%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC220+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 : n022.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 08:58:30 AM UTC 2026 % Result : Theorem 0.37s 0.73s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC220+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 : n022.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 19:26:08 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.73 % SZS status Theorem % 0.37/0.73 % SZS output start Proof % 0.37/0.73 ( % 0.37/0.73 (declare-sort $$unsorted 0) % 0.37/0.73 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.nil $$unsorted) % 0.37/0.73 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.73 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.73 (define @t3 () (= @t2 @t1)) % 0.37/0.73 (define @t4 () (not @t3)) % 0.37/0.73 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.37/0.73 (define @t6 () (tptp.ssItem @t1)) % 0.37/0.73 (define @t7 () (@list @t1)) % 0.37/0.73 (define @t8 () (tptp.ssItem @t2)) % 0.37/0.73 (define @t9 () (@list @t2)) % 0.37/0.73 (define @t10 () (@var "X" $$unsorted)) % 0.37/0.73 (define @t11 () (tptp.cons @t1 @t10)) % 0.37/0.73 (define @t12 () (@var "W" $$unsorted)) % 0.37/0.73 (define @t13 () (tptp.ssList @t10)) % 0.37/0.73 (define @t14 () (@list @t10)) % 0.37/0.73 (define @t15 () (tptp.ssList @t12)) % 0.37/0.73 (define @t16 () (@list @t12)) % 0.37/0.73 (define @t17 () (tptp.ssList @t2)) % 0.37/0.73 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.37/0.73 (define @t19 () (tptp.app @t1 @t12)) % 0.37/0.73 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.37/0.73 (define @t21 () (tptp.ssList @t1)) % 0.37/0.73 (define @t22 () (tptp.app @t12 @t1)) % 0.37/0.73 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.37/0.73 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.37/0.73 (define @t25 () (tptp.leq @t12 @t1)) % 0.37/0.73 (define @t26 () (tptp.leq @t1 @t12)) % 0.37/0.73 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.73 (define @t28 () (@var "Y" $$unsorted)) % 0.37/0.73 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.37/0.73 (define @t30 () (tptp.ssList @t27)) % 0.37/0.73 (define @t31 () (@list @t27)) % 0.37/0.73 (define @t32 () (tptp.ssList @t28)) % 0.37/0.73 (define @t33 () (@list @t28)) % 0.37/0.73 (define @t34 () (tptp.ssItem @t12)) % 0.37/0.73 (define @t35 () (tptp.lt @t1 @t12)) % 0.37/0.73 (define @t36 () (= @t1 @t12)) % 0.37/0.73 (define @t37 () (tptp.cons @t1 @t2)) % 0.37/0.73 (define @t38 () (= @t1 @t2)) % 0.37/0.73 (define @t39 () (tptp.cons @t12 @t1)) % 0.37/0.73 (define @t40 () (= tptp.nil @t2)) % 0.37/0.73 (define @t41 () (tptp.hd @t2)) % 0.37/0.73 (define @t42 () (not @t40)) % 0.37/0.73 (define @t43 () (tptp.tl @t2)) % 0.37/0.73 (define @t44 () (tptp.app @t2 @t1)) % 0.37/0.73 (define @t45 () (tptp.app @t1 @t2)) % 0.37/0.73 (define @t46 () (tptp.leq @t1 @t2)) % 0.37/0.73 (define @t47 () (tptp.leq @t2 @t1)) % 0.37/0.73 (define @t48 () (tptp.geq @t2 @t1)) % 0.37/0.73 (define @t49 () (tptp.lt @t1 @t2)) % 0.37/0.73 (define @t50 () (tptp.lt @t2 @t1)) % 0.37/0.73 (define @t51 () (tptp.lt @t2 @t12)) % 0.37/0.73 (define @t52 () (tptp.gt @t2 @t1)) % 0.37/0.73 (define @t53 () (tptp.memberP @t12 @t2)) % 0.37/0.73 (define @t54 () (tptp.app @t12 @t2)) % 0.37/0.73 (define @t55 () (tptp.cons @t2 tptp.nil)) % 0.37/0.73 (define @t56 () (tptp.hd @t1)) % 0.37/0.73 (define @t57 () (= tptp.nil @t1)) % 0.37/0.73 (define @t58 () (not @t57)) % 0.37/0.73 (define @t59 () (tptp.cons @t2 @t1)) % 0.37/0.73 (define @t60 () (= @t12 @t2)) % 0.37/0.73 (define @t61 () (@var "X6" $$unsorted)) % 0.37/0.73 (define @t62 () (@var "X3" $$unsorted)) % 0.37/0.73 (define @t63 () (tptp.leq @t62 @t61)) % 0.37/0.73 (define @t64 () (@var "X5" $$unsorted)) % 0.37/0.73 (define @t65 () (tptp.memberP @t64 @t61)) % 0.37/0.73 (define @t66 () (@var "X4" $$unsorted)) % 0.37/0.73 (define @t67 () (tptp.memberP @t66 @t61)) % 0.37/0.73 (define @t68 () (tptp.leq @t61 @t62)) % 0.37/0.73 (define @t69 () (not @t68)) % 0.37/0.73 (define @t70 () (tptp.ssItem @t61)) % 0.37/0.73 (define @t71 () (and @t70 @t69 @t67 @t65 @t63)) % 0.37/0.73 (define @t72 () (@list @t61)) % 0.37/0.73 (define @t73 () (exists @t72 @t71)) % 0.37/0.73 (define @t74 () (tptp.cons @t62 tptp.nil)) % 0.37/0.73 (define @t75 () (tptp.app @t66 @t74)) % 0.37/0.73 (define @t76 () (tptp.app @t75 @t64)) % 0.37/0.73 (define @t77 () (not (= @t76 @t12))) % 0.37/0.73 (define @t78 () (or @t77 @t73)) % 0.37/0.73 (define @t79 () (tptp.ssList @t64)) % 0.37/0.73 (define @t80 () (=> @t79 @t78)) % 0.37/0.73 (define @t81 () (@list @t64)) % 0.37/0.73 (define @t82 () (forall @t81 @t80)) % 0.37/0.73 (define @t83 () (tptp.ssList @t66)) % 0.37/0.73 (define @t84 () (=> @t83 @t82)) % 0.37/0.73 (define @t85 () (@list @t66)) % 0.37/0.73 (define @t86 () (forall @t85 @t84)) % 0.37/0.73 (define @t87 () (tptp.ssItem @t62)) % 0.37/0.73 (define @t88 () (=> @t87 @t86)) % 0.37/0.73 (define @t89 () (@list @t62)) % 0.37/0.73 (define @t90 () (forall @t89 @t88)) % 0.37/0.73 (define @t91 () (not (= tptp.nil @t12))) % 0.37/0.73 (define @t92 () (and @t91 @t90)) % 0.37/0.73 (define @t93 () (@var "X2" $$unsorted)) % 0.37/0.73 (define @t94 () (tptp.leq @t93 @t28)) % 0.37/0.73 (define @t95 () (not (tptp.leq @t28 @t93))) % 0.37/0.73 (define @t96 () (@var "X1" $$unsorted)) % 0.37/0.73 (define @t97 () (not (tptp.memberP @t96 @t93))) % 0.37/0.73 (define @t98 () (not (tptp.memberP @t27 @t93))) % 0.37/0.73 (define @t99 () (or @t98 @t97 @t95 @t94)) % 0.37/0.73 (define @t100 () (tptp.ssItem @t93)) % 0.37/0.73 (define @t101 () (@list @t93)) % 0.37/0.73 (define @t102 () (forall @t101 (=> @t100 @t99))) % 0.37/0.73 (define @t103 () (tptp.cons @t28 tptp.nil)) % 0.37/0.73 (define @t104 () (tptp.app @t27 @t103)) % 0.37/0.73 (define @t105 () (tptp.app @t104 @t96)) % 0.37/0.73 (define @t106 () (tptp.ssList @t96)) % 0.37/0.73 (define @t107 () (and @t106 (= @t105 @t2) @t102)) % 0.37/0.73 (define @t108 () (@list @t96)) % 0.37/0.73 (define @t109 () (exists @t108 @t107)) % 0.37/0.73 (define @t110 () (and @t30 @t109)) % 0.37/0.73 (define @t111 () (exists @t31 @t110)) % 0.37/0.73 (define @t112 () (tptp.ssItem @t28)) % 0.37/0.73 (define @t113 () (and @t112 @t111)) % 0.37/0.73 (define @t114 () (exists @t33 @t113)) % 0.37/0.73 (define @t115 () (not (= @t2 @t12))) % 0.37/0.73 (define @t116 () (not (= @t1 @t10))) % 0.37/0.73 (define @t117 () (or @t116 @t115 @t40 @t114 @t92)) % 0.37/0.73 (define @t118 () (=> @t13 @t117)) % 0.37/0.73 (define @t119 () (forall @t14 @t118)) % 0.37/0.73 (define @t120 () (=> @t15 @t119)) % 0.37/0.73 (define @t121 () (forall @t16 @t120)) % 0.37/0.73 (define @t122 () (=> @t21 @t121)) % 0.37/0.73 (define @t123 () (forall @t7 @t122)) % 0.37/0.73 (define @t124 () (=> @t17 @t123)) % 0.37/0.73 (define @t125 () (forall @t9 @t124)) % 0.37/0.73 (define @t126 () (not @t125)) % 0.37/0.73 (define @t127 () (@var "BOUND_VARIABLE_11231" $$unsorted)) % 0.37/0.73 (define @t128 () (@var "BOUND_VARIABLE_11235" $$unsorted)) % 0.37/0.73 (define @t129 () (@var "BOUND_VARIABLE_11233" $$unsorted)) % 0.37/0.73 (define @t130 () (not @t70)) % 0.37/0.73 (define @t131 () (or (not (tptp.ssItem @t127)) (not (tptp.ssList @t129)) (not (tptp.ssList @t128)) (not (= @t2 (tptp.app (tptp.app @t129 (tptp.cons @t127 tptp.nil)) @t128))) (not (forall @t72 (or @t130 (tptp.leq @t61 @t127) (not (tptp.memberP @t129 @t61)) (not (tptp.memberP @t128 @t61)) (not (tptp.leq @t127 @t61))))))) % 0.37/0.73 (define @t132 () (= @t2 tptp.nil)) % 0.37/0.73 (define @t133 () (not @t132)) % 0.37/0.73 (define @t134 () (and @t133 @t131)) % 0.37/0.73 (define @t135 () (@var "BOUND_VARIABLE_11022" $$unsorted)) % 0.37/0.73 (define @t136 () (@var "BOUND_VARIABLE_11020" $$unsorted)) % 0.37/0.73 (define @t137 () (not @t100)) % 0.37/0.73 (define @t138 () (not (forall @t101 (or @t137 (not (tptp.memberP @t136 @t93)) (not (tptp.memberP @t135 @t93)) @t95 @t94)))) % 0.37/0.73 (define @t139 () (tptp.app (tptp.app @t136 @t103) @t135)) % 0.37/0.73 (define @t140 () (not (= @t2 @t139))) % 0.37/0.73 (define @t141 () (not (tptp.ssList @t135))) % 0.37/0.73 (define @t142 () (not (tptp.ssList @t136))) % 0.37/0.73 (define @t143 () (not @t112)) % 0.37/0.73 (define @t144 () (or @t143 @t142 @t141 @t140 @t138)) % 0.37/0.73 (define @t145 () (@list @t28 @t136 @t135)) % 0.37/0.73 (define @t146 () (not (forall @t145 @t144))) % 0.37/0.73 (define @t147 () (not @t17)) % 0.37/0.73 (define @t148 () (or @t147 @t132 @t146 @t134)) % 0.37/0.73 (define @t149 () (forall (@list @t2 @t127 @t129 @t128) @t148)) % 0.37/0.73 (define @t150 () (@list @t127 @t129 @t128)) % 0.37/0.73 (define @t151 () (forall @t150 @t148)) % 0.37/0.73 (define @t152 () (forall @t150 @t131)) % 0.37/0.73 (define @t153 () (@var "BOUND_VARIABLE_11188" $$unsorted)) % 0.37/0.73 (define @t154 () (@var "BOUND_VARIABLE_11186" $$unsorted)) % 0.37/0.73 (define @t155 () (@var "BOUND_VARIABLE_11184" $$unsorted)) % 0.37/0.73 (define @t156 () (@list @t155 @t154 @t153)) % 0.37/0.73 (define @t157 () (forall @t150 @t133)) % 0.37/0.73 (define @t158 () (and @t157 @t152)) % 0.37/0.73 (define @t159 () (forall @t150 @t134)) % 0.37/0.73 (define @t160 () (or @t147 @t132 @t146 @t159)) % 0.37/0.73 (define @t161 () (and @t133 (forall (@list @t155 @t154 @t153) (or (not (tptp.ssItem @t155)) (not (tptp.ssList @t154)) (not (tptp.ssList @t153)) (not (= @t2 (tptp.app (tptp.app @t154 (tptp.cons @t155 tptp.nil)) @t153))) (not (forall @t72 (or @t130 (tptp.leq @t61 @t155) (not (tptp.memberP @t154 @t61)) (not (tptp.memberP @t153 @t61)) (not (tptp.leq @t155 @t61))))))))) % 0.37/0.73 (define @t162 () (or @t147 @t132 @t146 @t161)) % 0.37/0.73 (define @t163 () (forall @t9 @t162)) % 0.37/0.73 (define @t164 () (not @t21)) % 0.37/0.73 (define @t165 () (forall @t7 @t164)) % 0.37/0.73 (define @t166 () (or @t165 @t163)) % 0.37/0.73 (define @t167 () (or @t165 @t162)) % 0.37/0.73 (define @t168 () (or @t147 @t132 @t146 @t161 @t165)) % 0.37/0.73 (define @t169 () (or @t132 @t146 @t147 @t161 @t165)) % 0.37/0.73 (define @t170 () (or @t132 @t146 @t147 @t161 @t164)) % 0.37/0.73 (define @t171 () (or @t164 @t132 @t146 @t147 @t161)) % 0.37/0.73 (define @t172 () (or @t132 @t146 @t164 @t147 @t161)) % 0.37/0.73 (define @t173 () (@var "BOUND_VARIABLE_11138" $$unsorted)) % 0.37/0.73 (define @t174 () (@var "BOUND_VARIABLE_11142" $$unsorted)) % 0.37/0.73 (define @t175 () (@var "BOUND_VARIABLE_11140" $$unsorted)) % 0.37/0.73 (define @t176 () (not (forall @t72 (or @t130 (tptp.leq @t61 @t173) (not (tptp.memberP @t175 @t61)) (not (tptp.memberP @t174 @t61)) (not (tptp.leq @t173 @t61)))))) % 0.37/0.73 (define @t177 () (tptp.app (tptp.app @t175 (tptp.cons @t173 tptp.nil)) @t174)) % 0.37/0.73 (define @t178 () (not (tptp.ssList @t174))) % 0.37/0.73 (define @t179 () (not (tptp.ssList @t175))) % 0.37/0.73 (define @t180 () (not (tptp.ssItem @t173))) % 0.37/0.73 (define @t181 () (or @t180 @t179 @t178 (not (= @t2 @t177)) @t176)) % 0.37/0.73 (define @t182 () (@list @t173 @t175 @t174)) % 0.37/0.73 (define @t183 () (forall @t182 @t181)) % 0.37/0.73 (define @t184 () (@list @t173 @t175 @t174)) % 0.37/0.73 (define @t185 () (forall @t182 @t133)) % 0.37/0.73 (define @t186 () (and @t185 @t183)) % 0.37/0.73 (define @t187 () (and @t133 @t181)) % 0.37/0.73 (define @t188 () (forall @t182 @t187)) % 0.37/0.73 (define @t189 () (or @t147 @t188)) % 0.37/0.73 (define @t190 () (or @t147 @t187)) % 0.37/0.73 (define @t191 () (not (= @t2 @t2))) % 0.37/0.73 (define @t192 () (or @t147 @t191 @t187)) % 0.37/0.73 (define @t193 () (or @t180 @t179 @t178 (not (= @t12 @t177)) @t176)) % 0.37/0.73 (define @t194 () (not (= @t12 tptp.nil))) % 0.37/0.73 (define @t195 () (and @t194 @t193)) % 0.37/0.73 (define @t196 () (not @t15)) % 0.37/0.73 (define @t197 () (or @t115 @t196 @t115 @t195)) % 0.37/0.73 (define @t198 () (or @t196 @t115 @t195)) % 0.37/0.73 (define @t199 () (forall @t16 @t198)) % 0.37/0.73 (define @t200 () (forall @t182 @t199)) % 0.37/0.73 (define @t201 () (forall (@list @t173 @t175 @t174 @t12) @t198)) % 0.37/0.73 (define @t202 () (forall (@list @t12 @t173 @t175 @t174) @t198)) % 0.37/0.73 (define @t203 () (forall @t182 @t198)) % 0.37/0.73 (define @t204 () (forall @t182 @t193)) % 0.37/0.73 (define @t205 () (@var "BOUND_VARIABLE_11096" $$unsorted)) % 0.37/0.73 (define @t206 () (@var "BOUND_VARIABLE_11094" $$unsorted)) % 0.37/0.73 (define @t207 () (forall @t182 @t194)) % 0.37/0.73 (define @t208 () (and @t207 @t204)) % 0.37/0.73 (define @t209 () (forall @t182 @t195)) % 0.37/0.73 (define @t210 () (or @t196 @t115 @t209)) % 0.37/0.73 (define @t211 () (not @t63)) % 0.37/0.73 (define @t212 () (not (forall @t72 (or @t130 @t68 (not (tptp.memberP @t206 @t61)) (not (tptp.memberP @t205 @t61)) @t211)))) % 0.37/0.73 (define @t213 () (not (= @t12 (tptp.app (tptp.app @t206 @t74) @t205)))) % 0.37/0.73 (define @t214 () (not (tptp.ssList @t205))) % 0.37/0.73 (define @t215 () (not (tptp.ssList @t206))) % 0.37/0.73 (define @t216 () (not @t87)) % 0.37/0.73 (define @t217 () (or @t216 @t215 @t214 @t213 @t212)) % 0.37/0.73 (define @t218 () (@list @t62 @t206 @t205)) % 0.37/0.73 (define @t219 () (and @t194 (forall @t218 @t217))) % 0.37/0.73 (define @t220 () (or @t196 @t115 @t219)) % 0.37/0.73 (define @t221 () (forall @t16 @t220)) % 0.37/0.73 (define @t222 () (or @t132 @t146 @t164 @t221)) % 0.37/0.73 (define @t223 () (or @t132 @t146 @t164 @t220)) % 0.37/0.73 (define @t224 () (or @t196 @t115 @t132 @t146 @t219 @t164)) % 0.37/0.73 (define @t225 () (or @t115 @t132 @t146 @t219 @t164)) % 0.37/0.73 (define @t226 () (not (= @t1 @t1))) % 0.37/0.73 (define @t227 () (or @t164 @t226)) % 0.37/0.73 (define @t228 () (not @t13)) % 0.37/0.73 (define @t229 () (or @t116 @t228 @t116)) % 0.37/0.73 (define @t230 () (or @t228 @t116)) % 0.37/0.73 (define @t231 () (forall @t14 @t230)) % 0.37/0.73 (define @t232 () (or @t115 @t132 @t146 @t219 @t231)) % 0.37/0.73 (define @t233 () (or @t115 @t132 @t146 @t219 @t230)) % 0.37/0.73 (define @t234 () (or @t228 @t116 @t115 @t132 @t146 @t219)) % 0.37/0.73 (define @t235 () (or @t116 @t115 @t132 @t146 @t219)) % 0.37/0.73 (define @t236 () (or @t215 @t214 @t213 @t212)) % 0.37/0.73 (define @t237 () (or @t216 @t236)) % 0.37/0.73 (define @t238 () (forall @t218 @t237)) % 0.37/0.73 (define @t239 () (@list @t206 @t205)) % 0.37/0.73 (define @t240 () (forall @t239 @t237)) % 0.37/0.73 (define @t241 () (forall @t239 @t236)) % 0.37/0.73 (define @t242 () (@var "BOUND_VARIABLE_11071" $$unsorted)) % 0.37/0.73 (define @t243 () (or @t216 @t241)) % 0.37/0.73 (define @t244 () (not @t67)) % 0.37/0.73 (define @t245 () (not (forall @t72 (or @t130 @t68 @t244 (not (tptp.memberP @t242 @t61)) @t211)))) % 0.37/0.73 (define @t246 () (not (= @t12 (tptp.app @t75 @t242)))) % 0.37/0.73 (define @t247 () (not (tptp.ssList @t242))) % 0.37/0.73 (define @t248 () (not @t83)) % 0.37/0.73 (define @t249 () (or @t248 @t247 @t246 @t245)) % 0.37/0.73 (define @t250 () (@list @t66 @t242)) % 0.37/0.73 (define @t251 () (forall @t250 @t249)) % 0.37/0.73 (define @t252 () (or @t247 @t246 @t245)) % 0.37/0.73 (define @t253 () (or @t248 @t252)) % 0.37/0.73 (define @t254 () (forall @t250 @t253)) % 0.37/0.73 (define @t255 () (@list @t242)) % 0.37/0.73 (define @t256 () (forall @t255 @t253)) % 0.37/0.73 (define @t257 () (forall @t255 @t252)) % 0.37/0.73 (define @t258 () (or @t248 @t257)) % 0.37/0.73 (define @t259 () (not @t65)) % 0.37/0.73 (define @t260 () (not (forall @t72 (or @t130 @t68 @t244 @t259 @t211)))) % 0.37/0.73 (define @t261 () (not (= @t12 @t76))) % 0.37/0.73 (define @t262 () (not @t79)) % 0.37/0.73 (define @t263 () (or @t262 @t261 @t260)) % 0.37/0.73 (define @t264 () (forall @t81 @t263)) % 0.37/0.73 (define @t265 () (or @t261 @t260)) % 0.37/0.73 (define @t266 () (not @t69)) % 0.37/0.73 (define @t267 () (or @t130 @t266 @t244 @t259 @t211)) % 0.37/0.73 (define @t268 () (forall @t72 (not @t71))) % 0.37/0.73 (define @t269 () (not @t268)) % 0.37/0.73 (define @t270 () (or @t142 @t141 @t140 @t138)) % 0.37/0.73 (define @t271 () (or @t143 @t270)) % 0.37/0.73 (define @t272 () (forall @t145 @t271)) % 0.37/0.73 (define @t273 () (@list @t136 @t135)) % 0.37/0.73 (define @t274 () (forall @t273 @t271)) % 0.37/0.73 (define @t275 () (forall @t273 @t270)) % 0.37/0.73 (define @t276 () (@var "BOUND_VARIABLE_10993" $$unsorted)) % 0.37/0.73 (define @t277 () (or @t143 @t275)) % 0.37/0.73 (define @t278 () (not (forall @t101 (or @t137 @t98 (not (tptp.memberP @t276 @t93)) @t95 @t94)))) % 0.37/0.73 (define @t279 () (not (= @t2 (tptp.app @t104 @t276)))) % 0.37/0.73 (define @t280 () (not (tptp.ssList @t276))) % 0.37/0.73 (define @t281 () (not @t30)) % 0.37/0.73 (define @t282 () (or @t281 @t280 @t279 @t278)) % 0.37/0.73 (define @t283 () (@list @t27 @t276)) % 0.37/0.73 (define @t284 () (forall @t283 @t282)) % 0.37/0.73 (define @t285 () (not @t284)) % 0.37/0.73 (define @t286 () (and @t112 @t285)) % 0.37/0.73 (define @t287 () (forall @t33 (not @t286))) % 0.37/0.73 (define @t288 () (not @t287)) % 0.37/0.73 (define @t289 () (or @t280 @t279 @t278)) % 0.37/0.73 (define @t290 () (or @t281 @t289)) % 0.37/0.73 (define @t291 () (forall @t283 @t290)) % 0.37/0.73 (define @t292 () (@list @t276)) % 0.37/0.73 (define @t293 () (forall @t292 @t290)) % 0.37/0.73 (define @t294 () (forall @t292 @t289)) % 0.37/0.73 (define @t295 () (or @t281 @t294)) % 0.37/0.73 (define @t296 () (or @t137 @t98 @t97 @t95 @t94)) % 0.37/0.73 (define @t297 () (forall @t101 @t296)) % 0.37/0.73 (define @t298 () (not @t297)) % 0.37/0.73 (define @t299 () (= @t2 @t105)) % 0.37/0.73 (define @t300 () (not @t299)) % 0.37/0.73 (define @t301 () (not @t106)) % 0.37/0.73 (define @t302 () (or @t301 @t300 @t298)) % 0.37/0.73 (define @t303 () (forall @t108 @t302)) % 0.37/0.73 (define @t304 () (not @t303)) % 0.37/0.73 (define @t305 () (and @t30 @t304)) % 0.37/0.73 (define @t306 () (forall @t31 (not @t305))) % 0.37/0.73 (define @t307 () (not @t306)) % 0.37/0.73 (define @t308 () (and @t106 @t299 @t297)) % 0.37/0.73 (define @t309 () (forall @t108 (not @t308))) % 0.37/0.73 (define @t310 () (not @t309)) % 0.37/0.73 (define @t311 () (@quantifiers_skolemize @t149 1)) % 0.37/0.73 (define @t312 () (@quantifiers_skolemize @t149 3)) % 0.37/0.73 (define @t313 () (@quantifiers_skolemize @t149 2)) % 0.37/0.73 (define @t314 () (forall @t72 (or @t130 (tptp.leq @t61 @t311) (not (tptp.memberP @t313 @t61)) (not (tptp.memberP @t312 @t61)) (not (tptp.leq @t311 @t61))))) % 0.37/0.73 (define @t315 () (not @t314)) % 0.37/0.73 (define @t316 () (tptp.app (tptp.app @t313 (tptp.cons @t311 tptp.nil)) @t312)) % 0.37/0.73 (define @t317 () (@quantifiers_skolemize @t149 0)) % 0.37/0.73 (define @t318 () (= @t317 @t316)) % 0.37/0.73 (define @t319 () (not @t318)) % 0.37/0.73 (define @t320 () (tptp.ssList @t312)) % 0.37/0.73 (define @t321 () (not @t320)) % 0.37/0.73 (define @t322 () (tptp.ssList @t313)) % 0.37/0.73 (define @t323 () (not @t322)) % 0.37/0.73 (define @t324 () (tptp.ssItem @t311)) % 0.37/0.73 (define @t325 () (not @t324)) % 0.37/0.73 (define @t326 () (or @t325 @t323 @t321 @t319 @t315)) % 0.37/0.73 (define @t327 () (= tptp.nil @t317)) % 0.37/0.73 (define @t328 () (not @t327)) % 0.37/0.73 (define @t329 () (and @t328 @t326)) % 0.37/0.73 (define @t330 () (forall @t145 (or @t143 @t142 @t141 (not (= @t139 @t317)) @t138))) % 0.37/0.73 (define @t331 () (not @t330)) % 0.37/0.73 (define @t332 () (not (tptp.ssList @t317))) % 0.37/0.73 (define @t333 () (or @t332 @t327 @t331 @t329)) % 0.37/0.73 (define @t334 () (not @t333)) % 0.37/0.73 (define @t335 () (not @t149)) % 0.37/0.73 (define @t336 () (= @t317 tptp.nil)) % 0.37/0.73 (define @t337 () (not @t336)) % 0.37/0.73 (define @t338 () (and @t337 @t326)) % 0.37/0.73 (define @t339 () (not (= @t317 @t139))) % 0.37/0.73 (define @t340 () (or @t143 @t142 @t141 @t339 @t138)) % 0.37/0.73 (define @t341 () (forall @t145 @t340)) % 0.37/0.73 (define @t342 () (not @t341)) % 0.37/0.73 (define @t343 () (or @t332 @t336 @t342 @t338)) % 0.37/0.73 (define @t344 () (not @t343)) % 0.37/0.73 (define @t345 () (@list true)) % 0.37/0.73 (define @t346 () (@list @t333)) % 0.37/0.73 (define @t347 () (not @t326)) % 0.37/0.73 (define @t348 () (@list @t326)) % 0.37/0.73 (define @t349 () (not (tptp.leq @t311 @t93))) % 0.37/0.73 (define @t350 () (not (tptp.memberP @t312 @t93))) % 0.37/0.73 (define @t351 () (not (tptp.memberP @t313 @t93))) % 0.37/0.73 (define @t352 () (tptp.leq @t93 @t311)) % 0.37/0.73 (define @t353 () (or @t137 @t352 @t351 @t350 @t349)) % 0.37/0.73 (define @t354 () (or @t137 @t351 @t350 @t349 @t352)) % 0.37/0.73 (define @t355 () (forall @t101 @t354)) % 0.37/0.73 (define @t356 () (forall @t101 @t353)) % 0.37/0.73 (define @t357 () (@list false)) % 0.37/0.73 (define @t358 () (not @t355)) % 0.37/0.73 (define @t359 () (not (= @t316 @t317))) % 0.37/0.73 (define @t360 () (or @t325 @t323 @t321 @t359 @t358)) % 0.37/0.73 (define @t361 () (or @t325 @t323 @t321 @t319 @t358)) % 0.37/0.73 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.73 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.37/0.73 (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))))))))))) % 0.37/0.73 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.37/0.73 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.37/0.73 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.37/0.73 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.37/0.73 (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))))))))))))))))) % 0.37/0.73 (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)))))))))))))))) % 0.37/0.73 (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))))))))))))))))) % 0.37/0.73 (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))))))))))))))) % 0.37/0.73 (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))))))))))))))) % 0.37/0.73 (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 @t36)))))))))))))))) % 0.37/0.73 (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) @t36))))))))))))) % 0.37/0.73 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.37/0.73 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.37/0.73 (assume @p17 (tptp.ssList tptp.nil)) % 0.37/0.73 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.37/0.73 (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) @t38))))))))))) % 0.37/0.73 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.37/0.73 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.37/0.73 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.37/0.73 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.37/0.73 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.37/0.73 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.37/0.73 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.37/0.73 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.37/0.73 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.37/0.73 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.37/0.73 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.37/0.73 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.37/0.73 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.37/0.73 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 0.37/0.73 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 @t35) @t51)))))))) % 0.37/0.73 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t49)))))) % 0.37/0.73 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t53))))))))) % 0.37/0.73 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t53))))))))) % 0.37/0.73 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.37/0.73 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.37/0.73 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.37/0.73 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.37/0.73 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.37/0.73 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.37/0.73 (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)))))))))))) % 0.37/0.73 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.37/0.73 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t40)))) % 0.37/0.73 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.37/0.73 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.37/0.73 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.37/0.73 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t54 @t1))))))))) % 0.37/0.73 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.37/0.73 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.37/0.73 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.37/0.73 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.37/0.73 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.37/0.73 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t54 @t10) @t1))))))))))) % 0.37/0.73 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.37/0.73 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t40)))) % 0.37/0.73 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t55)))) % 0.37/0.73 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.37/0.73 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t55)))) % 0.37/0.73 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.37/0.73 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t55)))) % 0.37/0.73 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.37/0.73 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(step @p496 :rule refl :args (@t330)) % 0.37/0.74 (step @p497 :rule cong :premises (@p496 @p495) :args ((=> @t330 @t360))) % 0.37/0.74 (assume-push @p510 @t330) % 0.37/0.74 (step @p499 :rule instantiate :premises (@p488) :args ((@list @t311 @t313 @t312))) % 0.37/0.74 (step-pop @p511 :rule scope :premises (@p499)) % 0.37/0.74 (step @p500 :rule process_scope :premises (@p511) :args (@t360)) % 0.37/0.74 (step @p502 :rule eq_resolve :premises (@p500 @p497)) % 0.37/0.74 (step @p503 :rule implies_elim :premises (@p502)) % 0.37/0.74 (step @p504 :rule chain_m_resolution :premises (@p503 @p488) :args (@t361 @t357 (@list @t330))) % 0.37/0.74 (step @p505 :rule cnf_or_pos :args (@t361)) % 0.37/0.74 (step @p506 :rule reordering :premises (@p505) :args ((or @t325 @t323 @t321 @t319 @t358 (not @t361)))) % 0.37/0.74 (step @p507 false :rule chain_m_resolution :premises (@p506 @p504 @p481 @p462 @p456 @p450 @p444) :args (false (@list false false false false false false) (@list @t361 @t355 @t318 @t320 @t322 @t324))) % 0.37/0.74 ) % 0.37/0.74 % SZS output end Proof % 0.37/0.74 % cvc5 exiting %------------------------------------------------------------------------------