%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN041^4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:07:51 AM UTC 2026 % Result : Theorem 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN041^4 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n028.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 23:18:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.39/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.q (-> $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.p (-> $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mand () (let ((_let_1 (@var "U" $$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))))))) % 0.39/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.mbox_s4 () (let ((_let_1 (@var "Y" $$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)))))))) % 0.39/0.60 (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))))) % 0.39/0.60 (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))))) % 0.39/0.60 (define tptp.itrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.39/0.60 (define tptp.iand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.ior () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.39/0.60 (define tptp.iimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.iimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iimplies _let_3) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.iequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.ixor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.inot (_ (_ tptp.iequiv _let_3) _let_2)) _let_1)))))) % 0.39/0.60 (define tptp.ivalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.isatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.icountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.iinvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define @t1 () (@var "X" $$unsorted)) % 0.39/0.60 (define @t2 () (_ tptp.irel @t1)) % 0.39/0.60 (define @t3 () (@list @t1)) % 0.39/0.60 (define @t4 () (@var "Z" $$unsorted)) % 0.39/0.60 (define @t5 () (_ @t2 @t4)) % 0.39/0.60 (define @t6 () (@var "Y" $$unsorted)) % 0.39/0.60 (define @t7 () (_ (_ tptp.irel @t6) @t4)) % 0.39/0.60 (define @t8 () (_ @t2 @t6)) % 0.39/0.60 (define @t9 () (and @t8 @t7)) % 0.39/0.60 (define @t10 () (@list @t1 @t6 @t4)) % 0.39/0.60 (define @t11 () (forall @t10 (=> @t9 @t5))) % 0.39/0.60 (define @t12 () (_ tptp.iatom tptp.p)) % 0.39/0.60 (define @t13 () (_ tptp.iatom tptp.q)) % 0.39/0.60 (define @t14 () (not (_ tptp.ivalid (_ (_ tptp.iimplies (_ tptp.inot (_ (_ tptp.iimplies @t12) @t13))) (_ (_ tptp.iimplies @t13) @t12))))) % 0.39/0.60 (define @t15 () (@var "U" $$unsorted)) % 0.39/0.60 (define @t16 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.60 (define @t17 () (_ @t16 @t15)) % 0.39/0.60 (define @t18 () (lambda (@list @t16 @t15) (not @t17))) % 0.39/0.60 (define @t19 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.60 (define @t20 () (_ @t19 @t15)) % 0.39/0.60 (define @t21 () (@list @t16 @t19 @t15)) % 0.39/0.60 (define @t22 () (lambda @t21 (or @t17 @t20))) % 0.39/0.60 (define @t23 () (lambda @t21 (and @t17 @t20))) % 0.39/0.60 (define @t24 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.60 (define @t25 () (@var "V" (-> $$unsorted Bool))) % 0.39/0.60 (define @t26 () (@var "U" (-> $$unsorted Bool))) % 0.39/0.60 (define @t27 () (@list @t26 @t25 @t24)) % 0.39/0.60 (define @t28 () (lambda @t27 (_ (_ (_ tptp.mor (_ tptp.mnot @t26)) @t25) @t24))) % 0.39/0.60 (define @t29 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.60 (define @t30 () (_ @t29 @t6)) % 0.39/0.60 (define @t31 () (@list @t6)) % 0.39/0.60 (define @t32 () (forall @t31 (=> @t8 @t30))) % 0.39/0.60 (define @t33 () (@list @t29 @t1)) % 0.39/0.60 (define @t34 () (lambda @t33 @t32)) % 0.39/0.60 (define @t35 () (@list @t29 @t24)) % 0.39/0.60 (define @t36 () (lambda @t35 (_ @t29 @t24))) % 0.39/0.60 (define @t37 () (_ tptp.mbox_s4 @t29)) % 0.39/0.60 (define @t38 () (lambda @t35 (_ (_ tptp.mnot @t37) @t24))) % 0.39/0.60 (define @t39 () (@var "W" $$unsorted)) % 0.39/0.60 (define @t40 () (@list @t39)) % 0.39/0.60 (define @t41 () (lambda @t40 true)) % 0.39/0.60 (define @t42 () (@var "Q" (-> $$unsorted Bool))) % 0.39/0.60 (define @t43 () (@list @t29 @t42 @t24)) % 0.39/0.60 (define @t44 () (lambda @t43 (_ (_ (_ tptp.mand @t29) @t42) @t24))) % 0.39/0.60 (define @t45 () (_ tptp.mbox_s4 @t42)) % 0.39/0.60 (define @t46 () (lambda @t43 (_ (_ (_ tptp.mor @t37) @t45) @t24))) % 0.39/0.60 (define @t47 () (lambda @t43 (_ (_ (_ tptp.mimplies @t37) @t45) @t24))) % 0.39/0.60 (define @t48 () (_ (_ tptp.iimplies @t42) @t29)) % 0.39/0.60 (define @t49 () (lambda @t43 (_ @t48 @t24))) % 0.39/0.60 (define @t50 () (lambda @t43 (_ (_ (_ tptp.iand (_ (_ tptp.iimplies @t29) @t42)) @t48) @t24))) % 0.39/0.60 (define @t51 () (lambda @t43 (_ (_ tptp.inot (_ (_ tptp.iequiv @t29) @t42)) @t24))) % 0.39/0.60 (define @t52 () (@var "Phi" (-> $$unsorted Bool))) % 0.39/0.60 (define @t53 () (_ @t52 @t39)) % 0.39/0.60 (define @t54 () (forall @t40 @t53)) % 0.39/0.60 (define @t55 () (@list @t52)) % 0.39/0.60 (define @t56 () (lambda @t55 @t54)) % 0.39/0.60 (define @t57 () (lambda @t55 (exists @t40 @t53))) % 0.39/0.60 (define @t58 () (not @t53)) % 0.39/0.60 (define @t59 () (lambda @t55 (exists @t40 @t58))) % 0.39/0.60 (define @t60 () (lambda @t55 (forall @t40 @t58))) % 0.39/0.60 (define @t61 () (@var "BOUND_VARIABLE_8226" $$unsorted)) % 0.39/0.60 (define @t62 () (tptp.p @t61)) % 0.39/0.60 (define @t63 () (@var "BOUND_VARIABLE_8224" $$unsorted)) % 0.39/0.60 (define @t64 () (not (tptp.irel @t63 @t61))) % 0.39/0.60 (define @t65 () (@var "BOUND_VARIABLE_8174" $$unsorted)) % 0.39/0.60 (define @t66 () (tptp.q @t65)) % 0.39/0.60 (define @t67 () (@list @t65)) % 0.39/0.60 (define @t68 () (not (forall @t67 (or (not (tptp.irel @t63 @t65)) @t66)))) % 0.39/0.60 (define @t69 () (not (tptp.irel @t39 @t63))) % 0.39/0.60 (define @t70 () (@var "BOUND_VARIABLE_8099" $$unsorted)) % 0.39/0.60 (define @t71 () (tptp.q @t70)) % 0.39/0.60 (define @t72 () (@var "BOUND_VARIABLE_8119" $$unsorted)) % 0.39/0.60 (define @t73 () (not (tptp.irel @t72 @t70))) % 0.39/0.60 (define @t74 () (@var "BOUND_VARIABLE_8074" $$unsorted)) % 0.39/0.60 (define @t75 () (tptp.p @t74)) % 0.39/0.60 (define @t76 () (@list @t74)) % 0.39/0.60 (define @t77 () (not (forall @t76 (or (not (tptp.irel @t72 @t74)) @t75)))) % 0.39/0.60 (define @t78 () (@list @t72 @t70)) % 0.39/0.60 (define @t79 () (not (forall @t78 (or (not (tptp.irel @t6 @t72)) @t77 @t73 @t71)))) % 0.39/0.60 (define @t80 () (not (tptp.irel @t39 @t6))) % 0.39/0.60 (define @t81 () (not (forall @t31 (or @t80 @t79)))) % 0.39/0.60 (define @t82 () (or @t81 @t69 @t68 @t64 @t62)) % 0.39/0.60 (define @t83 () (or @t69 @t68 @t64 @t62)) % 0.39/0.60 (define @t84 () (or @t81 @t83)) % 0.39/0.60 (define @t85 () (@list @t39 @t63 @t61)) % 0.39/0.60 (define @t86 () (forall @t85 @t84)) % 0.39/0.60 (define @t87 () (@list @t63 @t61)) % 0.39/0.60 (define @t88 () (forall @t87 @t84)) % 0.39/0.60 (define @t89 () (forall @t87 @t83)) % 0.39/0.60 (define @t90 () (@var "BOUND_VARIABLE_8199" $$unsorted)) % 0.39/0.60 (define @t91 () (or @t81 @t89)) % 0.39/0.60 (define @t92 () (tptp.p @t90)) % 0.39/0.60 (define @t93 () (not (tptp.irel @t6 @t90))) % 0.39/0.60 (define @t94 () (not (forall @t67 (or (not (tptp.irel @t6 @t65)) @t66)))) % 0.39/0.60 (define @t95 () (@list @t6 @t90)) % 0.39/0.60 (define @t96 () (or @t81 (forall @t95 (or @t80 @t94 @t93 @t92)))) % 0.39/0.60 (define @t97 () (not (tptp.irel @t24 @t6))) % 0.39/0.60 (define @t98 () (or @t97 @t94 @t93 @t92)) % 0.39/0.60 (define @t99 () (not (forall @t31 (or @t97 @t79)))) % 0.39/0.60 (define @t100 () (@list @t24)) % 0.39/0.60 (define @t101 () (lambda @t100 (or @t99 (forall @t95 @t98)))) % 0.39/0.60 (define @t102 () (_ @t101 @t39)) % 0.39/0.60 (define @t103 () (forall @t40 @t102)) % 0.39/0.60 (define @t104 () (_ @t52 @t39)) % 0.39/0.60 (define @t105 () (lambda @t55 (forall @t40 @t104))) % 0.39/0.60 (define @t106 () (or @t93 @t92)) % 0.39/0.60 (define @t107 () (or @t97 @t94 @t106)) % 0.39/0.60 (define @t108 () (forall @t95 @t107)) % 0.39/0.60 (define @t109 () (@list @t90)) % 0.39/0.60 (define @t110 () (forall @t109 @t107)) % 0.39/0.60 (define @t111 () (forall @t109 @t106)) % 0.39/0.60 (define @t112 () (@var "BOUND_VARIABLE_8166" $$unsorted)) % 0.39/0.60 (define @t113 () (@list @t112)) % 0.39/0.60 (define @t114 () (or @t97 @t94 @t111)) % 0.39/0.60 (define @t115 () (tptp.p @t112)) % 0.39/0.60 (define @t116 () (@list @t112)) % 0.39/0.60 (define @t117 () (forall @t116 (or (not (tptp.irel @t6 @t112)) @t115))) % 0.39/0.60 (define @t118 () (or @t97 @t94 @t117)) % 0.39/0.60 (define @t119 () (or @t94 @t117)) % 0.39/0.60 (define @t120 () (tptp.p @t6)) % 0.39/0.60 (define @t121 () (forall @t31 (or @t97 @t120))) % 0.39/0.60 (define @t122 () (@list @t6)) % 0.39/0.60 (define @t123 () (tptp.q @t6)) % 0.39/0.60 (define @t124 () (forall @t31 (or @t97 @t123))) % 0.39/0.60 (define @t125 () (not @t124)) % 0.39/0.60 (define @t126 () (or @t125 @t121)) % 0.39/0.60 (define @t127 () (lambda @t100 @t126)) % 0.39/0.60 (define @t128 () (or @t97 (_ @t127 @t6))) % 0.39/0.60 (define @t129 () (forall @t31 @t128)) % 0.39/0.60 (define @t130 () (or @t99 @t129)) % 0.39/0.60 (define @t131 () (lambda @t100 @t130)) % 0.39/0.60 (define @t132 () (_ @t42 @t6)) % 0.39/0.60 (define @t133 () (forall @t31 (or @t97 @t132))) % 0.39/0.60 (define @t134 () (@list @t42 @t24)) % 0.39/0.60 (define @t135 () (_ tptp.p @t6)) % 0.39/0.60 (define @t136 () (or @t97 @t135)) % 0.39/0.60 (define @t137 () (lambda @t100 (_ tptp.p @t24))) % 0.39/0.60 (define @t138 () (_ @t137 @t6)) % 0.39/0.60 (define @t139 () (or @t97 @t138)) % 0.39/0.60 (define @t140 () (forall @t31 @t139)) % 0.39/0.60 (define @t141 () (or @t125 @t140)) % 0.39/0.60 (define @t142 () (lambda @t100 @t141)) % 0.39/0.60 (define @t143 () (_ @t36 tptp.p)) % 0.39/0.60 (define @t144 () (_ tptp.q @t6)) % 0.39/0.60 (define @t145 () (or @t97 @t144)) % 0.39/0.60 (define @t146 () (lambda @t100 (_ tptp.q @t24))) % 0.39/0.60 (define @t147 () (_ @t146 @t6)) % 0.39/0.60 (define @t148 () (or @t97 @t147)) % 0.39/0.60 (define @t149 () (forall @t31 @t148)) % 0.39/0.60 (define @t150 () (not @t149)) % 0.39/0.60 (define @t151 () (or @t150 @t133)) % 0.39/0.60 (define @t152 () (lambda @t134 @t151)) % 0.39/0.60 (define @t153 () (_ @t29 @t6)) % 0.39/0.60 (define @t154 () (forall @t31 (or @t97 @t153))) % 0.39/0.60 (define @t155 () (not @t154)) % 0.39/0.60 (define @t156 () (or @t155 @t133)) % 0.39/0.60 (define @t157 () (lambda @t43 @t156)) % 0.39/0.60 (define @t158 () (_ @t36 tptp.q)) % 0.39/0.60 (define @t159 () (not (tptp.irel @t6 @t70))) % 0.39/0.60 (define @t160 () (not (forall @t76 (or (not (tptp.irel @t6 @t74)) @t75)))) % 0.39/0.60 (define @t161 () (or @t97 @t160 @t159 @t71)) % 0.39/0.60 (define @t162 () (@list @t6 @t70)) % 0.39/0.60 (define @t163 () (forall @t162 @t161)) % 0.39/0.60 (define @t164 () (not @t163)) % 0.39/0.60 (define @t165 () (lambda @t100 @t164)) % 0.39/0.60 (define @t166 () (or @t97 (_ @t165 @t6))) % 0.39/0.60 (define @t167 () (forall @t31 @t166)) % 0.39/0.60 (define @t168 () (not @t167)) % 0.39/0.60 (define @t169 () (or @t168 @t133)) % 0.39/0.60 (define @t170 () (lambda @t134 @t169)) % 0.39/0.60 (define @t171 () (or @t159 @t71)) % 0.39/0.60 (define @t172 () (or @t97 @t160 @t171)) % 0.39/0.60 (define @t173 () (forall @t162 @t172)) % 0.39/0.60 (define @t174 () (@list @t70)) % 0.39/0.60 (define @t175 () (forall @t174 @t172)) % 0.39/0.60 (define @t176 () (forall @t174 @t171)) % 0.39/0.60 (define @t177 () (@var "BOUND_VARIABLE_8066" $$unsorted)) % 0.39/0.60 (define @t178 () (@list @t177)) % 0.39/0.60 (define @t179 () (or @t97 @t160 @t176)) % 0.39/0.60 (define @t180 () (tptp.q @t177)) % 0.39/0.60 (define @t181 () (@list @t177)) % 0.39/0.60 (define @t182 () (forall @t181 (or (not (tptp.irel @t6 @t177)) @t180))) % 0.39/0.60 (define @t183 () (or @t97 @t160 @t182)) % 0.39/0.60 (define @t184 () (or @t160 @t182)) % 0.39/0.60 (define @t185 () (not @t121)) % 0.39/0.60 (define @t186 () (or @t185 @t124)) % 0.39/0.60 (define @t187 () (lambda @t100 @t186)) % 0.39/0.60 (define @t188 () (or @t97 (_ @t187 @t6))) % 0.39/0.60 (define @t189 () (forall @t31 @t188)) % 0.39/0.60 (define @t190 () (not @t189)) % 0.39/0.60 (define @t191 () (lambda @t100 @t190)) % 0.39/0.60 (define @t192 () (lambda @t35 @t155)) % 0.39/0.60 (define @t193 () (or @t185 @t149)) % 0.39/0.60 (define @t194 () (lambda @t100 @t193)) % 0.39/0.60 (define @t195 () (not @t140)) % 0.39/0.60 (define @t196 () (or @t195 @t133)) % 0.39/0.60 (define @t197 () (lambda @t134 @t196)) % 0.39/0.60 (define @t198 () (tptp.irel @t1 @t6)) % 0.39/0.60 (define @t199 () (not @t198)) % 0.39/0.60 (define @t200 () (lambda @t3 (forall @t31 (or @t199 @t132)))) % 0.39/0.60 (define @t201 () (_ @t200 @t24)) % 0.39/0.60 (define @t202 () (or @t155 @t201)) % 0.39/0.60 (define @t203 () (lambda @t100 @t202)) % 0.39/0.60 (define @t204 () (_ @t25 @t24)) % 0.39/0.60 (define @t205 () (@list @t25 @t24)) % 0.39/0.60 (define @t206 () (forall @t31 (or @t199 @t153))) % 0.39/0.60 (define @t207 () (lambda @t33 @t206)) % 0.39/0.60 (define @t208 () (lambda @t3 @t206)) % 0.39/0.60 (define @t209 () (_ @t208 @t24)) % 0.39/0.60 (define @t210 () (not @t209)) % 0.39/0.60 (define @t211 () (or @t210 @t204)) % 0.39/0.60 (define @t212 () (lambda @t205 @t211)) % 0.39/0.60 (define @t213 () (or (not (_ @t26 @t24)) @t204)) % 0.39/0.60 (define @t214 () (lambda @t27 @t213)) % 0.39/0.60 (define @t215 () (not @t8)) % 0.39/0.60 (define @t216 () (or @t215 @t30)) % 0.39/0.60 (define @t217 () (not (_ @t26 @t15))) % 0.39/0.60 (define @t218 () (@list @t15)) % 0.39/0.60 (define @t219 () (lambda @t218 (or @t217 (_ @t25 @t15)))) % 0.39/0.60 (define @t220 () (@list @t19 @t15)) % 0.39/0.60 (define @t221 () (lambda @t218 @t217)) % 0.39/0.60 (define @t222 () (_ @t221 @t15)) % 0.39/0.60 (define @t223 () (or @t222 @t20)) % 0.39/0.60 (define @t224 () (lambda @t220 @t223)) % 0.39/0.60 (define @t225 () (forall @t31 (or (not (tptp.irel @t15 @t6)) @t153))) % 0.39/0.60 (define @t226 () (_ @t208 @t15)) % 0.39/0.60 (define @t227 () (not @t226)) % 0.39/0.60 (define @t228 () (lambda @t218 @t227)) % 0.39/0.60 (define @t229 () (forall @t85 @t82)) % 0.39/0.60 (define @t230 () (@quantifiers_skolemize @t229 0)) % 0.39/0.60 (define @t231 () (forall @t31 (or (not (tptp.irel @t230 @t6)) @t79))) % 0.39/0.60 (define @t232 () (@quantifiers_skolemize @t229 2)) % 0.39/0.60 (define @t233 () (@quantifiers_skolemize @t229 1)) % 0.39/0.60 (define @t234 () (forall @t67 (or (not (tptp.irel @t233 @t65)) @t66))) % 0.39/0.60 (define @t235 () (not @t234)) % 0.39/0.60 (define @t236 () (tptp.irel @t230 @t233)) % 0.39/0.60 (define @t237 () (not @t236)) % 0.39/0.60 (define @t238 () (not @t231)) % 0.39/0.60 (define @t239 () (or @t238 @t237 @t235 (not (tptp.irel @t233 @t232)) (tptp.p @t232))) % 0.39/0.60 (define @t240 () (@list true)) % 0.39/0.60 (define @t241 () (@list @t239)) % 0.39/0.60 (define @t242 () (forall @t78 (or (not (tptp.irel @t233 @t72)) @t77 @t73 @t71))) % 0.39/0.60 (define @t243 () (not @t242)) % 0.39/0.60 (define @t244 () (or @t237 @t243)) % 0.39/0.60 (define @t245 () (@quantifiers_skolemize @t242 1)) % 0.39/0.60 (define @t246 () (tptp.q @t245)) % 0.39/0.60 (define @t247 () (@quantifiers_skolemize @t242 0)) % 0.39/0.60 (define @t248 () (tptp.irel @t247 @t245)) % 0.39/0.60 (define @t249 () (not @t248)) % 0.39/0.60 (define @t250 () (tptp.irel @t233 @t247)) % 0.39/0.60 (define @t251 () (not @t250)) % 0.39/0.60 (define @t252 () (or @t251 (not (forall @t76 (or (not (tptp.irel @t247 @t74)) @t75))) @t249 @t246)) % 0.39/0.60 (define @t253 () (@list @t252)) % 0.39/0.60 (define @t254 () (tptp.irel @t1 @t4)) % 0.39/0.60 (define @t255 () (tptp.irel @t6 @t4)) % 0.39/0.60 (define @t256 () (not @t7)) % 0.39/0.60 (define @t257 () (or @t215 @t256 @t5)) % 0.39/0.60 (define @t258 () (tptp.irel @t233 @t245)) % 0.39/0.60 (define @t259 () (or @t251 @t249 @t258)) % 0.39/0.60 (define @t260 () (not @t258)) % 0.39/0.60 (define @t261 () (or @t260 @t246)) % 0.39/0.60 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.39/0.60 (assume @p2 @t11) % 0.39/0.60 (assume @p3 (= tptp.ifalse (_ tptp.inot tptp.itrue))) % 0.39/0.60 (assume @p4 @t14) % 0.39/0.60 (assume @p5 true) % 0.39/0.60 (step @p6 (= tptp.mnot @t18) :rule refl :args (@t18)) % 0.39/0.60 (step @p7 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.39/0.60 (step @p8 (= tptp.mand @t23) :rule refl :args (@t23)) % 0.39/0.60 (step @p9 (= tptp.mimplies @t28) :rule refl :args (@t28)) % 0.39/0.60 (step @p10 (= tptp.mbox_s4 @t34) :rule refl :args (@t34)) % 0.39/0.60 (step @p11 (= tptp.iatom @t36) :rule refl :args (@t36)) % 0.39/0.60 (step @p12 (= tptp.inot @t38) :rule refl :args (@t38)) % 0.39/0.60 (step @p13 (= tptp.itrue @t41) :rule refl :args (@t41)) % 0.39/0.60 (step @p14 (= tptp.iand @t44) :rule refl :args (@t44)) % 0.39/0.60 (step @p15 (= tptp.ior @t46) :rule refl :args (@t46)) % 0.39/0.60 (step @p16 (= tptp.iimplies @t47) :rule refl :args (@t47)) % 0.39/0.60 (step @p17 (= tptp.iimplied @t49) :rule refl :args (@t49)) % 0.39/0.60 (step @p18 (= tptp.iequiv @t50) :rule refl :args (@t50)) % 0.39/0.60 (step @p19 (= tptp.ixor @t51) :rule refl :args (@t51)) % 0.39/0.60 (step @p20 (= tptp.ivalid @t56) :rule refl :args (@t56)) % 0.39/0.60 (step @p21 (= tptp.isatisfiable @t57) :rule refl :args (@t57)) % 0.39/0.60 (step @p22 (= tptp.icountersatisfiable @t59) :rule refl :args (@t59)) % 0.39/0.60 (step @p23 (= tptp.iinvalid @t60) :rule refl :args (@t60)) % 0.39/0.60 (step @p24 :rule aci_norm :args ((= @t84 @t82))) % 0.39/0.60 (step @p25 :rule cong :premises (@p24) :args (@t86)) % 0.39/0.60 (step @p26 :rule quant-merge-prenex :args ((= (forall @t40 @t88) @t86))) % 0.39/0.60 (step @p27 :rule alpha_equiv :args (@t89 (@list @t63 @t61) (@list @t6 @t90))) % 0.39/0.60 (step @p28 :rule refl :args (@t81)) % 0.39/0.60 (step @p29 :rule nary_cong :premises (@p28 @p27) :args (@t91)) % 0.39/0.60 (step @p30 :rule quant-miniscope-or :args ((= @t88 @t91))) % 0.39/0.60 (step @p31 :rule trans :premises (@p30 @p29)) % 0.39/0.60 (step @p32 :rule symm :premises (@p31)) % 0.39/0.60 (step @p33 :rule cong :premises (@p32) :args ((forall @t40 @t96))) % 0.39/0.60 (step @p34 :rule trans :premises (@p33 @p26)) % 0.39/0.60 (step @p35 :rule trans :premises (@p34 @p25)) % 0.39/0.60 (step @p36 :rule beta-reduce :args ((= @t102 @t96))) % 0.39/0.60 (step @p37 :rule cong :premises (@p36) :args (@t103)) % 0.39/0.60 (step @p38 :rule trans :premises (@p37 @p35)) % 0.39/0.60 (step @p39 :rule beta-reduce :args ((= (_ @t105 @t101) @t103))) % 0.39/0.60 (step @p40 :rule trans :premises (@p39 @p38)) % 0.39/0.60 (step @p41 :rule aci_norm :args ((= @t107 @t98))) % 0.39/0.60 (step @p42 :rule cong :premises (@p41) :args (@t108)) % 0.39/0.60 (step @p43 :rule quant-merge-prenex :args ((= (forall @t31 @t110) @t108))) % 0.39/0.60 (step @p44 :rule alpha_equiv :args (@t111 (@list @t90) @t113)) % 0.39/0.60 (step @p45 :rule refl :args (@t94)) % 0.39/0.60 (step @p46 :rule refl :args (@t97)) % 0.39/0.60 (step @p47 :rule nary_cong :premises (@p46 @p45 @p44) :args (@t114)) % 0.39/0.60 (step @p48 :rule quant-miniscope-or :args ((= @t110 @t114))) % 0.39/0.60 (step @p49 :rule trans :premises (@p48 @p47)) % 0.39/0.60 (step @p50 :rule symm :premises (@p49)) % 0.39/0.60 (step @p51 :rule cong :premises (@p50) :args ((forall @t31 @t118))) % 0.39/0.60 (step @p52 :rule trans :premises (@p51 @p43)) % 0.39/0.60 (step @p53 :rule trans :premises (@p52 @p42)) % 0.39/0.60 (step @p54 :rule aci_norm :args ((= (or @t97 @t119) @t118))) % 0.39/0.60 (step @p55 :rule beta-reduce :args ((= (_ (lambda @t100 (or (not (forall @t67 (or (not (tptp.irel @t24 @t65)) @t66))) (forall @t116 (or (not (tptp.irel @t24 @t112)) @t115)))) @t6) @t119))) % 0.39/0.60 (step @p56 :rule refl :args (@t6)) % 0.39/0.60 (step @p57 :rule alpha_equiv :args (@t121 @t122 @t113)) % 0.39/0.60 (step @p58 :rule alpha_equiv :args (@t124 @t122 (@list @t65))) % 0.39/0.60 (step @p59 :rule cong :premises (@p58) :args (@t125)) % 0.39/0.60 (step @p60 :rule nary_cong :premises (@p59 @p57) :args (@t126)) % 0.39/0.60 (step @p61 :rule cong :premises (@p60) :args (@t127)) % 0.39/0.60 (step @p62 :rule ho_cong :premises (@p61 @p56)) % 0.39/0.60 (step @p63 :rule trans :premises (@p62 @p55)) % 0.39/0.60 (step @p64 :rule refl :args (@t97)) % 0.39/0.60 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t128)) % 0.39/0.60 (step @p66 :rule trans :premises (@p65 @p54)) % 0.39/0.60 (step @p67 :rule cong :premises (@p66) :args (@t129)) % 0.39/0.60 (step @p68 :rule trans :premises (@p67 @p53)) % 0.39/0.60 (step @p69 :rule refl :args (@t99)) % 0.39/0.60 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t130)) % 0.39/0.60 (step @p71 :rule cong :premises (@p70) :args (@t131)) % 0.39/0.60 (step @p72 :rule beta-reduce :args ((= (_ (lambda @t134 (or @t99 @t133)) @t127) @t131))) % 0.39/0.60 (step @p73 :rule trans :premises (@p72 @p71)) % 0.39/0.60 (step @p74 :rule refl :args (@t120)) % 0.39/0.60 (step @p75 :rule refl :args (@t135)) % 0.39/0.60 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t135 @t120))) % 0.39/0.60 (step @p77 :rule symm :premises (@p76)) % 0.39/0.60 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.39/0.60 (step @p79 :rule nary_cong :premises (@p46 @p78) :args (@t136)) % 0.39/0.60 (step @p80 :rule cong :premises (@p79) :args ((forall @t31 @t136))) % 0.39/0.60 (step @p81 :rule beta-reduce :args ((= @t138 @t135))) % 0.39/0.60 (step @p82 :rule nary_cong :premises (@p64 @p81) :args (@t139)) % 0.39/0.60 (step @p83 :rule cong :premises (@p82) :args (@t140)) % 0.39/0.60 (step @p84 :rule trans :premises (@p83 @p80)) % 0.39/0.60 (step @p85 :rule refl :args (@t125)) % 0.39/0.60 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t141)) % 0.39/0.60 (step @p87 :rule cong :premises (@p86) :args (@t142)) % 0.39/0.60 (step @p88 :rule beta-reduce :args ((= (_ (lambda @t134 (or @t125 @t133)) @t137) @t142))) % 0.39/0.60 (step @p89 :rule trans :premises (@p88 @p87)) % 0.39/0.60 (step @p90 :rule beta-reduce :args ((= @t143 @t137))) % 0.39/0.60 (step @p91 :rule refl :args (@t133)) % 0.39/0.60 (step @p92 :rule refl :args (@t123)) % 0.39/0.60 (step @p93 :rule refl :args (@t144)) % 0.39/0.60 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t144 @t123))) % 0.39/0.60 (step @p95 :rule symm :premises (@p94)) % 0.39/0.60 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.39/0.60 (step @p97 :rule nary_cong :premises (@p46 @p96) :args (@t145)) % 0.39/0.60 (step @p98 :rule cong :premises (@p97) :args ((forall @t31 @t145))) % 0.39/0.60 (step @p99 :rule beta-reduce :args ((= @t147 @t144))) % 0.39/0.60 (step @p100 :rule nary_cong :premises (@p64 @p99) :args (@t148)) % 0.39/0.60 (step @p101 :rule cong :premises (@p100) :args (@t149)) % 0.39/0.60 (step @p102 :rule trans :premises (@p101 @p98)) % 0.39/0.60 (step @p103 :rule cong :premises (@p102) :args (@t150)) % 0.39/0.60 (step @p104 :rule nary_cong :premises (@p103 @p91) :args (@t151)) % 0.39/0.60 (step @p105 :rule cong :premises (@p104) :args (@t152)) % 0.39/0.60 (step @p106 :rule beta-reduce :args ((= (_ @t157 @t146) @t152))) % 0.39/0.60 (step @p107 :rule trans :premises (@p106 @p105)) % 0.39/0.60 (step @p108 :rule beta-reduce :args ((= @t158 @t146))) % 0.39/0.60 (step @p109 :rule refl :args (@t157)) % 0.39/0.60 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.39/0.60 (step @p111 :rule trans :premises (@p110 @p107)) % 0.39/0.60 (step @p112 :rule ho_cong :premises (@p111 @p90)) % 0.39/0.60 (step @p113 :rule trans :premises (@p112 @p89)) % 0.39/0.60 (step @p114 :rule beta-reduce :args ((= (_ (lambda @t100 (not (forall @t78 (or (not (tptp.irel @t24 @t72)) @t77 @t73 @t71)))) @t6) @t79))) % 0.39/0.60 (step @p115 :rule alpha_equiv :args (@t163 @t122 (@list @t72))) % 0.39/0.60 (step @p116 :rule cong :premises (@p115) :args (@t164)) % 0.39/0.60 (step @p117 :rule cong :premises (@p116) :args (@t165)) % 0.39/0.60 (step @p118 :rule ho_cong :premises (@p117 @p56)) % 0.39/0.60 (step @p119 :rule trans :premises (@p118 @p114)) % 0.39/0.60 (step @p120 :rule nary_cong :premises (@p64 @p119) :args (@t166)) % 0.39/0.60 (step @p121 :rule cong :premises (@p120) :args (@t167)) % 0.39/0.60 (step @p122 :rule cong :premises (@p121) :args (@t168)) % 0.39/0.60 (step @p123 :rule nary_cong :premises (@p122 @p91) :args (@t169)) % 0.39/0.60 (step @p124 :rule cong :premises (@p123) :args (@t170)) % 0.39/0.60 (step @p125 :rule beta-reduce :args ((= (_ @t157 @t165) @t170))) % 0.39/0.60 (step @p126 :rule trans :premises (@p125 @p124)) % 0.39/0.60 (step @p127 :rule aci_norm :args ((= @t172 @t161))) % 0.39/0.60 (step @p128 :rule cong :premises (@p127) :args (@t173)) % 0.39/0.60 (step @p129 :rule quant-merge-prenex :args ((= (forall @t31 @t175) @t173))) % 0.39/0.60 (step @p130 :rule alpha_equiv :args (@t176 (@list @t70) @t178)) % 0.39/0.60 (step @p131 :rule refl :args (@t160)) % 0.39/0.60 (step @p132 :rule nary_cong :premises (@p46 @p131 @p130) :args (@t179)) % 0.39/0.60 (step @p133 :rule quant-miniscope-or :args ((= @t175 @t179))) % 0.39/0.60 (step @p134 :rule trans :premises (@p133 @p132)) % 0.39/0.60 (step @p135 :rule symm :premises (@p134)) % 0.39/0.60 (step @p136 :rule cong :premises (@p135) :args ((forall @t31 @t183))) % 0.39/0.60 (step @p137 :rule trans :premises (@p136 @p129)) % 0.39/0.60 (step @p138 :rule trans :premises (@p137 @p128)) % 0.39/0.60 (step @p139 :rule aci_norm :args ((= (or @t97 @t184) @t183))) % 0.39/0.60 (step @p140 :rule beta-reduce :args ((= (_ (lambda @t100 (or (not (forall @t76 (or (not (tptp.irel @t24 @t74)) @t75))) (forall @t181 (or (not (tptp.irel @t24 @t177)) @t180)))) @t6) @t184))) % 0.39/0.60 (step @p141 :rule alpha_equiv :args (@t124 @t122 @t178)) % 0.39/0.60 (step @p142 :rule alpha_equiv :args (@t121 @t122 (@list @t74))) % 0.39/0.60 (step @p143 :rule cong :premises (@p142) :args (@t185)) % 0.39/0.60 (step @p144 :rule nary_cong :premises (@p143 @p141) :args (@t186)) % 0.39/0.60 (step @p145 :rule cong :premises (@p144) :args (@t187)) % 0.39/0.60 (step @p146 :rule ho_cong :premises (@p145 @p56)) % 0.39/0.60 (step @p147 :rule trans :premises (@p146 @p140)) % 0.39/0.60 (step @p148 :rule nary_cong :premises (@p64 @p147) :args (@t188)) % 0.39/0.60 (step @p149 :rule trans :premises (@p148 @p139)) % 0.39/0.60 (step @p150 :rule cong :premises (@p149) :args (@t189)) % 0.39/0.60 (step @p151 :rule trans :premises (@p150 @p138)) % 0.39/0.60 (step @p152 :rule cong :premises (@p151) :args (@t190)) % 0.39/0.60 (step @p153 :rule cong :premises (@p152) :args (@t191)) % 0.39/0.60 (step @p154 :rule beta-reduce :args ((= (_ @t192 @t187) @t191))) % 0.39/0.60 (step @p155 :rule trans :premises (@p154 @p153)) % 0.39/0.60 (step @p156 :rule refl :args (@t185)) % 0.39/0.60 (step @p157 :rule nary_cong :premises (@p156 @p102) :args (@t193)) % 0.39/0.60 (step @p158 :rule cong :premises (@p157) :args (@t194)) % 0.39/0.60 (step @p159 :rule beta-reduce :args ((= (_ (lambda @t134 (or @t185 @t133)) @t146) @t194))) % 0.39/0.60 (step @p160 :rule trans :premises (@p159 @p158)) % 0.39/0.60 (step @p161 :rule cong :premises (@p84) :args (@t195)) % 0.39/0.60 (step @p162 :rule nary_cong :premises (@p161 @p91) :args (@t196)) % 0.39/0.60 (step @p163 :rule cong :premises (@p162) :args (@t197)) % 0.39/0.60 (step @p164 :rule beta-reduce :args ((= (_ @t157 @t137) @t197))) % 0.39/0.60 (step @p165 :rule trans :premises (@p164 @p163)) % 0.39/0.60 (step @p166 :rule ho_cong :premises (@p109 @p90)) % 0.39/0.60 (step @p167 :rule trans :premises (@p166 @p165)) % 0.39/0.60 (step @p168 :rule ho_cong :premises (@p167 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0.39/0.60 (step @p307 :rule nary_cong :premises (@p299 @p306) :args ((or @t239 (not @t237)))) % 0.39/0.60 (step @p308 :rule cnf_or_neg :args (@t239 1)) % 0.39/0.60 (step @p309 :rule eq_resolve :premises (@p308 @p307)) % 0.39/0.60 (step @p310 :rule reordering :premises (@p309) :args ((or @t236 @t239))) % 0.39/0.60 (step @p311 :rule chain_m_resolution :premises (@p310 @p297) :args (@t236 @t240 @t241)) % 0.39/0.60 (step @p312 :rule cnf_or_pos :args (@t244)) % 0.39/0.60 (step @p313 :rule reordering :premises (@p312) :args ((or @t237 @t243 (not @t244)))) % 0.39/0.60 (step @p314 :rule chain_m_resolution :premises (@p313 @p311 @p305) :args (@t243 (@list false false) (@list @t236 @t244))) % 0.39/0.60 (step @p315 :rule skolemize :premises (@p314)) % 0.39/0.60 (step @p316 :rule cnf_or_neg :args (@t252 3)) % 0.39/0.60 (step @p317 :rule chain_m_resolution :premises (@p316 @p315) :args ((not @t246) @t240 @t253)) % 0.39/0.60 (step @p318 :rule bool-double-not-elim :args (@t234)) % 0.39/0.60 (step 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(@t250 @t240 @t253)) % 0.39/0.60 (step @p361 :rule cnf_or_pos :args (@t259)) % 0.39/0.60 (step @p362 :rule reordering :premises (@p361) :args ((or @t251 @t249 @t258 (not @t259)))) % 0.39/0.60 (step @p363 :rule chain_m_resolution :premises (@p362 @p360 @p354 @p347) :args (@t258 (@list false false false) (@list @t250 @t248 @t259))) % 0.39/0.60 (step @p364 :rule cnf_or_pos :args (@t261)) % 0.39/0.60 (step @p365 :rule reordering :premises (@p364) :args ((or @t246 @t260 (not @t261)))) % 0.39/0.60 (step @p366 false :rule chain_m_resolution :premises (@p365 @p363 @p324 @p317) :args (false (@list false false true) (@list @t258 @t261 @t246))) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------