%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC276+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 : 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 08:58:42 AM UTC 2026 % Result : Theorem 0.37s 0.70s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC276+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n017.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 19:34:16 EDT 2026 % 0.15/0.34 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.70 % SZS status Theorem % 0.37/0.70 % SZS output start Proof % 0.37/0.70 ( % 0.37/0.70 (declare-sort $$unsorted 0) % 0.37/0.70 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.37/0.70 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.37/0.70 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.70 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.70 (declare-const tptp.nil $$unsorted) % 0.37/0.70 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.37/0.70 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.70 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.70 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.70 (define @t3 () (= @t2 @t1)) % 0.37/0.70 (define @t4 () (not @t3)) % 0.37/0.70 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.37/0.70 (define @t6 () (tptp.ssItem @t1)) % 0.37/0.70 (define @t7 () (@list @t1)) % 0.37/0.70 (define @t8 () (tptp.ssItem @t2)) % 0.37/0.70 (define @t9 () (@list @t2)) % 0.37/0.70 (define @t10 () (@var "X" $$unsorted)) % 0.37/0.70 (define @t11 () (tptp.cons @t1 @t10)) % 0.37/0.70 (define @t12 () (@var "W" $$unsorted)) % 0.37/0.70 (define @t13 () (tptp.ssList @t10)) % 0.37/0.70 (define @t14 () (@list @t10)) % 0.37/0.70 (define @t15 () (tptp.ssList @t12)) % 0.37/0.70 (define @t16 () (@list @t12)) % 0.37/0.70 (define @t17 () (tptp.ssList @t2)) % 0.37/0.70 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.37/0.70 (define @t19 () (tptp.app @t1 @t12)) % 0.37/0.70 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.37/0.70 (define @t21 () (tptp.ssList @t1)) % 0.37/0.70 (define @t22 () (tptp.app @t12 @t1)) % 0.37/0.70 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.37/0.70 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.37/0.70 (define @t25 () (tptp.leq @t12 @t1)) % 0.37/0.70 (define @t26 () (tptp.leq @t1 @t12)) % 0.37/0.70 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.70 (define @t28 () (@var "Y" $$unsorted)) % 0.37/0.70 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.37/0.70 (define @t30 () (tptp.ssList @t27)) % 0.37/0.70 (define @t31 () (@list @t27)) % 0.37/0.70 (define @t32 () (tptp.ssList @t28)) % 0.37/0.70 (define @t33 () (@list @t28)) % 0.37/0.70 (define @t34 () (tptp.ssItem @t12)) % 0.37/0.70 (define @t35 () (tptp.lt @t1 @t12)) % 0.37/0.70 (define @t36 () (tptp.totalorderedP @t2)) % 0.37/0.70 (define @t37 () (= @t1 @t12)) % 0.37/0.70 (define @t38 () (tptp.cons @t1 @t2)) % 0.37/0.70 (define @t39 () (= @t1 @t2)) % 0.37/0.70 (define @t40 () (tptp.cons @t12 @t1)) % 0.37/0.70 (define @t41 () (= tptp.nil @t2)) % 0.37/0.70 (define @t42 () (tptp.hd @t2)) % 0.37/0.70 (define @t43 () (not @t41)) % 0.37/0.70 (define @t44 () (tptp.tl @t2)) % 0.37/0.70 (define @t45 () (tptp.app @t2 @t1)) % 0.37/0.70 (define @t46 () (tptp.app @t1 @t2)) % 0.37/0.70 (define @t47 () (tptp.leq @t1 @t2)) % 0.37/0.70 (define @t48 () (tptp.leq @t2 @t1)) % 0.37/0.70 (define @t49 () (tptp.geq @t2 @t1)) % 0.37/0.70 (define @t50 () (tptp.lt @t1 @t2)) % 0.37/0.70 (define @t51 () (tptp.lt @t2 @t1)) % 0.37/0.70 (define @t52 () (tptp.lt @t2 @t12)) % 0.37/0.70 (define @t53 () (tptp.gt @t2 @t1)) % 0.37/0.70 (define @t54 () (tptp.memberP @t12 @t2)) % 0.37/0.70 (define @t55 () (tptp.app @t12 @t2)) % 0.37/0.70 (define @t56 () (tptp.cons @t2 tptp.nil)) % 0.37/0.70 (define @t57 () (tptp.totalorderedP @t56)) % 0.37/0.70 (define @t58 () (forall @t9 (=> @t8 @t57))) % 0.37/0.70 (define @t59 () (tptp.totalorderedP tptp.nil)) % 0.37/0.70 (define @t60 () (tptp.hd @t1)) % 0.37/0.70 (define @t61 () (= tptp.nil @t1)) % 0.37/0.70 (define @t62 () (not @t61)) % 0.37/0.70 (define @t63 () (tptp.cons @t2 @t1)) % 0.37/0.70 (define @t64 () (= @t12 @t2)) % 0.37/0.70 (define @t65 () (not (= tptp.nil @t12))) % 0.37/0.70 (define @t66 () (not (= tptp.nil @t10))) % 0.37/0.70 (define @t67 () (or @t66 @t65)) % 0.37/0.70 (define @t68 () (not (tptp.memberP @t10 @t28))) % 0.37/0.70 (define @t69 () (tptp.cons @t28 tptp.nil)) % 0.37/0.70 (define @t70 () (not (= @t69 @t12))) % 0.37/0.70 (define @t71 () (or @t70 @t68)) % 0.37/0.70 (define @t72 () (tptp.ssItem @t28)) % 0.37/0.70 (define @t73 () (=> @t72 @t71)) % 0.37/0.70 (define @t74 () (forall @t33 @t73)) % 0.37/0.70 (define @t75 () (and @t74 @t67)) % 0.37/0.70 (define @t76 () (not (= @t2 @t12))) % 0.37/0.70 (define @t77 () (not (= @t1 @t10))) % 0.37/0.70 (define @t78 () (or @t77 @t76 @t36 @t75)) % 0.37/0.70 (define @t79 () (=> @t13 @t78)) % 0.37/0.70 (define @t80 () (forall @t14 @t79)) % 0.37/0.70 (define @t81 () (=> @t15 @t80)) % 0.37/0.70 (define @t82 () (forall @t16 @t81)) % 0.37/0.70 (define @t83 () (=> @t21 @t82)) % 0.37/0.70 (define @t84 () (forall @t7 @t83)) % 0.37/0.70 (define @t85 () (=> @t17 @t84)) % 0.37/0.70 (define @t86 () (forall @t9 @t85)) % 0.37/0.70 (define @t87 () (not @t86)) % 0.37/0.70 (define @t88 () (not (= @t2 tptp.nil))) % 0.37/0.70 (define @t89 () (@var "BOUND_VARIABLE_11072" $$unsorted)) % 0.37/0.70 (define @t90 () (not (= @t89 tptp.nil))) % 0.37/0.70 (define @t91 () (or @t90 @t88)) % 0.37/0.70 (define @t92 () (@var "BOUND_VARIABLE_11074" $$unsorted)) % 0.37/0.70 (define @t93 () (or (not (tptp.ssItem @t92)) (not (= @t2 (tptp.cons @t92 tptp.nil))) (not (tptp.memberP @t89 @t92)))) % 0.37/0.70 (define @t94 () (and @t93 @t91)) % 0.37/0.70 (define @t95 () (not (tptp.ssList @t89))) % 0.37/0.70 (define @t96 () (not @t17)) % 0.37/0.70 (define @t97 () (or @t96 @t36 @t95 @t94)) % 0.37/0.70 (define @t98 () (or @t95 @t94)) % 0.37/0.70 (define @t99 () (or @t96 @t36 @t98)) % 0.37/0.70 (define @t100 () (@list @t2 @t89 @t92)) % 0.37/0.70 (define @t101 () (forall @t100 @t99)) % 0.37/0.70 (define @t102 () (@list @t89 @t92)) % 0.37/0.70 (define @t103 () (forall @t102 @t99)) % 0.37/0.70 (define @t104 () (forall @t102 @t98)) % 0.37/0.70 (define @t105 () (@var "BOUND_VARIABLE_11053" $$unsorted)) % 0.37/0.70 (define @t106 () (or @t96 @t36 @t104)) % 0.37/0.70 (define @t107 () (not (= @t1 tptp.nil))) % 0.37/0.70 (define @t108 () (or @t107 @t88)) % 0.37/0.70 (define @t109 () (or (not (tptp.ssItem @t105)) (not (= @t2 (tptp.cons @t105 tptp.nil))) (not (tptp.memberP @t1 @t105)))) % 0.37/0.70 (define @t110 () (and @t109 @t108)) % 0.37/0.70 (define @t111 () (not @t21)) % 0.37/0.70 (define @t112 () (or @t111 @t110)) % 0.37/0.70 (define @t113 () (forall (@list @t1 @t105) @t112)) % 0.37/0.70 (define @t114 () (or @t96 @t36 @t113)) % 0.37/0.70 (define @t115 () (or @t36 @t96 @t113)) % 0.37/0.70 (define @t116 () (@list @t105)) % 0.37/0.70 (define @t117 () (forall @t116 @t112)) % 0.37/0.70 (define @t118 () (forall @t116 @t108)) % 0.37/0.70 (define @t119 () (forall @t116 @t109)) % 0.37/0.70 (define @t120 () (@var "BOUND_VARIABLE_11028" $$unsorted)) % 0.37/0.70 (define @t121 () (@list @t120)) % 0.37/0.70 (define @t122 () (and @t119 @t118)) % 0.37/0.70 (define @t123 () (forall @t116 @t110)) % 0.37/0.70 (define @t124 () (or @t111 @t123)) % 0.37/0.70 (define @t125 () (and (forall (@list @t120) (or (not (tptp.ssItem @t120)) (not (= @t2 (tptp.cons @t120 tptp.nil))) (not (tptp.memberP @t1 @t120)))) @t108)) % 0.37/0.70 (define @t126 () (or @t111 @t125)) % 0.37/0.70 (define @t127 () (forall @t7 @t126)) % 0.37/0.70 (define @t128 () (or @t36 @t96 @t127)) % 0.37/0.70 (define @t129 () (or @t36 @t96 @t126)) % 0.37/0.70 (define @t130 () (or @t111 @t36 @t96 @t125)) % 0.37/0.70 (define @t131 () (or @t36 @t111 @t96 @t125)) % 0.37/0.70 (define @t132 () (@var "BOUND_VARIABLE_10999" $$unsorted)) % 0.37/0.70 (define @t133 () (@list @t132)) % 0.37/0.70 (define @t134 () (forall @t133 @t108)) % 0.37/0.70 (define @t135 () (not (tptp.memberP @t1 @t132))) % 0.37/0.70 (define @t136 () (tptp.cons @t132 tptp.nil)) % 0.37/0.70 (define @t137 () (not (tptp.ssItem @t132))) % 0.37/0.70 (define @t138 () (or @t137 (not (= @t2 @t136)) @t135)) % 0.37/0.70 (define @t139 () (forall @t133 @t138)) % 0.37/0.70 (define @t140 () (@list @t132)) % 0.37/0.70 (define @t141 () (and @t139 @t134)) % 0.37/0.70 (define @t142 () (and @t138 @t108)) % 0.37/0.70 (define @t143 () (forall @t133 @t142)) % 0.37/0.70 (define @t144 () (or @t96 @t143)) % 0.37/0.70 (define @t145 () (or @t96 @t142)) % 0.37/0.70 (define @t146 () (not (= @t2 @t2))) % 0.37/0.70 (define @t147 () (or @t96 @t146 @t142)) % 0.37/0.70 (define @t148 () (not (= @t12 tptp.nil))) % 0.37/0.70 (define @t149 () (or @t107 @t148)) % 0.37/0.70 (define @t150 () (or @t137 (not (= @t12 @t136)) @t135)) % 0.37/0.70 (define @t151 () (and @t150 @t149)) % 0.37/0.70 (define @t152 () (not @t15)) % 0.37/0.70 (define @t153 () (or @t76 @t152 @t76 @t151)) % 0.37/0.70 (define @t154 () (or @t152 @t76 @t151)) % 0.37/0.70 (define @t155 () (forall @t16 @t154)) % 0.37/0.70 (define @t156 () (forall @t133 @t155)) % 0.37/0.70 (define @t157 () (forall (@list @t132 @t12) @t154)) % 0.37/0.70 (define @t158 () (forall (@list @t12 @t132) @t154)) % 0.37/0.70 (define @t159 () (forall @t133 @t154)) % 0.37/0.70 (define @t160 () (forall @t133 @t149)) % 0.37/0.70 (define @t161 () (forall @t133 @t150)) % 0.37/0.70 (define @t162 () (@var "BOUND_VARIABLE_10974" $$unsorted)) % 0.37/0.70 (define @t163 () (@list @t162)) % 0.37/0.70 (define @t164 () (and @t161 @t160)) % 0.37/0.70 (define @t165 () (forall @t133 @t151)) % 0.37/0.70 (define @t166 () (or @t152 @t76 @t165)) % 0.37/0.70 (define @t167 () (and (forall (@list @t162) (or (not (tptp.ssItem @t162)) (not (= @t12 (tptp.cons @t162 tptp.nil))) (not (tptp.memberP @t1 @t162)))) @t149)) % 0.37/0.70 (define @t168 () (or @t152 @t76 @t167)) % 0.37/0.70 (define @t169 () (forall @t16 @t168)) % 0.37/0.70 (define @t170 () (or @t36 @t111 @t169)) % 0.37/0.70 (define @t171 () (or @t36 @t111 @t168)) % 0.37/0.70 (define @t172 () (or @t152 @t76 @t36 @t111 @t167)) % 0.37/0.70 (define @t173 () (or @t76 @t36 @t111 @t167)) % 0.37/0.70 (define @t174 () (@var "BOUND_VARIABLE_10947" $$unsorted)) % 0.37/0.70 (define @t175 () (@list @t174)) % 0.37/0.70 (define @t176 () (forall @t175 @t149)) % 0.37/0.70 (define @t177 () (not (= @t12 (tptp.cons @t174 tptp.nil)))) % 0.37/0.70 (define @t178 () (not (tptp.ssItem @t174))) % 0.37/0.70 (define @t179 () (or @t178 @t177 (not (tptp.memberP @t1 @t174)))) % 0.37/0.70 (define @t180 () (forall @t175 @t179)) % 0.37/0.70 (define @t181 () (@list @t174)) % 0.37/0.70 (define @t182 () (and @t180 @t176)) % 0.37/0.70 (define @t183 () (and @t179 @t149)) % 0.37/0.70 (define @t184 () (forall @t175 @t183)) % 0.37/0.70 (define @t185 () (or @t111 @t184)) % 0.37/0.70 (define @t186 () (or @t111 @t183)) % 0.37/0.70 (define @t187 () (not (= @t1 @t1))) % 0.37/0.70 (define @t188 () (or @t111 @t187 @t183)) % 0.37/0.70 (define @t189 () (or (not (= @t10 tptp.nil)) @t148)) % 0.37/0.70 (define @t190 () (or @t178 @t177 (not (tptp.memberP @t10 @t174)))) % 0.37/0.70 (define @t191 () (and @t190 @t189)) % 0.37/0.70 (define @t192 () (not @t13)) % 0.37/0.70 (define @t193 () (or @t77 @t192 @t77 @t191)) % 0.37/0.70 (define @t194 () (or @t192 @t77 @t191)) % 0.37/0.70 (define @t195 () (forall @t14 @t194)) % 0.37/0.70 (define @t196 () (forall @t175 @t195)) % 0.37/0.70 (define @t197 () (forall (@list @t174 @t10) @t194)) % 0.37/0.70 (define @t198 () (forall (@list @t10 @t174) @t194)) % 0.37/0.70 (define @t199 () (forall @t175 @t194)) % 0.37/0.70 (define @t200 () (forall @t175 @t189)) % 0.37/0.70 (define @t201 () (forall @t175 @t190)) % 0.37/0.70 (define @t202 () (and @t201 @t200)) % 0.37/0.70 (define @t203 () (forall @t175 @t191)) % 0.37/0.70 (define @t204 () (or @t192 @t77 @t203)) % 0.37/0.70 (define @t205 () (not (= @t12 @t69))) % 0.37/0.70 (define @t206 () (not @t72)) % 0.37/0.70 (define @t207 () (or @t206 @t205 @t68)) % 0.37/0.70 (define @t208 () (and (forall @t33 @t207) @t189)) % 0.37/0.70 (define @t209 () (or @t192 @t77 @t208)) % 0.37/0.70 (define @t210 () (forall @t14 @t209)) % 0.37/0.70 (define @t211 () (or @t76 @t36 @t210)) % 0.37/0.70 (define @t212 () (or @t76 @t36 @t209)) % 0.37/0.70 (define @t213 () (or @t192 @t77 @t76 @t36 @t208)) % 0.37/0.70 (define @t214 () (or @t77 @t76 @t36 @t208)) % 0.37/0.71 (define @t215 () (or @t205 @t68)) % 0.37/0.71 (define @t216 () (forall @t100 (or @t96 @t36 @t95 (and @t93 (or (not (= tptp.nil @t89)) @t88))))) % 0.37/0.71 (define @t217 () (@quantifiers_skolemize @t216 0)) % 0.37/0.71 (define @t218 () (= tptp.nil @t217)) % 0.37/0.71 (define @t219 () (not @t218)) % 0.37/0.71 (define @t220 () (@quantifiers_skolemize @t216 1)) % 0.37/0.71 (define @t221 () (not (= tptp.nil @t220))) % 0.37/0.71 (define @t222 () (or @t221 @t219)) % 0.37/0.71 (define @t223 () (@quantifiers_skolemize @t216 2)) % 0.37/0.71 (define @t224 () (tptp.cons @t223 tptp.nil)) % 0.37/0.71 (define @t225 () (= @t217 @t224)) % 0.37/0.71 (define @t226 () (not @t225)) % 0.37/0.71 (define @t227 () (tptp.ssItem @t223)) % 0.37/0.71 (define @t228 () (not @t227)) % 0.37/0.71 (define @t229 () (or @t228 @t226 (not (tptp.memberP @t220 @t223)))) % 0.37/0.71 (define @t230 () (and @t229 @t222)) % 0.37/0.71 (define @t231 () (not (tptp.ssList @t220))) % 0.37/0.71 (define @t232 () (tptp.totalorderedP @t217)) % 0.37/0.71 (define @t233 () (not (tptp.ssList @t217))) % 0.37/0.71 (define @t234 () (or @t233 @t232 @t231 @t230)) % 0.37/0.71 (define @t235 () (not @t234)) % 0.37/0.71 (define @t236 () (not @t216)) % 0.37/0.71 (define @t237 () (not (= @t217 tptp.nil))) % 0.37/0.71 (define @t238 () (or @t221 @t237)) % 0.37/0.71 (define @t239 () (and @t229 @t238)) % 0.37/0.71 (define @t240 () (or @t233 @t232 @t231 @t239)) % 0.37/0.71 (define @t241 () (not @t240)) % 0.37/0.71 (define @t242 () (@list true)) % 0.37/0.71 (define @t243 () (not @t232)) % 0.37/0.71 (define @t244 () (@list @t234)) % 0.37/0.71 (define @t245 () (not @t59)) % 0.37/0.71 (define @t246 () (not @t243)) % 0.37/0.71 (define @t247 () (= false true)) % 0.37/0.71 (define @t248 () (@list @t229)) % 0.37/0.71 (define @t249 () (tptp.totalorderedP @t224)) % 0.37/0.71 (define @t250 () (or @t228 @t249)) % 0.37/0.71 (define @t251 () (not @t249)) % 0.37/0.71 (define @t252 () (and @t249 @t225 @t243)) % 0.37/0.71 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.71 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.37/0.71 (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))))))))))) % 0.37/0.71 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.37/0.71 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.37/0.71 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.37/0.71 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.37/0.71 (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))))))))))))))))) % 0.37/0.71 (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)))))))))))))))) % 0.37/0.71 (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))))))))))))))))) % 0.37/0.71 (assume @p11 (forall @t9 (=> @t17 (= @t36 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t26))))))))))))))) % 0.37/0.71 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t35))))))))))))))) % 0.37/0.71 (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)))))))))))))))) % 0.37/0.71 (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))))))))))))) % 0.37/0.71 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.37/0.71 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.37/0.71 (assume @p17 (tptp.ssList tptp.nil)) % 0.37/0.71 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.37/0.71 (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))))))))))) % 0.37/0.71 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t40 @t2))))))))) % 0.37/0.71 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.37/0.71 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.37/0.71 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.37/0.71 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.37/0.71 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.37/0.71 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t45)))))) % 0.37/0.71 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.37/0.71 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.37/0.71 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.37/0.71 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t26) (tptp.leq @t2 @t12))))))))) % 0.37/0.71 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.37/0.71 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.37/0.71 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.37/0.71 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t52)))))))) % 0.37/0.71 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.37/0.71 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t54))))))))) % 0.37/0.71 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t54))))))))) % 0.37/0.71 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.37/0.71 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.37/0.71 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.37/0.71 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.37/0.71 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.37/0.71 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.37/0.71 (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)))))))))))) % 0.37/0.71 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.37/0.71 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t41)))) % 0.37/0.71 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.37/0.71 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.37/0.71 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.37/0.71 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t55 @t1))))))))) % 0.37/0.71 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.37/0.71 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t41)))) % 0.37/0.71 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.37/0.71 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.37/0.71 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.37/0.71 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t55 @t10) @t1))))))))))) % 0.37/0.71 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.37/0.71 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t41)))) % 0.37/0.71 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t56)))) % 0.37/0.71 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.37/0.71 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t56)))) % 0.37/0.71 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.37/0.71 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t56)))) % 0.37/0.71 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.37/0.71 (assume @p65 @t58) % 0.37/0.71 (assume @p66 @t59) % 0.37/0.71 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t63) (or @t61 (and @t62 (tptp.totalorderedP @t1) (tptp.leq @t2 @t60))))))))) % 0.37/0.71 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t56)))) % 0.37/0.71 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.37/0.71 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t63) (or @t61 (and @t62 (tptp.strictorderedP @t1) (tptp.lt @t2 @t60))))))))) % 0.37/0.71 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t56)))) % 0.37/0.71 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.37/0.71 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t56)))) % 0.37/0.71 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.37/0.71 (assume @p75 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t6 (= @t42 @t1))))))) % 0.37/0.71 (assume @p76 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t21 (= @t44 @t1))))))) % 0.37/0.71 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t62 @t43 (= @t60 @t42) (= (tptp.tl @t1) @t44)) @t39)))))) % 0.37/0.71 (assume @p78 (forall @t9 (=> @t17 (=> @t43 (= (tptp.cons @t42 @t44) @t2))))) % 0.37/0.71 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t45) @t64)))))))) % 0.37/0.71 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t46) @t64)))))))) % 0.37/0.71 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t38 (tptp.app @t18 @t2))))))) % 0.37/0.71 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t45 @t12) (tptp.app @t2 @t19))))))))) % 0.37/0.71 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t45) (and @t61 @t41))))))) % 0.37/0.71 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.37/0.71 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.hd @t45) @t42))))))) % 0.37/0.71 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.tl @t45) (tptp.app @t44 @t1)))))))) % 0.37/0.71 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 (tptp.geq @t1 @t2)) @t3)))))) % 0.37/0.71 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t49 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.37/0.71 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.37/0.71 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.37/0.71 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t35) @t52)))))))) % 0.37/0.71 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t48 (or @t3 @t51))))))) % 0.37/0.71 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t51 (and @t4 @t48))))))) % 0.37/0.71 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (not (tptp.gt @t1 @t2)))))))) % 0.37/0.71 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t53 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.37/0.71 (assume @p96 @t87) % 0.37/0.71 (assume @p97 true) % 0.37/0.71 (step @p98 :rule refl :args (@t88)) % 0.37/0.71 (step @p99 :rule eq-symm :args (@t89 tptp.nil)) % 0.37/0.71 (step @p100 :rule cong :premises (@p99) :args (@t90)) % 0.37/0.71 (step @p101 :rule nary_cong :premises (@p100 @p98) :args (@t91)) % 0.37/0.71 (step @p102 :rule refl :args (@t93)) % 0.37/0.71 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t94)) % 0.37/0.71 (step @p104 :rule refl :args (@t95)) % 0.37/0.71 (step @p105 :rule refl :args (@t36)) % 0.37/0.71 (step @p106 :rule refl :args (@t96)) % 0.37/0.71 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104 @p103) :args (@t97)) % 0.37/0.71 (step @p108 :rule aci_norm :args ((= @t99 @t97))) % 0.37/0.71 (step @p109 :rule trans :premises (@p108 @p107)) % 0.37/0.71 (step @p110 :rule cong :premises (@p109) :args (@t101)) % 0.37/0.71 (step @p111 :rule quant-merge-prenex :args ((= (forall @t9 @t103) @t101))) % 0.37/0.71 (step @p112 :rule alpha_equiv :args (@t104 (@list @t89 @t92) (@list @t1 @t105))) % 0.37/0.71 (step @p113 :rule refl :args (@t36)) % 0.37/0.71 (step @p114 :rule refl :args (@t96)) % 0.37/0.71 (step @p115 :rule nary_cong :premises (@p114 @p113 @p112) :args (@t106)) % 0.37/0.71 (step @p116 :rule quant-miniscope-or :args ((= @t103 @t106))) % 0.37/0.71 (step @p117 :rule trans :premises (@p116 @p115)) % 0.37/0.71 (step @p118 :rule symm :premises (@p117)) % 0.37/0.71 (step @p119 :rule cong :premises (@p118) :args ((forall @t9 @t114))) % 0.37/0.71 (step @p120 :rule trans :premises (@p119 @p111)) % 0.37/0.71 (step @p121 :rule trans :premises (@p120 @p110)) % 0.37/0.71 (step @p122 :rule aci_norm :args ((= (or @t96 @t115) 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@t229 (not @t228)))) % 0.37/0.71 (step @p384 :rule cnf_or_neg :args (@t229 0)) % 0.37/0.71 (step @p385 :rule eq_resolve :premises (@p384 @p383)) % 0.37/0.71 (step @p386 :rule reordering :premises (@p385) :args ((or @t227 @t229))) % 0.37/0.71 (step @p387 :rule chain_m_resolution :premises (@p386 @p371) :args (@t227 @t242 @t248)) % 0.37/0.71 (step @p388 :rule cnf_or_pos :args (@t250)) % 0.37/0.71 (step @p389 :rule reordering :premises (@p388) :args ((or @t228 @t249 (not @t250)))) % 0.37/0.71 (step @p390 :rule chain_m_resolution :premises (@p389 @p387 @p381) :args (@t249 (@list false false) (@list @t227 @t250))) % 0.37/0.71 (step @p391 :rule refl :args (@t251)) % 0.37/0.71 (step @p392 :rule refl :args (@t226)) % 0.37/0.71 (step @p393 :rule nary_cong :premises (@p392 @p338 @p391) :args ((or @t226 @t246 @t251))) % 0.37/0.71 (assume-push @p427 @t249) % 0.37/0.71 (assume-push @p428 @t225) % 0.37/0.71 (assume-push @p429 @t243) % 0.37/0.71 (step @p345 :rule evaluate :args (@t247)) % 0.37/0.71 (step @p397 :rule true_intro :premises (@p427)) % 0.37/0.71 (step @p398 :rule cong :premises (@p428) :args (@t232)) % 0.37/0.71 (step @p349 :rule false_intro :premises (@p337)) % 0.37/0.71 (step @p350 :rule symm :premises (@p349)) % 0.37/0.71 (step @p399 :rule trans :premises (@p350 @p398 @p397)) % 0.37/0.71 (step @p400 false :rule eq_resolve :premises (@p399 @p345)) % 0.37/0.71 (step-pop @p430 :rule scope :premises (@p400)) % 0.37/0.71 (step-pop @p431 :rule scope :premises (@p430)) % 0.37/0.71 (step-pop @p432 :rule scope :premises (@p431)) % 0.37/0.71 (step @p401 :rule process_scope :premises (@p432) :args (false)) % 0.37/0.71 (assume-push @p433 @t225) % 0.37/0.71 (assume-push @p434 @t243) % 0.37/0.71 (assume-push @p435 @t249) % 0.37/0.71 (step @p408 :rule and_intro :premises (@p435 @p433 @p337)) % 0.37/0.71 (step-pop @p436 :rule scope :premises (@p408)) % 0.37/0.71 (step-pop @p437 :rule scope :premises (@p436)) % 0.37/0.71 (step-pop @p438 :rule scope :premises (@p437)) % 0.37/0.71 (step @p409 :rule process_scope :premises (@p438) :args (@t252)) % 0.37/0.71 (step @p413 :rule implies_elim :premises (@p409)) % 0.37/0.71 (step @p414 :rule resolution :premises (@p413 @p401) :args (true @t252)) % 0.37/0.71 (step @p415 :rule not_and :premises (@p414)) % 0.37/0.71 (step @p416 :rule eq_resolve :premises (@p415 @p393)) % 0.37/0.71 (step @p417 :rule reordering :premises (@p416) :args ((or @t232 @t226 @t251))) % 0.37/0.71 (step @p418 false :rule chain_m_resolution :premises (@p417 @p390 @p377 @p337) :args (false (@list false false true) (@list @t249 @t225 @t232))) % 0.37/0.71 ) % 0.37/0.71 % SZS output end Proof % 0.37/0.71 % cvc5 exiting %------------------------------------------------------------------------------