%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.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 09:07:16 AM UTC 2026 % Result : Theorem 0.40s 0.59s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n003.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 23:03:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.50 %----Proving TH0 % 0.40/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.59 % SZS status Theorem % 0.40/0.59 % SZS output start Proof % 0.40/0.59 ( % 0.40/0.59 (declare-sort $$unsorted 0) % 0.40/0.59 (declare-sort tptp.d_unsorted 0) % 0.40/0.59 (declare-const tptp.mnot (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.mor (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.mand (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.mimplies (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.mbox_s4 (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.iatom (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.inot (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.iand (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.ior (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.d_unsorted_0 tptp.d_unsorted) % 0.40/0.59 (declare-const tptp.d2unsorted (-> tptp.d_unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.itrue (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.iinvalid (-> (-> $$unsorted Bool) Bool)) % 0.40/0.59 (declare-const tptp.icountersatisfiable (-> (-> $$unsorted Bool) Bool)) % 0.40/0.59 (declare-const tptp.isatisfiable (-> (-> $$unsorted Bool) Bool)) % 0.40/0.59 (declare-const tptp.ivalid (-> (-> $$unsorted Bool) Bool)) % 0.40/0.59 (declare-const tptp.ixor (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.iequiv (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.iimplied (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.iimplies (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) % 0.40/0.59 (define @t1 () (_ tptp.d2unsorted tptp.d_unsorted_0)) % 0.40/0.59 (define @t2 () (@var "W" $$unsorted)) % 0.40/0.59 (define @t3 () (@var "Phi" (-> $$unsorted Bool))) % 0.40/0.59 (define @t4 () (_ @t3 @t2)) % 0.40/0.59 (define @t5 () (@list @t2)) % 0.40/0.59 (define @t6 () (forall @t5 (not @t4))) % 0.40/0.59 (define @t7 () (@list @t3)) % 0.40/0.59 (define @t8 () (forall @t5 @t4)) % 0.40/0.59 (define @t9 () (@var "Bound_variable_754" $$unsorted)) % 0.40/0.59 (define @t10 () (@var "P" (-> $$unsorted Bool))) % 0.40/0.59 (define @t11 () (_ @t10 @t9)) % 0.40/0.59 (define @t12 () (@var "Y" $$unsorted)) % 0.40/0.59 (define @t13 () (_ tptp.irel @t12)) % 0.40/0.59 (define @t14 () (_ @t13 @t9)) % 0.40/0.59 (define @t15 () (not @t14)) % 0.40/0.59 (define @t16 () (@var "Bound_variable_717" $$unsorted)) % 0.40/0.59 (define @t17 () (@var "Q" (-> $$unsorted Bool))) % 0.40/0.59 (define @t18 () (_ @t17 @t16)) % 0.40/0.59 (define @t19 () (_ @t13 @t16)) % 0.40/0.59 (define @t20 () (not @t19)) % 0.40/0.59 (define @t21 () (or @t20 @t18)) % 0.40/0.59 (define @t22 () (@list @t16)) % 0.40/0.59 (define @t23 () (forall @t22 @t21)) % 0.40/0.59 (define @t24 () (not @t23)) % 0.40/0.59 (define @t25 () (or @t24 @t15 @t11)) % 0.40/0.59 (define @t26 () (@var "Bound_variable_747" $$unsorted)) % 0.40/0.59 (define @t27 () (_ @t17 @t26)) % 0.40/0.59 (define @t28 () (_ @t13 @t26)) % 0.40/0.59 (define @t29 () (not @t28)) % 0.40/0.59 (define @t30 () (@var "Bound_variable_709" $$unsorted)) % 0.40/0.59 (define @t31 () (_ @t10 @t30)) % 0.40/0.59 (define @t32 () (_ @t13 @t30)) % 0.40/0.59 (define @t33 () (not @t32)) % 0.40/0.59 (define @t34 () (or @t33 @t31)) % 0.40/0.59 (define @t35 () (@list @t30)) % 0.40/0.59 (define @t36 () (forall @t35 @t34)) % 0.40/0.59 (define @t37 () (not @t36)) % 0.40/0.59 (define @t38 () (or @t37 @t29 @t27)) % 0.40/0.59 (define @t39 () (and @t38 @t25)) % 0.40/0.59 (define @t40 () (@var "Flatten_var_0" $$unsorted)) % 0.40/0.59 (define @t41 () (_ (_ tptp.irel @t40) @t12)) % 0.40/0.59 (define @t42 () (not @t41)) % 0.40/0.59 (define @t43 () (or @t42 @t39)) % 0.40/0.59 (define @t44 () (@list @t12 @t26 @t9)) % 0.40/0.59 (define @t45 () (forall @t44 @t43)) % 0.40/0.59 (define @t46 () (not @t45)) % 0.40/0.59 (define @t47 () (@list @t10 @t17 @t40)) % 0.40/0.59 (define @t48 () (lambda @t47 @t46)) % 0.40/0.59 (define @t49 () (= tptp.ixor @t48)) % 0.40/0.59 (define @t50 () (_ @t10 @t12)) % 0.40/0.59 (define @t51 () (or @t42 @t50)) % 0.40/0.59 (define @t52 () (@list @t12)) % 0.40/0.59 (define @t53 () (forall @t52 @t51)) % 0.40/0.59 (define @t54 () (_ @t17 @t12)) % 0.40/0.59 (define @t55 () (or @t42 @t54)) % 0.40/0.59 (define @t56 () (forall @t52 @t55)) % 0.40/0.59 (define @t57 () (not @t56)) % 0.40/0.59 (define @t58 () (or @t57 @t53)) % 0.40/0.59 (define @t59 () (not @t53)) % 0.40/0.59 (define @t60 () (or @t59 @t56)) % 0.40/0.59 (define @t61 () (and @t60 @t58)) % 0.40/0.59 (define @t62 () (lambda @t47 @t61)) % 0.40/0.59 (define @t63 () (= tptp.iequiv @t62)) % 0.40/0.59 (define @t64 () (_ @t10 @t40)) % 0.40/0.59 (define @t65 () (@list @t10 @t40)) % 0.40/0.59 (define @t66 () (lambda @t65 @t59)) % 0.40/0.59 (define @t67 () (= tptp.inot @t66)) % 0.40/0.59 (define @t68 () (@var "X" $$unsorted)) % 0.40/0.59 (define @t69 () (@var "V" (-> $$unsorted Bool))) % 0.40/0.59 (define @t70 () (@var "U" (-> $$unsorted Bool))) % 0.40/0.59 (define @t71 () (@var "U" $$unsorted)) % 0.40/0.59 (define @t72 () (@var "Y" (-> $$unsorted Bool))) % 0.40/0.59 (define @t73 () (_ @t72 @t71)) % 0.40/0.59 (define @t74 () (@var "X" (-> $$unsorted Bool))) % 0.40/0.59 (define @t75 () (_ @t74 @t71)) % 0.40/0.59 (define @t76 () (@list @t74 @t72 @t71)) % 0.40/0.59 (define @t77 () (@var "DU2" tptp.d_unsorted)) % 0.40/0.59 (define @t78 () (@var "DU1" tptp.d_unsorted)) % 0.40/0.59 (define @t79 () (@var "DU" tptp.d_unsorted)) % 0.40/0.59 (define @t80 () (@list @t79)) % 0.40/0.59 (define @t81 () (@var "__flatten_var_0" $$unsorted)) % 0.40/0.59 (define @t82 () (@list @t10 @t17 @t81)) % 0.40/0.59 (define @t83 () (lambda @t82 (_ (_ tptp.inot (_ (_ tptp.iequiv @t10) @t17)) @t81))) % 0.40/0.59 (define @t84 () (= tptp.ixor @t83)) % 0.40/0.59 (define @t85 () (not @t84)) % 0.40/0.59 (define @t86 () (_ @t10 @t9)) % 0.40/0.59 (define @t87 () (tptp.irel @t12 @t9)) % 0.40/0.59 (define @t88 () (not @t87)) % 0.40/0.59 (define @t89 () (_ @t17 @t16)) % 0.40/0.59 (define @t90 () (tptp.irel @t12 @t16)) % 0.40/0.59 (define @t91 () (not @t90)) % 0.40/0.59 (define @t92 () (not (forall @t22 (or @t91 @t89)))) % 0.40/0.59 (define @t93 () (_ @t17 @t26)) % 0.40/0.59 (define @t94 () (tptp.irel @t12 @t26)) % 0.40/0.59 (define @t95 () (not @t94)) % 0.40/0.59 (define @t96 () (_ @t10 @t30)) % 0.40/0.59 (define @t97 () (tptp.irel @t12 @t30)) % 0.40/0.59 (define @t98 () (not @t97)) % 0.40/0.59 (define @t99 () (not (forall @t35 (or @t98 @t96)))) % 0.40/0.59 (define @t100 () (tptp.irel @t40 @t12)) % 0.40/0.59 (define @t101 () (not @t100)) % 0.40/0.59 (define @t102 () (lambda @t47 (not (forall @t44 (or @t101 (and (or @t99 @t95 @t93) (or @t92 @t88 @t86))))))) % 0.40/0.59 (define @t103 () (@purify @t102)) % 0.40/0.59 (define @t104 () (@var "BOUND_VARIABLE_7811" $$unsorted)) % 0.40/0.59 (define @t105 () (_ @t10 @t104)) % 0.40/0.59 (define @t106 () (not (tptp.irel @t12 @t104))) % 0.40/0.59 (define @t107 () (@var "BOUND_VARIABLE_7774" $$unsorted)) % 0.40/0.59 (define @t108 () (_ @t17 @t107)) % 0.40/0.59 (define @t109 () (not (tptp.irel @t12 @t107))) % 0.40/0.59 (define @t110 () (@list @t107)) % 0.40/0.59 (define @t111 () (forall @t110 (or @t109 @t108))) % 0.40/0.59 (define @t112 () (not @t111)) % 0.40/0.59 (define @t113 () (or @t112 @t106 @t105)) % 0.40/0.59 (define @t114 () (@var "BOUND_VARIABLE_7804" $$unsorted)) % 0.40/0.59 (define @t115 () (_ @t17 @t114)) % 0.40/0.59 (define @t116 () (not (tptp.irel @t12 @t114))) % 0.40/0.59 (define @t117 () (@var "BOUND_VARIABLE_7766" $$unsorted)) % 0.40/0.59 (define @t118 () (_ @t10 @t117)) % 0.40/0.59 (define @t119 () (not (tptp.irel @t12 @t117))) % 0.40/0.59 (define @t120 () (@list @t117)) % 0.40/0.59 (define @t121 () (forall @t120 (or @t119 @t118))) % 0.40/0.59 (define @t122 () (not @t121)) % 0.40/0.59 (define @t123 () (or @t122 @t116 @t115)) % 0.40/0.59 (define @t124 () (and @t123 @t113)) % 0.40/0.59 (define @t125 () (@list @t12 @t114 @t104)) % 0.40/0.59 (define @t126 () (not (forall @t125 (or (not (tptp.irel @t81 @t12)) @t124)))) % 0.40/0.59 (define @t127 () (lambda @t82 @t126)) % 0.40/0.59 (define @t128 () (@purify @t127)) % 0.40/0.59 (define @t129 () (= @t102 @t127)) % 0.40/0.59 (define @t130 () (@list @t40)) % 0.40/0.59 (define @t131 () (or @t106 @t105)) % 0.40/0.59 (define @t132 () (or @t112 @t131)) % 0.40/0.59 (define @t133 () (or @t116 @t115)) % 0.40/0.59 (define @t134 () (or @t122 @t133)) % 0.40/0.59 (define @t135 () (and @t134 @t132)) % 0.40/0.59 (define @t136 () (or @t101 @t135)) % 0.40/0.59 (define @t137 () (forall @t125 @t136)) % 0.40/0.59 (define @t138 () (@list @t114 @t104)) % 0.40/0.59 (define @t139 () (forall @t138 @t136)) % 0.40/0.59 (define @t140 () (@list @t104)) % 0.40/0.59 (define @t141 () (forall @t140 @t131)) % 0.40/0.59 (define @t142 () (@list @t117)) % 0.40/0.59 (define @t143 () (or @t112 @t141)) % 0.40/0.59 (define @t144 () (forall @t140 @t132)) % 0.40/0.59 (define @t145 () (forall @t138 @t132)) % 0.40/0.59 (define @t146 () (@list @t114)) % 0.40/0.59 (define @t147 () (forall @t146 @t133)) % 0.40/0.59 (define @t148 () (@list @t107)) % 0.40/0.59 (define @t149 () (or @t122 @t147)) % 0.40/0.59 (define @t150 () (forall @t146 @t134)) % 0.40/0.59 (define @t151 () (forall @t138 @t134)) % 0.40/0.59 (define @t152 () (and @t151 @t145)) % 0.40/0.59 (define @t153 () (forall @t138 @t135)) % 0.40/0.59 (define @t154 () (or @t101 @t153)) % 0.40/0.59 (define @t155 () (and (or @t122 @t111) (or @t112 @t121))) % 0.40/0.59 (define @t156 () (forall @t120 (or (not (tptp.irel @t40 @t117)) @t118))) % 0.40/0.59 (define @t157 () (forall @t110 (or (not (tptp.irel @t40 @t107)) @t108))) % 0.40/0.59 (define @t158 () (_ @t10 @t12)) % 0.40/0.59 (define @t159 () (forall @t52 (or @t101 @t158))) % 0.40/0.59 (define @t160 () (@list @t12)) % 0.40/0.59 (define @t161 () (_ @t17 @t12)) % 0.40/0.59 (define @t162 () (forall @t52 (or @t101 @t161))) % 0.40/0.59 (define @t163 () (not @t162)) % 0.40/0.59 (define @t164 () (or @t163 @t159)) % 0.40/0.59 (define @t165 () (not @t159)) % 0.40/0.59 (define @t166 () (or @t165 @t162)) % 0.40/0.59 (define @t167 () (and @t166 @t164)) % 0.40/0.59 (define @t168 () (lambda @t130 @t167)) % 0.40/0.59 (define @t169 () (or @t101 (_ @t168 @t12))) % 0.40/0.59 (define @t170 () (forall @t52 @t169)) % 0.40/0.59 (define @t171 () (not @t170)) % 0.40/0.59 (define @t172 () (lambda @t130 @t171)) % 0.40/0.59 (define @t173 () (lambda @t65 @t165)) % 0.40/0.59 (define @t174 () (lambda (@list @t17 @t40) @t167)) % 0.40/0.59 (define @t175 () (_ (lambda @t47 @t167) @t10)) % 0.40/0.59 (define @t176 () (lambda @t82 (_ (_ @t173 (_ @t175 @t17)) @t81))) % 0.40/0.59 (define @t177 () (= @t102 @t176)) % 0.40/0.59 (define @t178 () (or @t92 @t15 @t11)) % 0.40/0.59 (define @t179 () (or @t99 @t29 @t27)) % 0.40/0.59 (define @t180 () (and @t179 @t178)) % 0.40/0.59 (define @t181 () (or @t42 @t180)) % 0.40/0.59 (define @t182 () (@const 0 (-> $$unsorted Bool))) % 0.40/0.59 (define @t183 () (@const 1 (-> $$unsorted Bool))) % 0.40/0.59 (define @t184 () (@const 2 $$unsorted)) % 0.40/0.59 (define @t185 () (not (tptp.irel @t184 @t12))) % 0.40/0.59 (define @t186 () (forall @t125 (or @t185 (and (or (not (forall @t120 (or @t119 (_ @t182 @t117)))) @t116 (_ @t183 @t114)) (or (not (forall @t110 (or @t109 (_ @t183 @t107)))) @t106 (_ @t182 @t104)))))) % 0.40/0.59 (define @t187 () (not @t186)) % 0.40/0.59 (define @t188 () (forall @t44 (or @t185 (and (or (not (forall @t35 (or @t98 (_ @t182 @t30)))) @t95 (_ @t183 @t26)) (or (not (forall @t22 (or @t91 (_ @t183 @t16)))) @t88 (_ @t182 @t9)))))) % 0.40/0.59 (define @t189 () (not @t188)) % 0.40/0.59 (define @t190 () (= (_ @t102 @t182 @t183 @t184) @t189)) % 0.40/0.59 (define @t191 () (_ @t103 @t182 @t183 @t184)) % 0.40/0.59 (define @t192 () (= (_ @t127 @t182 @t183 @t184) @t187)) % 0.40/0.59 (define @t193 () (_ @t128 @t182 @t183 @t184)) % 0.40/0.59 (define @t194 () (= @t193 @t191)) % 0.40/0.59 (define @t195 () (not @t194)) % 0.40/0.59 (define @t196 () (= @t128 @t103)) % 0.40/0.59 (define @t197 () (or @t196 @t195)) % 0.40/0.59 (define @t198 () (= @t189 @t187)) % 0.40/0.59 (define @t199 () (@list true)) % 0.40/0.59 (define @t200 () (@var "BOUND_VARIABLE_8038" $$unsorted)) % 0.40/0.59 (define @t201 () (@var "BOUND_VARIABLE_8035" $$unsorted)) % 0.40/0.59 (define @t202 () (@var "BOUND_VARIABLE_8039" $$unsorted)) % 0.40/0.59 (define @t203 () (@var "BOUND_VARIABLE_8036" $$unsorted)) % 0.40/0.59 (define @t204 () (@var "BOUND_VARIABLE_8037" $$unsorted)) % 0.40/0.59 (define @t205 () (@list @t201 @t203 @t204 @t200 @t202)) % 0.40/0.59 (assume @p1 (and (forall (@list @t71) (exists @t80 (= @t71 (_ tptp.d2unsorted @t79)))) (forall @t80 (= @t79 tptp.d_unsorted_0)) (forall (@list @t78 @t77) (=> (= (_ tptp.d2unsorted @t78) (_ tptp.d2unsorted @t77)) (= @t78 @t77))) (= tptp.mnot (lambda (@list @t74 @t71) (not @t75))) (= tptp.mor (lambda @t76 (or @t75 @t73))) (= tptp.mand (lambda @t76 (and @t75 @t73))) (= tptp.mimplies (lambda (@list @t70 @t69 @t40) (or (not (_ @t70 @t40)) (_ @t69 @t40)))) (= tptp.mbox_s4 (lambda (@list @t10 @t68) (forall @t52 (or (not (_ (_ tptp.irel @t68) @t12)) @t50)))) (= tptp.iatom (lambda @t65 @t64)) @t67 (= tptp.iand (lambda @t47 (and @t64 (_ @t17 @t40)))) (= tptp.ior (lambda @t47 (or @t53 @t56))) (= tptp.iimplies (lambda @t47 @t60)) (= tptp.iimplied (lambda @t47 @t58)) @t63 @t49 (= tptp.ivalid (lambda @t7 @t8)) (= tptp.isatisfiable (lambda @t7 (not @t6))) (= tptp.icountersatisfiable (lambda @t7 (not @t8))) (= tptp.iinvalid (lambda @t7 @t6)) (_ (_ tptp.irel @t1) @t1) (_ tptp.itrue @t1) (not (_ tptp.ifalse @t1)))) % 0.40/0.59 (assume @p2 @t85) % 0.40/0.59 (assume @p3 true) % 0.40/0.59 (step @p4 :rule eq-symm :args (@t103 @t128)) % 0.40/0.59 (step @p5 :rule eq-refl :args (@t127)) % 0.40/0.59 (step @p6 :rule skolem_intro :args (@t128)) % 0.40/0.59 (step @p7 :rule refl :args (@t127)) % 0.40/0.59 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t127 @t128))) % 0.40/0.59 (step @p9 :rule trans :premises (@p8 @p5)) % 0.40/0.59 (step @p10 :rule true_elim :premises (@p9)) % 0.40/0.59 (step @p11 :rule eq-refl :args (@t102)) % 0.40/0.59 (step @p12 :rule skolem_intro :args (@t103)) % 0.40/0.59 (step @p13 :rule refl :args (@t102)) % 0.40/0.59 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t102 @t103))) % 0.40/0.59 (step @p15 :rule trans :premises (@p14 @p11)) % 0.40/0.59 (step @p16 :rule true_elim :premises (@p15)) % 0.40/0.59 (step @p17 :rule cong :premises (@p16 @p10) :args (@t129)) % 0.40/0.59 (step @p18 :rule trans :premises (@p17 @p4)) % 0.40/0.59 (step @p19 :rule cong :premises (@p18) :args ((not @t129))) % 0.40/0.59 (step @p20 :rule beta-reduce :args ((= (_ (lambda @t130 (not (forall @t125 (or @t101 @t124)))) @t81) @t126))) % 0.40/0.59 (step @p21 :rule refl :args (@t81)) % 0.40/0.59 (step @p22 :rule aci_norm :args ((= @t132 @t113))) % 0.40/0.59 (step @p23 :rule aci_norm :args ((= @t134 @t123))) % 0.40/0.59 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t135)) % 0.40/0.59 (step @p25 :rule refl :args (@t101)) % 0.40/0.59 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t136)) % 0.40/0.59 (step @p27 :rule cong :premises (@p26) :args (@t137)) % 0.40/0.59 (step @p28 :rule quant-merge-prenex :args ((= (forall @t52 @t139) @t137))) % 0.40/0.59 (step @p29 :rule alpha_equiv :args (@t141 (@list @t104) @t142)) % 0.40/0.59 (step @p30 :rule refl :args (@t112)) % 0.40/0.59 (step @p31 :rule nary_cong :premises (@p30 @p29) :args (@t143)) % 0.40/0.59 (step @p32 :rule quant-miniscope-or :args ((= @t144 @t143))) % 0.40/0.59 (step @p33 :rule quant-unused-vars :args ((= @t145 @t144))) % 0.40/0.59 (step @p34 :rule trans :premises (@p33 @p32)) % 0.40/0.59 (step @p35 :rule trans :premises (@p34 @p31)) % 0.40/0.59 (step @p36 :rule alpha_equiv :args (@t147 (@list @t114) @t148)) % 0.40/0.59 (step @p37 :rule refl :args (@t122)) % 0.40/0.59 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t149)) % 0.40/0.59 (step @p39 :rule quant-miniscope-or :args ((= @t150 @t149))) % 0.40/0.59 (step @p40 :rule quant-unused-vars :args ((= @t151 @t150))) % 0.40/0.59 (step @p41 :rule trans :premises (@p40 @p39)) % 0.40/0.59 (step @p42 :rule trans :premises (@p41 @p38)) % 0.40/0.59 (step @p43 :rule nary_cong :premises (@p42 @p35) :args (@t152)) % 0.40/0.59 (step @p44 :rule quant-miniscope-and :args ((= @t153 @t152))) % 0.40/0.59 (step @p45 :rule trans :premises (@p44 @p43)) % 0.40/0.59 (step @p46 :rule refl :args (@t101)) % 0.40/0.59 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t154)) % 0.40/0.59 (step @p48 :rule quant-miniscope-or :args ((= @t139 @t154))) % 0.40/0.59 (step @p49 :rule trans :premises (@p48 @p47)) % 0.40/0.59 (step @p50 :rule symm :premises (@p49)) % 0.40/0.59 (step @p51 :rule cong :premises (@p50) :args ((forall @t52 (or @t101 @t155)))) % 0.40/0.59 (step @p52 :rule trans :premises (@p51 @p28)) % 0.40/0.59 (step @p53 :rule trans :premises (@p52 @p27)) % 0.40/0.59 (step @p54 :rule beta-reduce :args ((= (_ (lambda @t130 (and (or (not @t156) @t157) (or (not @t157) @t156))) @t12) @t155))) % 0.40/0.59 (step @p55 :rule refl :args (@t12)) % 0.40/0.59 (step @p56 :rule alpha_equiv :args (@t159 @t160 @t142)) % 0.40/0.59 (step @p57 :rule alpha_equiv :args (@t162 @t160 @t148)) % 0.40/0.59 (step @p58 :rule cong :premises (@p57) :args (@t163)) % 0.40/0.59 (step @p59 :rule nary_cong :premises (@p58 @p56) :args (@t164)) % 0.40/0.59 (step @p60 :rule cong :premises (@p56) :args (@t165)) % 0.40/0.59 (step @p61 :rule nary_cong :premises (@p60 @p57) :args (@t166)) % 0.40/0.59 (step @p62 :rule nary_cong :premises (@p61 @p59) :args (@t167)) % 0.40/0.59 (step @p63 :rule cong :premises (@p62) :args (@t168)) % 0.40/0.59 (step @p64 :rule ho_cong :premises (@p63 @p55)) % 0.40/0.59 (step @p65 :rule trans :premises (@p64 @p54)) % 0.40/0.59 (step @p66 :rule nary_cong :premises (@p25 @p65) :args (@t169)) % 0.40/0.59 (step @p67 :rule cong :premises (@p66) :args (@t170)) % 0.40/0.59 (step @p68 :rule trans :premises (@p67 @p53)) % 0.40/0.59 (step @p69 :rule cong :premises (@p68) :args (@t171)) % 0.40/0.59 (step @p70 :rule cong :premises (@p69) :args (@t172)) % 0.40/0.59 (step @p71 :rule beta-reduce :args ((= (_ @t173 @t168) @t172))) % 0.40/0.59 (step @p72 :rule trans :premises (@p71 @p70)) % 0.40/0.59 (step @p73 :rule beta-reduce :args ((= (_ @t174 @t17) @t168))) % 0.40/0.59 (step @p74 :rule refl :args (@t17)) % 0.40/0.59 (step @p75 :rule beta-reduce :args ((= @t175 @t174))) % 0.40/0.59 (step @p76 :rule ho_cong :premises (@p75 @p74)) % 0.40/0.59 (step @p77 :rule trans :premises (@p76 @p73)) % 0.40/0.59 (step @p78 :rule refl :args (@t173)) % 0.40/0.59 (step @p79 :rule ho_cong :premises (@p78 @p77)) % 0.40/0.59 (step @p80 :rule trans :premises (@p79 @p72)) % 0.40/0.59 (step @p81 :rule ho_cong :premises (@p80 @p21)) % 0.40/0.59 (step @p82 :rule trans :premises (@p81 @p20)) % 0.40/0.59 (step @p83 :rule cong :premises (@p82) :args (@t176)) % 0.40/0.59 (step @p84 :rule cong :premises (@p13 @p83) :args (@t177)) % 0.40/0.59 (step @p85 :rule cong :premises (@p84) :args ((not @t177))) % 0.40/0.59 (step @p86 :rule refl :args (@t10)) % 0.40/0.59 (step @p87 :rule refl :args (@t158)) % 0.40/0.59 (step @p88 :rule refl :args (@t50)) % 0.40/0.59 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t50 @t158))) % 0.40/0.59 (step @p90 :rule symm :premises (@p89)) % 0.40/0.59 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.40/0.59 (step @p92 :rule refl :args (@t100)) % 0.40/0.59 (step @p93 :rule refl :args (@t41)) % 0.40/0.59 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t41 @t100))) % 0.40/0.59 (step @p95 :rule symm :premises (@p94)) % 0.40/0.59 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.40/0.59 (step @p97 :rule cong :premises (@p96) :args (@t42)) % 0.40/0.59 (step @p98 :rule nary_cong :premises (@p97 @p91) :args (@t51)) % 0.40/0.59 (step @p99 :rule cong :premises (@p98) :args (@t53)) % 0.40/0.59 (step @p100 :rule refl :args (@t161)) % 0.40/0.59 (step @p101 :rule refl :args (@t54)) % 0.40/0.59 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t54 @t161))) % 0.40/0.59 (step @p103 :rule symm :premises (@p102)) % 0.40/0.59 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.40/0.59 (step @p105 :rule nary_cong :premises (@p97 @p104) :args (@t55)) % 0.40/0.59 (step @p106 :rule cong :premises (@p105) :args (@t56)) % 0.40/0.59 (step @p107 :rule cong :premises (@p106) :args (@t57)) % 0.40/0.59 (step @p108 :rule nary_cong :premises (@p107 @p99) :args (@t58)) % 0.40/0.59 (step @p109 :rule cong :premises (@p99) :args (@t59)) % 0.40/0.59 (step @p110 :rule nary_cong :premises (@p109 @p106) :args (@t60)) % 0.40/0.59 (step @p111 :rule nary_cong :premises (@p110 @p108) :args (@t61)) % 0.40/0.59 (step @p112 :rule cong :premises (@p111) :args (@t62)) % 0.40/0.59 (step @p113 :rule refl :args (tptp.iequiv)) % 0.40/0.59 (step @p114 :rule cong :premises (@p113 @p112) :args (@t63)) % 0.40/0.59 (step @p115 :rule and_elim :premises (@p1) :args (14)) % 0.40/0.59 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 0.40/0.59 (step @p117 :rule ho_cong :premises (@p116 @p86)) % 0.40/0.59 (step @p118 :rule ho_cong :premises (@p117 @p74)) % 0.40/0.59 (step @p119 :rule cong :premises (@p109) :args (@t66)) % 0.40/0.59 (step @p120 :rule refl :args (tptp.inot)) % 0.40/0.59 (step @p121 :rule cong :premises (@p120 @p119) :args (@t67)) % 0.40/0.59 (step @p122 :rule and_elim :premises (@p1) :args (9)) % 0.40/0.59 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.40/0.59 (step @p124 :rule ho_cong :premises (@p123 @p118)) % 0.40/0.59 (step @p125 :rule ho_cong :premises (@p124 @p21)) % 0.40/0.59 (step @p126 :rule cong :premises (@p125) :args (@t83)) % 0.40/0.59 (step @p127 :rule refl :args (@t86)) % 0.40/0.59 (step @p128 :rule refl :args (@t11)) % 0.40/0.59 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t11 @t86))) % 0.40/0.59 (step @p130 :rule symm :premises (@p129)) % 0.40/0.59 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.40/0.59 (step @p132 :rule refl :args (@t87)) % 0.40/0.59 (step @p133 :rule refl :args (@t14)) % 0.40/0.59 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t14 @t87))) % 0.40/0.59 (step @p135 :rule symm :premises (@p134)) % 0.40/0.59 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.40/0.59 (step @p137 :rule cong :premises (@p136) :args (@t15)) % 0.40/0.59 (step @p138 :rule refl :args (@t92)) % 0.40/0.59 (step @p139 :rule nary_cong :premises (@p138 @p137 @p131) :args (@t178)) % 0.40/0.59 (step @p140 :rule refl :args (@t93)) % 0.40/0.59 (step @p141 :rule refl :args (@t27)) % 0.40/0.59 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t27 @t93))) % 0.40/0.59 (step @p143 :rule symm :premises (@p142)) % 0.40/0.59 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.40/0.59 (step @p145 :rule refl :args (@t94)) % 0.40/0.59 (step @p146 :rule refl :args (@t28)) % 0.40/0.59 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t28 @t94))) % 0.40/0.59 (step @p148 :rule symm :premises (@p147)) % 0.40/0.59 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.40/0.59 (step @p150 :rule cong :premises (@p149) :args (@t29)) % 0.40/0.59 (step @p151 :rule refl :args (@t99)) % 0.40/0.59 (step @p152 :rule nary_cong :premises (@p151 @p150 @p144) :args (@t179)) % 0.40/0.59 (step @p153 :rule nary_cong :premises (@p152 @p139) :args (@t180)) % 0.40/0.59 (step @p154 :rule nary_cong :premises (@p97 @p153) :args (@t181)) % 0.40/0.59 (step @p155 :rule cong :premises (@p154) :args ((forall @t44 @t181))) % 0.40/0.59 (step @p156 :rule refl :args (@t11)) % 0.40/0.59 (step @p157 :rule refl :args (@t15)) % 0.40/0.59 (step @p158 :rule refl :args (@t89)) % 0.40/0.59 (step @p159 :rule refl :args (@t18)) % 0.40/0.59 (step @p160 :rule cong :premises (@p159 @p158) :args ((= @t18 @t89))) % 0.40/0.59 (step @p161 :rule symm :premises (@p160)) % 0.40/0.59 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 0.40/0.59 (step @p163 :rule refl :args (@t90)) % 0.40/0.59 (step @p164 :rule refl :args (@t19)) % 0.40/0.59 (step @p165 :rule cong :premises (@p164 @p163) :args ((= @t19 @t90))) % 0.40/0.59 (step @p166 :rule symm :premises (@p165)) % 0.40/0.59 (step @p167 :rule eq_resolve :premises (@p164 @p166)) % 0.40/0.59 (step @p168 :rule cong :premises (@p167) :args (@t20)) % 0.40/0.59 (step @p169 :rule nary_cong :premises (@p168 @p162) :args (@t21)) % 0.40/0.59 (step @p170 :rule cong :premises (@p169) :args (@t23)) % 0.40/0.59 (step @p171 :rule cong :premises (@p170) :args (@t24)) % 0.40/0.59 (step @p172 :rule nary_cong :premises (@p171 @p157 @p156) :args (@t25)) % 0.40/0.59 (step @p173 :rule refl :args (@t27)) % 0.40/0.59 (step @p174 :rule refl :args (@t29)) % 0.40/0.59 (step @p175 :rule refl :args (@t96)) % 0.40/0.59 (step @p176 :rule refl :args (@t31)) % 0.40/0.59 (step @p177 :rule cong :premises (@p176 @p175) :args ((= @t31 @t96))) % 0.40/0.59 (step @p178 :rule symm :premises (@p177)) % 0.40/0.59 (step @p179 :rule eq_resolve :premises (@p176 @p178)) % 0.40/0.59 (step @p180 :rule refl :args (@t97)) % 0.40/0.59 (step @p181 :rule refl :args (@t32)) % 0.40/0.59 (step @p182 :rule cong :premises (@p181 @p180) :args ((= @t32 @t97))) % 0.40/0.59 (step @p183 :rule symm :premises (@p182)) % 0.40/0.59 (step @p184 :rule eq_resolve :premises (@p181 @p183)) % 0.40/0.59 (step @p185 :rule cong :premises (@p184) :args (@t33)) % 0.40/0.59 (step @p186 :rule nary_cong :premises (@p185 @p179) :args (@t34)) % 0.40/0.59 (step @p187 :rule cong :premises (@p186) :args (@t36)) % 0.40/0.59 (step @p188 :rule cong :premises (@p187) :args (@t37)) % 0.40/0.59 (step @p189 :rule nary_cong :premises (@p188 @p174 @p173) :args (@t38)) % 0.40/0.59 (step @p190 :rule nary_cong :premises (@p189 @p172) :args (@t39)) % 0.40/0.59 (step @p191 :rule refl :args (@t42)) % 0.40/0.59 (step @p192 :rule nary_cong :premises (@p191 @p190) :args (@t43)) % 0.40/0.59 (step @p193 :rule cong :premises (@p192) :args (@t45)) % 0.40/0.59 (step @p194 :rule trans :premises (@p193 @p155)) % 0.40/0.59 (step @p195 :rule cong :premises (@p194) :args (@t46)) % 0.40/0.59 (step @p196 :rule cong :premises (@p195) :args (@t48)) % 0.40/0.59 (step @p197 :rule refl :args (tptp.ixor)) % 0.40/0.59 (step @p198 :rule cong :premises (@p197 @p196) :args (@t49)) % 0.40/0.59 (step @p199 :rule and_elim :premises (@p1) :args (15)) % 0.40/0.59 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 0.40/0.59 (step @p201 :rule cong :premises (@p200 @p126) :args (@t84)) % 0.40/0.59 (step @p202 :rule cong :premises (@p201) :args (@t85)) % 0.40/0.59 (step @p203 :rule trans :premises (@p202 @p85)) % 0.40/0.59 (step @p204 :rule trans :premises (@p203 @p19)) % 0.40/0.59 (step @p205 :rule eq_resolve :premises (@p2 @p204)) % 0.40/0.59 (step @p206 :rule eq-symm :args (@t187 @t189)) % 0.40/0.59 (step @p207 :rule eq-refl :args (@t189)) % 0.40/0.59 (step @p208 :rule refl :args (@t189)) % 0.40/0.59 (step @p209 :rule beta-reduce :args (@t190)) % 0.40/0.59 (step @p210 :rule cong :premises (@p209 @p208) :args (@t190)) % 0.40/0.59 (step @p211 :rule trans :premises (@p210 @p207)) % 0.40/0.59 (step @p212 :rule refl :args (@t184)) % 0.40/0.59 (step @p213 :rule refl :args (@t183)) % 0.40/0.59 (step @p214 :rule refl :args (@t182)) % 0.40/0.59 (step @p215 :rule ho_cong :premises (@p12 @p214 @p213 @p212)) % 0.40/0.59 (step @p216 :rule cong :premises (@p215 @p208) :args ((= @t191 @t189))) % 0.40/0.59 (step @p217 :rule trans :premises (@p216 @p211)) % 0.40/0.59 (step @p218 :rule true_elim :premises (@p217)) % 0.40/0.59 (step @p219 :rule eq-refl :args (@t187)) % 0.40/0.59 (step @p220 :rule refl :args (@t187)) % 0.40/0.59 (step @p221 :rule beta-reduce :args (@t192)) % 0.40/0.59 (step @p222 :rule cong :premises (@p221 @p220) :args (@t192)) % 0.40/0.59 (step @p223 :rule trans :premises (@p222 @p219)) % 0.40/0.59 (step @p224 :rule ho_cong :premises (@p6 @p214 @p213 @p212)) % 0.40/0.59 (step @p225 :rule cong :premises (@p224 @p220) :args ((= @t193 @t187))) % 0.40/0.59 (step @p226 :rule trans :premises (@p225 @p223)) % 0.40/0.59 (step @p227 :rule true_elim :premises (@p226)) % 0.40/0.59 (step @p228 :rule cong :premises (@p227 @p218) :args (@t194)) % 0.40/0.59 (step @p229 :rule trans :premises (@p228 @p206)) % 0.40/0.59 (step @p230 :rule cong :premises (@p229) :args (@t195)) % 0.40/0.59 (step @p231 :rule refl :args (@t196)) % 0.40/0.59 (step @p232 :rule nary_cong :premises (@p231 @p230) :args (@t197)) % 0.40/0.59 ; WARNING: add trust step for TRUST % 0.40/0.59 ; trust TRUST THEORY_LEMMA % 0.40/0.59 (step @p233 :rule trust :premises () :args (@t197)) % 0.40/0.59 (step @p234 :rule eq_resolve :premises (@p233 @p232)) % 0.40/0.59 (step @p235 :rule chain_m_resolution :premises (@p234 @p205) :args ((not @t198) @t199 (@list @t196))) % 0.40/0.59 (step @p236 :rule alpha_equiv :args ((forall (@list @t201 @t203 @t200) (or (not (tptp.irel @t184 @t201)) (and (or (not (forall (@list @t204) (or (not (tptp.irel @t201 @t204)) (_ @t182 @t204)))) (not (tptp.irel @t201 @t203)) (_ @t183 @t203)) (or (not (forall (@list @t202) (or (not (tptp.irel @t201 @t202)) (_ @t183 @t202)))) (not (tptp.irel @t201 @t200)) (_ @t182 @t200))))) @t205 (@list @t12 @t114 @t117 @t104 @t107))) % 0.40/0.59 (step @p237 :rule alpha_equiv :args (@t188 (@list @t12 @t26 @t30 @t9 @t16) @t205)) % 0.40/0.59 (step @p238 :rule trans :premises (@p237 @p236)) % 0.40/0.59 (step @p239 :rule equiv_elim1 :premises (@p238)) % 0.40/0.59 (step @p240 :rule cnf_equiv_neg1 :args (@t198)) % 0.40/0.59 (step @p241 :rule reordering :premises (@p240) :args ((or @t189 @t187 @t198))) % 0.40/0.59 (step @p242 :rule chain_m_resolution :premises (@p241 @p235 @p239) :args (@t189 (@list true false) (@list @t198 @t186))) % 0.40/0.59 (step @p243 :rule equiv_elim2 :premises (@p238)) % 0.40/0.59 (step @p244 :rule chain_m_resolution :premises (@p243 @p242) :args (@t187 @t199 (@list @t188))) % 0.40/0.59 (step @p245 :rule bool-double-not-elim :args (@t186)) % 0.40/0.59 (step @p246 :rule bool-double-not-elim :args (@t188)) % 0.40/0.59 (step @p247 :rule refl :args (@t198)) % 0.40/0.59 (step @p248 :rule nary_cong :premises (@p247 @p246 @p245) :args ((or @t198 (not @t189) (not @t187)))) % 0.40/0.59 (step @p249 :rule cnf_equiv_neg2 :args (@t198)) % 0.40/0.59 (step @p250 :rule eq_resolve :premises (@p249 @p248)) % 0.40/0.59 (step @p251 :rule reordering :premises (@p250) :args ((or @t188 @t186 @t198))) % 0.40/0.59 (step @p252 false :rule chain_m_resolution :premises (@p251 @p244 @p242 @p235) :args (false (@list true true true) (@list @t186 @t188 @t198))) % 0.40/0.59 ) % 0.40/0.59 % SZS output end Proof % 0.40/0.59 % cvc5 exiting %------------------------------------------------------------------------------