%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC293+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:58:45 AM UTC 2026 % Result : Theorem 0.35s 0.68s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC293+1 : TPTP v9.2.1. Released v2.4.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n017.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 19:36:31 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.68 % SZS status Theorem % 0.35/0.68 % SZS output start Proof % 0.35/0.68 ( % 0.35/0.68 (declare-sort $$unsorted 0) % 0.35/0.68 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.35/0.68 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.35/0.68 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.68 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.68 (declare-const tptp.nil $$unsorted) % 0.35/0.68 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.35/0.68 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.35/0.68 (define @t1 () (@var "V" $$unsorted)) % 0.35/0.68 (define @t2 () (@var "U" $$unsorted)) % 0.35/0.68 (define @t3 () (= @t2 @t1)) % 0.35/0.68 (define @t4 () (not @t3)) % 0.35/0.68 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.35/0.68 (define @t6 () (tptp.ssItem @t1)) % 0.35/0.68 (define @t7 () (@list @t1)) % 0.35/0.68 (define @t8 () (tptp.ssItem @t2)) % 0.35/0.68 (define @t9 () (@list @t2)) % 0.35/0.68 (define @t10 () (@var "X" $$unsorted)) % 0.35/0.68 (define @t11 () (tptp.cons @t1 @t10)) % 0.35/0.68 (define @t12 () (@var "W" $$unsorted)) % 0.35/0.68 (define @t13 () (tptp.ssList @t10)) % 0.35/0.68 (define @t14 () (@list @t10)) % 0.35/0.68 (define @t15 () (tptp.ssList @t12)) % 0.35/0.68 (define @t16 () (@list @t12)) % 0.35/0.68 (define @t17 () (tptp.ssList @t2)) % 0.35/0.68 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.35/0.68 (define @t19 () (tptp.app @t1 @t12)) % 0.35/0.68 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.35/0.68 (define @t21 () (tptp.ssList @t1)) % 0.35/0.68 (define @t22 () (tptp.app @t12 @t1)) % 0.35/0.68 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.35/0.68 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.35/0.68 (define @t25 () (tptp.leq @t12 @t1)) % 0.35/0.68 (define @t26 () (tptp.leq @t1 @t12)) % 0.35/0.68 (define @t27 () (@var "Z" $$unsorted)) % 0.35/0.68 (define @t28 () (@var "Y" $$unsorted)) % 0.35/0.68 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.35/0.68 (define @t30 () (tptp.ssList @t27)) % 0.35/0.68 (define @t31 () (@list @t27)) % 0.35/0.68 (define @t32 () (tptp.ssList @t28)) % 0.35/0.68 (define @t33 () (@list @t28)) % 0.35/0.68 (define @t34 () (tptp.ssItem @t12)) % 0.35/0.68 (define @t35 () (tptp.lt @t1 @t12)) % 0.35/0.68 (define @t36 () (tptp.strictorderedP @t2)) % 0.35/0.68 (define @t37 () (= @t1 @t12)) % 0.35/0.68 (define @t38 () (tptp.cons @t1 @t2)) % 0.35/0.68 (define @t39 () (= @t1 @t2)) % 0.35/0.68 (define @t40 () (tptp.cons @t12 @t1)) % 0.35/0.68 (define @t41 () (= tptp.nil @t2)) % 0.35/0.68 (define @t42 () (tptp.hd @t2)) % 0.35/0.68 (define @t43 () (not @t41)) % 0.35/0.68 (define @t44 () (tptp.tl @t2)) % 0.35/0.68 (define @t45 () (tptp.app @t2 @t1)) % 0.35/0.68 (define @t46 () (tptp.app @t1 @t2)) % 0.35/0.68 (define @t47 () (tptp.leq @t1 @t2)) % 0.35/0.68 (define @t48 () (tptp.leq @t2 @t1)) % 0.35/0.68 (define @t49 () (tptp.geq @t2 @t1)) % 0.35/0.68 (define @t50 () (tptp.lt @t1 @t2)) % 0.35/0.68 (define @t51 () (tptp.lt @t2 @t1)) % 0.35/0.68 (define @t52 () (tptp.lt @t2 @t12)) % 0.35/0.68 (define @t53 () (tptp.gt @t2 @t1)) % 0.35/0.68 (define @t54 () (tptp.memberP @t12 @t2)) % 0.35/0.68 (define @t55 () (tptp.app @t12 @t2)) % 0.35/0.68 (define @t56 () (tptp.cons @t2 tptp.nil)) % 0.35/0.68 (define @t57 () (tptp.hd @t1)) % 0.35/0.68 (define @t58 () (= tptp.nil @t1)) % 0.35/0.68 (define @t59 () (not @t58)) % 0.35/0.68 (define @t60 () (tptp.cons @t2 @t1)) % 0.35/0.68 (define @t61 () (tptp.strictorderedP @t56)) % 0.35/0.68 (define @t62 () (forall @t9 (=> @t8 @t61))) % 0.35/0.68 (define @t63 () (tptp.strictorderedP tptp.nil)) % 0.35/0.68 (define @t64 () (= @t12 @t2)) % 0.35/0.68 (define @t65 () (not (= tptp.nil @t12))) % 0.35/0.68 (define @t66 () (not (= tptp.nil @t10))) % 0.35/0.68 (define @t67 () (or @t66 @t65)) % 0.35/0.68 (define @t68 () (not (tptp.memberP @t10 @t28))) % 0.35/0.68 (define @t69 () (tptp.cons @t28 tptp.nil)) % 0.35/0.68 (define @t70 () (not (= @t69 @t12))) % 0.35/0.68 (define @t71 () (not (tptp.ssItem @t28))) % 0.35/0.68 (define @t72 () (or @t71 @t70 @t68)) % 0.35/0.68 (define @t73 () (forall @t33 @t72)) % 0.35/0.68 (define @t74 () (and @t73 @t67)) % 0.35/0.68 (define @t75 () (not (= @t2 @t12))) % 0.35/0.68 (define @t76 () (not (= @t1 @t10))) % 0.35/0.68 (define @t77 () (not @t13)) % 0.35/0.68 (define @t78 () (or @t77 @t76 @t75 @t36 @t74)) % 0.35/0.68 (define @t79 () (forall @t14 @t78)) % 0.35/0.68 (define @t80 () (=> @t15 @t79)) % 0.35/0.68 (define @t81 () (forall @t16 @t80)) % 0.35/0.68 (define @t82 () (=> @t21 @t81)) % 0.35/0.68 (define @t83 () (forall @t7 @t82)) % 0.35/0.68 (define @t84 () (=> @t17 @t83)) % 0.35/0.68 (define @t85 () (forall @t9 @t84)) % 0.35/0.68 (define @t86 () (not @t85)) % 0.35/0.68 (define @t87 () (not (= @t2 tptp.nil))) % 0.35/0.68 (define @t88 () (@var "BOUND_VARIABLE_11064" $$unsorted)) % 0.35/0.68 (define @t89 () (not (= @t88 tptp.nil))) % 0.35/0.68 (define @t90 () (or @t89 @t87)) % 0.35/0.68 (define @t91 () (@var "BOUND_VARIABLE_11066" $$unsorted)) % 0.35/0.68 (define @t92 () (or (not (tptp.ssItem @t91)) (not (= @t2 (tptp.cons @t91 tptp.nil))) (not (tptp.memberP @t88 @t91)))) % 0.35/0.68 (define @t93 () (and @t92 @t90)) % 0.35/0.68 (define @t94 () (not (tptp.ssList @t88))) % 0.35/0.68 (define @t95 () (not @t17)) % 0.35/0.68 (define @t96 () (or @t95 @t36 @t94 @t93)) % 0.35/0.68 (define @t97 () (or @t94 @t93)) % 0.35/0.68 (define @t98 () (or @t95 @t36 @t97)) % 0.35/0.68 (define @t99 () (@list @t2 @t88 @t91)) % 0.35/0.68 (define @t100 () (forall @t99 @t98)) % 0.35/0.68 (define @t101 () (@list @t88 @t91)) % 0.35/0.68 (define @t102 () (forall @t101 @t98)) % 0.35/0.68 (define @t103 () (forall @t101 @t97)) % 0.35/0.68 (define @t104 () (@var "BOUND_VARIABLE_11045" $$unsorted)) % 0.35/0.68 (define @t105 () (or @t95 @t36 @t103)) % 0.35/0.68 (define @t106 () (not (= @t1 tptp.nil))) % 0.35/0.68 (define @t107 () (or @t106 @t87)) % 0.35/0.68 (define @t108 () (or (not (tptp.ssItem @t104)) (not (= @t2 (tptp.cons @t104 tptp.nil))) (not (tptp.memberP @t1 @t104)))) % 0.35/0.68 (define @t109 () (and @t108 @t107)) % 0.35/0.68 (define @t110 () (not @t21)) % 0.35/0.68 (define @t111 () (or @t110 @t109)) % 0.35/0.68 (define @t112 () (forall (@list @t1 @t104) @t111)) % 0.35/0.68 (define @t113 () (or @t95 @t36 @t112)) % 0.35/0.68 (define @t114 () (or @t36 @t95 @t112)) % 0.35/0.68 (define @t115 () (@list @t104)) % 0.35/0.68 (define @t116 () (forall @t115 @t111)) % 0.35/0.68 (define @t117 () (forall @t115 @t107)) % 0.35/0.68 (define @t118 () (forall @t115 @t108)) % 0.35/0.68 (define @t119 () (@var "BOUND_VARIABLE_11020" $$unsorted)) % 0.35/0.68 (define @t120 () (@list @t119)) % 0.35/0.68 (define @t121 () (and @t118 @t117)) % 0.35/0.68 (define @t122 () (forall @t115 @t109)) % 0.35/0.68 (define @t123 () (or @t110 @t122)) % 0.35/0.68 (define @t124 () (and (forall (@list @t119) (or (not (tptp.ssItem @t119)) (not (= @t2 (tptp.cons @t119 tptp.nil))) (not (tptp.memberP @t1 @t119)))) @t107)) % 0.35/0.68 (define @t125 () (or @t110 @t124)) % 0.35/0.68 (define @t126 () (forall @t7 @t125)) % 0.35/0.68 (define @t127 () (or @t36 @t95 @t126)) % 0.35/0.68 (define @t128 () (or @t36 @t95 @t125)) % 0.35/0.68 (define @t129 () (or @t110 @t36 @t95 @t124)) % 0.35/0.68 (define @t130 () (or @t36 @t110 @t95 @t124)) % 0.35/0.68 (define @t131 () (@var "BOUND_VARIABLE_10991" $$unsorted)) % 0.35/0.68 (define @t132 () (@list @t131)) % 0.35/0.68 (define @t133 () (forall @t132 @t107)) % 0.35/0.68 (define @t134 () (not (tptp.memberP @t1 @t131))) % 0.35/0.68 (define @t135 () (tptp.cons @t131 tptp.nil)) % 0.35/0.68 (define @t136 () (not (tptp.ssItem @t131))) % 0.35/0.68 (define @t137 () (or @t136 (not (= @t2 @t135)) @t134)) % 0.35/0.68 (define @t138 () (forall @t132 @t137)) % 0.35/0.68 (define @t139 () (@list @t131)) % 0.35/0.68 (define @t140 () (and @t138 @t133)) % 0.35/0.68 (define @t141 () (and @t137 @t107)) % 0.35/0.68 (define @t142 () (forall @t132 @t141)) % 0.35/0.68 (define @t143 () (or @t95 @t142)) % 0.35/0.68 (define @t144 () (or @t95 @t141)) % 0.35/0.68 (define @t145 () (not (= @t2 @t2))) % 0.35/0.68 (define @t146 () (or @t95 @t145 @t141)) % 0.35/0.68 (define @t147 () (not (= @t12 tptp.nil))) % 0.35/0.68 (define @t148 () (or @t106 @t147)) % 0.35/0.68 (define @t149 () (or @t136 (not (= @t12 @t135)) @t134)) % 0.35/0.68 (define @t150 () (and @t149 @t148)) % 0.35/0.68 (define @t151 () (not @t15)) % 0.35/0.68 (define @t152 () (or @t75 @t151 @t75 @t150)) % 0.35/0.68 (define @t153 () (or @t151 @t75 @t150)) % 0.35/0.68 (define @t154 () (forall @t16 @t153)) % 0.35/0.68 (define @t155 () (forall @t132 @t154)) % 0.35/0.68 (define @t156 () (forall (@list @t131 @t12) @t153)) % 0.35/0.68 (define @t157 () (forall (@list @t12 @t131) @t153)) % 0.35/0.68 (define @t158 () (forall @t132 @t153)) % 0.35/0.68 (define @t159 () (forall @t132 @t148)) % 0.35/0.68 (define @t160 () (forall @t132 @t149)) % 0.35/0.68 (define @t161 () (@var "BOUND_VARIABLE_10966" $$unsorted)) % 0.35/0.68 (define @t162 () (@list @t161)) % 0.35/0.68 (define @t163 () (and @t160 @t159)) % 0.35/0.68 (define @t164 () (forall @t132 @t150)) % 0.35/0.68 (define @t165 () (or @t151 @t75 @t164)) % 0.35/0.68 (define @t166 () (and (forall (@list @t161) (or (not (tptp.ssItem @t161)) (not (= @t12 (tptp.cons @t161 tptp.nil))) (not (tptp.memberP @t1 @t161)))) @t148)) % 0.35/0.68 (define @t167 () (or @t151 @t75 @t166)) % 0.35/0.68 (define @t168 () (forall @t16 @t167)) % 0.35/0.68 (define @t169 () (or @t36 @t110 @t168)) % 0.35/0.68 (define @t170 () (or @t36 @t110 @t167)) % 0.35/0.68 (define @t171 () (or @t151 @t75 @t36 @t110 @t166)) % 0.35/0.68 (define @t172 () (or @t75 @t36 @t110 @t166)) % 0.35/0.68 (define @t173 () (@var "BOUND_VARIABLE_10939" $$unsorted)) % 0.35/0.68 (define @t174 () (@list @t173)) % 0.35/0.68 (define @t175 () (forall @t174 @t148)) % 0.35/0.68 (define @t176 () (not (= @t12 (tptp.cons @t173 tptp.nil)))) % 0.35/0.68 (define @t177 () (not (tptp.ssItem @t173))) % 0.35/0.68 (define @t178 () (or @t177 @t176 (not (tptp.memberP @t1 @t173)))) % 0.35/0.68 (define @t179 () (forall @t174 @t178)) % 0.35/0.68 (define @t180 () (@list @t173)) % 0.35/0.68 (define @t181 () (and @t179 @t175)) % 0.35/0.68 (define @t182 () (and @t178 @t148)) % 0.35/0.68 (define @t183 () (forall @t174 @t182)) % 0.35/0.68 (define @t184 () (or @t110 @t183)) % 0.35/0.68 (define @t185 () (or @t110 @t182)) % 0.35/0.68 (define @t186 () (not (= @t1 @t1))) % 0.35/0.68 (define @t187 () (or @t110 @t186 @t182)) % 0.35/0.68 (define @t188 () (or (not (= @t10 tptp.nil)) @t147)) % 0.35/0.68 (define @t189 () (or @t177 @t176 (not (tptp.memberP @t10 @t173)))) % 0.35/0.68 (define @t190 () (and @t189 @t188)) % 0.35/0.68 (define @t191 () (or @t76 @t77 @t76 @t190)) % 0.35/0.68 (define @t192 () (or @t77 @t76 @t190)) % 0.35/0.68 (define @t193 () (forall @t14 @t192)) % 0.35/0.68 (define @t194 () (forall @t174 @t193)) % 0.35/0.68 (define @t195 () (forall (@list @t173 @t10) @t192)) % 0.35/0.68 (define @t196 () (forall (@list @t10 @t173) @t192)) % 0.35/0.68 (define @t197 () (forall @t174 @t192)) % 0.35/0.68 (define @t198 () (forall @t174 @t188)) % 0.35/0.68 (define @t199 () (forall @t174 @t189)) % 0.35/0.68 (define @t200 () (and @t199 @t198)) % 0.35/0.68 (define @t201 () (forall @t174 @t190)) % 0.35/0.68 (define @t202 () (or @t77 @t76 @t201)) % 0.35/0.68 (define @t203 () (and (forall @t33 (or @t71 (not (= @t12 @t69)) @t68)) @t188)) % 0.35/0.68 (define @t204 () (or @t77 @t76 @t203)) % 0.35/0.68 (define @t205 () (forall @t14 @t204)) % 0.35/0.68 (define @t206 () (or @t75 @t36 @t205)) % 0.35/0.68 (define @t207 () (or @t75 @t36 @t204)) % 0.35/0.68 (define @t208 () (or @t77 @t76 @t75 @t36 @t203)) % 0.35/0.68 (define @t209 () (forall @t99 (or @t95 @t36 @t94 (and @t92 (or (not (= tptp.nil @t88)) @t87))))) % 0.35/0.68 (define @t210 () (@quantifiers_skolemize @t209 0)) % 0.35/0.68 (define @t211 () (= tptp.nil @t210)) % 0.35/0.68 (define @t212 () (not @t211)) % 0.35/0.68 (define @t213 () (@quantifiers_skolemize @t209 1)) % 0.35/0.68 (define @t214 () (not (= tptp.nil @t213))) % 0.35/0.68 (define @t215 () (or @t214 @t212)) % 0.35/0.68 (define @t216 () (@quantifiers_skolemize @t209 2)) % 0.35/0.68 (define @t217 () (tptp.cons @t216 tptp.nil)) % 0.35/0.68 (define @t218 () (= @t210 @t217)) % 0.35/0.68 (define @t219 () (not @t218)) % 0.35/0.68 (define @t220 () (tptp.ssItem @t216)) % 0.35/0.68 (define @t221 () (not @t220)) % 0.35/0.68 (define @t222 () (or @t221 @t219 (not (tptp.memberP @t213 @t216)))) % 0.35/0.68 (define @t223 () (and @t222 @t215)) % 0.35/0.68 (define @t224 () (not (tptp.ssList @t213))) % 0.35/0.68 (define @t225 () (tptp.strictorderedP @t210)) % 0.35/0.68 (define @t226 () (not (tptp.ssList @t210))) % 0.35/0.68 (define @t227 () (or @t226 @t225 @t224 @t223)) % 0.35/0.68 (define @t228 () (not @t227)) % 0.35/0.68 (define @t229 () (not @t209)) % 0.35/0.68 (define @t230 () (not (= @t210 tptp.nil))) % 0.35/0.68 (define @t231 () (or @t214 @t230)) % 0.35/0.68 (define @t232 () (and @t222 @t231)) % 0.35/0.68 (define @t233 () (or @t226 @t225 @t224 @t232)) % 0.35/0.68 (define @t234 () (not @t233)) % 0.35/0.68 (define @t235 () (@list true)) % 0.35/0.68 (define @t236 () (not @t225)) % 0.35/0.68 (define @t237 () (@list @t227)) % 0.35/0.68 (define @t238 () (not @t63)) % 0.35/0.68 (define @t239 () (not @t236)) % 0.35/0.68 (define @t240 () (= false true)) % 0.35/0.68 (define @t241 () (@list @t222)) % 0.35/0.68 (define @t242 () (tptp.strictorderedP @t217)) % 0.35/0.68 (define @t243 () (or @t221 @t242)) % 0.35/0.68 (define @t244 () (not @t242)) % 0.35/0.68 (define @t245 () (and @t242 @t218 @t236)) % 0.35/0.68 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.35/0.68 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.35/0.68 (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))))))))))) % 0.35/0.68 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.35/0.68 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.35/0.68 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.35/0.68 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.35/0.68 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not (and @t26 @t25))))))))))))))))) % 0.35/0.68 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t26 @t25)))))))))))))))) % 0.35/0.68 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t35 (tptp.lt @t12 @t1))))))))))))))))) % 0.35/0.68 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t26))))))))))))))) % 0.35/0.68 (assume @p12 (forall @t9 (=> @t17 (= @t36 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t35))))))))))))))) % 0.35/0.68 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not @t37)))))))))))))))) % 0.35/0.68 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t28))) @t2) @t37))))))))))))) % 0.35/0.68 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.35/0.68 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.35/0.68 (assume @p17 (tptp.ssList tptp.nil)) % 0.35/0.68 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.35/0.68 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t39))))))))))) % 0.35/0.68 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t40 @t2))))))))) % 0.35/0.68 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.35/0.68 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.35/0.68 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.35/0.68 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.35/0.68 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.35/0.68 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t45)))))) % 0.35/0.68 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.35/0.68 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.35/0.68 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.35/0.68 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t26) (tptp.leq @t2 @t12))))))))) % 0.35/0.68 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.35/0.68 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.35/0.68 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.35/0.68 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t52)))))))) % 0.35/0.68 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.35/0.68 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t54))))))))) % 0.35/0.68 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t54))))))))) % 0.35/0.68 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.35/0.68 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.35/0.68 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.35/0.68 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.35/0.68 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.35/0.68 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.35/0.68 (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)))))))))))) % 0.35/0.68 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.35/0.68 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t41)))) % 0.35/0.68 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.35/0.68 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.35/0.68 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.35/0.68 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t55 @t1))))))))) % 0.35/0.68 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.35/0.68 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t41)))) % 0.35/0.68 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.35/0.68 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.35/0.68 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.35/0.68 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t55 @t10) @t1))))))))))) % 0.35/0.68 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.35/0.68 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t41)))) % 0.35/0.68 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t56)))) % 0.35/0.68 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.35/0.68 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t56)))) % 0.35/0.68 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.35/0.68 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t56)))) % 0.35/0.68 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.35/0.68 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t56)))) % 0.35/0.68 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.35/0.68 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t60) (or @t58 (and @t59 (tptp.totalorderedP @t1) (tptp.leq @t2 @t57))))))))) % 0.35/0.68 (assume @p68 @t62) % 0.35/0.68 (assume @p69 @t63) % 0.35/0.68 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t60) (or @t58 (and @t59 (tptp.strictorderedP @t1) (tptp.lt @t2 @t57))))))))) % 0.35/0.68 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t56)))) % 0.35/0.68 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.35/0.68 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t56)))) % 0.35/0.68 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.35/0.68 (assume @p75 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t6 (= @t42 @t1))))))) % 0.35/0.68 (assume @p76 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t21 (= @t44 @t1))))))) % 0.35/0.68 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t59 @t43 (= @t57 @t42) (= (tptp.tl @t1) @t44)) @t39)))))) % 0.35/0.68 (assume @p78 (forall @t9 (=> @t17 (=> @t43 (= (tptp.cons @t42 @t44) @t2))))) % 0.35/0.68 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t45) @t64)))))))) % 0.35/0.68 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t46) @t64)))))))) % 0.35/0.68 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t38 (tptp.app @t18 @t2))))))) % 0.35/0.68 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t45 @t12) (tptp.app @t2 @t19))))))))) % 0.35/0.68 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t45) (and @t58 @t41))))))) % 0.35/0.68 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.35/0.68 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.hd @t45) @t42))))))) % 0.35/0.68 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.tl @t45) (tptp.app @t44 @t1)))))))) % 0.35/0.68 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 (tptp.geq @t1 @t2)) @t3)))))) % 0.35/0.68 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t49 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.35/0.68 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.35/0.68 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.35/0.68 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t35) @t52)))))))) % 0.35/0.68 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t48 (or @t3 @t51))))))) % 0.35/0.68 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t51 (and @t4 @t48))))))) % 0.35/0.68 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (not (tptp.gt @t1 @t2)))))))) % 0.35/0.68 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t53 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.35/0.68 (assume @p96 @t86) % 0.35/0.68 (assume @p97 true) % 0.35/0.68 (step @p98 :rule refl :args (@t87)) % 0.35/0.68 (step @p99 :rule eq-symm :args (@t88 tptp.nil)) % 0.35/0.68 (step @p100 :rule cong :premises (@p99) :args (@t89)) % 0.35/0.68 (step @p101 :rule nary_cong :premises (@p100 @p98) :args (@t90)) % 0.35/0.68 (step @p102 :rule refl :args (@t92)) % 0.35/0.68 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t93)) % 0.35/0.68 (step @p104 :rule refl :args (@t94)) % 0.35/0.68 (step @p105 :rule refl :args (@t36)) % 0.35/0.68 (step @p106 :rule refl :args (@t95)) % 0.35/0.68 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104 @p103) :args (@t96)) % 0.35/0.68 (step @p108 :rule aci_norm :args ((= @t98 @t96))) % 0.35/0.68 (step @p109 :rule trans :premises (@p108 @p107)) % 0.35/0.68 (step @p110 :rule cong :premises (@p109) :args (@t100)) % 0.35/0.68 (step @p111 :rule quant-merge-prenex :args ((= (forall @t9 @t102) @t100))) % 0.35/0.68 (step @p112 :rule alpha_equiv :args (@t103 (@list @t88 @t91) (@list @t1 @t104))) % 0.35/0.68 (step @p113 :rule refl :args (@t36)) % 0.35/0.68 (step @p114 :rule refl :args (@t95)) % 0.35/0.68 (step @p115 :rule nary_cong :premises (@p114 @p113 @p112) :args (@t105)) % 0.35/0.68 (step @p116 :rule quant-miniscope-or :args ((= @t102 @t105))) % 0.35/0.68 (step @p117 :rule trans :premises (@p116 @p115)) % 0.35/0.68 (step @p118 :rule symm :premises (@p117)) % 0.35/0.68 (step @p119 :rule cong :premises (@p118) :args ((forall @t9 @t113))) % 0.35/0.68 (step @p120 :rule trans :premises (@p119 @p111)) % 0.35/0.68 (step @p121 :rule trans :premises (@p120 @p110)) % 0.35/0.68 (step @p122 :rule aci_norm :args ((= (or @t95 @t114) @t113))) % 0.35/0.68 (step @p123 :rule bool-impl-elim :args (@t17 @t114)) % 0.35/0.68 (step @p124 :rule trans :premises (@p123 @p122)) % 0.35/0.68 (step @p125 :rule cong :premises (@p124) :args ((forall @t9 (=> @t17 @t114)))) % 0.35/0.68 (step @p126 :rule trans :premises (@p125 @p121)) % 0.35/0.68 (step @p127 :rule 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@p337 :rule false_intro :premises (@p325)) % 0.35/0.69 (step @p338 :rule symm :premises (@p337)) % 0.35/0.69 (step @p387 :rule trans :premises (@p338 @p386 @p385)) % 0.35/0.69 (step @p388 false :rule eq_resolve :premises (@p387 @p333)) % 0.35/0.69 (step-pop @p418 :rule scope :premises (@p388)) % 0.35/0.69 (step-pop @p419 :rule scope :premises (@p418)) % 0.35/0.69 (step-pop @p420 :rule scope :premises (@p419)) % 0.35/0.69 (step @p389 :rule process_scope :premises (@p420) :args (false)) % 0.35/0.69 (assume-push @p421 @t218) % 0.35/0.69 (assume-push @p422 @t236) % 0.35/0.69 (assume-push @p423 @t242) % 0.35/0.69 (step @p396 :rule and_intro :premises (@p423 @p421 @p325)) % 0.35/0.69 (step-pop @p424 :rule scope :premises (@p396)) % 0.35/0.69 (step-pop @p425 :rule scope :premises (@p424)) % 0.35/0.69 (step-pop @p426 :rule scope :premises (@p425)) % 0.35/0.69 (step @p397 :rule process_scope :premises (@p426) :args (@t245)) % 0.35/0.69 (step @p401 :rule implies_elim :premises (@p397)) % 0.35/0.69 (step @p402 :rule resolution :premises (@p401 @p389) :args (true @t245)) % 0.35/0.69 (step @p403 :rule not_and :premises (@p402)) % 0.35/0.69 (step @p404 :rule eq_resolve :premises (@p403 @p381)) % 0.35/0.69 (step @p405 :rule reordering :premises (@p404) :args ((or @t225 @t219 @t244))) % 0.35/0.69 (step @p406 false :rule chain_m_resolution :premises (@p405 @p378 @p365 @p325) :args (false (@list false false true) (@list @t242 @t218 @t225))) % 0.35/0.69 ) % 0.35/0.69 % SZS output end Proof % 0.35/0.69 % cvc5 exiting %------------------------------------------------------------------------------