args ((= @t43 @t85))) % 0.19/0.53 (step @p181 :rule symm :premises (@p180)) % 0.19/0.53 (step @p182 :rule eq_resolve :premises (@p179 @p181)) % 0.19/0.53 (step @p183 :rule cong :premises (@p182) :args (@t45)) % 0.19/0.53 (step @p184 :rule cong :premises (@p183) :args (@t47)) % 0.19/0.53 (step @p185 :rule trans :premises (@p14 @p184)) % 0.19/0.53 (step @p186 :rule ho_cong :premises (@p185 @p177)) % 0.19/0.53 (step @p187 :rule cong :premises (@p186) :args (@t3)) % 0.19/0.53 (step @p188 :rule trans :premises (@p187 @p110)) % 0.19/0.53 (step @p189 :rule eq_resolve :premises (@p1 @p188)) % 0.19/0.53 (step @p190 :rule skolemize :premises (@p189)) % 0.19/0.53 (step @p191 :rule cnf_or_neg :args (@t156 0)) % 0.19/0.54 (step @p192 :rule chain_m_resolution :premises (@p191 @p190) :args ((not @t155) @t157 @t158)) % 0.19/0.54 (step @p193 :rule bool-double-not-elim :args (@t149)) % 0.19/0.54 (step @p194 :rule refl :args (@t156)) % 0.19/0.54 (step @p195 :rule nary_cong :premises (@p194 @p193) :args ((or @t156 (not @t150)))) % 0.19/0.54 (step @p196 :rule cnf_or_neg :args (@t156 1)) % 0.19/0.54 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 0.19/0.54 (step @p198 :rule reordering :premises (@p197) :args ((or @t149 @t156))) % 0.19/0.54 (step @p199 :rule chain_m_resolution :premises (@p198 @p190) :args (@t149 @t157 @t158)) % 0.19/0.54 (step @p200 :rule instantiate :premises (@p199) :args (@t159)) % 0.19/0.54 (step @p201 :rule bool-double-not-elim :args (@t146)) % 0.19/0.54 (step @p202 :rule nary_cong :premises (@p194 @p201) :args ((or @t156 (not @t147)))) % 0.19/0.54 (step @p203 :rule cnf_or_neg :args (@t156 2)) % 0.19/0.54 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.19/0.54 (step @p205 :rule reordering :premises (@p204) :args ((or @t146 @t156))) % 0.19/0.54 (step @p206 :rule chain_m_resolution :premises (@p205 @p190) :args (@t146 @t157 @t158)) % 0.19/0.54 (step @p207 :rule cnf_or_pos :args (@t161)) % 0.19/0.54 (step @p208 :rule reordering :premises (@p207) :args ((or @t147 @t160 (not @t161)))) % 0.19/0.54 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p200) :args (@t160 @t162 (@list @t146 @t161))) % 0.19/0.54 (step @p210 :rule cnf_or_pos :args (@t164)) % 0.19/0.54 (step @p211 :rule reordering :premises (@p210) :args ((or @t147 @t163 @t165))) % 0.19/0.54 (step @p212 :rule chain_m_resolution :premises (@p211 @p206 @p209) :args (@t165 @t162 (@list @t146 @t160))) % 0.19/0.54 (assume-push @p238 @t153) % 0.19/0.54 (step @p214 :rule instantiate :premises (@p238) :args (@t159)) % 0.19/0.54 (step-pop @p239 :rule scope :premises (@p214)) % 0.19/0.54 (step @p215 :rule process_scope :premises (@p239) :args (@t164)) % 0.19/0.54 (step @p217 :rule implies_elim :premises (@p215)) % 0.19/0.54 (step @p218 :rule chain_m_resolution :premises (@p217 @p212) :args (@t154 @t157 (@list @t164))) % 0.19/0.54 (step @p219 :rule bool-double-not-elim :args (@t151)) % 0.19/0.54 (step @p220 :rule bool-double-not-elim :args (@t153)) % 0.19/0.54 (step @p221 :rule refl :args (@t155)) % 0.19/0.54 (step @p222 :rule nary_cong :premises (@p221 @p220 @p219) :args ((or @t155 (not @t154) (not @t152)))) % 0.19/0.54 (step @p223 :rule cnf_and_neg :args (@t155)) % 0.19/0.54 (step @p224 :rule eq_resolve :premises (@p223 @p222)) % 0.19/0.54 (step @p225 :rule reordering :premises (@p224) :args ((or @t153 @t151 @t155))) % 0.19/0.54 (step @p226 :rule chain_m_resolution :premises (@p225 @p218 @p192) :args (@t151 (@list true true) (@list @t153 @t155))) % 0.19/0.54 (step @p227 :rule cnf_or_neg :args (@t156 3)) % 0.19/0.54 (step @p228 :rule chain_m_resolution :premises (@p227 @p190) :args ((not @t144) @t157 @t158)) % 0.19/0.54 (step @p229 :rule cnf_or_pos :args (@t166)) % 0.19/0.54 (step @p230 :rule reordering :premises (@p229) :args ((or @t147 @t144 @t167))) % 0.19/0.54 (step @p231 :rule chain_m_resolution :premises (@p230 @p206 @p228) :args (@t167 (@list false true) (@list @t146 @t144))) % 0.19/0.54 (assume-push @p240 @t151) % 0.19/0.54 (step @p233 :rule instantiate :premises (@p240) :args (@t159)) % 0.19/0.54 (step-pop @p241 :rule scope :premises (@p233)) % 0.19/0.54 (step @p234 :rule process_scope :premises (@p241) :args (@t166)) % 0.19/0.54 (step @p236 :rule implies_elim :premises (@p234)) % 0.19/0.54 (step @p237 false :rule chain_m_resolution :premises (@p236 @p231 @p226) :args (false (@list true false) (@list @t166 @t151))) % 0.19/0.54 ) % 0.19/0.54 % SZS output end Proof % 0.19/0.54 % cvc5 exiting %------------------------------------------------------------------------------