%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ150^18 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:44:19 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ150^18 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n013.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 : Tue Jun 2 13:19:30 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.38/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort tptp.mindex 0) % 0.38/0.60 (declare-sort tptp.mworld 0) % 0.38/0.60 (declare-const tptp.mactual tptp.mworld) % 0.38/0.60 (declare-const tptp.mrel (-> tptp.mindex tptp.mworld tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.a0 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.a1 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.a2 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const |tptp.'#c'| tptp.mindex) % 0.38/0.60 (declare-const tptp.cb (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const |tptp.'#b'| tptp.mindex) % 0.38/0.60 (declare-const |tptp.'#a'| tptp.mindex) % 0.38/0.60 (declare-const tptp.c2 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.c1 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.c0 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.b0 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.b2 (-> tptp.mworld Bool)) % 0.38/0.60 (declare-const tptp.b1 (-> tptp.mworld Bool)) % 0.38/0.60 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.38/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (let ((_let_4 (@var "R" tptp.mindex))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ (_ tptp.mrel _let_4) _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.38/0.60 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (let ((_let_4 (@var "R" tptp.mindex))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ (_ tptp.mrel _let_4) _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.38/0.60 (define @t1 () (@var "V" tptp.mworld)) % 0.38/0.60 (define @t2 () (@var "W" tptp.mworld)) % 0.38/0.60 (define @t3 () (_ (_ (_ tptp.mrel |tptp.'#c'|) @t2) @t1)) % 0.38/0.60 (define @t4 () (@list @t2 @t1)) % 0.38/0.60 (define @t5 () (forall @t4 @t3)) % 0.38/0.60 (define @t6 () (_ tptp.mbox |tptp.'#c'|)) % 0.38/0.60 (define @t7 () (_ (_ tptp.mor (_ @t6 tptp.c0)) (_ (_ tptp.mor (_ @t6 tptp.c1)) (_ @t6 tptp.c2)))) % 0.38/0.60 (define @t8 () (_ tptp.mbox |tptp.'#b'|)) % 0.38/0.60 (define @t9 () (_ tptp.mbox |tptp.'#a'|)) % 0.38/0.60 (define @t10 () (_ (_ tptp.mor (_ @t8 tptp.b1)) (_ @t8 tptp.b2))) % 0.38/0.60 (define @t11 () (_ (_ tptp.mor (_ @t9 tptp.a0)) (_ (_ tptp.mor (_ @t9 tptp.a1)) (_ @t9 tptp.a2)))) % 0.38/0.60 (define @t12 () (not (_ tptp.mlocal (_ @t8 (_ tptp.mnot (_ (_ tptp.mdia |tptp.'#a'|) (_ (_ tptp.mdia |tptp.'#b'|) (_ @t6 (_ tptp.mnot tptp.a0))))))))) % 0.38/0.60 (define @t13 () (@var "Phi" (-> tptp.mworld Bool))) % 0.38/0.60 (define @t14 () (lambda (@list @t13) (_ @t13 tptp.mactual))) % 0.38/0.60 (define @t15 () (@var "A" (-> tptp.mworld Bool))) % 0.38/0.60 (define @t16 () (_ @t15 @t2)) % 0.38/0.60 (define @t17 () (lambda (@list @t15 @t2) (not @t16))) % 0.38/0.60 (define @t18 () (@var "B" (-> tptp.mworld Bool))) % 0.38/0.60 (define @t19 () (_ @t18 @t2)) % 0.38/0.60 (define @t20 () (@list @t15 @t18 @t2)) % 0.38/0.60 (define @t21 () (lambda @t20 (and @t16 @t19))) % 0.38/0.60 (define @t22 () (lambda @t20 (or @t16 @t19))) % 0.38/0.60 (define @t23 () (lambda @t20 (=> @t16 @t19))) % 0.38/0.60 (define @t24 () (lambda @t20 (= @t16 @t19))) % 0.38/0.60 (define @t25 () (_ @t13 @t1)) % 0.38/0.60 (define @t26 () (@var "R" tptp.mindex)) % 0.38/0.60 (define @t27 () (_ (_ (_ tptp.mrel @t26) @t2) @t1)) % 0.38/0.60 (define @t28 () (@list @t1)) % 0.38/0.60 (define @t29 () (forall @t28 (=> @t27 @t25))) % 0.38/0.60 (define @t30 () (@list @t26 @t13 @t2)) % 0.38/0.60 (define @t31 () (lambda @t30 @t29)) % 0.38/0.60 (define @t32 () (and @t27 @t25)) % 0.38/0.60 (define @t33 () (exists @t28 @t32)) % 0.38/0.60 (define @t34 () (lambda @t30 @t33)) % 0.38/0.60 (define @t35 () (tptp.mrel |tptp.'#c'| @t2 @t1)) % 0.38/0.60 (define @t36 () (@var "BOUND_VARIABLE_8570" tptp.mworld)) % 0.38/0.60 (define @t37 () (not (tptp.a0 @t36))) % 0.38/0.60 (define @t38 () (@var "BOUND_VARIABLE_8668" tptp.mworld)) % 0.38/0.60 (define @t39 () (@list @t36)) % 0.38/0.60 (define @t40 () (not (forall @t39 (or (not (tptp.mrel |tptp.'#c'| @t38 @t36)) @t37)))) % 0.38/0.60 (define @t41 () (@var "BOUND_VARIABLE_8666" tptp.mworld)) % 0.38/0.60 (define @t42 () (not (tptp.mrel |tptp.'#b'| @t41 @t38))) % 0.38/0.60 (define @t43 () (not (tptp.mrel |tptp.'#a'| @t1 @t41))) % 0.38/0.60 (define @t44 () (@list @t1 @t41 @t38)) % 0.38/0.60 (define @t45 () (forall @t44 (or (not (tptp.mrel |tptp.'#b'| tptp.mactual @t1)) @t43 @t42 @t40))) % 0.38/0.60 (define @t46 () (not (tptp.mrel |tptp.'#b'| @t2 @t1))) % 0.38/0.60 (define @t47 () (or @t46 @t43 @t42 @t40)) % 0.38/0.60 (define @t48 () (@list @t2)) % 0.38/0.60 (define @t49 () (lambda @t48 (forall @t44 @t47))) % 0.38/0.60 (define @t50 () (_ @t49 tptp.mactual)) % 0.38/0.60 (define @t51 () (or @t43 @t42 @t40)) % 0.38/0.60 (define @t52 () (or @t46 @t51)) % 0.38/0.60 (define @t53 () (forall @t44 @t52)) % 0.38/0.60 (define @t54 () (@list @t41 @t38)) % 0.38/0.60 (define @t55 () (forall @t54 @t52)) % 0.38/0.60 (define @t56 () (forall @t54 @t51)) % 0.38/0.60 (define @t57 () (@var "BOUND_VARIABLE_8621" tptp.mworld)) % 0.38/0.60 (define @t58 () (@var "BOUND_VARIABLE_8649" tptp.mworld)) % 0.38/0.60 (define @t59 () (or @t46 @t56)) % 0.38/0.60 (define @t60 () (not (forall @t39 (or (not (tptp.mrel |tptp.'#c'| @t57 @t36)) @t37)))) % 0.38/0.60 (define @t61 () (not (tptp.mrel |tptp.'#b'| @t58 @t57))) % 0.38/0.60 (define @t62 () (@list @t58 @t57)) % 0.38/0.60 (define @t63 () (forall @t62 (or (not (tptp.mrel |tptp.'#a'| @t1 @t58)) @t61 @t60))) % 0.38/0.60 (define @t64 () (not (tptp.mrel |tptp.'#b'| @t1 @t57))) % 0.38/0.60 (define @t65 () (not (tptp.mrel |tptp.'#a'| @t2 @t1))) % 0.38/0.60 (define @t66 () (or @t65 @t64 @t60)) % 0.38/0.60 (define @t67 () (@list @t1 @t57)) % 0.38/0.60 (define @t68 () (forall @t67 @t66)) % 0.38/0.60 (define @t69 () (@list @t1)) % 0.38/0.60 (define @t70 () (lambda @t48 @t68)) % 0.38/0.60 (define @t71 () (or @t46 (_ @t70 @t1))) % 0.38/0.60 (define @t72 () (forall @t28 @t71)) % 0.38/0.60 (define @t73 () (lambda @t48 @t72)) % 0.38/0.60 (define @t74 () (_ @t13 @t1)) % 0.38/0.60 (define @t75 () (@list @t13 @t2)) % 0.38/0.60 (define @t76 () (lambda @t75 (forall @t28 (or @t46 @t74)))) % 0.38/0.60 (define @t77 () (not @t68)) % 0.38/0.60 (define @t78 () (lambda @t48 @t77)) % 0.38/0.60 (define @t79 () (_ @t78 @t2)) % 0.38/0.60 (define @t80 () (not @t79)) % 0.38/0.60 (define @t81 () (lambda @t48 @t80)) % 0.38/0.60 (define @t82 () (or @t64 @t60)) % 0.38/0.60 (define @t83 () (or @t65 @t82)) % 0.38/0.60 (define @t84 () (forall @t67 @t83)) % 0.38/0.60 (define @t85 () (@list @t57)) % 0.38/0.60 (define @t86 () (forall @t85 @t83)) % 0.38/0.60 (define @t87 () (forall @t85 @t82)) % 0.38/0.60 (define @t88 () (@var "BOUND_VARIABLE_8598" tptp.mworld)) % 0.38/0.60 (define @t89 () (@list @t88)) % 0.38/0.60 (define @t90 () (or @t65 @t87)) % 0.38/0.60 (define @t91 () (not (forall @t39 (or (not (tptp.mrel |tptp.'#c'| @t88 @t36)) @t37)))) % 0.38/0.60 (define @t92 () (@list @t88)) % 0.38/0.60 (define @t93 () (forall @t92 (or (not (tptp.mrel |tptp.'#b'| @t1 @t88)) @t91))) % 0.38/0.60 (define @t94 () (forall @t39 (or (not (tptp.mrel |tptp.'#c'| @t1 @t36)) @t37))) % 0.38/0.60 (define @t95 () (forall @t28 (or @t46 (not @t94)))) % 0.38/0.60 (define @t96 () (not @t95)) % 0.38/0.60 (define @t97 () (lambda @t48 @t96)) % 0.38/0.60 (define @t98 () (not (_ @t97 @t1))) % 0.38/0.60 (define @t99 () (or @t65 @t98)) % 0.38/0.60 (define @t100 () (forall @t28 @t99)) % 0.38/0.60 (define @t101 () (not @t100)) % 0.38/0.60 (define @t102 () (lambda @t48 @t101)) % 0.38/0.60 (define @t103 () (not @t74)) % 0.38/0.60 (define @t104 () (lambda @t75 (not (forall @t28 (or @t65 @t103))))) % 0.38/0.60 (define @t105 () (tptp.a0 @t1)) % 0.38/0.60 (define @t106 () (not @t35)) % 0.38/0.60 (define @t107 () (forall @t28 (or @t106 (not @t105)))) % 0.38/0.60 (define @t108 () (lambda @t48 @t107)) % 0.38/0.60 (define @t109 () (not (_ @t108 @t1))) % 0.38/0.60 (define @t110 () (or @t46 @t109)) % 0.38/0.60 (define @t111 () (forall @t28 @t110)) % 0.38/0.60 (define @t112 () (not @t111)) % 0.38/0.60 (define @t113 () (lambda @t48 @t112)) % 0.38/0.60 (define @t114 () (lambda @t75 (not (forall @t28 (or @t46 @t103))))) % 0.38/0.60 (define @t115 () (_ tptp.a0 @t1)) % 0.38/0.60 (define @t116 () (not @t115)) % 0.38/0.60 (define @t117 () (or @t106 @t116)) % 0.38/0.60 (define @t118 () (lambda @t48 (not (_ tptp.a0 @t2)))) % 0.38/0.60 (define @t119 () (_ @t118 @t1)) % 0.38/0.60 (define @t120 () (or @t106 @t119)) % 0.38/0.60 (define @t121 () (forall @t28 @t120)) % 0.38/0.60 (define @t122 () (lambda @t48 @t121)) % 0.38/0.60 (define @t123 () (lambda @t75 (forall @t28 (or @t106 @t74)))) % 0.38/0.60 (define @t124 () (_ @t17 tptp.a0)) % 0.38/0.60 (define @t125 () (tptp.mrel @t26 @t2 @t1)) % 0.38/0.60 (define @t126 () (not @t125)) % 0.38/0.60 (define @t127 () (lambda @t30 (forall @t28 (or @t126 @t74)))) % 0.38/0.60 (define @t128 () (_ @t127 |tptp.'#c'|)) % 0.38/0.60 (define @t129 () (lambda @t30 (not (forall @t28 (or @t126 @t103))))) % 0.38/0.60 (define @t130 () (_ @t129 |tptp.'#b'|)) % 0.38/0.60 (define @t131 () (_ @t129 |tptp.'#a'|)) % 0.38/0.60 (define @t132 () (_ @t127 |tptp.'#b'|)) % 0.38/0.60 (define @t133 () (not @t27)) % 0.38/0.60 (define @t134 () (or @t133 @t25)) % 0.38/0.60 (define @t135 () (not @t25)) % 0.38/0.60 (define @t136 () (or @t133 @t135)) % 0.38/0.60 (define @t137 () (forall @t28 (not @t32))) % 0.38/0.60 (define @t138 () (not @t137)) % 0.38/0.60 (define @t139 () (@quantifiers_skolemize @t45 2)) % 0.38/0.60 (define @t140 () (forall @t39 (or (not (tptp.mrel |tptp.'#c'| @t139 @t36)) @t37))) % 0.38/0.60 (define @t141 () (not @t140)) % 0.38/0.60 (define @t142 () (@quantifiers_skolemize @t45 1)) % 0.38/0.60 (define @t143 () (@quantifiers_skolemize @t45 0)) % 0.38/0.60 (define @t144 () (or (not (tptp.mrel |tptp.'#b'| tptp.mactual @t143)) (not (tptp.mrel |tptp.'#a'| @t143 @t142)) (not (tptp.mrel |tptp.'#b'| @t142 @t139)) @t141)) % 0.38/0.60 (define @t145 () (tptp.a0 tptp.mactual)) % 0.38/0.60 (define @t146 () (_ tptp.a0 tptp.mactual)) % 0.38/0.60 (define @t147 () (not @t145)) % 0.38/0.60 (define @t148 () (tptp.mrel |tptp.'#c'| @t139 tptp.mactual)) % 0.38/0.60 (define @t149 () (not @t148)) % 0.38/0.60 (define @t150 () (or @t149 @t147)) % 0.38/0.60 (define @t151 () (forall @t4 @t35)) % 0.38/0.60 (assume @p1 @t5) % 0.38/0.60 (assume @p2 (forall @t4 (_ (_ (_ tptp.mrel |tptp.'#b'|) @t2) @t1))) % 0.38/0.60 (assume @p3 (forall @t4 (_ (_ (_ tptp.mrel |tptp.'#a'|) @t2) @t1))) % 0.38/0.60 (assume @p4 (_ tptp.mlocal (_ @t9 (_ @t8 @t7)))) % 0.38/0.60 (assume @p5 (_ tptp.mlocal (_ @t8 (_ @t9 @t7)))) % 0.38/0.60 (assume @p6 (_ tptp.mlocal (_ @t9 (_ @t6 (_ (_ tptp.mor (_ @t8 tptp.b0)) @t10))))) % 0.38/0.60 (assume @p7 (_ tptp.mlocal (_ @t6 (_ @t9 (_ (_ tptp.mor (_ @t8 tptp.cb)) @t10))))) % 0.38/0.60 (assume @p8 (_ tptp.mlocal (_ @t6 (_ @t8 @t11)))) % 0.38/0.60 (assume @p9 (_ tptp.mlocal (_ @t8 (_ @t6 @t11)))) % 0.38/0.60 (assume @p10 (_ tptp.mlocal tptp.a0)) % 0.38/0.60 (assume @p11 @t12) % 0.38/0.60 (assume @p12 true) % 0.38/0.60 (step @p13 (= tptp.mlocal @t14) :rule refl :args (@t14)) % 0.38/0.60 (step @p14 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.38/0.60 (step @p15 (= tptp.mand @t21) :rule refl :args (@t21)) % 0.38/0.60 (step @p16 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.38/0.60 (step @p17 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.38/0.60 (step @p18 (= tptp.mequiv @t24) :rule refl :args (@t24)) % 0.38/0.60 (step @p19 (= tptp.mbox @t31) :rule refl :args (@t31)) % 0.38/0.60 (step @p20 (= tptp.mdia @t34) :rule refl :args (@t34)) % 0.38/0.60 (step @p21 :rule refl :args (@t35)) % 0.38/0.60 (step @p22 :rule refl :args (@t3)) % 0.38/0.60 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t3 @t35))) % 0.38/0.60 (step @p24 :rule symm :premises (@p23)) % 0.38/0.60 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.38/0.60 (step @p26 :rule cong :premises (@p25) :args (@t5)) % 0.38/0.60 (step @p27 :rule eq_resolve :premises (@p1 @p26)) % 0.38/0.60 (step @p28 :rule beta-reduce :args ((= @t50 @t45))) % 0.38/0.60 (step @p29 :rule beta-reduce :args ((= (_ @t14 @t49) @t50))) % 0.38/0.60 (step @p30 :rule trans :premises (@p29 @p28)) % 0.38/0.60 (step @p31 :rule aci_norm :args ((= @t52 @t47))) % 0.38/0.60 (step @p32 :rule cong :premises (@p31) :args (@t53)) % 0.38/0.60 (step @p33 :rule quant-merge-prenex :args ((= (forall @t28 @t55) @t53))) % 0.38/0.60 (step @p34 :rule alpha_equiv :args (@t56 (@list @t41 @t38) (@list @t58 @t57))) % 0.38/0.60 (step @p35 :rule refl :args (@t46)) % 0.38/0.60 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t59)) % 0.38/0.60 (step @p37 :rule quant-miniscope-or :args ((= @t55 @t59))) % 0.38/0.60 (step @p38 :rule trans :premises (@p37 @p36)) % 0.38/0.60 (step @p39 :rule symm :premises (@p38)) % 0.38/0.60 (step @p40 :rule cong :premises (@p39) :args ((forall @t28 (or @t46 @t63)))) % 0.38/0.60 (step @p41 :rule trans :premises (@p40 @p33)) % 0.38/0.60 (step @p42 :rule trans :premises (@p41 @p32)) % 0.38/0.60 (step @p43 :rule beta-reduce :args ((= (_ (lambda @t48 (forall @t62 (or (not (tptp.mrel |tptp.'#a'| @t2 @t58)) @t61 @t60))) @t1) @t63))) % 0.38/0.60 (step @p44 :rule refl :args (@t1)) % 0.38/0.60 (step @p45 :rule alpha_equiv :args (@t68 @t69 (@list @t58))) % 0.38/0.60 (step @p46 :rule cong :premises (@p45) :args (@t70)) % 0.38/0.60 (step @p47 :rule ho_cong :premises (@p46 @p44)) % 0.38/0.60 (step @p48 :rule trans :premises (@p47 @p43)) % 0.38/0.60 (step @p49 :rule refl :args (@t46)) % 0.38/0.60 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t71)) % 0.38/0.60 (step @p51 :rule cong :premises (@p50) :args (@t72)) % 0.38/0.60 (step @p52 :rule trans :premises (@p51 @p42)) % 0.38/0.60 (step @p53 :rule cong :premises (@p52) :args (@t73)) % 0.38/0.60 (step @p54 :rule beta-reduce :args ((= (_ @t76 @t70) @t73))) % 0.38/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.38/0.60 (step @p56 :rule bool-double-not-elim :args (@t68)) % 0.38/0.60 (step @p57 :rule beta-reduce :args ((= @t79 @t77))) % 0.38/0.60 (step @p58 :rule cong :premises (@p57) :args (@t80)) % 0.38/0.60 (step @p59 :rule trans :premises (@p58 @p56)) % 0.38/0.60 (step @p60 :rule cong :premises (@p59) :args (@t81)) % 0.38/0.60 (step @p61 :rule beta-reduce :args ((= (_ @t17 @t78) @t81))) % 0.38/0.60 (step @p62 :rule trans :premises (@p61 @p60)) % 0.38/0.60 (step @p63 :rule aci_norm :args ((= @t83 @t66))) % 0.38/0.60 (step @p64 :rule cong :premises (@p63) :args (@t84)) % 0.38/0.60 (step @p65 :rule quant-merge-prenex :args ((= (forall @t28 @t86) @t84))) % 0.38/0.60 (step @p66 :rule alpha_equiv :args (@t87 (@list @t57) @t89)) % 0.38/0.60 (step @p67 :rule refl :args (@t65)) % 0.38/0.60 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t90)) % 0.38/0.60 (step @p69 :rule quant-miniscope-or :args ((= @t86 @t90))) % 0.38/0.60 (step @p70 :rule trans :premises (@p69 @p68)) % 0.38/0.60 (step @p71 :rule symm :premises (@p70)) % 0.38/0.60 (step @p72 :rule cong :premises (@p71) :args ((forall @t28 (or @t65 @t93)))) % 0.38/0.60 (step @p73 :rule trans :premises (@p72 @p65)) % 0.38/0.60 (step @p74 :rule trans :premises (@p73 @p64)) % 0.38/0.60 (step @p75 :rule bool-double-not-elim :args (@t93)) % 0.38/0.60 (step @p76 :rule beta-reduce :args ((= (_ (lambda @t48 (not (forall @t92 (or (not (tptp.mrel |tptp.'#b'| @t2 @t88)) @t91)))) @t1) (not @t93)))) % 0.38/0.60 (step @p77 :rule alpha_equiv :args (@t95 @t69 @t89)) % 0.38/0.60 (step @p78 :rule cong :premises (@p77) :args (@t96)) % 0.38/0.60 (step @p79 :rule cong :premises (@p78) :args (@t97)) % 0.38/0.60 (step @p80 :rule ho_cong :premises (@p79 @p44)) % 0.38/0.60 (step @p81 :rule trans :premises (@p80 @p76)) % 0.38/0.60 (step @p82 :rule cong :premises (@p81) :args (@t98)) % 0.38/0.60 (step @p83 :rule trans :premises (@p82 @p75)) % 0.38/0.60 (step @p84 :rule refl :args (@t65)) % 0.38/0.60 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t99)) % 0.38/0.60 (step @p86 :rule cong :premises (@p85) :args (@t100)) % 0.38/0.60 (step @p87 :rule trans :premises (@p86 @p74)) % 0.38/0.60 (step @p88 :rule cong :premises (@p87) :args (@t101)) % 0.38/0.60 (step @p89 :rule cong :premises (@p88) :args (@t102)) % 0.38/0.60 (step @p90 :rule beta-reduce :args ((= (_ @t104 @t97) @t102))) % 0.38/0.60 (step @p91 :rule trans :premises (@p90 @p89)) % 0.38/0.60 (step @p92 :rule beta-reduce :args ((= (_ (lambda @t48 (forall @t39 (or (not (tptp.mrel |tptp.'#c'| @t2 @t36)) @t37))) @t1) @t94))) % 0.38/0.60 (step @p93 :rule alpha_equiv :args (@t107 @t69 (@list @t36))) % 0.38/0.60 (step @p94 :rule cong :premises (@p93) :args (@t108)) % 0.38/0.60 (step @p95 :rule ho_cong :premises (@p94 @p44)) % 0.38/0.60 (step @p96 :rule trans :premises (@p95 @p92)) % 0.38/0.60 (step @p97 :rule cong :premises (@p96) :args (@t109)) % 0.38/0.60 (step @p98 :rule nary_cong :premises (@p49 @p97) :args (@t110)) % 0.38/0.60 (step @p99 :rule cong :premises (@p98) :args (@t111)) % 0.38/0.60 (step @p100 :rule cong :premises (@p99) :args (@t112)) % 0.38/0.60 (step @p101 :rule cong :premises (@p100) :args (@t113)) % 0.38/0.60 (step @p102 :rule beta-reduce :args ((= (_ @t114 @t108) @t113))) % 0.38/0.60 (step @p103 :rule trans :premises (@p102 @p101)) % 0.38/0.60 (step @p104 :rule refl :args (@t105)) % 0.38/0.60 (step @p105 :rule refl :args (@t115)) % 0.38/0.60 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t115 @t105))) % 0.38/0.60 (step @p107 :rule symm :premises (@p106)) % 0.38/0.60 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.38/0.60 (step @p109 :rule cong :premises (@p108) :args (@t116)) % 0.38/0.60 (step @p110 :rule refl :args (@t106)) % 0.38/0.60 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t117)) % 0.38/0.60 (step @p112 :rule cong :premises (@p111) :args ((forall @t28 @t117))) % 0.38/0.60 (step @p113 :rule beta-reduce :args ((= @t119 @t116))) % 0.38/0.60 (step @p114 :rule refl :args (@t106)) % 0.38/0.60 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t120)) % 0.38/0.60 (step @p116 :rule cong :premises (@p115) :args (@t121)) % 0.38/0.60 (step @p117 :rule trans :premises (@p116 @p112)) % 0.38/0.60 (step @p118 :rule cong :premises (@p117) :args (@t122)) % 0.38/0.60 (step @p119 :rule beta-reduce :args ((= (_ @t123 @t118) @t122))) % 0.38/0.60 (step @p120 :rule trans :premises (@p119 @p118)) % 0.38/0.60 (step @p121 :rule beta-reduce :args ((= @t124 @t118))) % 0.38/0.60 (step @p122 :rule beta-reduce :args ((= @t128 @t123))) % 0.38/0.60 (step @p123 :rule ho_cong :premises (@p122 @p121)) % 0.38/0.60 (step @p124 :rule trans :premises (@p123 @p120)) % 0.38/0.60 (step @p125 :rule beta-reduce :args ((= @t130 @t114))) % 0.38/0.60 (step @p126 :rule ho_cong :premises (@p125 @p124)) % 0.38/0.60 (step @p127 :rule trans :premises (@p126 @p103)) % 0.38/0.60 (step @p128 :rule beta-reduce :args ((= @t131 @t104))) % 0.38/0.60 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.38/0.60 (step @p130 :rule trans :premises (@p129 @p91)) % 0.38/0.60 (step @p131 :rule refl :args (@t17)) % 0.38/0.60 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 0.38/0.60 (step @p133 :rule trans :premises (@p132 @p62)) % 0.38/0.60 (step @p134 :rule beta-reduce :args ((= @t132 @t76))) % 0.38/0.60 (step @p135 :rule ho_cong :premises (@p134 @p133)) % 0.38/0.60 (step @p136 :rule trans :premises (@p135 @p55)) % 0.38/0.60 (step @p137 :rule refl :args (@t14)) % 0.38/0.60 (step @p138 :rule ho_cong :premises (@p137 @p136)) % 0.38/0.60 (step @p139 :rule trans :premises (@p138 @p30)) % 0.38/0.60 (step @p140 :rule cong :premises (@p139) :args ((not (_ @t14 (_ @t132 (_ @t17 (_ @t131 (_ @t130 (_ @t128 @t124))))))))) % 0.38/0.60 (step @p141 :rule refl :args (tptp.a0)) % 0.38/0.60 (step @p142 :rule ho_cong :premises (@p14 @p141)) % 0.38/0.60 (step @p143 :rule refl :args (|tptp.'#c'|)) % 0.38/0.60 (step @p144 :rule refl :args (@t74)) % 0.38/0.60 (step @p145 :rule refl :args (@t25)) % 0.38/0.60 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t25 @t74))) % 0.38/0.60 (step @p147 :rule symm :premises (@p146)) % 0.38/0.60 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.38/0.60 (step @p149 :rule refl :args (@t125)) % 0.38/0.60 (step @p150 :rule refl :args (@t27)) % 0.38/0.60 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t27 @t125))) % 0.38/0.60 (step @p152 :rule symm :premises (@p151)) % 0.38/0.60 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.38/0.60 (step @p154 :rule cong :premises (@p153) :args (@t133)) % 0.38/0.60 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t134)) % 0.38/0.60 (step @p156 :rule cong :premises (@p155) :args ((forall @t28 @t134))) % 0.38/0.60 (step @p157 :rule bool-impl-elim :args (@t27 @t25)) % 0.38/0.60 (step @p158 :rule cong :premises (@p157) :args (@t29)) % 0.38/0.60 (step @p159 :rule trans :premises (@p158 @p156)) % 0.38/0.60 (step @p160 :rule cong :premises (@p159) :args (@t31)) % 0.38/0.60 (step @p161 :rule trans :premises (@p19 @p160)) % 0.38/0.60 (step @p162 :rule ho_cong :premises (@p161 @p143)) % 0.38/0.60 (step @p163 :rule ho_cong :premises (@p162 @p142)) % 0.38/0.60 (step @p164 :rule refl :args (|tptp.'#b'|)) % 0.38/0.60 (step @p165 :rule cong :premises (@p148) :args (@t135)) % 0.38/0.60 (step @p166 :rule nary_cong :premises (@p154 @p165) :args (@t136)) % 0.38/0.60 (step @p167 :rule cong :premises (@p166) :args ((forall @t28 @t136))) % 0.38/0.60 (step @p168 :rule bool-and-de-morgan :args (@t27 @t25 true)) % 0.38/0.60 (step @p169 :rule cong :premises (@p168) :args (@t137)) % 0.38/0.60 (step @p170 :rule trans :premises (@p169 @p167)) % 0.38/0.60 (step @p171 :rule cong :premises (@p170) :args (@t138)) % 0.38/0.60 (step @p172 :rule exists-elim :args ((= @t33 @t138))) % 0.38/0.60 (step @p173 :rule trans :premises (@p172 @p171)) % 0.38/0.60 (step @p174 :rule cong :premises (@p173) :args (@t34)) % 0.38/0.60 (step @p175 :rule trans :premises (@p20 @p174)) % 0.38/0.60 (step @p176 :rule ho_cong :premises (@p175 @p164)) % 0.38/0.60 (step @p177 :rule ho_cong :premises (@p176 @p163)) % 0.38/0.60 (step @p178 :rule refl :args (|tptp.'#a'|)) % 0.38/0.60 (step @p179 :rule ho_cong :premises (@p175 @p178)) % 0.38/0.60 (step @p180 :rule ho_cong :premises (@p179 @p177)) % 0.38/0.60 (step @p181 :rule ho_cong :premises (@p14 @p180)) % 0.38/0.60 (step @p182 :rule ho_cong :premises (@p161 @p164)) % 0.38/0.60 (step @p183 :rule ho_cong :premises (@p182 @p181)) % 0.38/0.60 (step @p184 :rule ho_cong :premises (@p13 @p183)) % 0.38/0.60 (step @p185 :rule cong :premises (@p184) :args (@t12)) % 0.38/0.60 (step @p186 :rule trans :premises (@p185 @p140)) % 0.38/0.60 (step @p187 :rule eq_resolve :premises (@p11 @p186)) % 0.38/0.60 (step @p188 :rule skolemize :premises (@p187)) % 0.38/0.60 (step @p189 :rule bool-double-not-elim :args (@t140)) % 0.38/0.60 (step @p190 :rule refl :args (@t144)) % 0.38/0.60 (step @p191 :rule nary_cong :premises (@p190 @p189) :args ((or @t144 (not @t141)))) % 0.38/0.60 (step @p192 :rule cnf_or_neg :args (@t144 3)) % 0.38/0.60 (step @p193 :rule eq_resolve :premises (@p192 @p191)) % 0.38/0.60 (step @p194 :rule reordering :premises (@p193) :args ((or @t140 @t144))) % 0.38/0.60 (step @p195 :rule chain_m_resolution :premises (@p194 @p188) :args (@t140 (@list true) (@list @t144))) % 0.38/0.60 (step @p196 :rule instantiate :premises (@p195) :args ((@list tptp.mactual))) % 0.38/0.60 (step @p197 :rule refl :args (@t145)) % 0.38/0.60 (step @p198 :rule refl :args (@t146)) % 0.38/0.60 (step @p199 :rule cong :premises (@p198 @p197) :args ((= @t146 @t145))) % 0.38/0.60 (step @p200 :rule symm :premises (@p199)) % 0.38/0.60 (step @p201 :rule eq_resolve :premises (@p198 @p200)) % 0.38/0.60 (step @p202 :rule beta-reduce :args ((= (_ @t14 tptp.a0) @t146))) % 0.38/0.60 (step @p203 :rule ho_cong :premises (@p13 @p141)) % 0.38/0.60 (step @p204 :rule trans :premises (@p203 @p202)) % 0.38/0.60 (step @p205 :rule trans :premises (@p204 @p201)) % 0.38/0.60 (step @p206 :rule eq_resolve :premises (@p10 @p205)) % 0.38/0.60 (step @p207 :rule cnf_or_pos :args (@t150)) % 0.38/0.60 (step @p208 :rule reordering :premises (@p207) :args ((or @t147 @t149 (not @t150)))) % 0.38/0.60 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p196) :args (@t149 (@list false false) (@list @t145 @t150))) % 0.38/0.60 (assume-push @p216 @t151) % 0.38/0.60 (step @p211 :rule instantiate :premises (@p27) :args ((@list @t139 tptp.mactual))) % 0.38/0.60 (step-pop @p217 :rule scope :premises (@p211)) % 0.38/0.60 (step @p212 :rule process_scope :premises (@p217) :args (@t148)) % 0.38/0.60 (step @p214 :rule implies_elim :premises (@p212)) % 0.38/0.60 (step @p215 false :rule chain_m_resolution :premises (@p214 @p209 @p27) :args (false (@list true false) (@list @t148 @t151))) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------