%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC288+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 08:58:44 AM UTC 2026 % Result : Theorem 0.35s 0.71s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC288+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.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 19:35:46 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.71 % SZS status Theorem % 0.35/0.71 % SZS output start Proof % 0.35/0.71 ( % 0.35/0.71 (declare-sort $$unsorted 0) % 0.35/0.71 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.35/0.71 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.35/0.71 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.71 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.71 (declare-const tptp.nil $$unsorted) % 0.35/0.71 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.35/0.71 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.35/0.71 (define @t1 () (@var "V" $$unsorted)) % 0.35/0.71 (define @t2 () (@var "U" $$unsorted)) % 0.35/0.71 (define @t3 () (= @t2 @t1)) % 0.35/0.71 (define @t4 () (not @t3)) % 0.35/0.71 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.35/0.71 (define @t6 () (tptp.ssItem @t1)) % 0.35/0.71 (define @t7 () (@list @t1)) % 0.35/0.71 (define @t8 () (tptp.ssItem @t2)) % 0.35/0.71 (define @t9 () (@list @t2)) % 0.35/0.71 (define @t10 () (@var "X" $$unsorted)) % 0.35/0.71 (define @t11 () (tptp.cons @t1 @t10)) % 0.35/0.71 (define @t12 () (@var "W" $$unsorted)) % 0.35/0.71 (define @t13 () (tptp.ssList @t10)) % 0.35/0.71 (define @t14 () (@list @t10)) % 0.35/0.71 (define @t15 () (tptp.ssList @t12)) % 0.35/0.71 (define @t16 () (@list @t12)) % 0.35/0.71 (define @t17 () (tptp.ssList @t2)) % 0.35/0.71 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.35/0.71 (define @t19 () (tptp.app @t1 @t12)) % 0.35/0.71 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.35/0.71 (define @t21 () (tptp.ssList @t1)) % 0.35/0.71 (define @t22 () (tptp.app @t12 @t1)) % 0.35/0.71 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.35/0.71 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.35/0.71 (define @t25 () (tptp.leq @t12 @t1)) % 0.35/0.71 (define @t26 () (tptp.leq @t1 @t12)) % 0.35/0.71 (define @t27 () (@var "Z" $$unsorted)) % 0.35/0.71 (define @t28 () (@var "Y" $$unsorted)) % 0.35/0.71 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.35/0.71 (define @t30 () (tptp.ssList @t27)) % 0.35/0.71 (define @t31 () (@list @t27)) % 0.35/0.71 (define @t32 () (tptp.ssList @t28)) % 0.35/0.71 (define @t33 () (@list @t28)) % 0.35/0.71 (define @t34 () (tptp.ssItem @t12)) % 0.35/0.71 (define @t35 () (tptp.lt @t1 @t12)) % 0.35/0.71 (define @t36 () (tptp.strictorderedP @t2)) % 0.35/0.71 (define @t37 () (= @t1 @t12)) % 0.35/0.71 (define @t38 () (tptp.cons @t1 @t2)) % 0.35/0.71 (define @t39 () (= @t1 @t2)) % 0.35/0.71 (define @t40 () (tptp.cons @t12 @t1)) % 0.35/0.71 (define @t41 () (= tptp.nil @t2)) % 0.35/0.71 (define @t42 () (tptp.hd @t2)) % 0.35/0.71 (define @t43 () (not @t41)) % 0.35/0.71 (define @t44 () (tptp.tl @t2)) % 0.35/0.71 (define @t45 () (tptp.app @t2 @t1)) % 0.35/0.71 (define @t46 () (tptp.app @t1 @t2)) % 0.35/0.71 (define @t47 () (tptp.leq @t1 @t2)) % 0.35/0.71 (define @t48 () (tptp.leq @t2 @t1)) % 0.35/0.71 (define @t49 () (tptp.geq @t2 @t1)) % 0.35/0.71 (define @t50 () (tptp.lt @t1 @t2)) % 0.35/0.71 (define @t51 () (tptp.lt @t2 @t1)) % 0.35/0.71 (define @t52 () (tptp.lt @t2 @t12)) % 0.35/0.71 (define @t53 () (tptp.gt @t2 @t1)) % 0.35/0.71 (define @t54 () (tptp.memberP @t12 @t2)) % 0.35/0.71 (define @t55 () (tptp.app @t12 @t2)) % 0.35/0.71 (define @t56 () (tptp.cons @t2 tptp.nil)) % 0.35/0.71 (define @t57 () (tptp.hd @t1)) % 0.35/0.71 (define @t58 () (= tptp.nil @t1)) % 0.35/0.71 (define @t59 () (not @t58)) % 0.35/0.71 (define @t60 () (tptp.cons @t2 @t1)) % 0.35/0.71 (define @t61 () (tptp.strictorderedP @t56)) % 0.35/0.71 (define @t62 () (forall @t9 (=> @t8 @t61))) % 0.35/0.71 (define @t63 () (tptp.strictorderedP tptp.nil)) % 0.35/0.71 (define @t64 () (= @t12 @t2)) % 0.35/0.71 (define @t65 () (not (= tptp.nil @t12))) % 0.35/0.71 (define @t66 () (not (= tptp.nil @t10))) % 0.35/0.71 (define @t67 () (or @t66 @t65)) % 0.35/0.71 (define @t68 () (@var "X3" $$unsorted)) % 0.35/0.71 (define @t69 () (tptp.lt @t68 @t28)) % 0.35/0.71 (define @t70 () (@var "X1" $$unsorted)) % 0.35/0.71 (define @t71 () (tptp.memberP @t70 @t68)) % 0.35/0.71 (define @t72 () (tptp.ssItem @t68)) % 0.35/0.71 (define @t73 () (and @t72 @t71 @t69)) % 0.35/0.71 (define @t74 () (@list @t68)) % 0.35/0.71 (define @t75 () (exists @t74 @t73)) % 0.35/0.71 (define @t76 () (@var "X2" $$unsorted)) % 0.35/0.71 (define @t77 () (tptp.lt @t28 @t76)) % 0.35/0.71 (define @t78 () (tptp.memberP @t27 @t76)) % 0.35/0.71 (define @t79 () (tptp.ssItem @t76)) % 0.35/0.71 (define @t80 () (and @t79 @t78 @t77)) % 0.35/0.71 (define @t81 () (@list @t76)) % 0.35/0.71 (define @t82 () (exists @t81 @t80)) % 0.35/0.71 (define @t83 () (tptp.app @t27 @t12)) % 0.35/0.71 (define @t84 () (tptp.app @t83 @t70)) % 0.35/0.71 (define @t85 () (not (= @t84 @t10))) % 0.35/0.71 (define @t86 () (tptp.cons @t28 tptp.nil)) % 0.35/0.71 (define @t87 () (not (= @t86 @t12))) % 0.35/0.71 (define @t88 () (not (tptp.ssList @t70))) % 0.35/0.71 (define @t89 () (or @t88 @t87 @t85 @t82 @t75)) % 0.35/0.71 (define @t90 () (@list @t70)) % 0.35/0.71 (define @t91 () (forall @t90 @t89)) % 0.35/0.71 (define @t92 () (=> @t30 @t91)) % 0.35/0.71 (define @t93 () (forall @t31 @t92)) % 0.35/0.71 (define @t94 () (tptp.ssItem @t28)) % 0.35/0.71 (define @t95 () (=> @t94 @t93)) % 0.35/0.71 (define @t96 () (forall @t33 @t95)) % 0.35/0.71 (define @t97 () (and @t96 @t67)) % 0.35/0.71 (define @t98 () (not (= @t2 @t12))) % 0.35/0.71 (define @t99 () (not (= @t1 @t10))) % 0.35/0.71 (define @t100 () (not @t13)) % 0.35/0.71 (define @t101 () (or @t100 @t99 @t98 @t36 @t97)) % 0.35/0.71 (define @t102 () (forall @t14 @t101)) % 0.35/0.71 (define @t103 () (=> @t15 @t102)) % 0.35/0.71 (define @t104 () (forall @t16 @t103)) % 0.35/0.71 (define @t105 () (=> @t21 @t104)) % 0.35/0.71 (define @t106 () (forall @t7 @t105)) % 0.35/0.71 (define @t107 () (=> @t17 @t106)) % 0.35/0.71 (define @t108 () (forall @t9 @t107)) % 0.35/0.71 (define @t109 () (not @t108)) % 0.35/0.71 (define @t110 () (not (= @t2 tptp.nil))) % 0.35/0.71 (define @t111 () (@var "BOUND_VARIABLE_11301" $$unsorted)) % 0.35/0.71 (define @t112 () (not (= @t111 tptp.nil))) % 0.35/0.71 (define @t113 () (or @t112 @t110)) % 0.35/0.71 (define @t114 () (@var "BOUND_VARIABLE_11303" $$unsorted)) % 0.35/0.71 (define @t115 () (@var "BOUND_VARIABLE_11307" $$unsorted)) % 0.35/0.71 (define @t116 () (not @t72)) % 0.35/0.71 (define @t117 () (@var "BOUND_VARIABLE_11305" $$unsorted)) % 0.35/0.71 (define @t118 () (not @t79)) % 0.35/0.71 (define @t119 () (or (not (tptp.ssItem @t114)) (not (= @t2 (tptp.cons @t114 tptp.nil))) (not (tptp.ssList @t117)) (not (forall @t81 (or @t118 (not (tptp.memberP @t117 @t76)) (not (tptp.lt @t114 @t76))))) (not (tptp.ssList @t115)) (not (= @t111 (tptp.app (tptp.app @t117 @t2) @t115))) (not (forall @t74 (or @t116 (not (tptp.memberP @t115 @t68)) (not (tptp.lt @t68 @t114))))))) % 0.35/0.71 (define @t120 () (and @t119 @t113)) % 0.35/0.71 (define @t121 () (not (tptp.ssList @t111))) % 0.35/0.71 (define @t122 () (not @t17)) % 0.35/0.71 (define @t123 () (or @t122 @t36 @t121 @t120)) % 0.35/0.71 (define @t124 () (or @t121 @t120)) % 0.35/0.71 (define @t125 () (or @t122 @t36 @t124)) % 0.35/0.71 (define @t126 () (@list @t2 @t111 @t114 @t117 @t115)) % 0.35/0.71 (define @t127 () (forall @t126 @t125)) % 0.35/0.71 (define @t128 () (@list @t111 @t114 @t117 @t115)) % 0.35/0.71 (define @t129 () (forall @t128 @t125)) % 0.35/0.71 (define @t130 () (forall @t128 @t124)) % 0.35/0.71 (define @t131 () (@var "BOUND_VARIABLE_11262" $$unsorted)) % 0.35/0.71 (define @t132 () (@var "BOUND_VARIABLE_11260" $$unsorted)) % 0.35/0.71 (define @t133 () (@var "BOUND_VARIABLE_11258" $$unsorted)) % 0.35/0.71 (define @t134 () (or @t122 @t36 @t130)) % 0.35/0.71 (define @t135 () (not (= @t1 tptp.nil))) % 0.35/0.71 (define @t136 () (or @t135 @t110)) % 0.35/0.71 (define @t137 () (or (not (tptp.ssItem @t133)) (not (= @t2 (tptp.cons @t133 tptp.nil))) (not (tptp.ssList @t132)) (not (forall @t81 (or @t118 (not (tptp.memberP @t132 @t76)) (not (tptp.lt @t133 @t76))))) (not (tptp.ssList @t131)) (not (= @t1 (tptp.app (tptp.app @t132 @t2) @t131))) (not (forall @t74 (or @t116 (not (tptp.memberP @t131 @t68)) (not (tptp.lt @t68 @t133))))))) % 0.35/0.71 (define @t138 () (and @t137 @t136)) % 0.35/0.71 (define @t139 () (not @t21)) % 0.35/0.71 (define @t140 () (or @t139 @t138)) % 0.35/0.71 (define @t141 () (forall (@list @t1 @t133 @t132 @t131) @t140)) % 0.35/0.71 (define @t142 () (or @t122 @t36 @t141)) % 0.35/0.71 (define @t143 () (or @t36 @t122 @t141)) % 0.35/0.71 (define @t144 () (@list @t133 @t132 @t131)) % 0.35/0.71 (define @t145 () (forall @t144 @t140)) % 0.35/0.71 (define @t146 () (forall @t144 @t136)) % 0.35/0.71 (define @t147 () (forall @t144 @t137)) % 0.35/0.71 (define @t148 () (@var "BOUND_VARIABLE_11209" $$unsorted)) % 0.35/0.71 (define @t149 () (@var "BOUND_VARIABLE_11207" $$unsorted)) % 0.35/0.71 (define @t150 () (@var "BOUND_VARIABLE_11205" $$unsorted)) % 0.35/0.71 (define @t151 () (@list @t150 @t149 @t148)) % 0.35/0.71 (define @t152 () (and @t147 @t146)) % 0.35/0.71 (define @t153 () (forall @t144 @t138)) % 0.35/0.71 (define @t154 () (or @t139 @t153)) % 0.35/0.71 (define @t155 () (and (forall (@list @t150 @t149 @t148) (or (not (tptp.ssItem @t150)) (not (= @t2 (tptp.cons @t150 tptp.nil))) (not (tptp.ssList @t149)) (not (forall @t81 (or @t118 (not (tptp.memberP @t149 @t76)) (not (tptp.lt @t150 @t76))))) (not (tptp.ssList @t148)) (not (= @t1 (tptp.app (tptp.app @t149 @t2) @t148))) (not (forall @t74 (or @t116 (not (tptp.memberP @t148 @t68)) (not (tptp.lt @t68 @t150))))))) @t136)) % 0.35/0.71 (define @t156 () (or @t139 @t155)) % 0.35/0.71 (define @t157 () (forall @t7 @t156)) % 0.35/0.71 (define @t158 () (or @t36 @t122 @t157)) % 0.35/0.71 (define @t159 () (or @t36 @t122 @t156)) % 0.35/0.71 (define @t160 () (or @t139 @t36 @t122 @t155)) % 0.35/0.71 (define @t161 () (or @t36 @t139 @t122 @t155)) % 0.35/0.71 (define @t162 () (@var "BOUND_VARIABLE_11152" $$unsorted)) % 0.35/0.71 (define @t163 () (@var "BOUND_VARIABLE_11150" $$unsorted)) % 0.35/0.71 (define @t164 () (@var "BOUND_VARIABLE_11148" $$unsorted)) % 0.35/0.71 (define @t165 () (@list @t164 @t163 @t162)) % 0.35/0.71 (define @t166 () (forall @t165 @t136)) % 0.35/0.71 (define @t167 () (not (forall @t74 (or @t116 (not (tptp.memberP @t162 @t68)) (not (tptp.lt @t68 @t164)))))) % 0.35/0.71 (define @t168 () (not (tptp.ssList @t162))) % 0.35/0.71 (define @t169 () (not (forall @t81 (or @t118 (not (tptp.memberP @t163 @t76)) (not (tptp.lt @t164 @t76)))))) % 0.35/0.71 (define @t170 () (not (tptp.ssList @t163))) % 0.35/0.71 (define @t171 () (tptp.cons @t164 tptp.nil)) % 0.35/0.71 (define @t172 () (not (tptp.ssItem @t164))) % 0.35/0.71 (define @t173 () (or @t172 (not (= @t2 @t171)) @t170 @t169 @t168 (not (= @t1 (tptp.app (tptp.app @t163 @t2) @t162))) @t167)) % 0.35/0.71 (define @t174 () (forall @t165 @t173)) % 0.35/0.71 (define @t175 () (@list @t164 @t163 @t162)) % 0.35/0.71 (define @t176 () (and @t174 @t166)) % 0.35/0.71 (define @t177 () (and @t173 @t136)) % 0.35/0.71 (define @t178 () (forall @t165 @t177)) % 0.35/0.71 (define @t179 () (or @t122 @t178)) % 0.35/0.71 (define @t180 () (or @t122 @t177)) % 0.35/0.71 (define @t181 () (not (= @t2 @t2))) % 0.35/0.71 (define @t182 () (or @t122 @t181 @t177)) % 0.35/0.71 (define @t183 () (not (= @t12 tptp.nil))) % 0.35/0.71 (define @t184 () (or @t135 @t183)) % 0.35/0.71 (define @t185 () (or @t172 (not (= @t12 @t171)) @t170 @t169 @t168 (not (= @t1 (tptp.app (tptp.app @t163 @t12) @t162))) @t167)) % 0.35/0.71 (define @t186 () (and @t185 @t184)) % 0.35/0.71 (define @t187 () (not @t15)) % 0.35/0.71 (define @t188 () (or @t98 @t187 @t98 @t186)) % 0.35/0.71 (define @t189 () (or @t187 @t98 @t186)) % 0.35/0.71 (define @t190 () (forall @t16 @t189)) % 0.35/0.71 (define @t191 () (forall @t165 @t190)) % 0.35/0.71 (define @t192 () (forall (@list @t164 @t163 @t162 @t12) @t189)) % 0.35/0.71 (define @t193 () (forall (@list @t12 @t164 @t163 @t162) @t189)) % 0.35/0.71 (define @t194 () (forall @t165 @t189)) % 0.35/0.71 (define @t195 () (forall @t165 @t184)) % 0.35/0.71 (define @t196 () (forall @t165 @t185)) % 0.35/0.71 (define @t197 () (@var "BOUND_VARIABLE_11099" $$unsorted)) % 0.35/0.71 (define @t198 () (@var "BOUND_VARIABLE_11097" $$unsorted)) % 0.35/0.71 (define @t199 () (@var "BOUND_VARIABLE_11095" $$unsorted)) % 0.35/0.71 (define @t200 () (@list @t199 @t198 @t197)) % 0.35/0.71 (define @t201 () (and @t196 @t195)) % 0.35/0.71 (define @t202 () (forall @t165 @t186)) % 0.35/0.71 (define @t203 () (or @t187 @t98 @t202)) % 0.35/0.71 (define @t204 () (and (forall (@list @t199 @t198 @t197) (or (not (tptp.ssItem @t199)) (not (= @t12 (tptp.cons @t199 tptp.nil))) (not (tptp.ssList @t198)) (not (forall @t81 (or @t118 (not (tptp.memberP @t198 @t76)) (not (tptp.lt @t199 @t76))))) (not (tptp.ssList @t197)) (not (= @t1 (tptp.app (tptp.app @t198 @t12) @t197))) (not (forall @t74 (or @t116 (not (tptp.memberP @t197 @t68)) (not (tptp.lt @t68 @t199))))))) @t184)) % 0.35/0.71 (define @t205 () (or @t187 @t98 @t204)) % 0.35/0.71 (define @t206 () (forall @t16 @t205)) % 0.35/0.71 (define @t207 () (or @t36 @t139 @t206)) % 0.35/0.71 (define @t208 () (or @t36 @t139 @t205)) % 0.35/0.71 (define @t209 () (or @t187 @t98 @t36 @t139 @t204)) % 0.35/0.71 (define @t210 () (or @t98 @t36 @t139 @t204)) % 0.35/0.71 (define @t211 () (@var "BOUND_VARIABLE_11048" $$unsorted)) % 0.35/0.71 (define @t212 () (@var "BOUND_VARIABLE_11046" $$unsorted)) % 0.35/0.71 (define @t213 () (@var "BOUND_VARIABLE_11044" $$unsorted)) % 0.35/0.71 (define @t214 () (@list @t213 @t212 @t211)) % 0.35/0.71 (define @t215 () (forall @t214 @t184)) % 0.35/0.71 (define @t216 () (not (forall @t74 (or @t116 (not (tptp.memberP @t211 @t68)) (not (tptp.lt @t68 @t213)))))) % 0.35/0.71 (define @t217 () (tptp.app (tptp.app @t212 @t12) @t211)) % 0.35/0.71 (define @t218 () (not (tptp.ssList @t211))) % 0.35/0.71 (define @t219 () (not (forall @t81 (or @t118 (not (tptp.memberP @t212 @t76)) (not (tptp.lt @t213 @t76)))))) % 0.35/0.71 (define @t220 () (not (tptp.ssList @t212))) % 0.35/0.71 (define @t221 () (not (= @t12 (tptp.cons @t213 tptp.nil)))) % 0.35/0.71 (define @t222 () (not (tptp.ssItem @t213))) % 0.35/0.71 (define @t223 () (or @t222 @t221 @t220 @t219 @t218 (not (= @t1 @t217)) @t216)) % 0.35/0.71 (define @t224 () (forall @t214 @t223)) % 0.35/0.71 (define @t225 () (@list @t213 @t212 @t211)) % 0.35/0.71 (define @t226 () (and @t224 @t215)) % 0.35/0.71 (define @t227 () (and @t223 @t184)) % 0.35/0.71 (define @t228 () (forall @t214 @t227)) % 0.35/0.71 (define @t229 () (or @t139 @t228)) % 0.35/0.71 (define @t230 () (or @t139 @t227)) % 0.35/0.71 (define @t231 () (not (= @t1 @t1))) % 0.35/0.71 (define @t232 () (or @t139 @t231 @t227)) % 0.35/0.71 (define @t233 () (or (not (= @t10 tptp.nil)) @t183)) % 0.35/0.71 (define @t234 () (or @t222 @t221 @t220 @t219 @t218 (not (= @t10 @t217)) @t216)) % 0.35/0.71 (define @t235 () (and @t234 @t233)) % 0.35/0.71 (define @t236 () (or @t99 @t100 @t99 @t235)) % 0.35/0.71 (define @t237 () (or @t100 @t99 @t235)) % 0.35/0.71 (define @t238 () (forall @t14 @t237)) % 0.35/0.71 (define @t239 () (forall @t214 @t238)) % 0.35/0.71 (define @t240 () (forall (@list @t213 @t212 @t211 @t10) @t237)) % 0.35/0.71 (define @t241 () (forall (@list @t10 @t213 @t212 @t211) @t237)) % 0.35/0.71 (define @t242 () (forall @t214 @t237)) % 0.35/0.71 (define @t243 () (forall @t214 @t233)) % 0.35/0.71 (define @t244 () (forall @t214 @t234)) % 0.35/0.71 (define @t245 () (@var "BOUND_VARIABLE_11007" $$unsorted)) % 0.35/0.71 (define @t246 () (@var "BOUND_VARIABLE_11005" $$unsorted)) % 0.35/0.71 (define @t247 () (and @t244 @t243)) % 0.35/0.71 (define @t248 () (forall @t214 @t235)) % 0.35/0.71 (define @t249 () (or @t100 @t99 @t248)) % 0.35/0.71 (define @t250 () (not @t69)) % 0.35/0.71 (define @t251 () (not (forall @t74 (or @t116 (not (tptp.memberP @t245 @t68)) @t250)))) % 0.35/0.71 (define @t252 () (not (= @t10 (tptp.app (tptp.app @t246 @t12) @t245)))) % 0.35/0.71 (define @t253 () (not (tptp.ssList @t245))) % 0.35/0.71 (define @t254 () (not @t77)) % 0.35/0.71 (define @t255 () (not (forall @t81 (or @t118 (not (tptp.memberP @t246 @t76)) @t254)))) % 0.35/0.71 (define @t256 () (not (tptp.ssList @t246))) % 0.35/0.71 (define @t257 () (not (= @t12 @t86))) % 0.35/0.71 (define @t258 () (not @t94)) % 0.35/0.71 (define @t259 () (or @t258 @t257 @t256 @t255 @t253 @t252 @t251)) % 0.35/0.71 (define @t260 () (@list @t28 @t246 @t245)) % 0.35/0.71 (define @t261 () (and (forall @t260 @t259) @t233)) % 0.35/0.71 (define @t262 () (or @t100 @t99 @t261)) % 0.35/0.71 (define @t263 () (forall @t14 @t262)) % 0.35/0.71 (define @t264 () (or @t98 @t36 @t263)) % 0.35/0.71 (define @t265 () (or @t98 @t36 @t262)) % 0.35/0.71 (define @t266 () (or @t100 @t99 @t98 @t36 @t261)) % 0.35/0.71 (define @t267 () (or @t256 @t255 @t253 @t252 @t251)) % 0.35/0.71 (define @t268 () (or @t258 @t257 @t267)) % 0.35/0.71 (define @t269 () (forall @t260 @t268)) % 0.35/0.71 (define @t270 () (@list @t246 @t245)) % 0.35/0.71 (define @t271 () (forall @t270 @t268)) % 0.35/0.71 (define @t272 () (forall @t270 @t267)) % 0.35/0.71 (define @t273 () (@var "BOUND_VARIABLE_10981" $$unsorted)) % 0.35/0.71 (define @t274 () (or @t258 @t257 @t272)) % 0.35/0.71 (define @t275 () (not (forall @t74 (or @t116 (not (tptp.memberP @t273 @t68)) @t250)))) % 0.35/0.71 (define @t276 () (not (= @t10 (tptp.app @t83 @t273)))) % 0.35/0.71 (define @t277 () (not (tptp.ssList @t273))) % 0.35/0.71 (define @t278 () (not @t78)) % 0.35/0.71 (define @t279 () (or @t118 @t278 @t254)) % 0.35/0.71 (define @t280 () (not (forall @t81 @t279))) % 0.35/0.71 (define @t281 () (not @t30)) % 0.35/0.71 (define @t282 () (or @t281 @t280 @t277 @t276 @t275)) % 0.35/0.71 (define @t283 () (@list @t27 @t273)) % 0.35/0.71 (define @t284 () (forall @t283 @t282)) % 0.35/0.71 (define @t285 () (or @t258 @t257 @t284)) % 0.35/0.71 (define @t286 () (or @t257 @t284)) % 0.35/0.71 (define @t287 () (or @t277 @t276 @t275)) % 0.35/0.71 (define @t288 () (or @t281 @t280 @t287)) % 0.35/0.71 (define @t289 () (forall @t283 @t288)) % 0.35/0.71 (define @t290 () (@list @t273)) % 0.35/0.71 (define @t291 () (forall @t290 @t288)) % 0.35/0.71 (define @t292 () (forall @t290 @t287)) % 0.35/0.71 (define @t293 () (or @t281 @t280 @t292)) % 0.35/0.71 (define @t294 () (not @t71)) % 0.35/0.71 (define @t295 () (or @t116 @t294 @t250)) % 0.35/0.71 (define @t296 () (not (forall @t74 @t295))) % 0.35/0.71 (define @t297 () (not (= @t10 @t84))) % 0.35/0.71 (define @t298 () (or @t88 @t297 @t296)) % 0.35/0.71 (define @t299 () (forall @t90 @t298)) % 0.35/0.71 (define @t300 () (or @t281 @t280 @t299)) % 0.35/0.71 (define @t301 () (forall @t31 @t300)) % 0.35/0.71 (define @t302 () (or @t257 @t301)) % 0.35/0.71 (define @t303 () (or @t257 @t300)) % 0.35/0.71 (define @t304 () (or @t281 @t257 @t280 @t299)) % 0.35/0.71 (define @t305 () (or @t257 @t280 @t299)) % 0.35/0.71 (define @t306 () (or @t257 @t280 @t298)) % 0.35/0.71 (define @t307 () (or @t88 @t257 @t297 @t280 @t296)) % 0.35/0.71 (define @t308 () (forall @t74 (not @t73))) % 0.35/0.71 (define @t309 () (not @t308)) % 0.35/0.71 (define @t310 () (forall @t81 (not @t80))) % 0.35/0.71 (define @t311 () (not @t310)) % 0.35/0.71 (define @t312 () (forall @t126 (or @t122 @t36 @t121 (and @t119 (or (not (= tptp.nil @t111)) @t110))))) % 0.35/0.71 (define @t313 () (@quantifiers_skolemize @t312 0)) % 0.35/0.71 (define @t314 () (= tptp.nil @t313)) % 0.35/0.71 (define @t315 () (not @t314)) % 0.35/0.71 (define @t316 () (@quantifiers_skolemize @t312 1)) % 0.35/0.71 (define @t317 () (not (= tptp.nil @t316))) % 0.35/0.71 (define @t318 () (or @t317 @t315)) % 0.35/0.71 (define @t319 () (@quantifiers_skolemize @t312 2)) % 0.35/0.71 (define @t320 () (@quantifiers_skolemize @t312 4)) % 0.35/0.71 (define @t321 () (@quantifiers_skolemize @t312 3)) % 0.35/0.71 (define @t322 () (tptp.cons @t319 tptp.nil)) % 0.35/0.71 (define @t323 () (= @t313 @t322)) % 0.35/0.71 (define @t324 () (not @t323)) % 0.35/0.71 (define @t325 () (tptp.ssItem @t319)) % 0.35/0.71 (define @t326 () (not @t325)) % 0.35/0.71 (define @t327 () (or @t326 @t324 (not (tptp.ssList @t321)) (not (forall @t81 (or @t118 (not (tptp.memberP @t321 @t76)) (not (tptp.lt @t319 @t76))))) (not (tptp.ssList @t320)) (not (= @t316 (tptp.app (tptp.app @t321 @t313) @t320))) (not (forall @t74 (or @t116 (not (tptp.memberP @t320 @t68)) (not (tptp.lt @t68 @t319))))))) % 0.35/0.71 (define @t328 () (and @t327 @t318)) % 0.35/0.71 (define @t329 () (not (tptp.ssList @t316))) % 0.35/0.71 (define @t330 () (tptp.strictorderedP @t313)) % 0.35/0.71 (define @t331 () (not (tptp.ssList @t313))) % 0.35/0.71 (define @t332 () (or @t331 @t330 @t329 @t328)) % 0.35/0.71 (define @t333 () (not @t332)) % 0.35/0.71 (define @t334 () (not @t312)) % 0.35/0.71 (define @t335 () (not (= @t313 tptp.nil))) % 0.35/0.71 (define @t336 () (or @t317 @t335)) % 0.35/0.71 (define @t337 () (and @t327 @t336)) % 0.35/0.71 (define @t338 () (or @t331 @t330 @t329 @t337)) % 0.35/0.71 (define @t339 () (not @t338)) % 0.35/0.71 (define @t340 () (@list true)) % 0.35/0.71 (define @t341 () (not @t330)) % 0.35/0.71 (define @t342 () (@list @t332)) % 0.35/0.71 (define @t343 () (not @t63)) % 0.35/0.71 (define @t344 () (not @t341)) % 0.35/0.71 (define @t345 () (= false true)) % 0.35/0.71 (define @t346 () (@list @t327)) % 0.35/0.71 (define @t347 () (tptp.strictorderedP @t322)) % 0.35/0.71 (define @t348 () (or @t326 @t347)) % 0.35/0.71 (define @t349 () (not @t347)) % 0.35/0.71 (define @t350 () (and @t347 @t323 @t341)) % 0.35/0.71 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.35/0.71 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.35/0.71 (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))))))))))) % 0.35/0.71 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.35/0.71 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.35/0.71 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.35/0.71 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.35/0.71 (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))))))))))))))))) % 0.35/0.71 (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)))))))))))))))) % 0.35/0.71 (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))))))))))))))))) % 0.35/0.71 (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))))))))))))))) % 0.35/0.71 (assume @p12 (forall @t9 (=> @t17 (= @t36 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t35))))))))))))))) % 0.35/0.71 (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)))))))))))))))) % 0.35/0.71 (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))))))))))))) % 0.35/0.71 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.35/0.71 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.35/0.71 (assume @p17 (tptp.ssList tptp.nil)) % 0.35/0.71 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.35/0.71 (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))))))))))) % 0.35/0.71 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t40 @t2))))))))) % 0.35/0.71 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.35/0.71 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.35/0.71 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.35/0.71 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.35/0.71 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.35/0.71 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t45)))))) % 0.35/0.71 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.35/0.71 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.35/0.71 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.35/0.71 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t26) (tptp.leq @t2 @t12))))))))) % 0.35/0.71 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.35/0.71 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.35/0.71 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.35/0.71 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t52)))))))) % 0.35/0.71 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.35/0.71 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t54))))))))) % 0.35/0.71 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t54))))))))) % 0.35/0.71 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.35/0.71 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.35/0.71 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.35/0.71 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.35/0.71 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.35/0.71 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.35/0.71 (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)))))))))))) % 0.35/0.71 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.35/0.71 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t41)))) % 0.35/0.71 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.35/0.71 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.35/0.71 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.35/0.71 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t55 @t1))))))))) % 0.35/0.71 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.35/0.71 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t41)))) % 0.35/0.71 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.35/0.71 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.35/0.71 (assume @p55 (forall @t9 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and_intro :premises (@p502 @p500 @p404)) % 0.35/0.71 (step-pop @p503 :rule scope :premises (@p475)) % 0.35/0.71 (step-pop @p504 :rule scope :premises (@p503)) % 0.35/0.71 (step-pop @p505 :rule scope :premises (@p504)) % 0.35/0.71 (step @p476 :rule process_scope :premises (@p505) :args (@t350)) % 0.35/0.71 (step @p480 :rule implies_elim :premises (@p476)) % 0.35/0.71 (step @p481 :rule resolution :premises (@p480 @p468) :args (true @t350)) % 0.35/0.71 (step @p482 :rule not_and :premises (@p481)) % 0.35/0.71 (step @p483 :rule eq_resolve :premises (@p482 @p460)) % 0.35/0.71 (step @p484 :rule reordering :premises (@p483) :args ((or @t330 @t324 @t349))) % 0.35/0.71 (step @p485 false :rule chain_m_resolution :premises (@p484 @p457 @p444 @p404) :args (false (@list false false true) (@list @t347 @t323 @t330))) % 0.35/0.71 ) % 0.35/0.71 % SZS output end Proof % 0.35/0.71 % cvc5 exiting %------------------------------------------------------------------------------