%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC200+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:58:26 AM UTC 2026 % Result : Theorem 14.61s 14.81s % Output : Proof 14.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC200+1 : TPTP v9.2.1. Released v2.4.0. % 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 : n014.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 19:23:28 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 14.61/14.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 14.61/14.81 % SZS status Theorem % 14.61/14.81 % SZS output start Proof % 14.61/14.81 ( % 14.61/14.81 (declare-sort $$unsorted 0) % 14.61/14.81 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 14.61/14.81 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 14.61/14.81 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 14.61/14.81 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 14.61/14.81 (declare-const tptp.nil $$unsorted) % 14.61/14.81 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.ssList (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 14.61/14.81 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 14.61/14.81 (define @t1 () (@var "V" $$unsorted)) % 14.61/14.81 (define @t2 () (@var "U" $$unsorted)) % 14.61/14.81 (define @t3 () (= @t2 @t1)) % 14.61/14.81 (define @t4 () (not @t3)) % 14.61/14.81 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 14.61/14.81 (define @t6 () (tptp.ssItem @t1)) % 14.61/14.81 (define @t7 () (@list @t1)) % 14.61/14.81 (define @t8 () (tptp.ssItem @t2)) % 14.61/14.81 (define @t9 () (@list @t2)) % 14.61/14.81 (define @t10 () (@var "X" $$unsorted)) % 14.61/14.81 (define @t11 () (tptp.cons @t1 @t10)) % 14.61/14.81 (define @t12 () (@var "W" $$unsorted)) % 14.61/14.81 (define @t13 () (tptp.ssList @t10)) % 14.61/14.81 (define @t14 () (@list @t10)) % 14.61/14.81 (define @t15 () (tptp.ssList @t12)) % 14.61/14.81 (define @t16 () (@list @t12)) % 14.61/14.81 (define @t17 () (tptp.ssList @t2)) % 14.61/14.81 (define @t18 () (tptp.cons @t1 tptp.nil)) % 14.61/14.81 (define @t19 () (and @t6 (= @t18 @t2))) % 14.61/14.81 (define @t20 () (exists @t7 @t19)) % 14.61/14.81 (define @t21 () (tptp.singletonP @t2)) % 14.61/14.81 (define @t22 () (= @t21 @t20)) % 14.61/14.81 (define @t23 () (=> @t17 @t22)) % 14.61/14.81 (define @t24 () (forall @t9 @t23)) % 14.61/14.81 (define @t25 () (tptp.app @t1 @t12)) % 14.61/14.81 (define @t26 () (tptp.frontsegP @t2 @t1)) % 14.61/14.81 (define @t27 () (tptp.ssList @t1)) % 14.61/14.81 (define @t28 () (tptp.app @t12 @t1)) % 14.61/14.81 (define @t29 () (tptp.rearsegP @t2 @t1)) % 14.61/14.81 (define @t30 () (tptp.segmentP @t2 @t1)) % 14.61/14.81 (define @t31 () (tptp.leq @t12 @t1)) % 14.61/14.81 (define @t32 () (tptp.leq @t1 @t12)) % 14.61/14.81 (define @t33 () (@var "Z" $$unsorted)) % 14.61/14.81 (define @t34 () (@var "Y" $$unsorted)) % 14.61/14.81 (define @t35 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t34)) (tptp.cons @t12 @t33)) @t2)) % 14.61/14.81 (define @t36 () (tptp.ssList @t33)) % 14.61/14.81 (define @t37 () (@list @t33)) % 14.61/14.81 (define @t38 () (tptp.ssList @t34)) % 14.61/14.81 (define @t39 () (@list @t34)) % 14.61/14.81 (define @t40 () (tptp.ssItem @t12)) % 14.61/14.81 (define @t41 () (tptp.lt @t1 @t12)) % 14.61/14.81 (define @t42 () (= @t1 @t12)) % 14.61/14.81 (define @t43 () (tptp.cons @t1 @t2)) % 14.61/14.81 (define @t44 () (tptp.ssList tptp.nil)) % 14.61/14.81 (define @t45 () (= @t1 @t2)) % 14.61/14.81 (define @t46 () (tptp.cons @t12 @t1)) % 14.61/14.81 (define @t47 () (= tptp.nil @t2)) % 14.61/14.81 (define @t48 () (tptp.hd @t2)) % 14.61/14.81 (define @t49 () (tptp.ssItem @t48)) % 14.61/14.81 (define @t50 () (not @t47)) % 14.61/14.81 (define @t51 () (=> @t50 @t49)) % 14.61/14.81 (define @t52 () (=> @t17 @t51)) % 14.61/14.81 (define @t53 () (forall @t9 @t52)) % 14.61/14.81 (define @t54 () (tptp.tl @t2)) % 14.61/14.81 (define @t55 () (tptp.ssList @t54)) % 14.61/14.81 (define @t56 () (=> @t50 @t55)) % 14.61/14.81 (define @t57 () (=> @t17 @t56)) % 14.61/14.81 (define @t58 () (forall @t9 @t57)) % 14.61/14.81 (define @t59 () (tptp.tl @t43)) % 14.61/14.81 (define @t60 () (=> @t6 (= @t59 @t2))) % 14.61/14.81 (define @t61 () (forall @t7 @t60)) % 14.61/14.81 (define @t62 () (=> @t17 @t61)) % 14.61/14.81 (define @t63 () (forall @t9 @t62)) % 14.61/14.81 (define @t64 () (tptp.app @t2 @t1)) % 14.61/14.81 (define @t65 () (tptp.app @t1 @t2)) % 14.61/14.81 (define @t66 () (tptp.leq @t1 @t2)) % 14.61/14.81 (define @t67 () (tptp.leq @t2 @t1)) % 14.61/14.81 (define @t68 () (tptp.geq @t2 @t1)) % 14.61/14.81 (define @t69 () (tptp.lt @t1 @t2)) % 14.61/14.81 (define @t70 () (tptp.lt @t2 @t1)) % 14.61/14.81 (define @t71 () (tptp.lt @t2 @t12)) % 14.61/14.81 (define @t72 () (tptp.gt @t2 @t1)) % 14.61/14.81 (define @t73 () (tptp.memberP @t12 @t2)) % 14.61/14.81 (define @t74 () (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t73))) % 14.61/14.81 (define @t75 () (forall @t16 (=> @t15 @t74))) % 14.61/14.81 (define @t76 () (=> @t6 @t75)) % 14.61/14.81 (define @t77 () (forall @t7 @t76)) % 14.61/14.81 (define @t78 () (=> @t8 @t77)) % 14.61/14.81 (define @t79 () (forall @t9 @t78)) % 14.61/14.81 (define @t80 () (not (tptp.memberP tptp.nil @t2))) % 14.61/14.81 (define @t81 () (forall @t9 (=> @t8 @t80))) % 14.61/14.81 (define @t82 () (tptp.singletonP tptp.nil)) % 14.61/14.81 (define @t83 () (not @t82)) % 14.61/14.81 (define @t84 () (tptp.app @t12 @t2)) % 14.61/14.81 (define @t85 () (tptp.cons @t2 tptp.nil)) % 14.61/14.81 (define @t86 () (tptp.hd @t1)) % 14.61/14.81 (define @t87 () (= tptp.nil @t1)) % 14.61/14.81 (define @t88 () (not @t87)) % 14.61/14.81 (define @t89 () (tptp.cons @t2 @t1)) % 14.61/14.81 (define @t90 () (tptp.cons @t48 @t54)) % 14.61/14.81 (define @t91 () (=> @t50 (= @t90 @t2))) % 14.61/14.81 (define @t92 () (=> @t17 @t91)) % 14.61/14.81 (define @t93 () (forall @t9 @t92)) % 14.61/14.81 (define @t94 () (= @t12 @t2)) % 14.61/14.81 (define @t95 () (= @t34 @t33)) % 14.61/14.81 (define @t96 () (not (tptp.memberP @t2 @t33))) % 14.61/14.81 (define @t97 () (or @t96 @t95)) % 14.61/14.81 (define @t98 () (tptp.ssItem @t33)) % 14.61/14.81 (define @t99 () (forall @t37 (=> @t98 @t97))) % 14.61/14.81 (define @t100 () (tptp.ssItem @t34)) % 14.61/14.81 (define @t101 () (and @t100 @t99)) % 14.61/14.81 (define @t102 () (exists @t39 @t101)) % 14.61/14.81 (define @t103 () (not (tptp.singletonP @t12))) % 14.61/14.81 (define @t104 () (not (= @t2 @t12))) % 14.61/14.81 (define @t105 () (not (= @t1 @t10))) % 14.61/14.81 (define @t106 () (or @t105 @t104 @t103 @t102)) % 14.61/14.81 (define @t107 () (=> @t13 @t106)) % 14.61/14.81 (define @t108 () (forall @t14 @t107)) % 14.61/14.81 (define @t109 () (=> @t15 @t108)) % 14.61/14.81 (define @t110 () (forall @t16 @t109)) % 14.61/14.81 (define @t111 () (=> @t27 @t110)) % 14.61/14.81 (define @t112 () (forall @t7 @t111)) % 14.61/14.81 (define @t113 () (=> @t17 @t112)) % 14.61/14.81 (define @t114 () (forall @t9 @t113)) % 14.61/14.81 (define @t115 () (not @t114)) % 14.61/14.81 (define @t116 () (not @t21)) % 14.61/14.81 (define @t117 () (not @t98)) % 14.61/14.81 (define @t118 () (or @t117 @t96 @t95)) % 14.61/14.81 (define @t119 () (forall @t37 @t118)) % 14.61/14.81 (define @t120 () (not @t100)) % 14.61/14.81 (define @t121 () (not (forall @t39 (or @t120 (not @t119))))) % 14.61/14.81 (define @t122 () (not @t17)) % 14.61/14.81 (define @t123 () (or @t122 @t121 @t116)) % 14.61/14.81 (define @t124 () (forall @t9 @t123)) % 14.61/14.81 (define @t125 () (not @t27)) % 14.61/14.81 (define @t126 () (forall @t7 @t125)) % 14.61/14.81 (define @t127 () (or @t126 @t123)) % 14.61/14.81 (define @t128 () (or @t122 @t121 @t116 @t126)) % 14.61/14.81 (define @t129 () (or @t121 @t122 @t116 @t126)) % 14.61/14.81 (define @t130 () (or @t121 @t122 @t116 @t125)) % 14.61/14.81 (define @t131 () (or @t125 @t121 @t122 @t116)) % 14.61/14.81 (define @t132 () (or @t121 @t125 @t122 @t116)) % 14.61/14.81 (define @t133 () (or @t122 @t116)) % 14.61/14.81 (define @t134 () (not (= @t2 @t2))) % 14.61/14.81 (define @t135 () (or @t122 @t134 @t116)) % 14.61/14.81 (define @t136 () (not @t15)) % 14.61/14.81 (define @t137 () (or @t104 @t136 @t104 @t103)) % 14.61/14.81 (define @t138 () (or @t136 @t104 @t103)) % 14.61/14.81 (define @t139 () (forall @t16 @t138)) % 14.61/14.81 (define @t140 () (or @t121 @t125 @t139)) % 14.61/14.81 (define @t141 () (or @t121 @t125 @t138)) % 14.61/14.81 (define @t142 () (or @t136 @t104 @t103 @t121 @t125)) % 14.61/14.81 (define @t143 () (or @t104 @t103 @t121 @t125)) % 14.61/14.81 (define @t144 () (not (= @t1 @t1))) % 14.61/14.81 (define @t145 () (or @t125 @t144)) % 14.61/14.81 (define @t146 () (not @t13)) % 14.61/14.81 (define @t147 () (or @t105 @t146 @t105)) % 14.61/14.81 (define @t148 () (or @t146 @t105)) % 14.61/14.81 (define @t149 () (forall @t14 @t148)) % 14.61/14.81 (define @t150 () (or @t104 @t103 @t121 @t149)) % 14.61/14.81 (define @t151 () (or @t104 @t103 @t121 @t148)) % 14.61/14.81 (define @t152 () (or @t146 @t105 @t104 @t103 @t121)) % 14.61/14.81 (define @t153 () (or @t105 @t104 @t103 @t121)) % 14.61/14.81 (define @t154 () (and @t100 @t119)) % 14.61/14.81 (define @t155 () (forall @t39 (not @t154))) % 14.61/14.81 (define @t156 () (not @t155)) % 14.61/14.81 (define @t157 () (@quantifiers_skolemize @t124 0)) % 14.61/14.81 (define @t158 () (not (tptp.memberP @t157 @t33))) % 14.61/14.81 (define @t159 () (forall @t39 (or @t120 (not (forall @t37 (or @t117 @t158 @t95)))))) % 14.61/14.81 (define @t160 () (tptp.singletonP @t157)) % 14.61/14.81 (define @t161 () (not @t160)) % 14.61/14.81 (define @t162 () (not @t159)) % 14.61/14.81 (define @t163 () (tptp.ssList @t157)) % 14.61/14.81 (define @t164 () (not @t163)) % 14.61/14.81 (define @t165 () (or @t164 @t162 @t161)) % 14.61/14.81 (define @t166 () (@list true)) % 14.61/14.81 (define @t167 () (@list @t165)) % 14.61/14.81 (define @t168 () (tptp.hd @t157)) % 14.61/14.81 (define @t169 () (or @t117 @t158 (= @t168 @t33))) % 14.61/14.81 (define @t170 () (forall @t37 @t169)) % 14.61/14.81 (define @t171 () (not @t170)) % 14.61/14.81 (define @t172 () (tptp.ssItem @t168)) % 14.61/14.81 (define @t173 () (not @t172)) % 14.61/14.81 (define @t174 () (or @t173 @t171)) % 14.61/14.81 (define @t175 () (forall @t37 (or @t117 @t158 (= @t33 @t168)))) % 14.61/14.81 (define @t176 () (not @t175)) % 14.61/14.81 (define @t177 () (or @t173 @t176)) % 14.61/14.81 (define @t178 () (@list false)) % 14.61/14.81 (define @t179 () (= @t2 tptp.nil)) % 14.61/14.81 (define @t180 () (or @t122 @t179 @t49)) % 14.61/14.81 (define @t181 () (not @t179)) % 14.61/14.81 (define @t182 () (not @t181)) % 14.61/14.81 (define @t183 () (=> @t181 @t49)) % 14.61/14.81 (define @t184 () (= @t157 tptp.nil)) % 14.61/14.81 (define @t185 () (or @t164 @t184 @t172)) % 14.61/14.81 (define @t186 () (forall @t9 @t180)) % 14.61/14.81 (define @t187 () (@list @t157)) % 14.61/14.81 (define @t188 () (= tptp.nil @t157)) % 14.61/14.81 (define @t189 () (or @t164 @t188 @t172)) % 14.61/14.81 (define @t190 () (not @t188)) % 14.61/14.81 (define @t191 () (and @t160 @t188 @t83)) % 14.61/14.81 (define @t192 () (@list false true false)) % 14.61/14.81 (define @t193 () (@list false false)) % 14.61/14.81 (define @t194 () (@quantifiers_skolemize @t175 0)) % 14.61/14.81 (define @t195 () (= @t168 @t194)) % 14.61/14.81 (define @t196 () (tptp.memberP @t157 @t194)) % 14.61/14.81 (define @t197 () (not @t196)) % 14.61/14.81 (define @t198 () (tptp.ssItem @t194)) % 14.61/14.81 (define @t199 () (not @t198)) % 14.61/14.81 (define @t200 () (or @t199 @t197 @t195)) % 14.61/14.81 (define @t201 () (not @t200)) % 14.61/14.81 (define @t202 () (= @t194 @t168)) % 14.61/14.81 (define @t203 () (or @t199 @t197 @t202)) % 14.61/14.81 (define @t204 () (not @t203)) % 14.61/14.81 (define @t205 () (@list @t200)) % 14.61/14.81 (define @t206 () (tptp.memberP tptp.nil @t194)) % 14.61/14.81 (define @t207 () (not @t206)) % 14.61/14.81 (define @t208 () (or @t199 @t207)) % 14.61/14.81 (define @t209 () (@var "BOUND_VARIABLE_9344" $$unsorted)) % 14.61/14.81 (define @t210 () (= @t2 (tptp.tl (tptp.cons @t209 @t2)))) % 14.61/14.81 (define @t211 () (not (tptp.ssItem @t209))) % 14.61/14.81 (define @t212 () (or @t211 @t210)) % 14.61/14.81 (define @t213 () (or @t122 @t212)) % 14.61/14.81 (define @t214 () (forall (@list @t2 @t209) @t213)) % 14.61/14.81 (define @t215 () (@list @t209)) % 14.61/14.81 (define @t216 () (forall @t215 @t213)) % 14.61/14.81 (define @t217 () (forall @t215 @t212)) % 14.61/14.81 (define @t218 () (or @t122 @t217)) % 14.61/14.81 (define @t219 () (= @t2 @t59)) % 14.61/14.81 (define @t220 () (not @t6)) % 14.61/14.81 (define @t221 () (forall @t7 (or @t220 @t219))) % 14.61/14.81 (define @t222 () (forall @t7 (or @t220 (not (= @t18 @t157))))) % 14.61/14.81 (define @t223 () (@quantifiers_skolemize @t222 0)) % 14.61/14.81 (define @t224 () (= @t2 @t18)) % 14.61/14.81 (define @t225 () (= @t21 (not (forall @t7 (or @t220 (not @t224)))))) % 14.61/14.81 (define @t226 () (and @t6 @t224)) % 14.61/14.81 (define @t227 () (forall @t7 (not @t226))) % 14.61/14.81 (define @t228 () (not @t227)) % 14.61/14.81 (define @t229 () (not (= @t157 @t18))) % 14.61/14.81 (define @t230 () (or @t220 @t229)) % 14.61/14.81 (define @t231 () (forall @t7 @t230)) % 14.61/14.81 (define @t232 () (not @t231)) % 14.61/14.81 (define @t233 () (= @t160 @t232)) % 14.61/14.81 (define @t234 () (or @t164 @t233)) % 14.61/14.81 (define @t235 () (forall @t9 (or @t122 @t225))) % 14.61/14.81 (define @t236 () (not @t222)) % 14.61/14.81 (define @t237 () (= @t160 @t236)) % 14.61/14.81 (define @t238 () (or @t164 @t237)) % 14.61/14.81 (define @t239 () (tptp.cons @t223 tptp.nil)) % 14.61/14.81 (define @t240 () (= @t157 @t239)) % 14.61/14.81 (define @t241 () (not @t240)) % 14.61/14.81 (define @t242 () (tptp.ssItem @t223)) % 14.61/14.81 (define @t243 () (not @t242)) % 14.61/14.81 (define @t244 () (or @t243 @t241)) % 14.61/14.81 (define @t245 () (not @t244)) % 14.61/14.81 (define @t246 () (not (= @t239 @t157))) % 14.61/14.81 (define @t247 () (or @t243 @t246)) % 14.61/14.81 (define @t248 () (not @t247)) % 14.61/14.81 (define @t249 () (@list @t244)) % 14.61/14.81 (define @t250 () (= tptp.nil (tptp.tl @t239))) % 14.61/14.81 (define @t251 () (not @t44)) % 14.61/14.81 (define @t252 () (or @t251 @t243 @t250)) % 14.61/14.81 (define @t253 () (tptp.tl @t157)) % 14.61/14.81 (define @t254 () (tptp.memberP @t253 @t194)) % 14.61/14.81 (define @t255 () (not @t254)) % 14.61/14.81 (define @t256 () (not @t250)) % 14.61/14.81 (define @t257 () (and @t240 @t250 @t207)) % 14.61/14.81 (define @t258 () (@var "BOUND_VARIABLE_9698" $$unsorted)) % 14.61/14.81 (define @t259 () (@var "BOUND_VARIABLE_9696" $$unsorted)) % 14.61/14.81 (define @t260 () (= (tptp.memberP (tptp.cons @t259 @t258) @t2) (or (= @t2 @t259) (tptp.memberP @t258 @t2)))) % 14.61/14.81 (define @t261 () (not (tptp.ssList @t258))) % 14.61/14.81 (define @t262 () (not (tptp.ssItem @t259))) % 14.61/14.81 (define @t263 () (not @t8)) % 14.61/14.81 (define @t264 () (or @t263 @t262 @t261 @t260)) % 14.61/14.81 (define @t265 () (or @t262 @t261 @t260)) % 14.61/14.81 (define @t266 () (or @t263 @t265)) % 14.61/14.81 (define @t267 () (@list @t2 @t259 @t258)) % 14.61/14.81 (define @t268 () (forall @t267 @t266)) % 14.61/14.81 (define @t269 () (@list @t259 @t258)) % 14.61/14.81 (define @t270 () (forall @t269 @t266)) % 14.61/14.81 (define @t271 () (forall @t269 @t265)) % 14.61/14.81 (define @t272 () (@var "BOUND_VARIABLE_9677" $$unsorted)) % 14.61/14.81 (define @t273 () (or @t263 @t271)) % 14.61/14.81 (define @t274 () (= (tptp.memberP (tptp.cons @t1 @t272) @t2) (or @t3 (tptp.memberP @t272 @t2)))) % 14.61/14.81 (define @t275 () (not (tptp.ssList @t272))) % 14.61/14.81 (define @t276 () (or @t220 @t275 @t274)) % 14.61/14.81 (define @t277 () (@list @t1 @t272)) % 14.61/14.81 (define @t278 () (forall @t277 @t276)) % 14.61/14.81 (define @t279 () (or @t275 @t274)) % 14.61/14.81 (define @t280 () (or @t220 @t279)) % 14.61/14.81 (define @t281 () (forall @t277 @t280)) % 14.61/14.81 (define @t282 () (@list @t272)) % 14.61/14.81 (define @t283 () (forall @t282 @t280)) % 14.61/14.81 (define @t284 () (forall @t282 @t279)) % 14.61/14.81 (define @t285 () (or @t220 @t284)) % 14.61/14.81 (define @t286 () (forall @t16 (or @t136 @t74))) % 14.61/14.81 (define @t287 () (or @t202 @t254)) % 14.61/14.81 (define @t288 () (tptp.cons @t168 @t253)) % 14.61/14.81 (define @t289 () (tptp.memberP @t288 @t194)) % 14.61/14.81 (define @t290 () (= @t289 @t287)) % 14.61/14.81 (define @t291 () (tptp.ssList @t253)) % 14.61/14.81 (define @t292 () (not @t291)) % 14.61/14.81 (define @t293 () (or @t199 @t173 @t292 @t290)) % 14.61/14.81 (define @t294 () (forall @t267 @t264)) % 14.61/14.81 (define @t295 () (or @t195 @t254)) % 14.61/14.81 (define @t296 () (= @t289 @t295)) % 14.61/14.81 (define @t297 () (or @t199 @t173 @t292 @t296)) % 14.61/14.81 (define @t298 () (or @t122 @t179 @t55)) % 14.61/14.81 (define @t299 () (=> @t181 @t55)) % 14.61/14.81 (define @t300 () (or @t164 @t184 @t291)) % 14.61/14.81 (define @t301 () (forall @t9 @t298)) % 14.61/14.81 (define @t302 () (or @t164 @t188 @t291)) % 14.61/14.81 (define @t303 () (= @t2 @t90)) % 14.61/14.81 (define @t304 () (or @t122 @t179 @t303)) % 14.61/14.81 (define @t305 () (=> @t181 @t303)) % 14.61/14.81 (define @t306 () (= @t157 @t288)) % 14.61/14.81 (define @t307 () (or @t164 @t184 @t306)) % 14.61/14.81 (define @t308 () (forall @t9 @t304)) % 14.61/14.81 (define @t309 () (or @t164 @t188 @t306)) % 14.61/14.81 (define @t310 () (and @t306 @t196)) % 14.61/14.81 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 14.61/14.81 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 14.61/14.81 (assume @p3 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.memberP @t2 @t1) (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t12 @t11) @t2))))))))))) % 14.61/14.81 (assume @p4 @t24) % 14.61/14.81 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= @t26 (exists @t16 (and @t15 (= @t25 @t2))))))))) % 14.61/14.81 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= @t29 (exists @t16 (and @t15 (= @t28 @t2))))))))) % 14.61/14.81 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= @t30 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t28 @t10) @t2))))))))))) % 14.61/14.81 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (not (and @t32 @t31))))))))))))))))) % 14.61/14.81 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (or @t32 @t31)))))))))))))))) % 14.61/14.81 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (or @t41 (tptp.lt @t12 @t1))))))))))))))))) % 14.61/14.81 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 @t32))))))))))))))) % 14.61/14.81 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 @t41))))))))))))))) % 14.61/14.81 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (not @t42)))))))))))))))) % 14.61/14.81 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t34))) @t2) @t42))))))))))))) % 14.61/14.81 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t27 @t5))))) % 14.61/14.81 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t43)))))) % 14.61/14.81 (assume @p17 @t44) % 14.61/14.81 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t43 @t2))))))) % 14.61/14.81 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t40 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t45))))))))))) % 14.61/14.81 (assume @p20 (forall @t9 (=> @t17 (or @t47 (exists @t7 (and @t27 (exists @t16 (and @t40 (= @t46 @t2))))))))) % 14.61/14.81 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t43))))))) % 14.61/14.81 (assume @p22 @t53) % 14.61/14.81 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t43) @t1)))))) % 14.61/14.81 (assume @p24 @t58) % 14.61/14.81 (assume @p25 @t63) % 14.61/14.81 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (tptp.ssList @t64)))))) % 14.61/14.81 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t40 (= (tptp.cons @t12 @t65) (tptp.app @t46 @t2))))))))) % 14.61/14.81 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 14.61/14.81 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t67 @t66) @t3)))))) % 14.61/14.81 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t67 @t32) (tptp.leq @t2 @t12))))))))) % 14.61/14.81 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 14.61/14.81 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t68 @t66)))))) % 14.61/14.81 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t70 (not @t69))))))) % 14.61/14.81 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t70 @t41) @t71)))))))) % 14.61/14.81 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t72 @t69)))))) % 14.61/14.81 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (= (tptp.memberP @t25 @t2) (or (tptp.memberP @t1 @t2) @t73))))))))) % 14.61/14.81 (assume @p37 @t79) % 14.61/14.81 (assume @p38 @t81) % 14.61/14.81 (assume @p39 @t83) % 14.61/14.81 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (and @t26 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 14.61/14.81 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t26 (tptp.frontsegP @t1 @t2)) @t3)))))) % 14.61/14.81 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 14.61/14.81 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> @t26 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 14.61/14.81 (assume @p44 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (= (tptp.frontsegP (tptp.cons @t2 @t12) @t11) (and @t3 (tptp.frontsegP @t12 @t10)))))))))))) % 14.61/14.81 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 14.61/14.81 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t47)))) % 14.61/14.81 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (and @t29 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 14.61/14.81 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t29 (tptp.rearsegP @t1 @t2)) @t3)))))) % 14.61/14.81 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 14.61/14.81 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> @t29 (tptp.rearsegP @t84 @t1))))))))) % 14.61/14.81 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 14.61/14.81 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t47)))) % 14.61/14.81 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (and @t30 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 14.61/14.81 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t30 (tptp.segmentP @t1 @t2)) @t3)))))) % 14.61/14.81 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 14.61/14.81 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t30 (tptp.segmentP (tptp.app @t84 @t10) @t1))))))))))) % 14.61/14.81 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 14.61/14.81 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t47)))) % 14.61/14.81 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t85)))) % 14.61/14.81 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 14.61/14.81 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t85)))) % 14.61/14.81 (assume @p62 (tptp.totalorderP tptp.nil)) % 14.61/14.81 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t85)))) % 14.61/14.81 (assume @p64 (tptp.strictorderP tptp.nil)) % 14.61/14.81 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t85)))) % 14.61/14.81 (assume @p66 (tptp.totalorderedP tptp.nil)) % 14.61/14.81 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t27 (= (tptp.totalorderedP @t89) (or @t87 (and @t88 (tptp.totalorderedP @t1) (tptp.leq @t2 @t86))))))))) % 14.61/14.81 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t85)))) % 14.61/14.81 (assume @p69 (tptp.strictorderedP tptp.nil)) % 14.61/14.81 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t27 (= (tptp.strictorderedP @t89) (or @t87 (and @t88 (tptp.strictorderedP @t1) (tptp.lt @t2 @t86))))))))) % 14.61/14.81 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t85)))) % 14.61/14.81 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 14.61/14.81 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t85)))) % 14.61/14.81 (assume @p74 (tptp.equalelemsP tptp.nil)) % 14.61/14.81 (assume @p75 (forall @t9 (=> @t17 (=> @t50 (exists @t7 (and @t6 (= @t48 @t1))))))) % 14.61/14.81 (assume @p76 (forall @t9 (=> @t17 (=> @t50 (exists @t7 (and @t27 (= @t54 @t1))))))) % 14.61/14.81 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t88 @t50 (= @t86 @t48) (= (tptp.tl @t1) @t54)) @t45)))))) % 14.61/14.81 (assume @p78 @t93) % 14.61/14.81 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (= @t28 @t64) @t94)))))))) % 14.61/14.81 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (= @t25 @t65) @t94)))))))) % 14.61/14.81 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t43 (tptp.app @t18 @t2))))))) % 14.61/14.81 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (= (tptp.app @t64 @t12) (tptp.app @t2 @t25))))))))) % 14.61/14.81 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= (= tptp.nil @t64) (and @t87 @t47))))))) % 14.61/14.81 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 14.61/14.81 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> @t50 (= (tptp.hd @t64) @t48))))))) % 14.61/14.81 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> @t50 (= (tptp.tl @t64) (tptp.app @t54 @t1)))))))) % 14.61/14.81 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t68 (tptp.geq @t1 @t2)) @t3)))))) % 14.61/14.81 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t68 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 14.61/14.81 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 14.61/14.81 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 14.61/14.81 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t67 @t41) @t71)))))))) % 14.61/14.81 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t67 (or @t3 @t70))))))) % 14.61/14.81 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t70 (and @t4 @t67))))))) % 14.61/14.81 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t72 (not (tptp.gt @t1 @t2)))))))) % 14.61/14.81 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t72 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 14.61/14.81 (assume @p96 @t115) % 14.61/14.81 (assume @p97 true) % 14.61/14.81 (step @p98 :rule quant-miniscope-or :args ((= (forall @t9 @t127) (or @t126 @t124)))) % 14.61/14.81 (step @p99 :rule aci_norm :args ((= @t128 @t127))) % 14.61/14.81 (step @p100 :rule cong :premises (@p99) :args ((forall @t9 @t128))) % 14.61/14.81 (step @p101 :rule trans :premises (@p100 @p98)) % 14.61/14.81 (step @p102 :rule aci_norm :args ((= (or @t122 @t129) @t128))) % 14.61/14.81 (step @p103 :rule bool-impl-elim :args (@t17 @t129)) % 14.61/14.81 (step @p104 :rule trans :premises (@p103 @p102)) % 14.61/14.81 (step @p105 :rule cong :premises (@p104) :args ((forall @t9 (=> @t17 @t129)))) % 14.61/14.81 (step @p106 :rule trans :premises (@p105 @p101)) % 14.61/14.81 (step @p107 :rule quant-miniscope-or :args ((= (forall @t7 @t130) @t129))) % 14.61/14.81 (step @p108 :rule aci_norm :args ((= @t131 @t130))) % 14.61/14.81 (step @p109 :rule cong :premises (@p108) :args ((forall @t7 @t131))) % 14.61/14.81 (step @p110 :rule trans :premises (@p109 @p107)) % 14.61/14.81 (step @p111 :rule aci_norm :args ((= (or @t125 @t132) @t131))) % 14.61/14.81 (step @p112 :rule bool-impl-elim :args (@t27 @t132)) % 14.61/14.81 (step @p113 :rule trans :premises (@p112 @p111)) % 14.61/14.81 (step @p114 :rule cong :premises (@p113) :args ((forall @t7 (=> @t27 @t132)))) % 14.61/14.81 (step @p115 :rule trans :premises (@p114 @p110)) % 14.61/14.81 (step @p116 :rule aci_norm :args ((= (or @t121 @t125 @t133) @t132))) % 14.61/14.81 (step @p117 :rule aci_norm :args ((= (or @t122 false @t116) @t133))) % 14.61/14.81 (step @p118 :rule refl :args (@t116)) % 14.61/14.81 (step @p119 :rule evaluate :args ((not true))) % 14.61/14.81 (step @p120 :rule eq-refl :args (@t2)) % 14.61/14.81 (step @p121 :rule cong :premises (@p120) :args (@t134)) % 14.61/14.81 (step @p122 :rule trans :premises (@p121 @p119)) % 14.61/14.81 (step @p123 :rule refl :args (@t122)) % 14.61/14.81 (step @p124 :rule nary_cong :premises (@p123 @p122 @p118) :args (@t135)) % 14.61/14.81 (step @p125 :rule trans :premises (@p124 @p117)) % 14.61/14.81 (step @p126 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t94) @t136 @t104 @t103)) @t135))) % 14.61/14.81 (step @p127 :rule refl :args (@t103)) % 14.61/14.81 (step @p128 :rule refl :args (@t104)) % 14.61/14.81 (step @p129 :rule refl :args (@t136)) % 14.61/14.81 (step @p130 :rule eq-symm :args (@t2 @t12)) % 14.61/14.81 (step @p131 :rule cong :premises (@p130) :args (@t104)) % 14.61/14.81 (step @p132 :rule nary_cong :premises (@p131 @p129 @p128 @p127) :args (@t137)) % 14.61/14.81 (step @p133 :rule aci_norm :args ((= @t138 @t137))) % 14.61/14.81 (step @p134 :rule trans :premises (@p133 @p132)) % 14.61/14.81 (step @p135 :rule cong :premises (@p134) :args (@t139)) % 14.61/14.81 (step @p136 :rule trans :premises (@p135 @p126)) % 14.61/14.81 (step @p137 :rule trans :premises (@p136 @p125)) % 14.61/14.81 (step @p138 :rule refl :args (@t125)) % 14.61/14.81 (step @p139 :rule refl :args (@t121)) % 14.61/14.81 (step @p140 :rule nary_cong :premises (@p139 @p138 @p137) :args (@t140)) % 14.61/14.81 (step @p141 :rule trans :premises (@p140 @p116)) % 14.61/14.81 (step @p142 :rule quant-miniscope-or :args ((= (forall @t16 @t141) @t140))) % 14.61/14.81 (step @p143 :rule aci_norm :args ((= @t142 @t141))) % 14.61/14.81 (step @p144 :rule cong :premises (@p143) :args ((forall @t16 @t142))) % 14.61/14.81 (step @p145 :rule trans :premises (@p144 @p142)) % 14.61/14.81 (step @p146 :rule trans :premises (@p145 @p141)) % 14.61/14.81 (step @p147 :rule aci_norm :args ((= (or @t136 @t143) @t142))) % 14.61/14.81 (step @p148 :rule bool-impl-elim :args (@t15 @t143)) % 14.61/14.81 (step @p149 :rule trans :premises (@p148 @p147)) % 14.61/14.81 (step @p150 :rule cong :premises (@p149) :args ((forall @t16 (=> @t15 @t143)))) % 14.61/14.81 (step @p151 :rule trans :premises (@p150 @p146)) % 14.61/14.81 (step @p152 :rule aci_norm :args ((= (or @t125 false) @t125))) % 14.61/14.81 (step @p153 :rule eq-refl :args (@t1)) % 14.61/14.81 (step @p154 :rule cong :premises (@p153) :args (@t144)) % 14.61/14.81 (step @p155 :rule trans :premises (@p154 @p119)) % 14.61/14.81 (step @p156 :rule nary_cong :premises (@p138 @p155) :args (@t145)) % 14.61/14.81 (step @p157 :rule trans :premises (@p156 @p152)) % 14.61/14.81 (step @p158 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t146 @t105)) @t145))) % 14.61/14.81 (step @p159 :rule refl :args (@t105)) % 14.61/14.81 (step @p160 :rule refl :args (@t146)) % 14.61/14.81 (step @p161 :rule eq-symm :args (@t1 @t10)) % 14.61/14.81 (step @p162 :rule cong :premises (@p161) :args (@t105)) % 14.61/14.81 (step @p163 :rule nary_cong :premises (@p162 @p160 @p159) :args (@t147)) % 14.61/14.81 (step @p164 :rule aci_norm :args ((= @t148 @t147))) % 14.61/14.81 (step @p165 :rule trans :premises (@p164 @p163)) % 14.61/14.81 (step @p166 :rule cong :premises (@p165) :args (@t149)) % 14.61/14.81 (step @p167 :rule trans :premises (@p166 @p158)) % 14.61/14.81 (step @p168 :rule trans :premises (@p167 @p157)) % 14.61/14.81 (step @p169 :rule refl :args (@t103)) % 14.61/14.81 (step @p170 :rule refl :args (@t104)) % 14.61/14.81 (step @p171 :rule nary_cong :premises (@p170 @p169 @p139 @p168) :args (@t150)) % 14.61/14.81 (step @p172 :rule quant-miniscope-or :args ((= (forall @t14 @t151) @t150))) % 14.61/14.81 (step @p173 :rule aci_norm :args ((= @t152 @t151))) % 14.61/14.81 (step @p174 :rule cong :premises (@p173) :args ((forall @t14 @t152))) % 14.61/14.81 (step @p175 :rule trans :premises (@p174 @p172)) % 14.61/14.81 (step @p176 :rule trans :premises (@p175 @p171)) % 14.61/14.81 (step @p177 :rule aci_norm :args ((= (or @t146 @t153) @t152))) % 14.61/14.81 (step @p178 :rule bool-impl-elim :args (@t13 @t153)) % 14.61/14.81 (step @p179 :rule trans :premises (@p178 @p177)) % 14.61/14.81 (step @p180 :rule cong :premises (@p179) :args ((forall @t14 (=> @t13 @t153)))) % 14.61/14.81 (step @p181 :rule trans :premises (@p180 @p176)) % 14.61/14.81 (step @p182 :rule bool-and-de-morgan :args (@t100 @t119 true)) % 14.61/14.81 (step @p183 :rule cong :premises (@p182) :args (@t155)) % 14.61/14.81 (step @p184 :rule cong :premises (@p183) :args (@t156)) % 14.61/14.81 (step @p185 :rule exists-elim :args ((= (exists @t39 @t154) @t156))) % 14.61/14.81 (step @p186 :rule trans :premises (@p185 @p184)) % 14.61/14.81 (step @p187 :rule aci_norm :args ((= (or @t117 @t97) @t118))) % 14.61/14.81 (step @p188 :rule bool-impl-elim :args (@t98 @t97)) % 14.61/14.81 (step @p189 :rule trans :premises (@p188 @p187)) % 14.61/14.81 (step @p190 :rule cong :premises (@p189) :args (@t99)) % 14.61/14.81 (step @p191 :rule refl :args (@t100)) % 14.61/14.81 (step @p192 :rule nary_cong :premises (@p191 @p190) :args (@t101)) % 14.61/14.81 (step @p193 :rule cong :premises (@p192) :args (@t102)) % 14.61/14.81 (step @p194 :rule trans :premises (@p193 @p186)) % 14.61/14.81 (step @p195 :rule refl :args (@t105)) % 14.61/14.81 (step @p196 :rule nary_cong :premises (@p195 @p170 @p169 @p194) :args (@t106)) % 14.61/14.81 (step @p197 :rule refl :args (@t13)) % 14.61/14.81 (step @p198 :rule cong :premises (@p197 @p196) :args (@t107)) % 14.61/14.81 (step @p199 :rule cong :premises (@p198) :args (@t108)) % 14.61/14.81 (step @p200 :rule trans :premises (@p199 @p181)) % 14.61/14.81 (step @p201 :rule refl :args (@t15)) % 14.61/14.81 (step @p202 :rule cong :premises (@p201 @p200) :args (@t109)) % 14.61/14.81 (step @p203 :rule cong :premises (@p202) :args (@t110)) % 14.61/14.81 (step @p204 :rule trans :premises (@p203 @p151)) % 14.61/14.81 (step @p205 :rule refl :args (@t27)) % 14.61/14.81 (step @p206 :rule cong :premises (@p205 @p204) :args (@t111)) % 14.61/14.81 (step @p207 :rule cong :premises (@p206) :args (@t112)) % 14.61/14.81 (step @p208 :rule trans :premises (@p207 @p115)) % 14.61/14.81 (step @p209 :rule refl :args (@t17)) % 14.61/14.81 (step @p210 :rule cong :premises (@p209 @p208) :args (@t113)) % 14.61/14.81 (step @p211 :rule cong :premises (@p210) :args (@t114)) % 14.61/14.81 (step @p212 :rule trans :premises (@p211 @p106)) % 14.61/14.81 (step @p213 :rule cong :premises (@p212) :args (@t115)) % 14.61/14.81 (step @p214 :rule eq_resolve :premises (@p96 @p213)) % 14.61/14.81 (step @p215 :rule not_or_elim :premises (@p214) :args (1)) % 14.61/14.81 (step @p216 :rule skolemize :premises (@p215)) % 14.61/14.81 (step @p217 :rule bool-double-not-elim :args (@t159)) % 14.61/14.81 (step @p218 :rule refl :args (@t165)) % 14.61/14.81 (step @p219 :rule nary_cong :premises (@p218 @p217) :args ((or @t165 (not @t162)))) % 14.61/14.81 (step @p220 :rule cnf_or_neg :args (@t165 1)) % 14.61/14.81 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 14.61/14.81 (step @p222 :rule reordering :premises (@p221) :args ((or @t159 @t165))) % 14.61/14.81 (step @p223 :rule chain_m_resolution :premises (@p222 @p216) :args (@t159 @t166 @t167)) % 14.61/14.81 (step @p224 :rule eq-symm :args (@t168 @t33)) % 14.61/14.81 (step @p225 :rule refl :args (@t158)) % 14.61/14.81 (step @p226 :rule refl :args (@t117)) % 14.61/14.81 (step @p227 :rule nary_cong :premises (@p226 @p225 @p224) :args (@t169)) % 14.61/14.81 (step @p228 :rule cong :premises (@p227) :args (@t170)) % 14.61/14.81 (step @p229 :rule cong :premises (@p228) :args (@t171)) % 14.61/14.81 (step @p230 :rule refl :args (@t173)) % 14.61/14.81 (step @p231 :rule nary_cong :premises (@p230 @p229) :args (@t174)) % 14.61/14.81 (step @p232 :rule refl :args (@t159)) % 14.61/14.81 (step @p233 :rule cong :premises (@p232 @p231) :args ((=> @t159 @t174))) % 14.61/14.81 (assume-push @p643 @t159) % 14.61/14.81 (step @p235 :rule instantiate :premises (@p223) :args ((@list @t168))) % 14.61/14.81 (step-pop @p644 :rule scope :premises (@p235)) % 14.61/14.81 (step @p236 :rule process_scope :premises (@p644) :args (@t174)) % 14.61/14.81 (step @p238 :rule eq_resolve :premises (@p236 @p233)) % 14.61/14.81 (step @p239 :rule implies_elim :premises (@p238)) % 14.61/14.81 (step @p240 :rule chain_m_resolution :premises (@p239 @p223) :args (@t177 @t178 (@list @t159))) % 14.61/14.81 (step @p241 :rule aci_norm :args ((= (or @t122 (or @t179 @t49)) @t180))) % 14.61/14.81 (step @p242 :rule refl :args (@t49)) % 14.61/14.81 (step @p243 :rule bool-double-not-elim :args (@t179)) % 14.61/14.81 (step @p244 :rule nary_cong :premises (@p243 @p242) :args ((or @t182 @t49))) % 14.61/14.81 (step @p245 :rule bool-impl-elim :args (@t181 @t49)) % 14.61/14.81 (step @p246 :rule trans :premises (@p245 @p244)) % 14.61/14.81 (step @p247 :rule refl :args (@t122)) % 14.61/14.81 (step @p248 :rule nary_cong :premises (@p247 @p246) :args ((or @t122 @t183))) % 14.61/14.81 (step @p249 :rule trans :premises (@p248 @p241)) % 14.61/14.81 (step @p250 :rule bool-impl-elim :args (@t17 @t183)) % 14.61/14.81 (step @p251 :rule trans :premises (@p250 @p249)) % 14.61/14.81 (step @p252 :rule cong :premises (@p251) :args ((forall @t9 (=> @t17 @t183)))) % 14.61/14.81 (step @p253 :rule refl :args (@t49)) % 14.61/14.81 (step @p254 :rule eq-symm :args (tptp.nil @t2)) % 14.61/14.81 (step @p255 :rule cong :premises (@p254) :args (@t50)) % 14.61/14.81 (step @p256 :rule cong :premises (@p255 @p253) :args (@t51)) % 14.61/14.81 (step @p257 :rule cong :premises (@p209 @p256) :args (@t52)) % 14.61/14.81 (step @p258 :rule cong :premises (@p257) :args (@t53)) % 14.61/14.81 (step @p259 :rule trans :premises (@p258 @p252)) % 14.61/14.81 (step @p260 :rule eq_resolve :premises (@p22 @p259)) % 14.61/14.81 (step @p261 :rule refl :args (@t172)) % 14.61/14.81 (step @p262 :rule eq-symm :args (@t157 tptp.nil)) % 14.61/14.81 (step @p263 :rule refl :args (@t164)) % 14.61/14.81 (step @p264 :rule nary_cong :premises (@p263 @p262 @p261) :args (@t185)) % 14.61/14.81 (step @p265 :rule refl :args (@t186)) % 14.61/14.81 (step @p266 :rule cong :premises (@p265 @p264) :args ((=> @t186 @t185))) % 14.61/14.81 (assume-push @p645 @t186) % 14.61/14.81 (step @p268 :rule instantiate :premises (@p260) :args (@t187)) % 14.61/14.81 (step-pop @p646 :rule scope :premises (@p268)) % 14.61/14.81 (step @p269 :rule process_scope :premises (@p646) :args (@t185)) % 14.61/14.81 (step @p271 :rule eq_resolve :premises (@p269 @p266)) % 14.61/14.81 (step @p272 :rule implies_elim :premises (@p271)) % 14.61/14.81 (step @p273 :rule chain_m_resolution :premises (@p272 @p260) :args (@t189 @t178 (@list @t186))) % 14.61/14.81 (step @p274 :rule bool-double-not-elim :args (@t160)) % 14.61/14.81 (step @p275 :rule nary_cong :premises (@p218 @p274) :args ((or @t165 (not @t161)))) % 14.61/14.81 (step @p276 :rule cnf_or_neg :args (@t165 2)) % 14.61/14.81 (step @p277 :rule eq_resolve :premises (@p276 @p275)) % 14.61/14.81 (step @p278 :rule reordering :premises (@p277) :args ((or @t160 @t165))) % 14.61/14.81 (step @p279 :rule chain_m_resolution :premises (@p278 @p216) :args (@t160 @t166 @t167)) % 14.61/14.81 (step @p280 :rule refl :args (@t190)) % 14.61/14.81 (step @p281 :rule refl :args (@t161)) % 14.61/14.81 (step @p282 :rule bool-double-not-elim :args (@t82)) % 14.61/14.81 (step @p283 :rule nary_cong :premises (@p282 @p281 @p280) :args ((or (not @t83) @t161 @t190))) % 14.61/14.81 (assume-push @p647 @t160) % 14.61/14.81 (assume-push @p648 @t188) % 14.61/14.81 (assume-push @p649 @t83) % 14.61/14.81 (step @p287 :rule evaluate :args ((= false true))) % 14.61/14.81 (step @p288 :rule true_intro :premises (@p279)) % 14.61/14.81 (step @p289 :rule cong :premises (@p648) :args (@t82)) % 14.61/14.81 (step @p290 :rule false_intro :premises (@p39)) % 14.61/14.81 (step @p291 :rule symm :premises (@p290)) % 14.61/14.81 (step @p292 :rule trans :premises (@p291 @p289 @p288)) % 14.61/14.81 (step @p293 false :rule eq_resolve :premises (@p292 @p287)) % 14.61/14.81 (step-pop @p650 :rule scope :premises (@p293)) % 14.61/14.81 (step-pop @p651 :rule scope :premises (@p650)) % 14.61/14.81 (step-pop @p652 :rule scope :premises (@p651)) % 14.61/14.81 (step @p294 :rule process_scope :premises (@p652) :args (false)) % 14.61/14.81 (assume-push @p653 @t83) % 14.61/14.81 (assume-push @p654 @t160) % 14.61/14.81 (assume-push @p655 @t188) % 14.61/14.81 (step @p301 :rule and_intro :premises (@p279 @p655 @p39)) % 14.61/14.81 (step-pop @p656 :rule scope :premises (@p301)) % 14.61/14.81 (step-pop @p657 :rule scope :premises (@p656)) % 14.61/14.81 (step-pop @p658 :rule scope :premises (@p657)) % 14.61/14.81 (step @p302 :rule process_scope :premises (@p658) :args (@t191)) % 14.61/14.81 (step @p306 :rule implies_elim :premises (@p302)) % 14.61/14.81 (step @p307 :rule resolution :premises (@p306 @p294) :args (true @t191)) % 14.61/14.81 (step @p308 :rule not_and :premises (@p307)) % 14.61/14.81 (step @p309 :rule eq_resolve :premises (@p308 @p283)) % 14.61/14.81 (step @p310 :rule chain_m_resolution :premises (@p309 @p39 @p279) :args (@t190 (@list true false) (@list @t82 @t160))) % 14.61/14.81 (step @p311 :rule bool-double-not-elim :args 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14.61/14.81 (step @p546 :rule chain_m_resolution :premises (@p545 @p531) :args (@t297 @t178 (@list @t294))) % 14.61/14.81 (step @p547 :rule aci_norm :args ((= (or @t122 (or @t179 @t55)) @t298))) % 14.61/14.81 (step @p548 :rule refl :args (@t55)) % 14.61/14.81 (step @p549 :rule nary_cong :premises (@p243 @p548) :args ((or @t182 @t55))) % 14.61/14.81 (step @p550 :rule bool-impl-elim :args (@t181 @t55)) % 14.61/14.81 (step @p551 :rule trans :premises (@p550 @p549)) % 14.61/14.81 (step @p552 :rule nary_cong :premises (@p247 @p551) :args ((or @t122 @t299))) % 14.61/14.81 (step @p553 :rule trans :premises (@p552 @p547)) % 14.61/14.81 (step @p554 :rule bool-impl-elim :args (@t17 @t299)) % 14.61/14.81 (step @p555 :rule trans :premises (@p554 @p553)) % 14.61/14.81 (step @p556 :rule cong :premises (@p555) :args ((forall @t9 (=> @t17 @t299)))) % 14.61/14.81 (step @p557 :rule refl :args (@t55)) % 14.61/14.81 (step @p558 :rule cong :premises (@p255 @p557) :args (@t56)) % 14.61/14.81 (step @p559 :rule cong :premises (@p209 @p558) :args (@t57)) % 14.61/14.81 (step @p560 :rule cong :premises (@p559) :args (@t58)) % 14.61/14.81 (step @p561 :rule trans :premises (@p560 @p556)) % 14.61/14.81 (step @p562 :rule eq_resolve :premises (@p24 @p561)) % 14.61/14.81 (step @p563 :rule refl :args (@t291)) % 14.61/14.81 (step @p564 :rule nary_cong :premises (@p263 @p262 @p563) :args (@t300)) % 14.61/14.81 (step @p565 :rule refl :args (@t301)) % 14.61/14.81 (step @p566 :rule cong :premises (@p565 @p564) :args ((=> @t301 @t300))) % 14.61/14.81 (assume-push @p679 @t301) % 14.61/14.81 (step @p568 :rule instantiate :premises (@p562) :args (@t187)) % 14.61/14.81 (step-pop @p680 :rule scope :premises (@p568)) % 14.61/14.81 (step @p569 :rule process_scope :premises (@p680) :args (@t300)) % 14.61/14.81 (step @p571 :rule eq_resolve :premises (@p569 @p566)) % 14.61/14.81 (step @p572 :rule implies_elim :premises (@p571)) % 14.61/14.81 (step @p573 :rule chain_m_resolution :premises (@p572 @p562) :args (@t302 @t178 (@list @t301))) % 14.61/14.81 (step @p574 :rule cnf_or_pos :args (@t302)) % 14.61/14.81 (step @p575 :rule reordering :premises (@p574) :args ((or @t164 @t188 @t291 (not @t302)))) % 14.61/14.81 (step @p576 :rule chain_m_resolution :premises (@p575 @p316 @p310 @p573) :args (@t291 @t192 (@list @t163 @t188 @t302))) % 14.61/14.81 (step @p577 :rule cnf_or_pos :args (@t297)) % 14.61/14.81 (step @p578 :rule reordering :premises (@p577) :args ((or @t173 @t292 @t199 @t296 (not @t297)))) % 14.61/14.81 (step @p579 :rule chain_m_resolution :premises (@p578 @p319 @p576 @p353 @p546) :args (@t296 (@list false false false false) (@list @t172 @t291 @t198 @t297))) % 14.61/14.81 (step @p580 :rule bool-double-not-elim :args (@t196)) % 14.61/14.81 (step @p581 :rule nary_cong :premises (@p348 @p580) :args ((or @t200 (not @t197)))) % 14.61/14.81 (step @p582 :rule cnf_or_neg :args (@t200 1)) % 14.61/14.81 (step @p583 :rule eq_resolve :premises (@p582 @p581)) % 14.61/14.81 (step @p584 :rule reordering :premises (@p583) :args ((or @t196 @t200))) % 14.61/14.81 (step @p585 :rule chain_m_resolution :premises (@p584 @p340) :args (@t196 @t166 @t205)) % 14.61/14.81 (step @p586 :rule aci_norm :args ((= (or @t122 (or @t179 @t303)) @t304))) % 14.61/14.81 (step @p587 :rule refl :args (@t303)) % 14.61/14.81 (step @p588 :rule nary_cong :premises (@p243 @p587) :args ((or @t182 @t303))) % 14.61/14.81 (step @p589 :rule bool-impl-elim :args (@t181 @t303)) % 14.61/14.81 (step @p590 :rule trans :premises (@p589 @p588)) % 14.61/14.81 (step @p591 :rule nary_cong :premises (@p247 @p590) :args ((or @t122 @t305))) % 14.61/14.81 (step @p592 :rule trans :premises (@p591 @p586)) % 14.61/14.81 (step @p593 :rule bool-impl-elim :args (@t17 @t305)) % 14.61/14.81 (step @p594 :rule trans :premises (@p593 @p592)) % 14.61/14.81 (step @p595 :rule cong :premises (@p594) :args ((forall @t9 (=> @t17 @t305)))) % 14.61/14.81 (step @p596 :rule eq-symm :args (@t90 @t2)) % 14.61/14.81 (step @p597 :rule cong :premises (@p255 @p596) :args (@t91)) % 14.61/14.81 (step @p598 :rule cong :premises (@p209 @p597) :args (@t92)) % 14.61/14.81 (step @p599 :rule cong :premises (@p598) :args (@t93)) % 14.61/14.81 (step @p600 :rule trans :premises (@p599 @p595)) % 14.61/14.81 (step @p601 :rule eq_resolve :premises (@p78 @p600)) % 14.61/14.81 (step @p602 :rule refl :args (@t306)) % 14.61/14.81 (step @p603 :rule nary_cong :premises (@p263 @p262 @p602) :args (@t307)) % 14.61/14.81 (step @p604 :rule refl :args (@t308)) % 14.61/14.81 (step @p605 :rule cong :premises (@p604 @p603) :args ((=> @t308 @t307))) % 14.61/14.81 (assume-push @p681 @t308) % 14.61/14.81 (step @p607 :rule instantiate :premises (@p601) :args (@t187)) % 14.61/14.81 (step-pop @p682 :rule scope :premises (@p607)) % 14.61/14.81 (step @p608 :rule process_scope :premises (@p682) :args (@t307)) % 14.61/14.81 (step @p610 :rule eq_resolve :premises (@p608 @p605)) % 14.61/14.81 (step @p611 :rule implies_elim :premises (@p610)) % 14.61/14.81 (step @p612 :rule chain_m_resolution :premises (@p611 @p601) :args (@t309 @t178 (@list @t308))) % 14.61/14.81 (step @p613 :rule cnf_or_pos :args (@t309)) % 14.61/14.81 (step @p614 :rule reordering :premises (@p613) :args ((or @t164 @t188 @t306 (not @t309)))) % 14.61/14.81 (step @p615 :rule chain_m_resolution :premises (@p614 @p316 @p310 @p612) :args (@t306 @t192 (@list @t163 @t188 @t309))) % 14.61/14.81 (assume-push @p683 @t306) % 14.61/14.81 (assume-push @p684 @t196) % 14.61/14.81 (assume-push @p685 @t196) % 14.61/14.81 (assume-push @p686 @t306) % 14.61/14.81 (step @p620 :rule true_intro :premises (@p684)) % 14.61/14.81 (step @p470 :rule refl :args (@t194)) % 14.61/14.81 (step @p621 :rule symm :premises (@p683)) % 14.61/14.81 (step @p622 :rule cong :premises (@p621 @p470) :args (@t289)) % 14.61/14.81 (step @p623 :rule trans :premises (@p622 @p620)) % 14.61/14.81 (step @p624 :rule true_elim :premises (@p623)) % 14.61/14.81 (step-pop @p687 :rule scope :premises (@p624)) % 14.61/14.81 (step-pop @p688 :rule scope :premises (@p687)) % 14.61/14.81 (step @p625 :rule process_scope :premises (@p688) :args (@t289)) % 14.61/14.81 (step @p628 :rule and_intro :premises (@p684 @p683)) % 14.61/14.81 (step @p629 :rule modus_ponens :premises (@p628 @p625)) % 14.61/14.81 (step-pop @p689 :rule scope :premises (@p629)) % 14.61/14.81 (step-pop @p690 :rule scope :premises (@p689)) % 14.61/14.81 (step @p630 :rule process_scope :premises (@p690) :args (@t289)) % 14.61/14.81 (step @p633 :rule implies_elim :premises (@p630)) % 14.61/14.81 (step @p634 :rule cnf_and_neg :args (@t310)) % 14.61/14.81 (step @p635 :rule resolution :premises (@p634 @p633) :args (true @t310)) % 14.61/14.87 (step @p636 :rule chain_m_resolution :premises (@p635 @p615 @p585) :args (@t289 @t193 (@list @t306 @t196))) % 14.61/14.87 (step @p637 :rule cnf_equiv_pos1 :args (@t296)) % 14.61/14.87 (step @p638 :rule reordering :premises (@p637) :args ((or @t295 (not @t289) (not @t296)))) % 14.61/14.87 (step @p639 :rule chain_m_resolution :premises (@p638 @p636 @p579) :args (@t295 @t193 (@list @t289 @t296))) % 14.61/14.87 (step @p640 :rule cnf_or_pos :args (@t295)) % 14.61/14.87 (step @p641 :rule reordering :premises (@p640) :args ((or @t195 @t254 (not @t295)))) % 14.61/14.87 (step @p642 false :rule chain_m_resolution :premises (@p641 @p639 @p491 @p342) :args (false (@list false true true) (@list @t295 @t254 @t195))) % 14.61/14.87 ) % 14.61/14.87 % SZS output end Proof % 14.61/14.87 % cvc5 exiting %------------------------------------------------------------------------------