%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN978^4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:10:11 AM UTC 2026 % Result : Theorem 0.38s 0.62s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN978^4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n023.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 23:51:28 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.38/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.62 % SZS status Theorem % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort $$unsorted 0) % 0.38/0.62 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.a (-> $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.b (-> $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.38/0.62 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.62 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.62 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.62 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.62 (define tptp.mbox_s4 () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.irel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.62 (define tptp.iatom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.38/0.62 (define tptp.inot () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 _let_2)) _let_1))))) % 0.38/0.62 (define tptp.itrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.62 (define tptp.iand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.38/0.62 (define tptp.ior () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.38/0.62 (define tptp.iimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mimplies (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.38/0.62 (define tptp.iimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iimplies _let_3) _let_2) _let_1)))))) % 0.38/0.62 (define tptp.iequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iand (_ (_ tptp.iimplies _let_2) _let_3)) (_ (_ tptp.iimplies _let_3) _let_2)) _let_1)))))) % 0.38/0.62 (define tptp.ixor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.inot (_ (_ tptp.iequiv _let_3) _let_2)) _let_1)))))) % 0.38/0.62 (define tptp.ivalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.62 (define tptp.isatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.62 (define tptp.icountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.62 (define tptp.iinvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.62 (define @t1 () (@var "X" $$unsorted)) % 0.38/0.62 (define @t2 () (_ tptp.irel @t1)) % 0.38/0.62 (define @t3 () (@list @t1)) % 0.38/0.62 (define @t4 () (@var "Z" $$unsorted)) % 0.38/0.62 (define @t5 () (_ @t2 @t4)) % 0.38/0.62 (define @t6 () (@var "Y" $$unsorted)) % 0.38/0.62 (define @t7 () (_ (_ tptp.irel @t6) @t4)) % 0.38/0.62 (define @t8 () (_ @t2 @t6)) % 0.38/0.62 (define @t9 () (and @t8 @t7)) % 0.38/0.62 (define @t10 () (@list @t1 @t6 @t4)) % 0.38/0.62 (define @t11 () (forall @t10 (=> @t9 @t5))) % 0.38/0.62 (define @t12 () (_ tptp.iatom tptp.b)) % 0.38/0.62 (define @t13 () (_ tptp.iatom tptp.a)) % 0.38/0.62 (define @t14 () (not (_ tptp.ivalid (_ (_ tptp.iimplies (_ (_ tptp.iand @t13) @t12)) (_ (_ tptp.iequiv @t13) @t12))))) % 0.38/0.62 (define @t15 () (@var "U" $$unsorted)) % 0.38/0.62 (define @t16 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.62 (define @t17 () (_ @t16 @t15)) % 0.38/0.62 (define @t18 () (lambda (@list @t16 @t15) (not @t17))) % 0.38/0.62 (define @t19 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.62 (define @t20 () (_ @t19 @t15)) % 0.38/0.62 (define @t21 () (@list @t16 @t19 @t15)) % 0.38/0.62 (define @t22 () (lambda @t21 (or @t17 @t20))) % 0.38/0.62 (define @t23 () (lambda @t21 (and @t17 @t20))) % 0.38/0.62 (define @t24 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.62 (define @t25 () (@var "V" (-> $$unsorted Bool))) % 0.38/0.62 (define @t26 () (@var "U" (-> $$unsorted Bool))) % 0.38/0.62 (define @t27 () (@list @t26 @t25 @t24)) % 0.38/0.62 (define @t28 () (lambda @t27 (_ (_ (_ tptp.mor (_ tptp.mnot @t26)) @t25) @t24))) % 0.38/0.62 (define @t29 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.62 (define @t30 () (_ @t29 @t6)) % 0.38/0.62 (define @t31 () (@list @t6)) % 0.38/0.62 (define @t32 () (forall @t31 (=> @t8 @t30))) % 0.38/0.62 (define @t33 () (@list @t29 @t1)) % 0.38/0.62 (define @t34 () (lambda @t33 @t32)) % 0.38/0.62 (define @t35 () (_ @t29 @t24)) % 0.38/0.62 (define @t36 () (@list @t29 @t24)) % 0.38/0.62 (define @t37 () (lambda @t36 @t35)) % 0.38/0.62 (define @t38 () (_ tptp.mbox_s4 @t29)) % 0.38/0.62 (define @t39 () (lambda @t36 (_ (_ tptp.mnot @t38) @t24))) % 0.38/0.62 (define @t40 () (@var "W" $$unsorted)) % 0.38/0.62 (define @t41 () (@list @t40)) % 0.38/0.62 (define @t42 () (lambda @t41 true)) % 0.38/0.62 (define @t43 () (@var "Q" (-> $$unsorted Bool))) % 0.38/0.62 (define @t44 () (@list @t29 @t43 @t24)) % 0.38/0.62 (define @t45 () (lambda @t44 (_ (_ (_ tptp.mand @t29) @t43) @t24))) % 0.38/0.62 (define @t46 () (_ tptp.mbox_s4 @t43)) % 0.38/0.62 (define @t47 () (lambda @t44 (_ (_ (_ tptp.mor @t38) @t46) @t24))) % 0.38/0.62 (define @t48 () (lambda @t44 (_ (_ (_ tptp.mimplies @t38) @t46) @t24))) % 0.38/0.62 (define @t49 () (_ (_ tptp.iimplies @t43) @t29)) % 0.38/0.62 (define @t50 () (lambda @t44 (_ @t49 @t24))) % 0.38/0.62 (define @t51 () (lambda @t44 (_ (_ (_ tptp.iand (_ (_ tptp.iimplies @t29) @t43)) @t49) @t24))) % 0.38/0.62 (define @t52 () (lambda @t44 (_ (_ tptp.inot (_ (_ tptp.iequiv @t29) @t43)) @t24))) % 0.38/0.62 (define @t53 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.62 (define @t54 () (_ @t53 @t40)) % 0.38/0.62 (define @t55 () (forall @t41 @t54)) % 0.38/0.62 (define @t56 () (@list @t53)) % 0.38/0.62 (define @t57 () (lambda @t56 @t55)) % 0.38/0.62 (define @t58 () (lambda @t56 (exists @t41 @t54))) % 0.38/0.62 (define @t59 () (not @t54)) % 0.38/0.62 (define @t60 () (lambda @t56 (exists @t41 @t59))) % 0.38/0.62 (define @t61 () (lambda @t56 (forall @t41 @t59))) % 0.38/0.62 (define @t62 () (@var "BOUND_VARIABLE_8183" $$unsorted)) % 0.38/0.62 (define @t63 () (@var "BOUND_VARIABLE_8179" $$unsorted)) % 0.38/0.62 (define @t64 () (@var "BOUND_VARIABLE_8112" $$unsorted)) % 0.38/0.62 (define @t65 () (tptp.b @t64)) % 0.38/0.62 (define @t66 () (@list @t64)) % 0.38/0.62 (define @t67 () (@var "BOUND_VARIABLE_8181" $$unsorted)) % 0.38/0.62 (define @t68 () (@var "BOUND_VARIABLE_8104" $$unsorted)) % 0.38/0.62 (define @t69 () (tptp.a @t68)) % 0.38/0.62 (define @t70 () (@list @t68)) % 0.38/0.62 (define @t71 () (and (or (not (forall @t70 (or (not (tptp.irel @t63 @t68)) @t69))) (not (tptp.irel @t63 @t67)) (tptp.b @t67)) (or (not (forall @t66 (or (not (tptp.irel @t63 @t64)) @t65))) (not (tptp.irel @t63 @t62)) (tptp.a @t62)))) % 0.38/0.62 (define @t72 () (not (tptp.irel @t40 @t63))) % 0.38/0.62 (define @t73 () (tptp.b @t6)) % 0.38/0.62 (define @t74 () (tptp.a @t6)) % 0.38/0.62 (define @t75 () (and @t74 @t73)) % 0.38/0.62 (define @t76 () (not (tptp.irel @t40 @t6))) % 0.38/0.62 (define @t77 () (not (forall @t31 (or @t76 @t75)))) % 0.38/0.62 (define @t78 () (or @t77 @t72 @t71)) % 0.38/0.62 (define @t79 () (or @t72 @t71)) % 0.38/0.62 (define @t80 () (or @t77 @t79)) % 0.38/0.62 (define @t81 () (@list @t40 @t63 @t67 @t62)) % 0.38/0.62 (define @t82 () (forall @t81 @t80)) % 0.38/0.62 (define @t83 () (@list @t63 @t67 @t62)) % 0.38/0.62 (define @t84 () (forall @t83 @t80)) % 0.38/0.62 (define @t85 () (forall @t83 @t79)) % 0.38/0.62 (define @t86 () (@var "BOUND_VARIABLE_8149" $$unsorted)) % 0.38/0.62 (define @t87 () (@var "BOUND_VARIABLE_8142" $$unsorted)) % 0.38/0.62 (define @t88 () (or @t77 @t85)) % 0.38/0.62 (define @t89 () (tptp.a @t86)) % 0.38/0.62 (define @t90 () (not (tptp.irel @t6 @t86))) % 0.38/0.62 (define @t91 () (forall @t66 (or (not (tptp.irel @t6 @t64)) @t65))) % 0.38/0.62 (define @t92 () (not @t91)) % 0.38/0.62 (define @t93 () (or @t92 @t90 @t89)) % 0.38/0.62 (define @t94 () (tptp.b @t87)) % 0.38/0.62 (define @t95 () (not (tptp.irel @t6 @t87))) % 0.38/0.62 (define @t96 () (forall @t70 (or (not (tptp.irel @t6 @t68)) @t69))) % 0.38/0.62 (define @t97 () (not @t96)) % 0.38/0.62 (define @t98 () (or @t97 @t95 @t94)) % 0.38/0.62 (define @t99 () (and @t98 @t93)) % 0.38/0.62 (define @t100 () (@list @t6 @t87 @t86)) % 0.38/0.62 (define @t101 () (or @t77 (forall @t100 (or @t76 @t99)))) % 0.38/0.62 (define @t102 () (not (tptp.irel @t24 @t6))) % 0.38/0.62 (define @t103 () (not (forall @t31 (or @t102 @t75)))) % 0.38/0.62 (define @t104 () (@list @t24)) % 0.38/0.62 (define @t105 () (lambda @t104 (or @t103 (forall @t100 (or @t102 @t99))))) % 0.38/0.62 (define @t106 () (_ @t105 @t40)) % 0.38/0.62 (define @t107 () (forall @t41 @t106)) % 0.38/0.62 (define @t108 () (_ @t53 @t40)) % 0.38/0.62 (define @t109 () (lambda @t56 (forall @t41 @t108))) % 0.38/0.62 (define @t110 () (or @t90 @t89)) % 0.38/0.62 (define @t111 () (or @t92 @t110)) % 0.38/0.62 (define @t112 () (or @t95 @t94)) % 0.38/0.62 (define @t113 () (or @t97 @t112)) % 0.38/0.62 (define @t114 () (and @t113 @t111)) % 0.38/0.62 (define @t115 () (or @t102 @t114)) % 0.38/0.62 (define @t116 () (forall @t100 @t115)) % 0.38/0.62 (define @t117 () (@list @t87 @t86)) % 0.38/0.62 (define @t118 () (forall @t117 @t115)) % 0.38/0.62 (define @t119 () (@list @t86)) % 0.38/0.62 (define @t120 () (forall @t119 @t110)) % 0.38/0.62 (define @t121 () (@list @t68)) % 0.38/0.62 (define @t122 () (or @t92 @t120)) % 0.38/0.62 (define @t123 () (forall @t119 @t111)) % 0.38/0.62 (define @t124 () (forall @t117 @t111)) % 0.38/0.62 (define @t125 () (@list @t87)) % 0.38/0.62 (define @t126 () (forall @t125 @t112)) % 0.38/0.62 (define @t127 () (@list @t64)) % 0.38/0.62 (define @t128 () (or @t97 @t126)) % 0.38/0.62 (define @t129 () (forall @t125 @t113)) % 0.38/0.62 (define @t130 () (forall @t117 @t113)) % 0.38/0.62 (define @t131 () (and @t130 @t124)) % 0.38/0.62 (define @t132 () (forall @t117 @t114)) % 0.38/0.62 (define @t133 () (or @t102 @t132)) % 0.38/0.62 (define @t134 () (and (or @t97 @t91) (or @t92 @t96))) % 0.38/0.62 (define @t135 () (forall @t70 (or (not (tptp.irel @t24 @t68)) @t69))) % 0.38/0.62 (define @t136 () (forall @t66 (or (not (tptp.irel @t24 @t64)) @t65))) % 0.38/0.62 (define @t137 () (forall @t31 (or @t102 @t74))) % 0.38/0.62 (define @t138 () (@list @t6)) % 0.38/0.62 (define @t139 () (forall @t31 (or @t102 @t73))) % 0.38/0.62 (define @t140 () (not @t139)) % 0.38/0.62 (define @t141 () (or @t140 @t137)) % 0.38/0.62 (define @t142 () (not @t137)) % 0.38/0.62 (define @t143 () (or @t142 @t139)) % 0.38/0.62 (define @t144 () (and @t143 @t141)) % 0.38/0.62 (define @t145 () (lambda @t104 @t144)) % 0.38/0.62 (define @t146 () (or @t102 (_ @t145 @t6))) % 0.38/0.62 (define @t147 () (forall @t31 @t146)) % 0.38/0.62 (define @t148 () (or @t103 @t147)) % 0.38/0.62 (define @t149 () (lambda @t104 @t148)) % 0.38/0.62 (define @t150 () (_ @t43 @t6)) % 0.38/0.62 (define @t151 () (forall @t31 (or @t102 @t150))) % 0.38/0.62 (define @t152 () (@list @t43 @t24)) % 0.38/0.62 (define @t153 () (_ tptp.b @t6)) % 0.38/0.62 (define @t154 () (or @t102 @t153)) % 0.38/0.62 (define @t155 () (_ tptp.b @t24)) % 0.38/0.62 (define @t156 () (lambda @t104 @t155)) % 0.38/0.62 (define @t157 () (_ @t156 @t6)) % 0.38/0.62 (define @t158 () (or @t102 @t157)) % 0.38/0.62 (define @t159 () (forall @t31 @t158)) % 0.38/0.62 (define @t160 () (not @t159)) % 0.38/0.62 (define @t161 () (or @t160 @t137)) % 0.38/0.62 (define @t162 () (or @t142 @t159)) % 0.38/0.62 (define @t163 () (and @t162 @t161)) % 0.38/0.62 (define @t164 () (lambda @t104 @t163)) % 0.38/0.62 (define @t165 () (not @t151)) % 0.38/0.62 (define @t166 () (_ @t37 tptp.b)) % 0.38/0.62 (define @t167 () (_ tptp.a @t6)) % 0.38/0.62 (define @t168 () (or @t102 @t167)) % 0.38/0.62 (define @t169 () (_ tptp.a @t24)) % 0.38/0.62 (define @t170 () (lambda @t104 @t169)) % 0.38/0.62 (define @t171 () (_ @t170 @t6)) % 0.38/0.62 (define @t172 () (or @t102 @t171)) % 0.38/0.62 (define @t173 () (forall @t31 @t172)) % 0.38/0.62 (define @t174 () (or @t165 @t173)) % 0.38/0.62 (define @t175 () (not @t173)) % 0.38/0.62 (define @t176 () (or @t175 @t151)) % 0.38/0.62 (define @t177 () (and @t176 @t174)) % 0.38/0.62 (define @t178 () (lambda @t152 @t177)) % 0.38/0.62 (define @t179 () (_ @t29 @t6)) % 0.38/0.62 (define @t180 () (forall @t31 (or @t102 @t179))) % 0.38/0.62 (define @t181 () (or @t165 @t180)) % 0.38/0.62 (define @t182 () (not @t180)) % 0.38/0.62 (define @t183 () (or @t182 @t151)) % 0.38/0.62 (define @t184 () (and @t183 @t181)) % 0.38/0.62 (define @t185 () (lambda @t44 @t184)) % 0.38/0.62 (define @t186 () (_ @t37 tptp.a)) % 0.38/0.62 (define @t187 () (and @t167 @t153)) % 0.38/0.62 (define @t188 () (or @t102 @t187)) % 0.38/0.62 (define @t189 () (lambda @t104 (and @t169 @t155))) % 0.38/0.62 (define @t190 () (_ @t189 @t6)) % 0.38/0.62 (define @t191 () (or @t102 @t190)) % 0.38/0.62 (define @t192 () (forall @t31 @t191)) % 0.38/0.62 (define @t193 () (not @t192)) % 0.38/0.62 (define @t194 () (or @t193 @t151)) % 0.38/0.62 (define @t195 () (lambda @t152 @t194)) % 0.38/0.62 (define @t196 () (lambda @t44 @t183)) % 0.38/0.62 (define @t197 () (_ @t156 @t24)) % 0.38/0.62 (define @t198 () (and @t169 @t197)) % 0.38/0.62 (define @t199 () (lambda @t104 @t198)) % 0.38/0.62 (define @t200 () (_ @t43 @t24)) % 0.38/0.62 (define @t201 () (_ @t170 @t24)) % 0.38/0.62 (define @t202 () (and @t201 @t200)) % 0.38/0.62 (define @t203 () (lambda @t152 @t202)) % 0.38/0.62 (define @t204 () (and @t35 @t200)) % 0.38/0.62 (define @t205 () (lambda @t44 @t204)) % 0.38/0.62 (define @t206 () (lambda @t104 @t181)) % 0.38/0.62 (define @t207 () (_ @t206 @t24)) % 0.38/0.62 (define @t208 () (and @t183 @t207)) % 0.38/0.62 (define @t209 () (lambda @t104 @t208)) % 0.38/0.62 (define @t210 () (@var "BOUND_VARIABLE_7728" (-> $$unsorted Bool))) % 0.38/0.62 (define @t211 () (_ @t210 @t24)) % 0.38/0.62 (define @t212 () (@list @t210 @t24)) % 0.38/0.62 (define @t213 () (@var "BOUND_VARIABLE_7685" (-> $$unsorted Bool))) % 0.38/0.62 (define @t214 () (forall @t31 (or @t102 (_ @t213 @t6)))) % 0.38/0.62 (define @t215 () (lambda (@list @t213 @t24) (or @t165 @t214))) % 0.38/0.62 (define @t216 () (@list @t43)) % 0.38/0.62 (define @t217 () (lambda @t104 @t183)) % 0.38/0.62 (define @t218 () (_ @t217 @t24)) % 0.38/0.62 (define @t219 () (and @t218 @t211)) % 0.38/0.62 (define @t220 () (lambda @t212 @t219)) % 0.38/0.62 (define @t221 () (lambda @t152 @t183)) % 0.38/0.62 (define @t222 () (tptp.irel @t1 @t6)) % 0.38/0.62 (define @t223 () (not @t222)) % 0.38/0.62 (define @t224 () (lambda @t3 (forall @t31 (or @t223 @t150)))) % 0.38/0.62 (define @t225 () (_ @t224 @t24)) % 0.38/0.62 (define @t226 () (or @t182 @t225)) % 0.38/0.62 (define @t227 () (lambda @t104 @t226)) % 0.38/0.62 (define @t228 () (_ @t25 @t24)) % 0.38/0.62 (define @t229 () (@list @t25 @t24)) % 0.38/0.62 (define @t230 () (forall @t31 (or @t223 @t179))) % 0.38/0.62 (define @t231 () (lambda @t33 @t230)) % 0.38/0.62 (define @t232 () (lambda @t3 @t230)) % 0.38/0.62 (define @t233 () (_ @t232 @t24)) % 0.38/0.62 (define @t234 () (not @t233)) % 0.38/0.62 (define @t235 () (or @t234 @t228)) % 0.38/0.62 (define @t236 () (lambda @t229 @t235)) % 0.38/0.62 (define @t237 () (or (not (_ @t26 @t24)) @t228)) % 0.38/0.62 (define @t238 () (lambda @t27 @t237)) % 0.38/0.62 (define @t239 () (not @t8)) % 0.38/0.62 (define @t240 () (or @t239 @t30)) % 0.38/0.62 (define @t241 () (not (_ @t26 @t15))) % 0.38/0.62 (define @t242 () (@list @t15)) % 0.38/0.62 (define @t243 () (lambda @t242 (or @t241 (_ @t25 @t15)))) % 0.38/0.62 (define @t244 () (@list @t19 @t15)) % 0.38/0.62 (define @t245 () (lambda @t242 @t241)) % 0.38/0.62 (define @t246 () (_ @t245 @t15)) % 0.38/0.62 (define @t247 () (or @t246 @t20)) % 0.38/0.62 (define @t248 () (lambda @t244 @t247)) % 0.38/0.62 (define @t249 () (_ @t29 @t15)) % 0.38/0.62 (define @t250 () (lambda @t242 (and @t249 (_ @t43 @t15)))) % 0.38/0.62 (define @t251 () (lambda @t244 (and @t249 @t20))) % 0.38/0.62 (define @t252 () (forall @t81 @t78)) % 0.38/0.62 (define @t253 () (@quantifiers_skolemize @t252 0)) % 0.38/0.62 (define @t254 () (forall @t31 (or (not (tptp.irel @t253 @t6)) @t75))) % 0.38/0.62 (define @t255 () (@quantifiers_skolemize @t252 3)) % 0.38/0.62 (define @t256 () (tptp.a @t255)) % 0.38/0.62 (define @t257 () (@quantifiers_skolemize @t252 1)) % 0.38/0.62 (define @t258 () (tptp.irel @t257 @t255)) % 0.38/0.62 (define @t259 () (not @t258)) % 0.38/0.62 (define @t260 () (or (not (forall @t66 (or (not (tptp.irel @t257 @t64)) @t65))) @t259 @t256)) % 0.38/0.62 (define @t261 () (@quantifiers_skolemize @t252 2)) % 0.38/0.62 (define @t262 () (tptp.b @t261)) % 0.38/0.62 (define @t263 () (tptp.irel @t257 @t261)) % 0.38/0.62 (define @t264 () (not @t263)) % 0.38/0.62 (define @t265 () (or (not (forall @t70 (or (not (tptp.irel @t257 @t68)) @t69))) @t264 @t262)) % 0.38/0.62 (define @t266 () (and @t265 @t260)) % 0.38/0.62 (define @t267 () (tptp.irel @t253 @t257)) % 0.38/0.62 (define @t268 () (not @t267)) % 0.38/0.62 (define @t269 () (not @t254)) % 0.38/0.62 (define @t270 () (or @t269 @t268 @t266)) % 0.38/0.62 (define @t271 () (@list true)) % 0.38/0.62 (define @t272 () (@list @t270)) % 0.38/0.62 (define @t273 () (tptp.irel @t1 @t4)) % 0.38/0.62 (define @t274 () (tptp.irel @t6 @t4)) % 0.38/0.62 (define @t275 () (not @t7)) % 0.38/0.62 (define @t276 () (or @t239 @t275 @t5)) % 0.38/0.62 (define @t277 () (tptp.irel @t253 @t261)) % 0.38/0.62 (define @t278 () (or @t268 @t264 @t277)) % 0.38/0.62 (define @t279 () (and (tptp.a @t261) @t262)) % 0.38/0.62 (define @t280 () (not @t277)) % 0.38/0.62 (define @t281 () (or @t280 @t279)) % 0.38/0.62 (define @t282 () (@list @t260)) % 0.38/0.62 (define @t283 () (and @t256 (tptp.b @t255))) % 0.38/0.62 (define @t284 () (not @t283)) % 0.38/0.62 (define @t285 () (tptp.irel @t253 @t255)) % 0.38/0.62 (define @t286 () (or @t268 @t259 @t285)) % 0.38/0.62 (define @t287 () (not @t285)) % 0.38/0.62 (define @t288 () (or @t287 @t283)) % 0.38/0.62 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.38/0.62 (assume @p2 @t11) % 0.38/0.62 (assume @p3 (= tptp.ifalse (_ tptp.inot tptp.itrue))) % 0.38/0.62 (assume @p4 @t14) % 0.38/0.62 (assume @p5 true) % 0.38/0.62 (step @p6 (= tptp.mnot @t18) :rule refl :args (@t18)) % 0.38/0.62 (step @p7 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.38/0.62 (step @p8 (= tptp.mand @t23) :rule refl :args (@t23)) % 0.38/0.62 (step @p9 (= tptp.mimplies @t28) :rule refl :args (@t28)) % 0.38/0.62 (step @p10 (= tptp.mbox_s4 @t34) :rule refl :args (@t34)) % 0.38/0.62 (step @p11 (= tptp.iatom @t37) :rule refl :args (@t37)) % 0.38/0.62 (step @p12 (= tptp.inot @t39) :rule refl :args (@t39)) % 0.38/0.62 (step @p13 (= tptp.itrue @t42) :rule refl :args (@t42)) % 0.38/0.62 (step @p14 (= tptp.iand @t45) :rule refl :args (@t45)) % 0.38/0.62 (step @p15 (= tptp.ior @t47) :rule refl :args (@t47)) % 0.38/0.62 (step @p16 (= tptp.iimplies @t48) :rule refl :args (@t48)) % 0.38/0.62 (step @p17 (= tptp.iimplied @t50) :rule refl :args (@t50)) % 0.38/0.62 (step @p18 (= tptp.iequiv @t51) :rule refl :args (@t51)) % 0.38/0.62 (step @p19 (= tptp.ixor @t52) :rule refl :args (@t52)) % 0.38/0.62 (step @p20 (= tptp.ivalid @t57) :rule refl :args (@t57)) % 0.38/0.62 (step @p21 (= tptp.isatisfiable @t58) :rule refl :args (@t58)) % 0.38/0.62 (step @p22 (= tptp.icountersatisfiable @t60) :rule refl :args (@t60)) % 0.38/0.62 (step @p23 (= tptp.iinvalid @t61) :rule refl :args (@t61)) % 0.38/0.62 (step @p24 :rule aci_norm :args ((= @t80 @t78))) % 0.38/0.62 (step @p25 :rule cong :premises (@p24) :args (@t82)) % 0.38/0.62 (step @p26 :rule quant-merge-prenex :args ((= (forall @t41 @t84) @t82))) % 0.38/0.62 (step @p27 :rule alpha_equiv :args (@t85 (@list @t63 @t67 @t62) (@list @t6 @t87 @t86))) % 0.38/0.62 (step @p28 :rule refl :args (@t77)) % 0.38/0.62 (step @p29 :rule nary_cong :premises (@p28 @p27) :args (@t88)) % 0.38/0.62 (step @p30 :rule quant-miniscope-or :args ((= @t84 @t88))) % 0.38/0.62 (step @p31 :rule trans :premises (@p30 @p29)) % 0.38/0.62 (step @p32 :rule symm :premises (@p31)) % 0.38/0.62 (step @p33 :rule cong :premises (@p32) :args ((forall @t41 @t101))) % 0.38/0.62 (step @p34 :rule trans :premises (@p33 @p26)) % 0.38/0.62 (step @p35 :rule trans :premises (@p34 @p25)) % 0.38/0.62 (step @p36 :rule beta-reduce :args ((= @t106 @t101))) % 0.38/0.62 (step @p37 :rule cong :premises (@p36) :args (@t107)) % 0.38/0.62 (step @p38 :rule trans :premises (@p37 @p35)) % 0.38/0.62 (step @p39 :rule beta-reduce :args ((= (_ @t109 @t105) @t107))) % 0.38/0.62 (step @p40 :rule trans :premises (@p39 @p38)) % 0.38/0.62 (step @p41 :rule aci_norm :args ((= @t111 @t93))) % 0.38/0.62 (step @p42 :rule aci_norm :args ((= @t113 @t98))) % 0.38/0.62 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t114)) % 0.38/0.62 (step @p44 :rule refl :args (@t102)) % 0.38/0.62 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t115)) % 0.38/0.62 (step @p46 :rule cong :premises (@p45) :args (@t116)) % 0.38/0.62 (step @p47 :rule quant-merge-prenex :args ((= (forall @t31 @t118) @t116))) % 0.38/0.62 (step @p48 :rule alpha_equiv :args (@t120 (@list @t86) @t121)) % 0.38/0.62 (step @p49 :rule refl :args (@t92)) % 0.38/0.62 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t122)) % 0.38/0.62 (step @p51 :rule quant-miniscope-or :args ((= @t123 @t122))) % 0.38/0.62 (step @p52 :rule quant-unused-vars :args ((= @t124 @t123))) % 0.38/0.62 (step @p53 :rule trans :premises (@p52 @p51)) % 0.38/0.62 (step @p54 :rule trans :premises (@p53 @p50)) % 0.38/0.62 (step @p55 :rule alpha_equiv :args (@t126 (@list @t87) @t127)) % 0.38/0.62 (step @p56 :rule refl :args (@t97)) % 0.38/0.62 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t128)) % 0.38/0.62 (step @p58 :rule quant-miniscope-or :args ((= @t129 @t128))) % 0.38/0.62 (step @p59 :rule quant-unused-vars :args ((= @t130 @t129))) % 0.38/0.62 (step @p60 :rule trans :premises (@p59 @p58)) % 0.38/0.62 (step @p61 :rule trans :premises (@p60 @p57)) % 0.38/0.62 (step @p62 :rule nary_cong :premises (@p61 @p54) :args (@t131)) % 0.38/0.62 (step @p63 :rule quant-miniscope-and :args ((= @t132 @t131))) % 0.38/0.62 (step @p64 :rule trans :premises (@p63 @p62)) % 0.38/0.62 (step @p65 :rule refl :args (@t102)) % 0.38/0.62 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t133)) % 0.38/0.62 (step @p67 :rule quant-miniscope-or :args ((= @t118 @t133))) % 0.38/0.62 (step @p68 :rule trans :premises (@p67 @p66)) % 0.38/0.62 (step @p69 :rule symm :premises (@p68)) % 0.38/0.62 (step @p70 :rule cong :premises (@p69) :args ((forall @t31 (or @t102 @t134)))) % 0.38/0.62 (step @p71 :rule trans :premises (@p70 @p47)) % 0.38/0.62 (step @p72 :rule trans :premises (@p71 @p46)) % 0.38/0.62 (step @p73 :rule beta-reduce :args ((= (_ (lambda @t104 (and (or (not @t135) @t136) (or (not @t136) @t135))) @t6) @t134))) % 0.38/0.62 (step @p74 :rule refl :args (@t6)) % 0.38/0.62 (step @p75 :rule alpha_equiv :args (@t137 @t138 @t121)) % 0.38/0.62 (step @p76 :rule alpha_equiv :args (@t139 @t138 @t127)) % 0.38/0.62 (step @p77 :rule cong :premises (@p76) :args (@t140)) % 0.38/0.62 (step @p78 :rule nary_cong :premises (@p77 @p75) :args (@t141)) % 0.38/0.62 (step @p79 :rule cong :premises (@p75) :args (@t142)) % 0.38/0.62 (step @p80 :rule nary_cong :premises (@p79 @p76) :args (@t143)) % 0.38/0.62 (step @p81 :rule nary_cong :premises (@p80 @p78) :args (@t144)) % 0.38/0.62 (step @p82 :rule cong :premises (@p81) :args (@t145)) % 0.38/0.62 (step @p83 :rule ho_cong :premises (@p82 @p74)) % 0.38/0.62 (step @p84 :rule trans :premises (@p83 @p73)) % 0.38/0.62 (step @p85 :rule nary_cong :premises (@p44 @p84) :args (@t146)) % 0.38/0.62 (step @p86 :rule cong :premises (@p85) :args (@t147)) % 0.38/0.62 (step @p87 :rule trans :premises (@p86 @p72)) % 0.38/0.62 (step @p88 :rule refl :args (@t103)) % 0.38/0.62 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t148)) % 0.38/0.62 (step @p90 :rule cong :premises (@p89) :args (@t149)) % 0.38/0.62 (step @p91 :rule beta-reduce :args ((= (_ (lambda @t152 (or @t103 @t151)) @t145) @t149))) % 0.38/0.62 (step @p92 :rule trans :premises (@p91 @p90)) % 0.38/0.62 (step @p93 :rule refl :args (@t137)) % 0.38/0.62 (step @p94 :rule refl :args (@t73)) % 0.38/0.62 (step @p95 :rule refl :args (@t153)) % 0.38/0.62 (step @p96 :rule cong :premises (@p95 @p94) :args ((= @t153 @t73))) % 0.38/0.62 (step @p97 :rule symm :premises (@p96)) % 0.38/0.62 (step @p98 :rule eq_resolve :premises (@p95 @p97)) % 0.38/0.62 (step @p99 :rule nary_cong :premises (@p65 @p98) :args (@t154)) % 0.38/0.62 (step @p100 :rule cong :premises (@p99) :args ((forall @t31 @t154))) % 0.38/0.62 (step @p101 :rule beta-reduce :args ((= @t157 @t153))) % 0.38/0.62 (step @p102 :rule nary_cong :premises (@p44 @p101) :args (@t158)) % 0.38/0.62 (step @p103 :rule cong :premises (@p102) :args (@t159)) % 0.38/0.62 (step @p104 :rule trans :premises (@p103 @p100)) % 0.38/0.62 (step @p105 :rule cong :premises (@p104) :args (@t160)) % 0.38/0.62 (step @p106 :rule nary_cong :premises (@p105 @p93) :args (@t161)) % 0.38/0.62 (step @p107 :rule refl :args (@t142)) % 0.38/0.62 (step @p108 :rule nary_cong :premises (@p107 @p104) :args (@t162)) % 0.38/0.62 (step @p109 :rule nary_cong :premises (@p108 @p106) :args (@t163)) % 0.38/0.62 (step @p110 :rule cong :premises (@p109) :args (@t164)) % 0.38/0.62 (step @p111 :rule beta-reduce :args ((= (_ (lambda @t152 (and (or @t142 @t151) (or @t165 @t137))) @t156) @t164))) % 0.38/0.62 (step @p112 :rule trans :premises (@p111 @p110)) % 0.38/0.62 (step @p113 :rule beta-reduce :args ((= @t166 @t156))) % 0.38/0.62 (step @p114 :rule refl :args (@t74)) % 0.38/0.62 (step @p115 :rule refl :args (@t167)) % 0.38/0.62 (step @p116 :rule cong :premises (@p115 @p114) :args ((= @t167 @t74))) % 0.38/0.62 (step @p117 :rule symm :premises (@p116)) % 0.38/0.62 (step @p118 :rule eq_resolve :premises (@p115 @p117)) % 0.38/0.62 (step @p119 :rule nary_cong :premises (@p65 @p118) :args (@t168)) % 0.38/0.62 (step @p120 :rule cong :premises (@p119) :args ((forall @t31 @t168))) % 0.38/0.62 (step @p121 :rule beta-reduce :args ((= @t171 @t167))) % 0.38/0.62 (step @p122 :rule nary_cong :premises (@p44 @p121) :args (@t172)) % 0.38/0.62 (step @p123 :rule cong :premises (@p122) 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cnf_and_neg :args (@t266)) % 0.38/0.62 (step @p390 :rule chain_m_resolution :premises (@p389 @p388 @p386) :args ((not @t260) (@list true false) (@list @t266 @t265))) % 0.38/0.62 (step @p391 :rule cnf_or_neg :args (@t260 2)) % 0.38/0.62 (step @p392 :rule chain_m_resolution :premises (@p391 @p390) :args ((not @t256) @t271 @t282)) % 0.38/0.62 (step @p393 :rule cnf_and_pos :args (@t283 0)) % 0.38/0.62 (step @p394 :rule reordering :premises (@p393) :args ((or @t256 @t284))) % 0.38/0.62 (step @p395 :rule chain_m_resolution :premises (@p394 @p392) :args (@t284 @t271 (@list @t256))) % 0.38/0.62 (step @p396 :rule instantiate :premises (@p377) :args ((@list @t253 @t257 @t255))) % 0.38/0.62 (step @p397 :rule bool-double-not-elim :args (@t258)) % 0.38/0.62 (step @p398 :rule refl :args (@t260)) % 0.38/0.62 (step @p399 :rule nary_cong :premises (@p398 @p397) :args ((or @t260 (not @t259)))) % 0.38/0.62 (step @p400 :rule cnf_or_neg :args (@t260 1)) % 0.38/0.62 (step @p401 :rule eq_resolve :premises (@p400 @p399)) % 0.38/0.62 (step @p402 :rule reordering :premises (@p401) :args ((or @t258 @t260))) % 0.38/0.62 (step @p403 :rule chain_m_resolution :premises (@p402 @p390) :args (@t258 @t271 @t282)) % 0.38/0.62 (step @p404 :rule cnf_or_pos :args (@t286)) % 0.38/0.62 (step @p405 :rule reordering :premises (@p404) :args ((or @t268 @t259 @t285 (not @t286)))) % 0.38/0.62 (step @p406 :rule chain_m_resolution :premises (@p405 @p355 @p403 @p396) :args (@t285 (@list false false false) (@list @t267 @t258 @t286))) % 0.38/0.62 (step @p407 :rule cnf_or_pos :args (@t288)) % 0.38/0.62 (step @p408 :rule reordering :premises (@p407) :args ((or @t287 @t283 (not @t288)))) % 0.38/0.62 (step @p409 false :rule chain_m_resolution :premises (@p408 @p406 @p395 @p342) :args (false (@list false true false) (@list @t285 @t283 @t288))) % 0.38/0.62 ) % 0.38/0.62 % SZS output end Proof % 0.38/0.62 % cvc5 exiting %------------------------------------------------------------------------------