%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC377+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 : n009.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 08:59:05 AM UTC 2026 % Result : Theorem 0.36s 0.74s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC377+1 : TPTP v9.2.1. Released v2.4.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 19:44:14 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.74 % SZS status Theorem % 0.36/0.74 % SZS output start Proof % 0.36/0.74 ( % 0.36/0.74 (declare-sort $$unsorted 0) % 0.36/0.74 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.nil $$unsorted) % 0.36/0.74 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.74 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.74 (define @t3 () (= @t2 @t1)) % 0.36/0.74 (define @t4 () (not @t3)) % 0.36/0.74 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.36/0.74 (define @t6 () (tptp.ssItem @t1)) % 0.36/0.74 (define @t7 () (@list @t1)) % 0.36/0.74 (define @t8 () (tptp.ssItem @t2)) % 0.36/0.74 (define @t9 () (@list @t2)) % 0.36/0.74 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.74 (define @t11 () (tptp.cons @t1 @t10)) % 0.36/0.74 (define @t12 () (@var "W" $$unsorted)) % 0.36/0.74 (define @t13 () (tptp.ssList @t10)) % 0.36/0.74 (define @t14 () (@list @t10)) % 0.36/0.74 (define @t15 () (tptp.ssList @t12)) % 0.36/0.74 (define @t16 () (@list @t12)) % 0.36/0.74 (define @t17 () (tptp.ssList @t2)) % 0.36/0.74 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.36/0.74 (define @t19 () (tptp.app @t1 @t12)) % 0.36/0.74 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.36/0.74 (define @t21 () (tptp.ssList @t1)) % 0.36/0.74 (define @t22 () (tptp.app @t12 @t1)) % 0.36/0.74 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.36/0.74 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.36/0.74 (define @t25 () (tptp.leq @t12 @t1)) % 0.36/0.74 (define @t26 () (tptp.leq @t1 @t12)) % 0.36/0.74 (define @t27 () (@var "Z" $$unsorted)) % 0.36/0.74 (define @t28 () (@var "Y" $$unsorted)) % 0.36/0.74 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.36/0.74 (define @t30 () (tptp.ssList @t27)) % 0.36/0.74 (define @t31 () (@list @t27)) % 0.36/0.74 (define @t32 () (tptp.ssList @t28)) % 0.36/0.74 (define @t33 () (@list @t28)) % 0.36/0.74 (define @t34 () (tptp.ssItem @t12)) % 0.36/0.74 (define @t35 () (tptp.lt @t1 @t12)) % 0.36/0.74 (define @t36 () (= @t1 @t12)) % 0.36/0.74 (define @t37 () (forall @t7 (=> @t21 @t5))) % 0.36/0.74 (define @t38 () (=> @t17 @t37)) % 0.36/0.74 (define @t39 () (forall @t9 @t38)) % 0.36/0.74 (define @t40 () (tptp.cons @t1 @t2)) % 0.36/0.74 (define @t41 () (tptp.ssList @t40)) % 0.36/0.74 (define @t42 () (forall @t7 (=> @t6 @t41))) % 0.36/0.74 (define @t43 () (=> @t17 @t42)) % 0.36/0.74 (define @t44 () (forall @t9 @t43)) % 0.36/0.74 (define @t45 () (tptp.ssList tptp.nil)) % 0.36/0.74 (define @t46 () (= @t1 @t2)) % 0.36/0.74 (define @t47 () (tptp.cons @t12 @t1)) % 0.36/0.74 (define @t48 () (= tptp.nil @t2)) % 0.36/0.74 (define @t49 () (tptp.hd @t2)) % 0.36/0.74 (define @t50 () (not @t48)) % 0.36/0.74 (define @t51 () (tptp.tl @t2)) % 0.36/0.74 (define @t52 () (tptp.app @t2 @t1)) % 0.36/0.74 (define @t53 () (tptp.app @t1 @t2)) % 0.36/0.74 (define @t54 () (tptp.leq @t1 @t2)) % 0.36/0.74 (define @t55 () (tptp.leq @t2 @t1)) % 0.36/0.74 (define @t56 () (tptp.geq @t2 @t1)) % 0.36/0.74 (define @t57 () (tptp.lt @t1 @t2)) % 0.36/0.74 (define @t58 () (tptp.lt @t2 @t1)) % 0.36/0.74 (define @t59 () (tptp.lt @t2 @t12)) % 0.36/0.74 (define @t60 () (tptp.gt @t2 @t1)) % 0.36/0.74 (define @t61 () (tptp.memberP @t12 @t2)) % 0.36/0.74 (define @t62 () (tptp.memberP @t1 @t2)) % 0.36/0.74 (define @t63 () (= (tptp.memberP @t19 @t2) (or @t62 @t61))) % 0.36/0.74 (define @t64 () (forall @t16 (=> @t15 @t63))) % 0.36/0.74 (define @t65 () (=> @t21 @t64)) % 0.36/0.74 (define @t66 () (forall @t7 @t65)) % 0.36/0.74 (define @t67 () (=> @t8 @t66)) % 0.36/0.74 (define @t68 () (forall @t9 @t67)) % 0.36/0.74 (define @t69 () (not (tptp.memberP tptp.nil @t2))) % 0.36/0.74 (define @t70 () (forall @t9 (=> @t8 @t69))) % 0.36/0.74 (define @t71 () (tptp.app @t12 @t2)) % 0.36/0.74 (define @t72 () (tptp.cons @t2 tptp.nil)) % 0.36/0.74 (define @t73 () (tptp.hd @t1)) % 0.36/0.74 (define @t74 () (= tptp.nil @t1)) % 0.36/0.74 (define @t75 () (not @t74)) % 0.36/0.74 (define @t76 () (tptp.cons @t2 @t1)) % 0.36/0.74 (define @t77 () (= @t12 @t2)) % 0.36/0.74 (define @t78 () (tptp.neq @t10 tptp.nil)) % 0.36/0.74 (define @t79 () (tptp.cons @t27 tptp.nil)) % 0.36/0.74 (define @t80 () (@var "X1" $$unsorted)) % 0.36/0.74 (define @t81 () (tptp.app @t80 @t79)) % 0.36/0.74 (define @t82 () (not (= @t81 @t10))) % 0.36/0.74 (define @t83 () (tptp.app @t79 @t80)) % 0.36/0.74 (define @t84 () (not (= @t83 @t12))) % 0.36/0.74 (define @t85 () (or @t84 @t82)) % 0.36/0.74 (define @t86 () (tptp.ssList @t80)) % 0.36/0.74 (define @t87 () (=> @t86 @t85)) % 0.36/0.74 (define @t88 () (@list @t80)) % 0.36/0.74 (define @t89 () (forall @t88 @t87)) % 0.36/0.74 (define @t90 () (tptp.ssItem @t27)) % 0.36/0.74 (define @t91 () (=> @t90 @t89)) % 0.36/0.74 (define @t92 () (forall @t31 @t91)) % 0.36/0.74 (define @t93 () (and @t92 @t78)) % 0.36/0.74 (define @t94 () (not (= tptp.nil @t12))) % 0.36/0.74 (define @t95 () (and @t94 (= tptp.nil @t10))) % 0.36/0.74 (define @t96 () (tptp.memberP @t2 @t28)) % 0.36/0.74 (define @t97 () (tptp.memberP @t1 @t28)) % 0.36/0.74 (define @t98 () (and @t97 @t96)) % 0.36/0.74 (define @t99 () (and (not @t97) (not @t96))) % 0.36/0.74 (define @t100 () (or @t99 @t98)) % 0.36/0.74 (define @t101 () (tptp.ssItem @t28)) % 0.36/0.74 (define @t102 () (forall @t33 (=> @t101 @t100))) % 0.36/0.74 (define @t103 () (not (= @t2 @t12))) % 0.36/0.74 (define @t104 () (not (= @t1 @t10))) % 0.36/0.74 (define @t105 () (or @t104 @t103 @t102 @t95 @t93)) % 0.36/0.74 (define @t106 () (=> @t13 @t105)) % 0.36/0.74 (define @t107 () (forall @t14 @t106)) % 0.36/0.74 (define @t108 () (=> @t15 @t107)) % 0.36/0.74 (define @t109 () (forall @t16 @t108)) % 0.36/0.74 (define @t110 () (=> @t21 @t109)) % 0.36/0.74 (define @t111 () (forall @t7 @t110)) % 0.36/0.74 (define @t112 () (=> @t17 @t111)) % 0.36/0.74 (define @t113 () (forall @t9 @t112)) % 0.36/0.74 (define @t114 () (not @t113)) % 0.36/0.74 (define @t115 () (@var "BOUND_VARIABLE_11163" $$unsorted)) % 0.36/0.74 (define @t116 () (tptp.memberP @t2 @t115)) % 0.36/0.74 (define @t117 () (@var "BOUND_VARIABLE_11161" $$unsorted)) % 0.36/0.74 (define @t118 () (tptp.memberP @t117 @t115)) % 0.36/0.74 (define @t119 () (and @t118 @t116)) % 0.36/0.74 (define @t120 () (and (not @t118) (not @t116))) % 0.36/0.74 (define @t121 () (not (tptp.ssItem @t115))) % 0.36/0.74 (define @t122 () (@var "BOUND_VARIABLE_11165" $$unsorted)) % 0.36/0.74 (define @t123 () (tptp.cons @t122 tptp.nil)) % 0.36/0.74 (define @t124 () (@var "BOUND_VARIABLE_11167" $$unsorted)) % 0.36/0.74 (define @t125 () (and (or (not (tptp.ssItem @t122)) (not (tptp.ssList @t124)) (not (= @t2 (tptp.app @t123 @t124))) (not (= @t117 (tptp.app @t124 @t123)))) (tptp.neq @t117 tptp.nil))) % 0.36/0.74 (define @t126 () (not (= @t2 tptp.nil))) % 0.36/0.74 (define @t127 () (and @t126 (= @t117 tptp.nil))) % 0.36/0.74 (define @t128 () (not (tptp.ssList @t117))) % 0.36/0.74 (define @t129 () (not @t17)) % 0.36/0.74 (define @t130 () (or @t129 @t128 @t127 @t125 @t121 @t120 @t119)) % 0.36/0.74 (define @t131 () (or @t128 @t127 @t125 @t121 @t120 @t119)) % 0.36/0.74 (define @t132 () (or @t129 @t131)) % 0.36/0.74 (define @t133 () (@list @t2 @t117 @t115 @t122 @t124)) % 0.36/0.74 (define @t134 () (forall @t133 @t132)) % 0.36/0.74 (define @t135 () (@list @t117 @t115 @t122 @t124)) % 0.36/0.74 (define @t136 () (forall @t135 @t132)) % 0.36/0.74 (define @t137 () (forall @t135 @t131)) % 0.36/0.74 (define @t138 () (@var "BOUND_VARIABLE_11137" $$unsorted)) % 0.36/0.74 (define @t139 () (@var "BOUND_VARIABLE_11135" $$unsorted)) % 0.36/0.74 (define @t140 () (@var "BOUND_VARIABLE_11124" $$unsorted)) % 0.36/0.74 (define @t141 () (or @t129 @t137)) % 0.36/0.74 (define @t142 () (tptp.memberP @t2 @t140)) % 0.36/0.74 (define @t143 () (tptp.memberP @t1 @t140)) % 0.36/0.74 (define @t144 () (and @t143 @t142)) % 0.36/0.74 (define @t145 () (and (not @t143) (not @t142))) % 0.36/0.74 (define @t146 () (not (tptp.ssItem @t140))) % 0.36/0.74 (define @t147 () (tptp.neq @t1 tptp.nil)) % 0.36/0.74 (define @t148 () (tptp.cons @t139 tptp.nil)) % 0.36/0.74 (define @t149 () (or (not (tptp.ssItem @t139)) (not (tptp.ssList @t138)) (not (= @t2 (tptp.app @t148 @t138))) (not (= @t1 (tptp.app @t138 @t148))))) % 0.36/0.74 (define @t150 () (and @t149 @t147)) % 0.36/0.74 (define @t151 () (= @t1 tptp.nil)) % 0.36/0.74 (define @t152 () (and @t126 @t151)) % 0.36/0.74 (define @t153 () (not @t21)) % 0.36/0.74 (define @t154 () (or @t153 @t152 @t150 @t146 @t145 @t144)) % 0.36/0.74 (define @t155 () (@list @t1 @t140 @t139 @t138)) % 0.36/0.74 (define @t156 () (or @t129 (forall @t155 @t154))) % 0.36/0.74 (define @t157 () (or @t146 @t145 @t144)) % 0.36/0.74 (define @t158 () (or @t153 @t157 @t152 @t150)) % 0.36/0.74 (define @t159 () (forall @t155 @t158)) % 0.36/0.74 (define @t160 () (forall (@list @t140 @t139 @t138) @t158)) % 0.36/0.74 (define @t161 () (@list @t139 @t138)) % 0.36/0.74 (define @t162 () (forall @t161 @t147)) % 0.36/0.74 (define @t163 () (forall @t161 @t149)) % 0.36/0.74 (define @t164 () (@var "BOUND_VARIABLE_11093" $$unsorted)) % 0.36/0.74 (define @t165 () (@var "BOUND_VARIABLE_11091" $$unsorted)) % 0.36/0.74 (define @t166 () (@list @t165 @t164)) % 0.36/0.74 (define @t167 () (and @t163 @t162)) % 0.36/0.74 (define @t168 () (forall @t161 @t150)) % 0.36/0.74 (define @t169 () (forall (@list @t140) @t157)) % 0.36/0.74 (define @t170 () (or @t153 @t169 @t152 @t168)) % 0.36/0.74 (define @t171 () (tptp.cons @t165 tptp.nil)) % 0.36/0.74 (define @t172 () (and (forall (@list @t165 @t164) (or (not (tptp.ssItem @t165)) (not (tptp.ssList @t164)) (not (= @t2 (tptp.app @t171 @t164))) (not (= @t1 (tptp.app @t164 @t171))))) @t147)) % 0.36/0.74 (define @t173 () (not @t101)) % 0.36/0.74 (define @t174 () (or @t173 @t99 @t98)) % 0.36/0.74 (define @t175 () (forall @t33 @t174)) % 0.36/0.74 (define @t176 () (or @t153 @t175 @t152 @t172)) % 0.36/0.74 (define @t177 () (forall @t7 @t176)) % 0.36/0.74 (define @t178 () (or @t129 @t177)) % 0.36/0.74 (define @t179 () (or @t129 @t176)) % 0.36/0.74 (define @t180 () (or @t153 @t175 @t129 @t152 @t172)) % 0.36/0.74 (define @t181 () (or @t175 @t153 @t129 @t152 @t172)) % 0.36/0.74 (define @t182 () (@var "BOUND_VARIABLE_11058" $$unsorted)) % 0.36/0.74 (define @t183 () (@var "BOUND_VARIABLE_11056" $$unsorted)) % 0.36/0.74 (define @t184 () (@list @t183 @t182)) % 0.36/0.74 (define @t185 () (forall @t184 @t147)) % 0.36/0.74 (define @t186 () (tptp.cons @t183 tptp.nil)) % 0.36/0.74 (define @t187 () (not (= @t1 (tptp.app @t182 @t186)))) % 0.36/0.74 (define @t188 () (tptp.app @t186 @t182)) % 0.36/0.74 (define @t189 () (not (tptp.ssList @t182))) % 0.36/0.74 (define @t190 () (not (tptp.ssItem @t183))) % 0.36/0.74 (define @t191 () (or @t190 @t189 (not (= @t2 @t188)) @t187)) % 0.36/0.74 (define @t192 () (forall @t184 @t191)) % 0.36/0.74 (define @t193 () (@list @t183 @t182)) % 0.36/0.74 (define @t194 () (and @t192 @t185)) % 0.36/0.74 (define @t195 () (and @t191 @t147)) % 0.36/0.74 (define @t196 () (forall @t184 @t195)) % 0.36/0.74 (define @t197 () (or @t129 @t152 @t196)) % 0.36/0.74 (define @t198 () (or @t129 @t152 @t195)) % 0.36/0.74 (define @t199 () (not (= @t2 @t2))) % 0.36/0.74 (define @t200 () (or @t129 @t199 @t152 @t195)) % 0.36/0.74 (define @t201 () (or @t190 @t189 (not (= @t12 @t188)) @t187)) % 0.36/0.74 (define @t202 () (and @t201 @t147)) % 0.36/0.74 (define @t203 () (not (= @t12 tptp.nil))) % 0.36/0.74 (define @t204 () (and @t203 @t151)) % 0.36/0.74 (define @t205 () (not @t15)) % 0.36/0.74 (define @t206 () (or @t103 @t205 @t103 @t204 @t202)) % 0.36/0.74 (define @t207 () (or @t205 @t103 @t204 @t202)) % 0.36/0.74 (define @t208 () (forall @t16 @t207)) % 0.36/0.74 (define @t209 () (forall @t184 @t208)) % 0.36/0.74 (define @t210 () (forall (@list @t183 @t182 @t12) @t207)) % 0.36/0.74 (define @t211 () (forall (@list @t12 @t183 @t182) @t207)) % 0.36/0.74 (define @t212 () (forall @t184 @t207)) % 0.36/0.74 (define @t213 () (forall @t184 @t201)) % 0.36/0.74 (define @t214 () (@var "BOUND_VARIABLE_11025" $$unsorted)) % 0.36/0.74 (define @t215 () (@var "BOUND_VARIABLE_11023" $$unsorted)) % 0.36/0.74 (define @t216 () (@list @t215 @t214)) % 0.36/0.74 (define @t217 () (and @t213 @t185)) % 0.36/0.74 (define @t218 () (forall @t184 @t202)) % 0.36/0.74 (define @t219 () (or @t205 @t103 @t204 @t218)) % 0.36/0.74 (define @t220 () (tptp.cons @t215 tptp.nil)) % 0.36/0.74 (define @t221 () (and (forall (@list @t215 @t214) (or (not (tptp.ssItem @t215)) (not (tptp.ssList @t214)) (not (= @t12 (tptp.app @t220 @t214))) (not (= @t1 (tptp.app @t214 @t220))))) @t147)) % 0.36/0.74 (define @t222 () (or @t205 @t103 @t204 @t221)) % 0.36/0.74 (define @t223 () (forall @t16 @t222)) % 0.36/0.74 (define @t224 () (or @t175 @t153 @t223)) % 0.36/0.74 (define @t225 () (or @t175 @t153 @t222)) % 0.36/0.74 (define @t226 () (or @t205 @t103 @t175 @t153 @t204 @t221)) % 0.36/0.74 (define @t227 () (or @t103 @t175 @t153 @t204 @t221)) % 0.36/0.74 (define @t228 () (@var "BOUND_VARIABLE_10991" $$unsorted)) % 0.36/0.74 (define @t229 () (@var "BOUND_VARIABLE_10989" $$unsorted)) % 0.36/0.74 (define @t230 () (@list @t229 @t228)) % 0.36/0.74 (define @t231 () (forall @t230 @t147)) % 0.36/0.74 (define @t232 () (tptp.cons @t229 tptp.nil)) % 0.36/0.74 (define @t233 () (tptp.app @t228 @t232)) % 0.36/0.74 (define @t234 () (not (= @t12 (tptp.app @t232 @t228)))) % 0.36/0.74 (define @t235 () (not (tptp.ssList @t228))) % 0.36/0.74 (define @t236 () (not (tptp.ssItem @t229))) % 0.36/0.74 (define @t237 () (or @t236 @t235 @t234 (not (= @t1 @t233)))) % 0.36/0.74 (define @t238 () (forall @t230 @t237)) % 0.36/0.74 (define @t239 () (@list @t229 @t228)) % 0.36/0.74 (define @t240 () (and @t238 @t231)) % 0.36/0.74 (define @t241 () (and @t237 @t147)) % 0.36/0.74 (define @t242 () (forall @t230 @t241)) % 0.36/0.74 (define @t243 () (or @t153 @t204 @t242)) % 0.36/0.74 (define @t244 () (or @t153 @t204 @t241)) % 0.36/0.74 (define @t245 () (not (= @t1 @t1))) % 0.36/0.74 (define @t246 () (or @t153 @t245 @t204 @t241)) % 0.36/0.74 (define @t247 () (or @t236 @t235 @t234 (not (= @t10 @t233)))) % 0.36/0.74 (define @t248 () (and @t247 @t78)) % 0.36/0.74 (define @t249 () (and @t203 (= @t10 tptp.nil))) % 0.36/0.74 (define @t250 () (not @t13)) % 0.36/0.74 (define @t251 () (or @t104 @t250 @t104 @t249 @t248)) % 0.36/0.74 (define @t252 () (or @t250 @t104 @t249 @t248)) % 0.36/0.74 (define @t253 () (forall @t14 @t252)) % 0.36/0.74 (define @t254 () (forall @t230 @t253)) % 0.36/0.74 (define @t255 () (forall (@list @t229 @t228 @t10) @t252)) % 0.36/0.74 (define @t256 () (forall (@list @t10 @t229 @t228) @t252)) % 0.36/0.74 (define @t257 () (forall @t230 @t252)) % 0.36/0.74 (define @t258 () (forall @t230 @t78)) % 0.36/0.74 (define @t259 () (forall @t230 @t247)) % 0.36/0.74 (define @t260 () (@var "BOUND_VARIABLE_10964" $$unsorted)) % 0.36/0.74 (define @t261 () (and @t259 @t258)) % 0.36/0.74 (define @t262 () (forall @t230 @t248)) % 0.36/0.74 (define @t263 () (or @t250 @t104 @t249 @t262)) % 0.36/0.74 (define @t264 () (not (= @t10 (tptp.app @t260 @t79)))) % 0.36/0.74 (define @t265 () (not (= @t12 (tptp.app @t79 @t260)))) % 0.36/0.74 (define @t266 () (not (tptp.ssList @t260))) % 0.36/0.74 (define @t267 () (not @t90)) % 0.36/0.74 (define @t268 () (or @t267 @t266 @t265 @t264)) % 0.36/0.74 (define @t269 () (@list @t27 @t260)) % 0.36/0.74 (define @t270 () (and (forall @t269 @t268) @t78)) % 0.36/0.74 (define @t271 () (or @t250 @t104 @t249 @t270)) % 0.36/0.74 (define @t272 () (forall @t14 @t271)) % 0.36/0.74 (define @t273 () (or @t103 @t175 @t272)) % 0.36/0.74 (define @t274 () (or @t103 @t175 @t271)) % 0.36/0.74 (define @t275 () (or @t250 @t104 @t103 @t175 @t249 @t270)) % 0.36/0.74 (define @t276 () (or @t104 @t103 @t175 @t249 @t270)) % 0.36/0.74 (define @t277 () (or @t266 @t265 @t264)) % 0.36/0.74 (define @t278 () (or @t267 @t277)) % 0.36/0.74 (define @t279 () (forall @t269 @t278)) % 0.36/0.74 (define @t280 () (@list @t260)) % 0.36/0.74 (define @t281 () (forall @t280 @t278)) % 0.36/0.74 (define @t282 () (forall @t280 @t277)) % 0.36/0.74 (define @t283 () (or @t267 @t282)) % 0.36/0.74 (define @t284 () (not (= @t10 @t81))) % 0.36/0.74 (define @t285 () (not (= @t12 @t83))) % 0.36/0.74 (define @t286 () (not @t86)) % 0.36/0.74 (define @t287 () (or @t286 @t285 @t284)) % 0.36/0.74 (define @t288 () (forall @t88 @t287)) % 0.36/0.74 (define @t289 () (or @t285 @t284)) % 0.36/0.74 (define @t290 () (forall @t133 (or @t129 @t128 (and @t126 (= tptp.nil @t117)) @t125 @t121 @t120 @t119))) % 0.36/0.74 (define @t291 () (@quantifiers_skolemize @t290 2)) % 0.36/0.74 (define @t292 () (@quantifiers_skolemize @t290 0)) % 0.36/0.74 (define @t293 () (tptp.memberP @t292 @t291)) % 0.36/0.74 (define @t294 () (@quantifiers_skolemize @t290 1)) % 0.36/0.74 (define @t295 () (tptp.memberP @t294 @t291)) % 0.36/0.74 (define @t296 () (and @t295 @t293)) % 0.36/0.74 (define @t297 () (not @t293)) % 0.36/0.74 (define @t298 () (not @t295)) % 0.36/0.74 (define @t299 () (and @t298 @t297)) % 0.36/0.74 (define @t300 () (tptp.ssItem @t291)) % 0.36/0.74 (define @t301 () (not @t300)) % 0.36/0.74 (define @t302 () (tptp.neq @t294 tptp.nil)) % 0.36/0.74 (define @t303 () (@quantifiers_skolemize @t290 3)) % 0.36/0.74 (define @t304 () (tptp.cons @t303 tptp.nil)) % 0.36/0.74 (define @t305 () (@quantifiers_skolemize @t290 4)) % 0.36/0.74 (define @t306 () (tptp.app @t305 @t304)) % 0.36/0.74 (define @t307 () (= @t294 @t306)) % 0.36/0.74 (define @t308 () (not @t307)) % 0.36/0.74 (define @t309 () (tptp.app @t304 @t305)) % 0.36/0.74 (define @t310 () (= @t292 @t309)) % 0.36/0.74 (define @t311 () (not @t310)) % 0.36/0.74 (define @t312 () (tptp.ssList @t305)) % 0.36/0.74 (define @t313 () (not @t312)) % 0.36/0.74 (define @t314 () (tptp.ssItem @t303)) % 0.36/0.74 (define @t315 () (not @t314)) % 0.36/0.74 (define @t316 () (or @t315 @t313 @t311 @t308)) % 0.36/0.74 (define @t317 () (and @t316 @t302)) % 0.36/0.74 (define @t318 () (= tptp.nil @t294)) % 0.36/0.74 (define @t319 () (= tptp.nil @t292)) % 0.36/0.74 (define @t320 () (not @t319)) % 0.36/0.74 (define @t321 () (and @t320 @t318)) % 0.36/0.74 (define @t322 () (tptp.ssList @t294)) % 0.36/0.74 (define @t323 () (not @t322)) % 0.36/0.74 (define @t324 () (not (tptp.ssList @t292))) % 0.36/0.74 (define @t325 () (or @t324 @t323 @t321 @t317 @t301 @t299 @t296)) % 0.36/0.74 (define @t326 () (not @t325)) % 0.36/0.74 (define @t327 () (not @t290)) % 0.36/0.74 (define @t328 () (not (= @t292 tptp.nil))) % 0.36/0.74 (define @t329 () (and @t328 @t318)) % 0.36/0.74 (define @t330 () (or @t324 @t323 @t329 @t317 @t301 @t299 @t296)) % 0.36/0.74 (define @t331 () (not @t330)) % 0.36/0.74 (define @t332 () (@list true)) % 0.36/0.74 (define @t333 () (@list @t325)) % 0.36/0.74 (define @t334 () (tptp.memberP tptp.nil @t291)) % 0.36/0.74 (define @t335 () (not @t334)) % 0.36/0.74 (define @t336 () (or @t301 @t335)) % 0.36/0.74 (define @t337 () (@var "BOUND_VARIABLE_9119" $$unsorted)) % 0.36/0.74 (define @t338 () (= (tptp.neq @t2 @t337) (not (= @t2 @t337)))) % 0.36/0.74 (define @t339 () (not (tptp.ssList @t337))) % 0.36/0.74 (define @t340 () (or @t129 @t339 @t338)) % 0.36/0.74 (define @t341 () (or @t339 @t338)) % 0.36/0.74 (define @t342 () (or @t129 @t341)) % 0.36/0.74 (define @t343 () (@list @t2 @t337)) % 0.36/0.74 (define @t344 () (forall @t343 @t342)) % 0.36/0.74 (define @t345 () (@list @t337)) % 0.36/0.74 (define @t346 () (forall @t345 @t342)) % 0.36/0.74 (define @t347 () (forall @t345 @t341)) % 0.36/0.74 (define @t348 () (@list @t1)) % 0.36/0.74 (define @t349 () (or @t129 @t347)) % 0.36/0.74 (define @t350 () (forall @t7 (or @t153 @t5))) % 0.36/0.74 (define @t351 () (not (= @t294 tptp.nil))) % 0.36/0.74 (define @t352 () (= @t302 @t351)) % 0.36/0.74 (define @t353 () (not @t45)) % 0.36/0.74 (define @t354 () (or @t323 @t353 @t352)) % 0.36/0.74 (define @t355 () (forall @t343 @t340)) % 0.36/0.74 (define @t356 () (not @t318)) % 0.36/0.74 (define @t357 () (= @t302 @t356)) % 0.36/0.74 (define @t358 () (or @t323 @t353 @t357)) % 0.36/0.74 (define @t359 () (@var "BOUND_VARIABLE_9140" $$unsorted)) % 0.36/0.74 (define @t360 () (tptp.ssList (tptp.cons @t359 @t2))) % 0.36/0.74 (define @t361 () (not (tptp.ssItem @t359))) % 0.36/0.74 (define @t362 () (or @t361 @t360)) % 0.36/0.74 (define @t363 () (or @t129 @t362)) % 0.36/0.74 (define @t364 () (forall (@list @t2 @t359) @t363)) % 0.36/0.74 (define @t365 () (@list @t359)) % 0.36/0.74 (define @t366 () (forall @t365 @t363)) % 0.36/0.74 (define @t367 () (forall @t365 @t362)) % 0.36/0.74 (define @t368 () (or @t129 @t367)) % 0.36/0.74 (define @t369 () (forall @t7 (or (not @t6) @t41))) % 0.36/0.74 (define @t370 () (tptp.ssList @t304)) % 0.36/0.74 (define @t371 () (or @t353 @t315 @t370)) % 0.36/0.74 (define @t372 () (@var "BOUND_VARIABLE_9672" $$unsorted)) % 0.36/0.74 (define @t373 () (@var "BOUND_VARIABLE_9670" $$unsorted)) % 0.36/0.74 (define @t374 () (= (tptp.memberP (tptp.app @t373 @t372) @t2) (or (tptp.memberP @t373 @t2) (tptp.memberP @t372 @t2)))) % 0.36/0.74 (define @t375 () (not (tptp.ssList @t372))) % 0.36/0.74 (define @t376 () (not (tptp.ssList @t373))) % 0.36/0.74 (define @t377 () (not @t8)) % 0.36/0.74 (define @t378 () (or @t376 @t375 @t374)) % 0.36/0.74 (define @t379 () (or @t377 @t378)) % 0.36/0.74 (define @t380 () (forall (@list @t2 @t373 @t372) @t379)) % 0.36/0.74 (define @t381 () (@list @t373 @t372)) % 0.36/0.74 (define @t382 () (forall @t381 @t379)) % 0.36/0.74 (define @t383 () (forall @t381 @t378)) % 0.36/0.74 (define @t384 () (@var "BOUND_VARIABLE_9651" $$unsorted)) % 0.36/0.74 (define @t385 () (or @t377 @t383)) % 0.36/0.74 (define @t386 () (= (tptp.memberP (tptp.app @t1 @t384) @t2) (or @t62 (tptp.memberP @t384 @t2)))) % 0.36/0.74 (define @t387 () (not (tptp.ssList @t384))) % 0.36/0.74 (define @t388 () (or @t153 @t387 @t386)) % 0.36/0.74 (define @t389 () (@list @t1 @t384)) % 0.36/0.74 (define @t390 () (forall @t389 @t388)) % 0.36/0.74 (define @t391 () (or @t387 @t386)) % 0.36/0.74 (define @t392 () (or @t153 @t391)) % 0.36/0.74 (define @t393 () (forall @t389 @t392)) % 0.36/0.74 (define @t394 () (@list @t384)) % 0.36/0.74 (define @t395 () (forall @t394 @t392)) % 0.36/0.74 (define @t396 () (forall @t394 @t391)) % 0.36/0.74 (define @t397 () (or @t153 @t396)) % 0.36/0.74 (define @t398 () (forall @t16 (or @t205 @t63))) % 0.36/0.74 (define @t399 () (tptp.memberP @t304 @t291)) % 0.36/0.74 (define @t400 () (tptp.memberP @t305 @t291)) % 0.36/0.74 (define @t401 () (or @t400 @t399)) % 0.36/0.74 (define @t402 () (tptp.memberP @t306 @t291)) % 0.36/0.74 (define @t403 () (= @t402 @t401)) % 0.36/0.74 (define @t404 () (not @t370)) % 0.36/0.74 (define @t405 () (or @t301 @t313 @t404 @t403)) % 0.36/0.74 (define @t406 () (or @t399 @t400)) % 0.36/0.74 (define @t407 () (tptp.memberP @t309 @t291)) % 0.36/0.74 (define @t408 () (= @t407 @t406)) % 0.36/0.74 (define @t409 () (or @t301 @t404 @t313 @t408)) % 0.36/0.74 (define @t410 () (and @t307 @t295)) % 0.36/0.74 (define @t411 () (not @t407)) % 0.36/0.74 (define @t412 () (not @t297)) % 0.36/0.74 (define @t413 () (and @t310 @t297)) % 0.36/0.74 (define @t414 () (not @t403)) % 0.36/0.74 (define @t415 () (not @t402)) % 0.36/0.74 (define @t416 () (not @t408)) % 0.36/0.74 (define @t417 () (not @t406)) % 0.36/0.74 (define @t418 () (not @t401)) % 0.36/0.74 (define @t419 () (not @t298)) % 0.36/0.74 (define @t420 () (and @t307 @t298)) % 0.36/0.74 (define @t421 () (and @t310 @t293)) % 0.36/0.74 (define @t422 () (@list true false)) % 0.36/0.74 (define @t423 () (not @t357)) % 0.36/0.74 (define @t424 () (not @t335)) % 0.36/0.74 (define @t425 () (and @t318 @t335)) % 0.36/0.74 (define @t426 () (@list false true)) % 0.36/0.74 (define @t427 () (and @t319 @t335)) % 0.36/0.74 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.36/0.74 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.36/0.74 (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))))))))))) % 0.36/0.74 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.36/0.74 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.36/0.74 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.36/0.74 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.36/0.74 (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))))))))))))))))) % 0.36/0.74 (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)))))))))))))))) % 0.36/0.74 (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))))))))))))))))) % 0.36/0.74 (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))))))))))))))) % 0.36/0.74 (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))))))))))))))) % 0.36/0.74 (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)))))))))))))))) % 0.36/0.74 (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))))))))))))) % 0.36/0.74 (assume @p15 @t39) % 0.36/0.74 (assume @p16 @t44) % 0.36/0.74 (assume @p17 @t45) % 0.36/0.74 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t40 @t2))))))) % 0.36/0.74 (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) @t46))))))))))) % 0.36/0.74 (assume @p20 (forall @t9 (=> @t17 (or @t48 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t47 @t2))))))))) % 0.36/0.74 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t40))))))) % 0.36/0.74 (assume @p22 (forall @t9 (=> @t17 (=> @t50 (tptp.ssItem @t49))))) % 0.36/0.74 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t40) @t1)))))) % 0.36/0.74 (assume @p24 (forall @t9 (=> @t17 (=> @t50 (tptp.ssList @t51))))) % 0.36/0.74 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t40) @t2)))))) % 0.36/0.74 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t52)))))) % 0.36/0.74 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t53) (tptp.app @t47 @t2))))))))) % 0.36/0.74 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.36/0.74 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t55 @t54) @t3)))))) % 0.36/0.74 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t55 @t26) (tptp.leq @t2 @t12))))))))) % 0.36/0.74 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.36/0.74 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t56 @t54)))))) % 0.36/0.74 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t58 (not @t57))))))) % 0.36/0.74 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t58 @t35) @t59)))))))) % 0.36/0.74 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= 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(@p680 @p674 @p645) :args (@t319 @t422 (@list @t321 @t318))) % 0.36/0.74 (step @p682 :rule refl :args (@t297)) % 0.36/0.74 (step @p683 :rule refl :args (@t320)) % 0.36/0.74 (step @p684 :rule nary_cong :premises (@p683 @p647 @p682) :args ((or @t320 @t424 @t297))) % 0.36/0.74 (assume-push @p752 @t319) % 0.36/0.74 (assume-push @p753 @t335) % 0.36/0.74 (assume-push @p754 @t335) % 0.36/0.74 (assume-push @p755 @t319) % 0.36/0.74 (step @p654 :rule false_intro :premises (@p384)) % 0.36/0.74 (step @p527 :rule refl :args (@t291)) % 0.36/0.74 (step @p689 :rule symm :premises (@p752)) % 0.36/0.74 (step @p690 :rule cong :premises (@p689 @p527) :args (@t293)) % 0.36/0.74 (step @p691 :rule trans :premises (@p690 @p654)) % 0.36/0.74 (step @p692 :rule false_elim :premises (@p691)) % 0.36/0.74 (step-pop @p756 :rule scope :premises (@p692)) % 0.36/0.74 (step-pop @p757 :rule scope :premises (@p756)) % 0.36/0.74 (step @p693 :rule process_scope :premises (@p757) :args (@t297)) % 0.36/0.74 (step @p696 :rule and_intro :premises (@p384 @p752)) % 0.36/0.74 (step @p697 :rule modus_ponens :premises (@p696 @p693)) % 0.36/0.74 (step-pop @p758 :rule scope :premises (@p697)) % 0.36/0.74 (step-pop @p759 :rule scope :premises (@p758)) % 0.36/0.74 (step @p698 :rule process_scope :premises (@p759) :args (@t297)) % 0.36/0.74 (step @p701 :rule implies_elim :premises (@p698)) % 0.36/0.74 (step @p702 :rule cnf_and_neg :args (@t427)) % 0.36/0.74 (step @p703 :rule resolution :premises (@p702 @p701) :args (true @t427)) % 0.36/0.74 (step @p704 :rule eq_resolve :premises (@p703 @p684)) % 0.36/0.74 (step @p705 :rule reordering :premises (@p704) :args ((or @t297 @t320 @t334))) % 0.36/0.74 (step @p706 :rule chain_m_resolution :premises (@p705 @p681 @p384) :args (@t297 @t426 (@list @t319 @t334))) % 0.36/0.74 (step @p707 false :rule chain_m_resolution :premises (@p581 @p706 @p672 @p370) :args (false (@list true true true) (@list @t293 @t295 @t299))) % 0.36/0.74 ) % 0.36/0.74 % SZS output end Proof % 0.36/0.74 % cvc5 exiting %------------------------------------------------------------------------------