%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM022+1 : 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 : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:10:26 AM UTC 2026 % Result : Theorem 0.52s 0.74s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM022+1 : 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 : n020.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 : Mon Jun 1 20:28:55 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.52/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.52/0.74 % SZS status Theorem % 0.52/0.74 % SZS output start Proof % 0.52/0.74 ( % 0.52/0.74 (declare-sort $$unsorted 0) % 0.52/0.74 (declare-const tptp.xa $$unsorted) % 0.52/0.74 (declare-const tptp.xb $$unsorted) % 0.52/0.74 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.aRewritingSystem0 (-> $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.sdtmndtplgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.sdtmndtasgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.xc $$unsorted) % 0.52/0.74 (declare-const tptp.aReductOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.isLocallyConfluent0 (-> $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.isConfluent0 (-> $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.xR $$unsorted) % 0.52/0.74 (declare-const tptp.isTerminating0 (-> $$unsorted Bool)) % 0.52/0.74 (declare-const tptp.aNormalFormOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.74 (define @t1 () (@var "W0" $$unsorted)) % 0.52/0.74 (define @t2 () (tptp.aElement0 @t1)) % 0.52/0.74 (define @t3 () (@list @t1)) % 0.52/0.74 (define @t4 () (tptp.aRewritingSystem0 @t1)) % 0.52/0.74 (define @t5 () (@var "W2" $$unsorted)) % 0.52/0.74 (define @t6 () (tptp.aElement0 @t5)) % 0.52/0.74 (define @t7 () (@var "W1" $$unsorted)) % 0.52/0.74 (define @t8 () (tptp.aReductOfIn0 @t5 @t1 @t7)) % 0.52/0.74 (define @t9 () (@list @t5)) % 0.52/0.74 (define @t10 () (tptp.aRewritingSystem0 @t7)) % 0.52/0.74 (define @t11 () (and @t2 @t10)) % 0.52/0.74 (define @t12 () (@list @t1 @t7)) % 0.52/0.74 (define @t13 () (tptp.aElement0 @t7)) % 0.52/0.74 (define @t14 () (tptp.sdtmndtplgtdt0 @t1 @t7 @t5)) % 0.52/0.74 (define @t15 () (and @t2 @t10 @t6)) % 0.52/0.74 (define @t16 () (@list @t1 @t7 @t5)) % 0.52/0.74 (define @t17 () (@var "W3" $$unsorted)) % 0.52/0.74 (define @t18 () (tptp.aElement0 @t17)) % 0.52/0.74 (define @t19 () (@list @t17)) % 0.52/0.74 (define @t20 () (and @t2 @t10 @t6 @t18)) % 0.52/0.74 (define @t21 () (@list @t1 @t7 @t5 @t17)) % 0.52/0.74 (define @t22 () (tptp.sdtmndtasgtdt0 @t1 @t7 @t5)) % 0.52/0.74 (define @t23 () (= @t22 (or (= @t1 @t5) @t14))) % 0.52/0.74 (define @t24 () (forall @t16 (=> @t15 @t23))) % 0.52/0.74 (define @t25 () (@var "W4" $$unsorted)) % 0.52/0.74 (define @t26 () (exists (@list @t25) (and (tptp.aElement0 @t25) (tptp.sdtmndtasgtdt0 @t5 @t1 @t25) (tptp.sdtmndtasgtdt0 @t17 @t1 @t25)))) % 0.52/0.74 (define @t27 () (@list @t7 @t5 @t17)) % 0.52/0.74 (define @t28 () (tptp.isTerminating0 @t1)) % 0.52/0.74 (define @t29 () (tptp.aReductOfIn0 @t17 @t5 @t7)) % 0.52/0.74 (define @t30 () (exists @t19 @t29)) % 0.52/0.74 (define @t31 () (not @t30)) % 0.52/0.74 (define @t32 () (and @t6 @t22 @t31)) % 0.52/0.74 (define @t33 () (tptp.aNormalFormOfIn0 @t5 @t1 @t7)) % 0.52/0.74 (define @t34 () (= @t33 @t32)) % 0.52/0.74 (define @t35 () (forall @t9 @t34)) % 0.52/0.74 (define @t36 () (=> @t11 @t35)) % 0.52/0.74 (define @t37 () (forall @t12 @t36)) % 0.52/0.74 (define @t38 () (@list @t7)) % 0.52/0.74 (define @t39 () (tptp.aRewritingSystem0 tptp.xR)) % 0.52/0.74 (define @t40 () (tptp.aElement0 tptp.xc)) % 0.52/0.74 (define @t41 () (tptp.aElement0 tptp.xb)) % 0.52/0.74 (define @t42 () (tptp.aElement0 tptp.xa)) % 0.52/0.74 (define @t43 () (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t5)) % 0.52/0.74 (define @t44 () (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR @t1)) % 0.52/0.74 (define @t45 () (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t1)) % 0.52/0.74 (define @t46 () (and @t2 @t45 @t44)) % 0.52/0.74 (define @t47 () (exists @t3 @t46)) % 0.52/0.74 (define @t48 () (tptp.sdtmndtasgtdt0 tptp.xa tptp.xR tptp.xc)) % 0.52/0.74 (define @t49 () (tptp.sdtmndtasgtdt0 tptp.xa tptp.xR tptp.xb)) % 0.52/0.74 (define @t50 () (and @t49 @t48)) % 0.52/0.74 (define @t51 () (=> @t50 @t47)) % 0.52/0.74 (define @t52 () (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR @t17)) % 0.52/0.74 (define @t53 () (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t17)) % 0.52/0.74 (define @t54 () (tptp.aNormalFormOfIn0 @t17 @t5 tptp.xR)) % 0.52/0.74 (define @t55 () (and @t54 @t53 @t52)) % 0.52/0.74 (define @t56 () (exists @t19 @t55)) % 0.52/0.74 (define @t57 () (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t5)) % 0.52/0.74 (define @t58 () (and @t6 @t43 @t57 @t56)) % 0.52/0.74 (define @t59 () (exists @t9 @t58)) % 0.52/0.74 (define @t60 () (tptp.sdtmndtasgtdt0 @t7 tptp.xR tptp.xc)) % 0.52/0.74 (define @t61 () (tptp.aReductOfIn0 @t7 tptp.xa tptp.xR)) % 0.52/0.74 (define @t62 () (and @t13 @t61 @t60 @t59)) % 0.52/0.74 (define @t63 () (exists @t38 @t62)) % 0.52/0.74 (define @t64 () (tptp.sdtmndtasgtdt0 @t1 tptp.xR tptp.xb)) % 0.52/0.74 (define @t65 () (tptp.aReductOfIn0 @t1 tptp.xa tptp.xR)) % 0.52/0.74 (define @t66 () (and @t2 @t65 @t64 @t63)) % 0.52/0.74 (define @t67 () (exists @t3 @t66)) % 0.52/0.74 (define @t68 () (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xc)) % 0.52/0.74 (define @t69 () (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xb)) % 0.52/0.74 (define @t70 () (and @t69 @t68)) % 0.52/0.74 (define @t71 () (=> @t70 @t67)) % 0.52/0.74 (define @t72 () (=> @t71 @t51)) % 0.52/0.74 (define @t73 () (not @t72)) % 0.52/0.74 (define @t74 () (not @t44)) % 0.52/0.74 (define @t75 () (not @t45)) % 0.52/0.74 (define @t76 () (not @t2)) % 0.52/0.74 (define @t77 () (forall @t3 (not @t46))) % 0.52/0.74 (define @t78 () (not @t77)) % 0.52/0.74 (define @t79 () (@var "BOUND_VARIABLE_7864" $$unsorted)) % 0.52/0.74 (define @t80 () (not (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR @t79))) % 0.52/0.74 (define @t81 () (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t79))) % 0.52/0.74 (define @t82 () (@var "BOUND_VARIABLE_7862" $$unsorted)) % 0.52/0.74 (define @t83 () (not (tptp.aNormalFormOfIn0 @t79 @t82 tptp.xR))) % 0.52/0.74 (define @t84 () (@var "BOUND_VARIABLE_7860" $$unsorted)) % 0.52/0.74 (define @t85 () (not (tptp.sdtmndtasgtdt0 @t84 tptp.xR @t82))) % 0.52/0.74 (define @t86 () (not (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t82))) % 0.52/0.74 (define @t87 () (not (tptp.aElement0 @t82))) % 0.52/0.74 (define @t88 () (not (tptp.sdtmndtasgtdt0 @t84 tptp.xR tptp.xc))) % 0.52/0.74 (define @t89 () (not (tptp.aReductOfIn0 @t84 tptp.xa tptp.xR))) % 0.52/0.74 (define @t90 () (not (tptp.aElement0 @t84))) % 0.52/0.74 (define @t91 () (not @t64)) % 0.52/0.74 (define @t92 () (not @t65)) % 0.52/0.74 (define @t93 () (or @t76 @t92 @t91 @t90 @t89 @t88 @t87 @t86 @t85 @t83 @t81 @t80)) % 0.52/0.74 (define @t94 () (or @t90 @t89 @t88 @t87 @t86 @t85 @t83 @t81 @t80)) % 0.52/0.74 (define @t95 () (or @t76 @t92 @t91 @t94)) % 0.52/0.74 (define @t96 () (@list @t1 @t84 @t82 @t79)) % 0.52/0.74 (define @t97 () (forall @t96 @t95)) % 0.52/0.74 (define @t98 () (@list @t84 @t82 @t79)) % 0.52/0.74 (define @t99 () (forall @t98 @t95)) % 0.52/0.74 (define @t100 () (forall @t98 @t94)) % 0.52/0.74 (define @t101 () (@var "BOUND_VARIABLE_7830" $$unsorted)) % 0.52/0.74 (define @t102 () (@var "BOUND_VARIABLE_7828" $$unsorted)) % 0.52/0.74 (define @t103 () (or @t76 @t92 @t91 @t100)) % 0.52/0.74 (define @t104 () (not (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR @t101))) % 0.52/0.74 (define @t105 () (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t101))) % 0.52/0.74 (define @t106 () (not (tptp.aNormalFormOfIn0 @t101 @t102 tptp.xR))) % 0.52/0.74 (define @t107 () (not (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t102))) % 0.52/0.74 (define @t108 () (not (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t102))) % 0.52/0.74 (define @t109 () (not (tptp.aElement0 @t102))) % 0.52/0.74 (define @t110 () (not @t60)) % 0.52/0.74 (define @t111 () (not @t61)) % 0.52/0.74 (define @t112 () (not @t13)) % 0.52/0.74 (define @t113 () (or @t112 @t111 @t110 @t109 @t108 @t107 @t106 @t105 @t104)) % 0.52/0.74 (define @t114 () (@list @t7 @t102 @t101)) % 0.52/0.74 (define @t115 () (forall @t114 @t113)) % 0.52/0.74 (define @t116 () (not @t115)) % 0.52/0.74 (define @t117 () (not @t116)) % 0.52/0.74 (define @t118 () (or @t76 @t92 @t91 @t117)) % 0.52/0.74 (define @t119 () (and @t2 @t65 @t64 @t116)) % 0.52/0.74 (define @t120 () (forall @t3 (not @t119))) % 0.52/0.74 (define @t121 () (not @t120)) % 0.52/0.74 (define @t122 () (or @t109 @t108 @t107 @t106 @t105 @t104)) % 0.52/0.74 (define @t123 () (or @t112 @t111 @t110 @t122)) % 0.52/0.74 (define @t124 () (forall @t114 @t123)) % 0.52/0.74 (define @t125 () (@list @t102 @t101)) % 0.52/0.74 (define @t126 () (forall @t125 @t123)) % 0.52/0.74 (define @t127 () (forall @t125 @t122)) % 0.52/0.74 (define @t128 () (@var "BOUND_VARIABLE_7804" $$unsorted)) % 0.52/0.74 (define @t129 () (or @t112 @t111 @t110 @t127)) % 0.52/0.74 (define @t130 () (not (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR @t128))) % 0.52/0.74 (define @t131 () (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t128))) % 0.52/0.74 (define @t132 () (not (tptp.aNormalFormOfIn0 @t128 @t5 tptp.xR))) % 0.52/0.74 (define @t133 () (not @t57)) % 0.52/0.74 (define @t134 () (not @t43)) % 0.52/0.74 (define @t135 () (not @t6)) % 0.52/0.74 (define @t136 () (or @t135 @t134 @t133 @t132 @t131 @t130)) % 0.52/0.74 (define @t137 () (@list @t5 @t128)) % 0.52/0.74 (define @t138 () (forall @t137 @t136)) % 0.52/0.74 (define @t139 () (not @t138)) % 0.52/0.74 (define @t140 () (not @t139)) % 0.52/0.74 (define @t141 () (or @t112 @t111 @t110 @t140)) % 0.52/0.74 (define @t142 () (and @t13 @t61 @t60 @t139)) % 0.52/0.74 (define @t143 () (forall @t38 (not @t142))) % 0.52/0.74 (define @t144 () (not @t143)) % 0.52/0.74 (define @t145 () (or @t132 @t131 @t130)) % 0.52/0.74 (define @t146 () (or @t135 @t134 @t133 @t145)) % 0.52/0.74 (define @t147 () (forall @t137 @t146)) % 0.52/0.74 (define @t148 () (@list @t128)) % 0.52/0.74 (define @t149 () (forall @t148 @t146)) % 0.52/0.74 (define @t150 () (forall @t148 @t145)) % 0.52/0.74 (define @t151 () (or @t135 @t134 @t133 @t150)) % 0.52/0.74 (define @t152 () (not @t52)) % 0.52/0.74 (define @t153 () (not @t53)) % 0.52/0.74 (define @t154 () (not @t54)) % 0.52/0.74 (define @t155 () (or @t154 @t153 @t152)) % 0.52/0.74 (define @t156 () (forall @t19 @t155)) % 0.52/0.74 (define @t157 () (not @t156)) % 0.52/0.74 (define @t158 () (not @t157)) % 0.52/0.74 (define @t159 () (or @t135 @t134 @t133 @t158)) % 0.52/0.74 (define @t160 () (and @t6 @t43 @t57 @t157)) % 0.52/0.74 (define @t161 () (forall @t9 (not @t160))) % 0.52/0.74 (define @t162 () (not @t161)) % 0.52/0.74 (define @t163 () (forall @t19 (not @t55))) % 0.52/0.74 (define @t164 () (not @t163)) % 0.52/0.74 (define @t165 () (forall @t96 @t93)) % 0.52/0.74 (define @t166 () (@quantifiers_skolemize @t165 3)) % 0.52/0.74 (define @t167 () (not @t10)) % 0.52/0.74 (define @t168 () (or @t76 @t167 @t135 @t23)) % 0.52/0.74 (define @t169 () (or @t76 @t167 @t135)) % 0.52/0.74 (define @t170 () (= tptp.xa tptp.xc)) % 0.52/0.74 (define @t171 () (or @t170 @t68)) % 0.52/0.74 (define @t172 () (= @t48 @t171)) % 0.52/0.74 (define @t173 () (not @t40)) % 0.52/0.74 (define @t174 () (not @t39)) % 0.52/0.74 (define @t175 () (not @t42)) % 0.52/0.74 (define @t176 () (or @t175 @t174 @t173 @t172)) % 0.52/0.74 (define @t177 () (@list false false false false)) % 0.52/0.74 (define @t178 () (not @t48)) % 0.52/0.74 (define @t179 () (@list false false)) % 0.52/0.74 (define @t180 () (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR tptp.xb)) % 0.52/0.74 (define @t181 () (or (= tptp.xc tptp.xb) @t180)) % 0.52/0.74 (define @t182 () (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR tptp.xb)) % 0.52/0.74 (define @t183 () (= @t182 @t181)) % 0.52/0.74 (define @t184 () (not @t41)) % 0.52/0.74 (define @t185 () (or @t173 @t174 @t184 @t183)) % 0.52/0.74 (define @t186 () (forall @t16 @t168)) % 0.52/0.74 (define @t187 () (or (= tptp.xb tptp.xc) @t180)) % 0.52/0.74 (define @t188 () (= @t182 @t187)) % 0.52/0.74 (define @t189 () (or @t173 @t174 @t184 @t188)) % 0.52/0.74 (define @t190 () (@list false)) % 0.52/0.74 (define @t191 () (@list @t186)) % 0.52/0.74 (define @t192 () (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR tptp.xb)) % 0.52/0.74 (define @t193 () (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR tptp.xb)) % 0.52/0.74 (define @t194 () (or (= tptp.xb tptp.xb) @t193)) % 0.52/0.74 (define @t195 () (= @t192 @t194)) % 0.52/0.74 (define @t196 () (or @t184 @t174 @t184 @t195)) % 0.52/0.74 (define @t197 () (or @t184 @t174 @t184 @t192)) % 0.52/0.74 (define @t198 () (@list false false false)) % 0.52/0.74 (define @t199 () (not @t182)) % 0.52/0.74 (define @t200 () (not @t192)) % 0.52/0.74 (define @t201 () (or @t184 @t200 @t199)) % 0.52/0.74 (define @t202 () (not @t187)) % 0.52/0.74 (define @t203 () (@list true false)) % 0.52/0.74 (define @t204 () (not @t180)) % 0.52/0.74 (define @t205 () (@list true)) % 0.52/0.74 (define @t206 () (= tptp.xa tptp.xb)) % 0.52/0.74 (define @t207 () (or @t206 @t69)) % 0.52/0.74 (define @t208 () (= @t49 @t207)) % 0.52/0.74 (define @t209 () (or @t175 @t174 @t184 @t208)) % 0.52/0.74 (define @t210 () (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR tptp.xc)) % 0.52/0.74 (define @t211 () (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR tptp.xc)) % 0.52/0.74 (define @t212 () (or (= tptp.xc tptp.xc) @t211)) % 0.52/0.74 (define @t213 () (= @t210 @t212)) % 0.52/0.74 (define @t214 () (or @t173 @t174 @t173 @t213)) % 0.52/0.74 (define @t215 () (or @t173 @t174 @t173 @t210)) % 0.52/0.74 (define @t216 () (not @t210)) % 0.52/0.74 (define @t217 () (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR tptp.xc)) % 0.52/0.74 (define @t218 () (not @t217)) % 0.52/0.74 (define @t219 () (or @t173 @t218 @t216)) % 0.52/0.74 (define @t220 () (not @t206)) % 0.52/0.74 (define @t221 () (and @t218 @t206 @t48)) % 0.52/0.74 (define @t222 () (@list false true)) % 0.52/0.74 (define @t223 () (not @t170)) % 0.52/0.74 (define @t224 () (not @t69)) % 0.52/0.74 (define @t225 () (not @t165)) % 0.52/0.74 (define @t226 () (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR @t166)) % 0.52/0.74 (define @t227 () (not @t226)) % 0.52/0.74 (define @t228 () (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t166)) % 0.52/0.74 (define @t229 () (not @t228)) % 0.52/0.74 (define @t230 () (@quantifiers_skolemize @t165 2)) % 0.52/0.74 (define @t231 () (tptp.aNormalFormOfIn0 @t166 @t230 tptp.xR)) % 0.52/0.74 (define @t232 () (not @t231)) % 0.52/0.74 (define @t233 () (@quantifiers_skolemize @t165 1)) % 0.52/0.74 (define @t234 () (@quantifiers_skolemize @t165 0)) % 0.52/0.74 (define @t235 () (tptp.aElement0 @t230)) % 0.52/0.74 (define @t236 () (not @t235)) % 0.52/0.74 (define @t237 () (or (not (tptp.aElement0 @t234)) (not (tptp.aReductOfIn0 @t234 tptp.xa tptp.xR)) (not (tptp.sdtmndtasgtdt0 @t234 tptp.xR tptp.xb)) (not (tptp.aElement0 @t233)) (not (tptp.aReductOfIn0 @t233 tptp.xa tptp.xR)) (not (tptp.sdtmndtasgtdt0 @t233 tptp.xR tptp.xc)) @t236 (not (tptp.sdtmndtasgtdt0 @t234 tptp.xR @t230)) (not (tptp.sdtmndtasgtdt0 @t233 tptp.xR @t230)) @t232 @t229 @t227)) % 0.52/0.74 (define @t238 () (not @t237)) % 0.52/0.74 (define @t239 () (@list @t237)) % 0.52/0.74 (define @t240 () (tptp.aElement0 @t166)) % 0.52/0.74 (define @t241 () (not @t240)) % 0.52/0.74 (define @t242 () (or @t241 @t229 @t227)) % 0.52/0.74 (define @t243 () (@var "BOUND_VARIABLE_7724" $$unsorted)) % 0.52/0.74 (define @t244 () (= (tptp.aNormalFormOfIn0 @t243 @t1 @t7) (and (tptp.aElement0 @t243) (tptp.sdtmndtasgtdt0 @t1 @t7 @t243) (forall @t19 (not (tptp.aReductOfIn0 @t17 @t243 @t7)))))) % 0.52/0.74 (define @t245 () (or @t76 @t167 @t244)) % 0.52/0.74 (define @t246 () (@list @t243)) % 0.52/0.74 (define @t247 () (forall @t246 @t245)) % 0.52/0.74 (define @t248 () (forall @t246 @t244)) % 0.52/0.74 (define @t249 () (or @t76 @t167 @t248)) % 0.52/0.74 (define @t250 () (forall @t19 (not @t29))) % 0.52/0.74 (define @t251 () (forall @t9 (= @t33 (and @t6 @t22 @t250)))) % 0.52/0.74 (define @t252 () (or @t76 @t167 @t251)) % 0.52/0.74 (define @t253 () (and @t240 (tptp.sdtmndtasgtdt0 @t230 tptp.xR @t166) (forall @t19 (not (tptp.aReductOfIn0 @t17 @t166 tptp.xR))))) % 0.52/0.74 (define @t254 () (= @t231 @t253)) % 0.52/0.74 (define @t255 () (or @t236 @t174 @t254)) % 0.52/0.74 (assume @p1 (forall @t3 (=> @t2 true))) % 0.52/0.74 (assume @p2 (forall @t3 (=> @t4 true))) % 0.52/0.74 (assume @p3 (forall @t12 (=> @t11 (forall @t9 (=> @t8 @t6))))) % 0.52/0.74 (assume @p4 (forall @t12 (=> (and @t2 @t13) (=> (tptp.iLess0 @t1 @t7) true)))) % 0.52/0.74 (assume @p5 (forall @t16 (=> @t15 (=> @t14 true)))) % 0.52/0.74 (assume @p6 (forall @t16 (=> @t15 (= @t14 (or @t8 (exists @t19 (and @t18 (tptp.aReductOfIn0 @t17 @t1 @t7) (tptp.sdtmndtplgtdt0 @t17 @t7 @t5)))))))) % 0.52/0.74 (assume @p7 (forall @t21 (=> @t20 (=> (and @t14 (tptp.sdtmndtplgtdt0 @t5 @t7 @t17)) (tptp.sdtmndtplgtdt0 @t1 @t7 @t17))))) % 0.52/0.74 (assume @p8 @t24) % 0.52/0.74 (assume @p9 (forall @t21 (=> @t20 (=> (and @t22 (tptp.sdtmndtasgtdt0 @t5 @t7 @t17)) (tptp.sdtmndtasgtdt0 @t1 @t7 @t17))))) % 0.52/0.74 (assume @p10 (forall @t3 (=> @t4 (= (tptp.isConfluent0 @t1) (forall @t27 (=> (and @t13 @t6 @t18 (tptp.sdtmndtasgtdt0 @t7 @t1 @t5) (tptp.sdtmndtasgtdt0 @t7 @t1 @t17)) @t26)))))) % 0.52/0.74 (assume @p11 (forall @t3 (=> @t4 (= (tptp.isLocallyConfluent0 @t1) (forall @t27 (=> (and @t13 @t6 @t18 (tptp.aReductOfIn0 @t5 @t7 @t1) (tptp.aReductOfIn0 @t17 @t7 @t1)) @t26)))))) % 0.52/0.74 (assume @p12 (forall @t3 (=> @t4 (= @t28 (forall (@list @t7 @t5) (=> (and @t13 @t6) (=> (tptp.sdtmndtplgtdt0 @t7 @t1 @t5) (tptp.iLess0 @t5 @t7)))))))) % 0.52/0.74 (assume @p13 @t37) % 0.52/0.74 (assume @p14 (forall @t3 (=> (and @t4 @t28) (forall @t38 (=> @t13 (exists @t9 (tptp.aNormalFormOfIn0 @t5 @t7 @t1))))))) % 0.52/0.74 (assume @p15 @t39) % 0.52/0.74 (assume @p16 (and (tptp.isLocallyConfluent0 tptp.xR) (tptp.isTerminating0 tptp.xR))) % 0.52/0.74 (assume @p17 (and @t42 @t41 @t40)) % 0.52/0.74 (assume @p18 (forall @t16 (=> (and @t2 @t13 @t6 (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t7) @t43) (=> (tptp.iLess0 @t1 tptp.xa) (exists @t19 (and @t18 (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t17) (tptp.sdtmndtasgtdt0 @t5 tptp.xR @t17))))))) % 0.52/0.74 (assume @p19 @t73) % 0.52/0.74 (assume @p20 true) % 0.52/0.74 (step @p21 :rule aci_norm :args ((= (or @t76 (or @t75 @t74)) (or @t76 @t75 @t74)))) % 0.52/0.74 (step @p22 :rule bool-and-de-morgan :args (@t45 @t44 true)) % 0.52/0.74 (step @p23 :rule refl :args (@t76)) % 0.52/0.74 (step @p24 :rule nary_cong :premises (@p23 @p22) :args ((or @t76 (not (and @t45 @t44))))) % 0.52/0.74 (step @p25 :rule bool-and-de-morgan :args (@t2 @t45 (and @t44))) % 0.52/0.74 (step @p26 :rule trans :premises (@p25 @p24)) % 0.52/0.74 (step @p27 :rule trans :premises (@p26 @p21)) % 0.52/0.74 (step @p28 :rule cong :premises (@p27) :args (@t77)) % 0.52/0.74 (step @p29 :rule cong :premises (@p28) :args (@t78)) % 0.52/0.74 (step @p30 :rule exists-elim :args ((= @t47 @t78))) % 0.52/0.74 (step @p31 :rule trans :premises (@p30 @p29)) % 0.52/0.74 (step @p32 :rule refl :args (@t50)) % 0.52/0.74 (step @p33 :rule cong :premises (@p32 @p31) :args (@t51)) % 0.52/0.74 (step @p34 :rule aci_norm :args ((= @t95 @t93))) % 0.52/0.74 (step @p35 :rule cong :premises (@p34) :args (@t97)) % 0.52/0.74 (step @p36 :rule quant-merge-prenex :args ((= (forall @t3 @t99) @t97))) % 0.52/0.74 (step @p37 :rule alpha_equiv :args (@t100 (@list @t84 @t82 @t79) (@list @t7 @t102 @t101))) % 0.52/0.74 (step @p38 :rule refl :args (@t91)) % 0.52/0.74 (step @p39 :rule refl :args (@t92)) % 0.52/0.74 (step @p40 :rule nary_cong :premises (@p23 @p39 @p38 @p37) :args (@t103)) % 0.52/0.74 (step @p41 :rule quant-miniscope-or :args ((= @t99 @t103))) % 0.52/0.74 (step @p42 :rule trans :premises (@p41 @p40)) % 0.52/0.74 (step @p43 :rule symm :premises (@p42)) % 0.52/0.74 (step @p44 :rule cong :premises (@p43) :args ((forall @t3 (or @t76 @t92 @t91 @t115)))) % 0.52/0.74 (step @p45 :rule trans :premises (@p44 @p36)) % 0.52/0.74 (step @p46 :rule trans :premises (@p45 @p35)) % 0.52/0.74 (step @p47 :rule bool-double-not-elim :args (@t115)) % 0.52/0.74 (step @p48 :rule nary_cong :premises (@p23 @p39 @p38 @p47) :args (@t118)) % 0.52/0.74 (step @p49 :rule aci_norm :args ((= (or @t76 (or @t92 (or @t91 @t117))) @t118))) % 0.52/0.74 (step @p50 :rule trans :premises (@p49 @p48)) % 0.52/0.74 (step @p51 :rule bool-and-de-morgan :args (@t64 @t116 true)) % 0.52/0.74 (step @p52 :rule nary_cong :premises (@p39 @p51) :args ((or @t92 (not (and @t64 @t116))))) % 0.52/0.74 (step @p53 :rule bool-and-de-morgan :args (@t65 @t64 (and @t116))) % 0.52/0.74 (step @p54 :rule trans :premises (@p53 @p52)) % 0.52/0.74 (step @p55 :rule nary_cong :premises (@p23 @p54) :args ((or @t76 (not (and @t65 @t64 @t116))))) % 0.52/0.74 (step @p56 :rule bool-and-de-morgan :args (@t2 @t65 (and @t64 @t116))) % 0.52/0.74 (step @p57 :rule trans :premises (@p56 @p55)) % 0.52/0.74 (step @p58 :rule trans :premises (@p57 @p50)) % 0.52/0.74 (step @p59 :rule cong :premises (@p58) :args (@t120)) % 0.52/0.74 (step @p60 :rule trans :premises (@p59 @p46)) % 0.52/0.74 (step @p61 :rule cong :premises (@p60) :args (@t121)) % 0.52/0.74 (step @p62 :rule exists-elim :args ((= (exists @t3 @t119) @t121))) % 0.52/0.74 (step @p63 :rule trans :premises (@p62 @p61)) % 0.52/0.74 (step @p64 :rule aci_norm :args ((= @t123 @t113))) % 0.52/0.74 (step @p65 :rule cong :premises (@p64) :args (@t124)) % 0.52/0.74 (step @p66 :rule quant-merge-prenex :args ((= (forall @t38 @t126) @t124))) % 0.52/0.74 (step @p67 :rule alpha_equiv :args (@t127 (@list @t102 @t101) (@list @t5 @t128))) % 0.52/0.74 (step @p68 :rule refl :args (@t110)) % 0.52/0.74 (step @p69 :rule refl :args (@t111)) % 0.52/0.74 (step @p70 :rule refl :args (@t112)) % 0.52/0.74 (step @p71 :rule nary_cong :premises (@p70 @p69 @p68 @p67) :args (@t129)) % 0.52/0.74 (step @p72 :rule quant-miniscope-or :args ((= @t126 @t129))) % 0.52/0.74 (step @p73 :rule trans :premises (@p72 @p71)) % 0.52/0.74 (step @p74 :rule symm :premises (@p73)) % 0.52/0.74 (step @p75 :rule cong :premises (@p74) :args ((forall @t38 (or @t112 @t111 @t110 @t138)))) % 0.52/0.74 (step @p76 :rule trans :premises (@p75 @p66)) % 0.52/0.74 (step @p77 :rule trans :premises (@p76 @p65)) % 0.52/0.74 (step @p78 :rule bool-double-not-elim :args (@t138)) % 0.52/0.74 (step @p79 :rule nary_cong :premises (@p70 @p69 @p68 @p78) :args (@t141)) % 0.52/0.74 (step @p80 :rule aci_norm :args ((= (or @t112 (or @t111 (or @t110 @t140))) @t141))) % 0.52/0.74 (step @p81 :rule trans :premises (@p80 @p79)) % 0.52/0.74 (step @p82 :rule bool-and-de-morgan :args (@t60 @t139 true)) % 0.52/0.74 (step @p83 :rule nary_cong :premises (@p69 @p82) :args ((or @t111 (not (and @t60 @t139))))) % 0.52/0.74 (step @p84 :rule bool-and-de-morgan :args (@t61 @t60 (and @t139))) % 0.52/0.74 (step @p85 :rule trans :premises (@p84 @p83)) % 0.52/0.74 (step @p86 :rule nary_cong :premises (@p70 @p85) :args ((or @t112 (not (and @t61 @t60 @t139))))) % 0.52/0.74 (step @p87 :rule bool-and-de-morgan :args (@t13 @t61 (and @t60 @t139))) % 0.52/0.74 (step @p88 :rule trans :premises (@p87 @p86)) % 0.52/0.74 (step @p89 :rule trans :premises (@p88 @p81)) % 0.52/0.74 (step @p90 :rule cong :premises (@p89) :args (@t143)) % 0.52/0.74 (step @p91 :rule trans :premises (@p90 @p77)) % 0.52/0.74 (step @p92 :rule cong :premises (@p91) :args (@t144)) % 0.52/0.74 (step @p93 :rule exists-elim :args ((= (exists @t38 @t142) @t144))) % 0.52/0.74 (step @p94 :rule trans :premises (@p93 @p92)) % 0.52/0.74 (step @p95 :rule aci_norm :args ((= @t146 @t136))) % 0.52/0.74 (step @p96 :rule cong :premises (@p95) :args (@t147)) % 0.52/0.74 (step @p97 :rule quant-merge-prenex :args ((= (forall @t9 @t149) @t147))) % 0.52/0.74 (step @p98 :rule alpha_equiv :args (@t150 (@list @t128) (@list @t17))) % 0.52/0.74 (step @p99 :rule refl :args (@t133)) % 0.52/0.74 (step @p100 :rule refl :args (@t134)) % 0.52/0.74 (step @p101 :rule refl :args (@t135)) % 0.52/0.74 (step @p102 :rule nary_cong :premises (@p101 @p100 @p99 @p98) :args (@t151)) % 0.52/0.74 (step @p103 :rule quant-miniscope-or :args ((= @t149 @t151))) % 0.52/0.74 (step @p104 :rule trans :premises (@p103 @p102)) % 0.52/0.74 (step @p105 :rule symm :premises (@p104)) % 0.52/0.74 (step @p106 :rule cong :premises (@p105) :args ((forall @t9 (or @t135 @t134 @t133 @t156)))) % 0.52/0.74 (step @p107 :rule trans :premises (@p106 @p97)) % 0.52/0.74 (step @p108 :rule trans :premises (@p107 @p96)) % 0.52/0.74 (step @p109 :rule bool-double-not-elim :args (@t156)) % 0.52/0.74 (step @p110 :rule nary_cong :premises (@p101 @p100 @p99 @p109) :args (@t159)) % 0.52/0.74 (step @p111 :rule aci_norm :args ((= (or @t135 (or @t134 (or @t133 @t158))) @t159))) % 0.52/0.74 (step @p112 :rule trans :premises (@p111 @p110)) % 0.52/0.74 (step @p113 :rule bool-and-de-morgan :args (@t57 @t157 true)) % 0.52/0.74 (step @p114 :rule nary_cong :premises (@p100 @p113) :args ((or @t134 (not (and @t57 @t157))))) % 0.52/0.74 (step @p115 :rule bool-and-de-morgan :args (@t43 @t57 (and @t157))) % 0.52/0.74 (step @p116 :rule trans :premises (@p115 @p114)) % 0.52/0.74 (step @p117 :rule nary_cong :premises (@p101 @p116) :args ((or @t135 (not (and @t43 @t57 @t157))))) % 0.52/0.74 (step @p118 :rule bool-and-de-morgan :args (@t6 @t43 (and @t57 @t157))) % 0.52/0.74 (step @p119 :rule trans :premises (@p118 @p117)) % 0.52/0.74 (step @p120 :rule trans :premises (@p119 @p112)) % 0.52/0.74 (step @p121 :rule cong :premises (@p120) :args (@t161)) % 0.52/0.74 (step @p122 :rule trans :premises (@p121 @p108)) % 0.52/0.74 (step @p123 :rule cong :premises (@p122) :args (@t162)) % 0.52/0.74 (step @p124 :rule exists-elim :args ((= (exists @t9 @t160) @t162))) % 0.52/0.74 (step @p125 :rule trans :premises (@p124 @p123)) % 0.52/0.74 (step @p126 :rule aci_norm :args ((= (or @t154 (or @t153 @t152)) @t155))) % 0.52/0.74 (step @p127 :rule bool-and-de-morgan :args (@t53 @t52 true)) % 0.52/0.74 (step @p128 :rule refl :args (@t154)) % 0.52/0.74 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or @t154 (not (and @t53 @t52))))) % 0.52/0.74 (step @p130 :rule bool-and-de-morgan :args (@t54 @t53 (and @t52))) % 0.52/0.74 (step @p131 :rule trans :premises (@p130 @p129)) % 0.52/0.74 (step @p132 :rule trans :premises (@p131 @p126)) % 0.52/0.74 (step @p133 :rule cong :premises (@p132) :args (@t163)) % 0.52/0.74 (step @p134 :rule cong :premises (@p133) :args (@t164)) % 0.52/0.74 (step @p135 :rule exists-elim :args ((= @t56 @t164))) % 0.52/0.74 (step @p136 :rule trans :premises (@p135 @p134)) % 0.52/0.74 (step @p137 :rule refl :args (@t57)) % 0.52/0.74 (step @p138 :rule refl :args (@t43)) % 0.52/0.74 (step @p139 :rule refl :args (@t6)) % 0.52/0.74 (step @p140 :rule nary_cong :premises (@p139 @p138 @p137 @p136) :args (@t58)) % 0.52/0.74 (step @p141 :rule cong :premises (@p140) :args (@t59)) % 0.52/0.74 (step @p142 :rule trans :premises (@p141 @p125)) % 0.52/0.74 (step @p143 :rule refl :args (@t60)) % 0.52/0.74 (step @p144 :rule refl :args (@t61)) % 0.52/0.74 (step @p145 :rule refl :args (@t13)) % 0.52/0.74 (step @p146 :rule nary_cong :premises (@p145 @p144 @p143 @p142) :args (@t62)) % 0.52/0.74 (step @p147 :rule cong :premises (@p146) :args (@t63)) % 0.52/0.74 (step @p148 :rule trans :premises (@p147 @p94)) % 0.52/0.74 (step @p149 :rule refl :args (@t64)) % 0.52/0.74 (step @p150 :rule refl :args (@t65)) % 0.52/0.74 (step @p151 :rule refl :args (@t2)) % 0.52/0.74 (step @p152 :rule nary_cong :premises (@p151 @p150 @p149 @p148) :args (@t66)) % 0.52/0.74 (step @p153 :rule cong :premises (@p152) :args (@t67)) % 0.52/0.74 (step @p154 :rule trans :premises (@p153 @p63)) % 0.52/0.74 (step @p155 :rule refl :args (@t70)) % 0.52/0.74 (step @p156 :rule cong :premises (@p155 @p154) :args (@t71)) % 0.52/0.74 (step @p157 :rule cong :premises (@p156 @p33) :args (@t72)) % 0.52/0.74 (step @p158 :rule cong :premises (@p157) :args (@t73)) % 0.52/0.74 (step @p159 :rule eq_resolve :premises (@p19 @p158)) % 0.52/0.74 (step @p160 :rule not_implies_elim2 :premises (@p159)) % 0.52/0.74 (step @p161 :rule not_implies_elim2 :premises (@p160)) % 0.52/0.74 (step @p162 :rule not_not_elim :premises (@p161)) % 0.52/0.74 (step @p163 :rule instantiate :premises (@p162) :args ((@list @t166))) % 0.52/0.74 (step @p164 :rule aci_norm :args ((= (or @t169 @t23) @t168))) % 0.52/0.74 (step @p165 :rule refl :args (@t23)) % 0.52/0.74 (step @p166 :rule aci_norm :args ((= (or @t76 (or @t167 @t135)) @t169))) % 0.52/0.74 (step @p167 :rule bool-and-de-morgan :args (@t10 @t6 true)) % 0.52/0.74 (step @p168 :rule nary_cong :premises (@p23 @p167) :args ((or @t76 (not (and @t10 @t6))))) % 0.52/0.74 (step @p169 :rule bool-and-de-morgan :args (@t2 @t10 (and @t6))) % 0.52/0.74 (step @p170 :rule trans :premises (@p169 @p168)) % 0.52/0.74 (step @p171 :rule trans :premises (@p170 @p166)) % 0.52/0.74 (step @p172 :rule nary_cong :premises (@p171 @p165) :args ((or (not @t15) @t23))) % 0.52/0.74 (step @p173 :rule trans :premises (@p172 @p164)) % 0.52/0.74 (step @p174 :rule bool-impl-elim :args (@t15 @t23)) % 0.52/0.74 (step @p175 :rule trans :premises (@p174 @p173)) % 0.52/0.74 (step @p176 :rule cong :premises (@p175) :args (@t24)) % 0.52/0.74 (step @p177 :rule eq_resolve :premises (@p8 @p176)) % 0.52/0.74 (step @p178 :rule instantiate :premises (@p177) :args ((@list tptp.xa tptp.xR tptp.xc))) % 0.52/0.74 (step @p179 :rule and_elim :premises (@p17) :args (2)) % 0.52/0.74 (step @p180 :rule and_elim :premises (@p17) :args (0)) % 0.52/0.74 (step @p181 :rule cnf_or_pos :args (@t176)) % 0.52/0.74 (step @p182 :rule reordering :premises (@p181) :args ((or @t174 @t175 @t173 @t172 (not @t176)))) % 0.52/0.74 (step @p183 :rule chain_m_resolution :premises (@p182 @p15 @p180 @p179 @p178) :args (@t172 @t177 (@list @t39 @t42 @t40 @t176))) % 0.52/0.74 (step @p184 :rule not_implies_elim1 :premises (@p160)) % 0.52/0.74 (step @p185 :rule and_elim :premises (@p184) :args (1)) % 0.52/0.74 (step @p186 :rule cnf_equiv_pos1 :args (@t172)) % 0.52/0.74 (step @p187 :rule reordering :premises (@p186) :args ((or @t178 @t171 (not @t172)))) % 0.52/0.74 (step @p188 :rule chain_m_resolution :premises (@p187 @p185 @p183) :args (@t171 @t179 (@list @t48 @t172))) % 0.52/0.74 (step @p189 :rule refl :args (@t180)) % 0.52/0.74 (step @p190 :rule eq-symm :args (tptp.xc tptp.xb)) % 0.52/0.74 (step @p191 :rule nary_cong :premises (@p190 @p189) :args (@t181)) % 0.52/0.74 (step @p192 :rule refl :args (@t182)) % 0.52/0.74 (step @p193 :rule cong :premises (@p192 @p191) :args (@t183)) % 0.52/0.74 (step @p194 :rule refl :args (@t184)) % 0.52/0.74 (step @p195 :rule refl :args (@t174)) % 0.52/0.74 (step @p196 :rule refl :args (@t173)) % 0.52/0.74 (step @p197 :rule nary_cong :premises (@p196 @p195 @p194 @p193) :args (@t185)) % 0.52/0.74 (step @p198 :rule refl :args (@t186)) % 0.52/0.74 (step @p199 :rule cong :premises (@p198 @p197) :args ((=> @t186 @t185))) % 0.52/0.74 (assume-push @p425 @t186) % 0.52/0.74 (step @p201 :rule instantiate :premises (@p177) :args ((@list tptp.xc tptp.xR tptp.xb))) % 0.52/0.74 (step-pop @p426 :rule scope :premises (@p201)) % 0.52/0.74 (step @p202 :rule process_scope :premises (@p426) :args (@t185)) % 0.52/0.74 (step @p204 :rule eq_resolve :premises (@p202 @p199)) % 0.52/0.74 (step @p205 :rule implies_elim :premises (@p204)) % 0.52/0.74 (step @p206 :rule chain_m_resolution :premises (@p205 @p177) :args (@t189 @t190 @t191)) % 0.52/0.74 (step @p207 :rule and_elim :premises (@p17) :args (1)) % 0.52/0.74 (step @p208 :rule cnf_or_pos :args (@t189)) % 0.52/0.74 (step @p209 :rule reordering :premises (@p208) :args ((or @t174 @t184 @t173 @t188 (not @t189)))) % 0.52/0.74 (step @p210 :rule chain_m_resolution :premises (@p209 @p15 @p207 @p179 @p206) :args (@t188 @t177 (@list @t39 @t41 @t40 @t189))) % 0.52/0.74 (step @p211 :rule instantiate :premises (@p162) :args ((@list tptp.xb))) % 0.52/0.74 (step @p212 :rule bool-eq-true :args (@t192)) % 0.52/0.74 (step @p213 :rule absorb :args ((= (or true @t193) true))) % 0.52/0.74 (step @p214 :rule refl :args (@t193)) % 0.52/0.74 (step @p215 :rule eq-refl :args (tptp.xb)) % 0.52/0.74 (step @p216 :rule nary_cong :premises (@p215 @p214) :args (@t194)) % 0.52/0.74 (step @p217 :rule trans :premises (@p216 @p213)) % 0.52/0.74 (step @p218 :rule refl :args (@t192)) % 0.52/0.74 (step @p219 :rule cong :premises (@p218 @p217) :args (@t195)) % 0.52/0.74 (step @p220 :rule trans :premises (@p219 @p212)) % 0.52/0.74 (step @p221 :rule nary_cong :premises (@p194 @p195 @p194 @p220) :args (@t196)) % 0.52/0.74 (step @p222 :rule cong :premises (@p198 @p221) :args ((=> @t186 @t196))) % 0.52/0.74 (assume-push @p427 @t186) % 0.52/0.74 (step @p224 :rule instantiate :premises (@p177) :args ((@list tptp.xb tptp.xR tptp.xb))) % 0.52/0.74 (step-pop @p428 :rule scope :premises (@p224)) % 0.52/0.74 (step @p225 :rule process_scope :premises (@p428) :args (@t196)) % 0.52/0.74 (step @p227 :rule eq_resolve :premises (@p225 @p222)) % 0.52/0.74 (step @p228 :rule implies_elim :premises (@p227)) % 0.52/0.74 (step @p229 :rule chain_m_resolution :premises (@p228 @p177) :args (@t197 @t190 @t191)) % 0.52/0.74 (step @p230 :rule cnf_or_pos :args (@t197)) % 0.52/0.74 (step @p231 :rule factoring :premises (@p230)) % 0.52/0.74 (step @p232 :rule reordering :premises (@p231) :args ((or @t174 @t184 @t192 (not @t197)))) % 0.52/0.74 (step @p233 :rule chain_m_resolution :premises (@p232 @p15 @p207 @p229) :args (@t192 @t198 (@list @t39 @t41 @t197))) % 0.52/0.74 (step @p234 :rule cnf_or_pos :args (@t201)) % 0.52/0.74 (step @p235 :rule reordering :premises (@p234) :args ((or @t184 @t200 @t199 (not @t201)))) % 0.52/0.74 (step @p236 :rule chain_m_resolution :premises (@p235 @p207 @p233 @p211) :args (@t199 @t198 (@list @t41 @t192 @t201))) % 0.52/0.74 (step @p237 :rule cnf_equiv_pos2 :args (@t188)) % 0.52/0.74 (step @p238 :rule reordering :premises (@p237) :args ((or @t182 @t202 (not @t188)))) % 0.52/0.74 (step @p239 :rule chain_m_resolution :premises (@p238 @p236 @p210) :args (@t202 @t203 (@list @t182 @t188))) % 0.52/0.74 (step @p240 :rule cnf_or_neg :args (@t187 1)) % 0.52/0.74 (step @p241 :rule chain_m_resolution :premises (@p240 @p239) :args (@t204 @t205 (@list @t187))) % 0.52/0.74 (step @p242 :rule instantiate :premises (@p177) :args ((@list tptp.xa tptp.xR tptp.xb))) % 0.52/0.74 (step @p243 :rule cnf_or_pos :args (@t209)) % 0.52/0.74 (step @p244 :rule reordering :premises (@p243) :args ((or @t174 @t175 @t184 @t208 (not @t209)))) % 0.52/0.74 (step @p245 :rule chain_m_resolution :premises (@p244 @p15 @p180 @p207 @p242) :args (@t208 @t177 (@list @t39 @t42 @t41 @t209))) % 0.52/0.74 (step @p246 :rule and_elim :premises (@p184) :args (0)) % 0.52/0.74 (step @p247 :rule cnf_equiv_pos1 :args (@t208)) % 0.52/0.74 (step @p248 :rule reordering :premises (@p247) :args ((or (not @t49) @t207 (not @t208)))) % 0.52/0.74 (step @p249 :rule chain_m_resolution :premises (@p248 @p246 @p245) :args (@t207 @t179 (@list @t49 @t208))) % 0.52/0.74 (step @p250 :rule instantiate :premises (@p162) :args ((@list tptp.xc))) % 0.52/0.74 (step @p251 :rule bool-eq-true :args (@t210)) % 0.52/0.74 (step @p252 :rule absorb :args ((= (or true @t211) true))) % 0.52/0.74 (step @p253 :rule refl :args (@t211)) % 0.52/0.74 (step @p254 :rule eq-refl :args (tptp.xc)) % 0.52/0.74 (step @p255 :rule nary_cong :premises (@p254 @p253) :args (@t212)) % 0.52/0.74 (step @p256 :rule trans :premises (@p255 @p252)) % 0.52/0.74 (step @p257 :rule refl :args (@t210)) % 0.52/0.74 (step @p258 :rule cong :premises (@p257 @p256) :args (@t213)) % 0.52/0.74 (step @p259 :rule trans :premises (@p258 @p251)) % 0.52/0.74 (step @p260 :rule nary_cong :premises (@p196 @p195 @p196 @p259) :args (@t214)) % 0.52/0.74 (step @p261 :rule cong :premises (@p198 @p260) :args ((=> @t186 @t214))) % 0.52/0.74 (assume-push @p429 @t186) % 0.52/0.74 (step @p263 :rule instantiate :premises (@p177) :args ((@list tptp.xc tptp.xR tptp.xc))) % 0.52/0.74 (step-pop @p430 :rule scope :premises (@p263)) % 0.52/0.74 (step @p264 :rule process_scope :premises (@p430) :args (@t214)) % 0.52/0.74 (step @p266 :rule eq_resolve :premises (@p264 @p261)) % 0.52/0.74 (step @p267 :rule implies_elim :premises (@p266)) % 0.52/0.74 (step @p268 :rule chain_m_resolution :premises (@p267 @p177) :args (@t215 @t190 @t191)) % 0.52/0.74 (step @p269 :rule cnf_or_pos :args (@t215)) % 0.52/0.74 (step @p270 :rule factoring :premises (@p269)) % 0.52/0.74 (step @p271 :rule reordering :premises (@p270) :args ((or @t174 @t173 @t210 (not @t215)))) % 0.52/0.74 (step @p272 :rule chain_m_resolution :premises (@p271 @p15 @p179 @p268) :args (@t210 @t198 (@list @t39 @t40 @t215))) % 0.52/0.74 (step @p273 :rule cnf_or_pos :args (@t219)) % 0.52/0.74 (step @p274 :rule reordering :premises (@p273) :args ((or @t173 @t216 @t218 (not @t219)))) % 0.52/0.74 (step @p275 :rule chain_m_resolution :premises (@p274 @p179 @p272 @p250) :args (@t218 @t198 (@list @t40 @t210 @t219))) % 0.52/0.74 (step @p276 :rule bool-double-not-elim :args (@t217)) % 0.52/0.74 (step @p277 :rule refl :args (@t220)) % 0.52/0.74 (step @p278 :rule refl :args (@t178)) % 0.52/0.74 (step @p279 :rule nary_cong :premises (@p278 @p277 @p276) :args ((or @t178 @t220 (not @t218)))) % 0.52/0.74 (assume-push @p431 @t218) % 0.52/0.74 (assume-push @p432 @t206) % 0.52/0.74 (assume-push @p433 @t48) % 0.52/0.74 (step @p283 :rule evaluate :args ((= true false))) % 0.52/0.74 (step @p284 :rule false_intro :premises (@p275)) % 0.52/0.74 (step @p285 :rule refl :args (tptp.xc)) % 0.52/0.74 (step @p286 :rule refl :args (tptp.xR)) % 0.52/0.74 (step @p287 :rule cong :premises (@p432 @p286 @p285) :args (@t48)) % 0.52/0.74 (step @p288 :rule true_intro :premises (@p185)) % 0.52/0.74 (step @p289 :rule symm :premises (@p288)) % 0.52/0.74 (step @p290 :rule trans :premises (@p289 @p287 @p284)) % 0.52/0.74 (step @p291 false :rule eq_resolve :premises (@p290 @p283)) % 0.52/0.74 (step-pop @p434 :rule scope :premises (@p291)) % 0.52/0.74 (step-pop @p435 :rule scope :premises (@p434)) % 0.52/0.74 (step-pop @p436 :rule scope :premises (@p435)) % 0.52/0.74 (step @p292 :rule process_scope :premises (@p436) :args (false)) % 0.52/0.74 (assume-push @p437 @t48) % 0.52/0.74 (assume-push @p438 @t206) % 0.52/0.74 (assume-push @p439 @t218) % 0.52/0.74 (step @p299 :rule and_intro :premises (@p275 @p438 @p185)) % 0.52/0.74 (step-pop @p440 :rule scope :premises (@p299)) % 0.52/0.74 (step-pop @p441 :rule scope :premises (@p440)) % 0.52/0.74 (step-pop @p442 :rule scope :premises (@p441)) % 0.52/0.74 (step @p300 :rule process_scope :premises (@p442) :args (@t221)) % 0.52/0.74 (step @p304 :rule implies_elim :premises (@p300)) % 0.52/0.74 (step @p305 :rule resolution :premises (@p304 @p292) :args (true @t221)) % 0.52/0.74 (step @p306 :rule not_and :premises (@p305)) % 0.52/0.74 (step @p307 :rule eq_resolve :premises (@p306 @p279)) % 0.52/0.74 (step @p308 :rule reordering :premises (@p307) :args ((or @t178 @t217 @t220))) % 0.52/0.74 (step @p309 :rule chain_m_resolution :premises (@p308 @p185 @p275) :args (@t220 @t222 (@list @t48 @t217))) % 0.52/0.74 (step @p310 :rule cnf_or_pos :args (@t207)) % 0.52/0.74 (step @p311 :rule reordering :premises (@p310) :args ((or @t69 @t206 (not @t207)))) % 0.52/0.74 (step @p312 :rule chain_m_resolution :premises (@p311 @p309 @p249) :args (@t69 @t203 (@list @t206 @t207))) % 0.52/0.74 (step @p313 :rule bool-double-not-elim :args (@t180)) % 0.52/0.74 (step @p314 :rule refl :args (@t223)) % 0.52/0.74 (step @p315 :rule refl :args (@t224)) % 0.52/0.74 (step @p316 :rule nary_cong :premises (@p315 @p314 @p313) :args ((or @t224 @t223 (not @t204)))) % 0.52/0.74 (assume-push @p443 @t69) % 0.52/0.74 (assume-push @p444 @t170) % 0.52/0.74 (assume-push @p445 @t204) % 0.52/0.74 (step @p320 :rule evaluate :args ((= false true))) % 0.52/0.74 (step @p321 :rule true_intro :premises (@p443)) % 0.52/0.74 (step @p322 :rule refl :args (tptp.xb)) % 0.52/0.74 (step @p286 :rule refl :args (tptp.xR)) % 0.52/0.74 (step @p323 :rule symm :premises (@p444)) % 0.52/0.74 (step @p324 :rule cong :premises (@p323 @p286 @p322) :args (@t180)) % 0.52/0.74 (step @p325 :rule false_intro :premises (@p241)) % 0.52/0.74 (step @p326 :rule symm :premises (@p325)) % 0.52/0.74 (step @p327 :rule trans :premises (@p326 @p324 @p321)) % 0.52/0.74 (step @p328 false :rule eq_resolve :premises (@p327 @p320)) % 0.52/0.74 (step-pop @p446 :rule scope :premises (@p328)) % 0.52/0.74 (step-pop @p447 :rule scope :premises (@p446)) % 0.52/0.74 (step-pop @p448 :rule scope :premises (@p447)) % 0.52/0.74 (step @p329 :rule process_scope :premises (@p448) :args (false)) % 0.52/0.74 (step @p333 :rule not_and :premises (@p329)) % 0.52/0.74 (step @p334 :rule eq_resolve :premises (@p333 @p316)) % 0.52/0.74 (step @p335 :rule chain_m_resolution :premises (@p334 @p312 @p241) :args (@t223 @t222 (@list @t69 @t180))) % 0.52/0.74 (step @p336 :rule cnf_or_pos :args (@t171)) % 0.52/0.74 (step @p337 :rule reordering :premises (@p336) :args ((or @t68 @t170 (not @t171)))) % 0.52/0.74 (step @p338 :rule chain_m_resolution :premises (@p337 @p335 @p188) :args (@t68 @t203 (@list @t170 @t171))) % 0.52/0.74 (step @p339 :rule cnf_and_neg :args (@t70)) % 0.52/0.74 (step @p340 :rule chain_m_resolution :premises (@p339 @p312 @p338) :args (@t70 @t179 (@list @t69 @t68))) % 0.52/0.74 (step @p341 :rule not_implies_elim1 :premises (@p159)) % 0.52/0.74 (step @p342 :rule implies_elim :premises (@p341)) % 0.52/0.74 (step @p343 :rule reordering :premises (@p342) :args ((or @t225 (not @t70)))) % 0.52/0.74 (step @p344 :rule chain_m_resolution :premises (@p343 @p340) :args (@t225 @t190 (@list @t70))) % 0.52/0.74 (step @p345 :rule refl :args (@t238)) % 0.52/0.74 (step @p346 :rule bool-double-not-elim :args (@t165)) % 0.52/0.74 (step @p347 :rule nary_cong :premises (@p346 @p345) :args ((or (not @t225) @t238))) % 0.52/0.74 (assume-push @p449 @t225) % 0.52/0.74 (step @p349 :rule skolemize :premises (@p449)) % 0.52/0.74 (step-pop @p450 :rule scope :premises (@p349)) % 0.52/0.74 (step @p350 :rule process_scope :premises (@p450) :args (@t238)) % 0.52/0.74 (step @p352 :rule implies_elim :premises (@p350)) % 0.52/0.74 (step @p353 :rule eq_resolve :premises (@p352 @p347)) % 0.52/0.74 (step @p354 :rule chain_m_resolution :premises (@p353 @p344) :args (@t238 @t205 (@list @t165))) % 0.52/0.74 (step @p355 :rule bool-double-not-elim :args (@t226)) % 0.52/0.74 (step @p356 :rule refl :args (@t237)) % 0.52/0.74 (step @p357 :rule nary_cong :premises (@p356 @p355) :args ((or @t237 (not @t227)))) % 0.52/0.74 (step @p358 :rule cnf_or_neg :args (@t237 11)) % 0.52/0.74 (step @p359 :rule eq_resolve :premises (@p358 @p357)) % 0.52/0.74 (step @p360 :rule reordering :premises (@p359) :args ((or @t226 @t237))) % 0.52/0.74 (step @p361 :rule chain_m_resolution :premises (@p360 @p354) :args (@t226 @t205 @t239)) % 0.52/0.74 (step @p362 :rule bool-double-not-elim :args (@t228)) % 0.52/0.74 (step @p363 :rule nary_cong :premises (@p356 @p362) :args ((or @t237 (not @t229)))) % 0.52/0.74 (step @p364 :rule cnf_or_neg :args (@t237 10)) % 0.52/0.74 (step @p365 :rule eq_resolve :premises (@p364 @p363)) % 0.52/0.74 (step @p366 :rule reordering :premises (@p365) :args ((or @t228 @t237))) % 0.52/0.74 (step @p367 :rule chain_m_resolution :premises (@p366 @p354) :args (@t228 @t205 @t239)) % 0.52/0.74 (step @p368 :rule cnf_or_pos :args (@t242)) % 0.52/0.74 (step @p369 :rule reordering :premises (@p368) :args ((or @t229 @t227 @t241 (not @t242)))) % 0.52/0.74 (step @p370 :rule chain_m_resolution :premises (@p369 @p367 @p361 @p163) :args (@t241 @t198 (@list @t228 @t226 @t242))) % 0.52/0.74 (step @p371 :rule quant-merge-prenex :args ((= (forall @t12 @t247) (forall (@list @t1 @t7 @t243) @t245)))) % 0.52/0.74 (step @p372 :rule alpha_equiv :args (@t248 (@list @t243) (@list @t5))) % 0.52/0.74 (step @p373 :rule refl :args (@t167)) % 0.52/0.74 (step @p374 :rule nary_cong :premises (@p23 @p373 @p372) :args (@t249)) % 0.52/0.74 (step @p375 :rule quant-miniscope-or :args ((= @t247 @t249))) % 0.52/0.74 (step @p376 :rule trans :premises (@p375 @p374)) % 0.52/0.74 (step @p377 :rule symm :premises (@p376)) % 0.52/0.74 (step @p378 :rule cong :premises (@p377) :args ((forall @t12 @t252))) % 0.52/0.74 (step @p379 :rule trans :premises (@p378 @p371)) % 0.52/0.74 (step @p380 :rule aci_norm :args ((= (or (or @t76 @t167) @t251) @t252))) % 0.52/0.74 (step @p381 :rule refl :args (@t251)) % 0.52/0.74 (step @p382 :rule bool-and-de-morgan :args (@t2 @t10 true)) % 0.52/0.74 (step @p383 :rule nary_cong :premises (@p382 @p381) :args ((or (not @t11) @t251))) % 0.52/0.74 (step @p384 :rule trans :premises (@p383 @p380)) % 0.52/0.74 (step @p385 :rule bool-impl-elim :args (@t11 @t251)) % 0.52/0.74 (step @p386 :rule trans :premises (@p385 @p384)) % 0.52/0.74 (step @p387 :rule cong :premises (@p386) :args ((forall @t12 (=> @t11 @t251)))) % 0.52/0.74 (step @p388 :rule trans :premises (@p387 @p379)) % 0.52/0.74 (step @p389 :rule bool-double-not-elim :args (@t250)) % 0.52/0.74 (step @p390 :rule exists-elim :args ((= @t30 (not @t250)))) % 0.52/0.74 (step @p391 :rule cong :premises (@p390) :args (@t31)) % 0.52/0.74 (step @p392 :rule trans :premises (@p391 @p389)) % 0.52/0.74 (step @p393 :rule refl :args (@t22)) % 0.52/0.74 (step @p394 :rule nary_cong :premises (@p139 @p393 @p392) :args (@t32)) % 0.52/0.74 (step @p395 :rule refl :args (@t33)) % 0.52/0.74 (step @p396 :rule cong :premises (@p395 @p394) :args (@t34)) % 0.52/0.74 (step @p397 :rule cong :premises (@p396) :args (@t35)) % 0.52/0.74 (step @p398 :rule refl :args (@t11)) % 0.52/0.74 (step @p399 :rule cong :premises (@p398 @p397) :args (@t36)) % 0.52/0.74 (step @p400 :rule cong :premises (@p399) :args (@t37)) % 0.52/0.74 (step @p401 :rule trans :premises (@p400 @p388)) % 0.52/0.74 (step @p402 :rule eq_resolve :premises (@p13 @p401)) % 0.52/0.74 (step @p403 :rule instantiate :premises (@p402) :args ((@list @t230 tptp.xR @t166))) % 0.52/0.74 (step @p404 :rule bool-double-not-elim :args (@t235)) % 0.52/0.74 (step @p405 :rule nary_cong :premises (@p356 @p404) :args ((or @t237 (not @t236)))) % 0.52/0.74 (step @p406 :rule cnf_or_neg :args (@t237 6)) % 0.52/0.74 (step @p407 :rule eq_resolve :premises (@p406 @p405)) % 0.52/0.74 (step @p408 :rule reordering :premises (@p407) :args ((or @t235 @t237))) % 0.52/0.74 (step @p409 :rule chain_m_resolution :premises (@p408 @p354) :args (@t235 @t205 @t239)) % 0.52/0.74 (step @p410 :rule cnf_or_pos :args (@t255)) % 0.52/0.74 (step @p411 :rule reordering :premises (@p410) :args ((or @t174 @t236 @t254 (not @t255)))) % 0.52/0.74 (step @p412 :rule chain_m_resolution :premises (@p411 @p15 @p409 @p403) :args (@t254 @t198 (@list @t39 @t235 @t255))) % 0.52/0.74 (step @p413 :rule bool-double-not-elim :args (@t231)) % 0.52/0.74 (step @p414 :rule nary_cong :premises (@p356 @p413) :args ((or @t237 (not @t232)))) % 0.52/0.74 (step @p415 :rule cnf_or_neg :args (@t237 9)) % 0.52/0.74 (step @p416 :rule eq_resolve :premises (@p415 @p414)) % 0.52/0.74 (step @p417 :rule reordering :premises (@p416) :args ((or @t231 @t237))) % 0.52/0.74 (step @p418 :rule chain_m_resolution :premises (@p417 @p354) :args (@t231 @t205 @t239)) % 0.52/0.74 (step @p419 :rule cnf_equiv_pos1 :args (@t254)) % 0.52/0.74 (step @p420 :rule reordering :premises (@p419) :args ((or @t232 @t253 (not @t254)))) % 0.52/0.74 (step @p421 :rule chain_m_resolution :premises (@p420 @p418 @p412) :args (@t253 @t179 (@list @t231 @t254))) % 0.52/0.74 (step @p422 :rule cnf_and_pos :args (@t253 0)) % 0.52/0.74 (step @p423 :rule reordering :premises (@p422) :args ((or @t240 (not @t253)))) % 0.52/0.74 (step @p424 false :rule chain_m_resolution :premises (@p423 @p421 @p370) :args (false @t222 (@list @t253 @t240))) % 0.52/0.74 ) % 0.52/0.74 % SZS output end Proof % 0.52/0.74 % cvc5 exiting %------------------------------------------------------------------------------