%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC094+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 : n007.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 08:58:01 AM UTC 2026 % Result : Theorem 0.36s 0.91s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC094+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n007.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 19:13:56 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.91 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.91 % SZS status Theorem % 0.36/0.91 % SZS output start Proof % 0.36/0.91 ( % 0.36/0.91 (declare-sort $$unsorted 0) % 0.36/0.91 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.36/0.91 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.36/0.91 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.91 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.91 (declare-const tptp.nil $$unsorted) % 0.36/0.91 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.36/0.91 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.91 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.91 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.91 (define @t3 () (= @t2 @t1)) % 0.36/0.91 (define @t4 () (not @t3)) % 0.36/0.91 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.36/0.91 (define @t6 () (tptp.ssItem @t1)) % 0.36/0.91 (define @t7 () (@list @t1)) % 0.36/0.91 (define @t8 () (tptp.ssItem @t2)) % 0.36/0.91 (define @t9 () (@list @t2)) % 0.36/0.91 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.91 (define @t11 () (tptp.cons @t1 @t10)) % 0.36/0.91 (define @t12 () (@var "W" $$unsorted)) % 0.36/0.91 (define @t13 () (tptp.ssList @t10)) % 0.36/0.91 (define @t14 () (@list @t10)) % 0.36/0.91 (define @t15 () (tptp.ssList @t12)) % 0.36/0.91 (define @t16 () (@list @t12)) % 0.36/0.91 (define @t17 () (tptp.ssList @t2)) % 0.36/0.91 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.36/0.91 (define @t19 () (tptp.app @t1 @t12)) % 0.36/0.91 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.36/0.91 (define @t21 () (tptp.ssList @t1)) % 0.36/0.91 (define @t22 () (tptp.app @t12 @t1)) % 0.36/0.91 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.36/0.91 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.36/0.91 (define @t25 () (tptp.leq @t12 @t1)) % 0.36/0.91 (define @t26 () (tptp.leq @t1 @t12)) % 0.36/0.91 (define @t27 () (@var "Z" $$unsorted)) % 0.36/0.91 (define @t28 () (@var "Y" $$unsorted)) % 0.36/0.91 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.36/0.91 (define @t30 () (tptp.ssList @t27)) % 0.36/0.91 (define @t31 () (@list @t27)) % 0.36/0.91 (define @t32 () (tptp.ssList @t28)) % 0.36/0.91 (define @t33 () (@list @t28)) % 0.36/0.91 (define @t34 () (tptp.ssItem @t12)) % 0.36/0.91 (define @t35 () (tptp.lt @t1 @t12)) % 0.36/0.91 (define @t36 () (= @t1 @t12)) % 0.36/0.91 (define @t37 () (not @t36)) % 0.36/0.91 (define @t38 () (tptp.cons @t1 @t2)) % 0.36/0.91 (define @t39 () (tptp.ssList tptp.nil)) % 0.36/0.91 (define @t40 () (= @t1 @t2)) % 0.36/0.91 (define @t41 () (= @t12 @t10)) % 0.36/0.91 (define @t42 () (tptp.cons @t12 @t1)) % 0.36/0.91 (define @t43 () (= tptp.nil @t2)) % 0.36/0.91 (define @t44 () (tptp.hd @t2)) % 0.36/0.91 (define @t45 () (not @t43)) % 0.36/0.91 (define @t46 () (tptp.tl @t2)) % 0.36/0.91 (define @t47 () (tptp.app @t2 @t1)) % 0.36/0.91 (define @t48 () (tptp.app @t1 @t2)) % 0.36/0.91 (define @t49 () (tptp.app tptp.nil @t2)) % 0.36/0.91 (define @t50 () (=> @t17 (= @t49 @t2))) % 0.36/0.91 (define @t51 () (forall @t9 @t50)) % 0.36/0.91 (define @t52 () (tptp.leq @t1 @t2)) % 0.36/0.91 (define @t53 () (tptp.leq @t2 @t1)) % 0.36/0.91 (define @t54 () (tptp.geq @t2 @t1)) % 0.36/0.91 (define @t55 () (tptp.lt @t1 @t2)) % 0.36/0.91 (define @t56 () (tptp.lt @t2 @t1)) % 0.36/0.91 (define @t57 () (tptp.lt @t2 @t12)) % 0.36/0.91 (define @t58 () (tptp.gt @t2 @t1)) % 0.36/0.91 (define @t59 () (tptp.memberP @t12 @t2)) % 0.36/0.91 (define @t60 () (tptp.app @t12 @t2)) % 0.36/0.91 (define @t61 () (tptp.cons @t2 tptp.nil)) % 0.36/0.91 (define @t62 () (tptp.hd @t1)) % 0.36/0.91 (define @t63 () (= tptp.nil @t1)) % 0.36/0.91 (define @t64 () (not @t63)) % 0.36/0.91 (define @t65 () (tptp.cons @t2 @t1)) % 0.36/0.91 (define @t66 () (= @t12 @t2)) % 0.36/0.91 (define @t67 () (@var "X1" $$unsorted)) % 0.36/0.91 (define @t68 () (tptp.app @t28 @t67)) % 0.36/0.91 (define @t69 () (tptp.app @t28 @t27)) % 0.36/0.91 (define @t70 () (tptp.app @t69 @t67)) % 0.36/0.91 (define @t71 () (tptp.ssList @t67)) % 0.36/0.91 (define @t72 () (and @t71 (= @t70 @t2) (= @t68 @t1))) % 0.36/0.91 (define @t73 () (@list @t67)) % 0.36/0.91 (define @t74 () (exists @t73 @t72)) % 0.36/0.91 (define @t75 () (and @t30 @t74)) % 0.36/0.91 (define @t76 () (exists @t31 @t75)) % 0.36/0.91 (define @t77 () (and @t32 @t76)) % 0.36/0.91 (define @t78 () (exists @t33 @t77)) % 0.36/0.91 (define @t79 () (not (= @t10 @t12))) % 0.36/0.91 (define @t80 () (not (= @t2 @t12))) % 0.36/0.91 (define @t81 () (not (= @t1 @t10))) % 0.36/0.91 (define @t82 () (or @t81 @t80 @t79 @t78)) % 0.36/0.91 (define @t83 () (=> @t13 @t82)) % 0.36/0.91 (define @t84 () (forall @t14 @t83)) % 0.36/0.91 (define @t85 () (=> @t15 @t84)) % 0.36/0.91 (define @t86 () (forall @t16 @t85)) % 0.36/0.91 (define @t87 () (=> @t21 @t86)) % 0.36/0.91 (define @t88 () (forall @t7 @t87)) % 0.36/0.91 (define @t89 () (=> @t17 @t88)) % 0.36/0.91 (define @t90 () (forall @t9 @t89)) % 0.36/0.91 (define @t91 () (not @t90)) % 0.36/0.91 (define @t92 () (= @t2 @t49)) % 0.36/0.91 (define @t93 () (tptp.app tptp.nil tptp.nil)) % 0.36/0.91 (define @t94 () (= tptp.nil @t93)) % 0.36/0.91 (define @t95 () (not @t39)) % 0.36/0.91 (define @t96 () (or @t95 @t94)) % 0.36/0.91 (define @t97 () (@list false false)) % 0.36/0.91 (define @t98 () (@var "BOUND_VARIABLE_10973" $$unsorted)) % 0.36/0.91 (define @t99 () (tptp.app @t28 @t98)) % 0.36/0.91 (define @t100 () (@var "BOUND_VARIABLE_10971" $$unsorted)) % 0.36/0.91 (define @t101 () (tptp.app (tptp.app @t28 @t100) @t98)) % 0.36/0.91 (define @t102 () (not (= @t2 @t101))) % 0.36/0.91 (define @t103 () (not (tptp.ssList @t98))) % 0.36/0.91 (define @t104 () (not (tptp.ssList @t100))) % 0.36/0.91 (define @t105 () (not @t32)) % 0.36/0.91 (define @t106 () (@list @t28 @t100 @t98)) % 0.36/0.91 (define @t107 () (not (forall @t106 (or @t105 @t104 @t103 @t102 (not (= @t2 @t99)))))) % 0.36/0.91 (define @t108 () (not @t17)) % 0.36/0.91 (define @t109 () (or @t108 @t107)) % 0.36/0.91 (define @t110 () (forall @t9 @t109)) % 0.36/0.91 (define @t111 () (@quantifiers_skolemize @t110 0)) % 0.36/0.91 (define @t112 () (not (= @t2 @t2))) % 0.36/0.91 (define @t113 () (or @t108 @t107 @t112)) % 0.36/0.91 (define @t114 () (not (= @t1 @t99))) % 0.36/0.91 (define @t115 () (or @t105 @t104 @t103 @t102 @t114)) % 0.36/0.91 (define @t116 () (not (forall @t106 @t115))) % 0.36/0.91 (define @t117 () (not @t21)) % 0.36/0.91 (define @t118 () (not @t40)) % 0.36/0.91 (define @t119 () (or @t4 @t117 @t116 @t4)) % 0.36/0.91 (define @t120 () (or @t117 @t116 @t4)) % 0.36/0.91 (define @t121 () (forall @t7 @t120)) % 0.36/0.91 (define @t122 () (or @t108 @t121)) % 0.36/0.91 (define @t123 () (or @t108 @t120)) % 0.36/0.91 (define @t124 () (or @t117 @t116 @t108 @t4)) % 0.36/0.91 (define @t125 () (or @t116 @t117 @t108 @t4)) % 0.36/0.91 (define @t126 () (or @t108 @t4)) % 0.36/0.91 (define @t127 () (or @t108 @t112 @t118)) % 0.36/0.91 (define @t128 () (not @t15)) % 0.36/0.91 (define @t129 () (or @t80 @t128 @t80 @t37)) % 0.36/0.91 (define @t130 () (or @t128 @t80 @t37)) % 0.36/0.91 (define @t131 () (forall @t16 @t130)) % 0.36/0.91 (define @t132 () (or @t116 @t117 @t131)) % 0.36/0.91 (define @t133 () (or @t116 @t117 @t130)) % 0.36/0.91 (define @t134 () (or @t128 @t80 @t116 @t117 @t37)) % 0.36/0.91 (define @t135 () (or @t80 @t116 @t117 @t37)) % 0.36/0.91 (define @t136 () (or @t117 @t37)) % 0.36/0.91 (define @t137 () (not (= @t12 @t1))) % 0.36/0.91 (define @t138 () (not (= @t1 @t1))) % 0.36/0.91 (define @t139 () (or @t117 @t138 @t137)) % 0.36/0.91 (define @t140 () (not @t41)) % 0.36/0.91 (define @t141 () (not @t13)) % 0.36/0.91 (define @t142 () (or @t81 @t141 @t81 @t140)) % 0.36/0.91 (define @t143 () (or @t141 @t81 @t140)) % 0.36/0.91 (define @t144 () (forall @t14 @t143)) % 0.36/0.91 (define @t145 () (or @t80 @t116 @t144)) % 0.36/0.91 (define @t146 () (or @t80 @t116 @t143)) % 0.36/0.91 (define @t147 () (or @t141 @t81 @t80 @t140 @t116)) % 0.36/0.91 (define @t148 () (or @t81 @t80 @t140 @t116)) % 0.36/0.91 (define @t149 () (or @t104 @t103 @t102 @t114)) % 0.36/0.91 (define @t150 () (or @t105 @t149)) % 0.36/0.91 (define @t151 () (forall @t106 @t150)) % 0.36/0.91 (define @t152 () (@list @t100 @t98)) % 0.36/0.91 (define @t153 () (forall @t152 @t150)) % 0.36/0.91 (define @t154 () (forall @t152 @t149)) % 0.36/0.91 (define @t155 () (@var "BOUND_VARIABLE_10947" $$unsorted)) % 0.36/0.91 (define @t156 () (or @t105 @t154)) % 0.36/0.91 (define @t157 () (not (= @t1 (tptp.app @t28 @t155)))) % 0.36/0.91 (define @t158 () (not (= @t2 (tptp.app @t69 @t155)))) % 0.36/0.91 (define @t159 () (not (tptp.ssList @t155))) % 0.36/0.91 (define @t160 () (not @t30)) % 0.36/0.91 (define @t161 () (or @t160 @t159 @t158 @t157)) % 0.36/0.91 (define @t162 () (@list @t27 @t155)) % 0.36/0.91 (define @t163 () (forall @t162 @t161)) % 0.36/0.91 (define @t164 () (not @t163)) % 0.36/0.91 (define @t165 () (and @t32 @t164)) % 0.36/0.91 (define @t166 () (forall @t33 (not @t165))) % 0.36/0.91 (define @t167 () (not @t166)) % 0.36/0.91 (define @t168 () (or @t159 @t158 @t157)) % 0.36/0.91 (define @t169 () (or @t160 @t168)) % 0.36/0.91 (define @t170 () (forall @t162 @t169)) % 0.36/0.91 (define @t171 () (@list @t155)) % 0.36/0.91 (define @t172 () (forall @t171 @t169)) % 0.36/0.91 (define @t173 () (forall @t171 @t168)) % 0.36/0.91 (define @t174 () (or @t160 @t173)) % 0.36/0.91 (define @t175 () (= @t1 @t68)) % 0.36/0.91 (define @t176 () (not @t175)) % 0.36/0.91 (define @t177 () (= @t2 @t70)) % 0.36/0.91 (define @t178 () (not @t177)) % 0.36/0.91 (define @t179 () (not @t71)) % 0.36/0.91 (define @t180 () (or @t179 @t178 @t176)) % 0.36/0.91 (define @t181 () (forall @t73 @t180)) % 0.36/0.91 (define @t182 () (not @t181)) % 0.36/0.91 (define @t183 () (and @t30 @t182)) % 0.36/0.91 (define @t184 () (forall @t31 (not @t183))) % 0.36/0.91 (define @t185 () (not @t184)) % 0.36/0.91 (define @t186 () (and @t71 @t177 @t175)) % 0.36/0.91 (define @t187 () (forall @t73 (not @t186))) % 0.36/0.91 (define @t188 () (not @t187)) % 0.36/0.91 (define @t189 () (forall @t106 (or @t105 @t104 @t103 (not (= @t101 @t111)) (not (= @t99 @t111))))) % 0.36/0.91 (define @t190 () (not @t189)) % 0.36/0.91 (define @t191 () (tptp.ssList @t111)) % 0.36/0.91 (define @t192 () (not @t191)) % 0.36/0.91 (define @t193 () (or @t192 @t190)) % 0.36/0.91 (define @t194 () (not @t193)) % 0.36/0.91 (define @t195 () (not @t110)) % 0.36/0.91 (define @t196 () (not (= @t111 @t99))) % 0.36/0.91 (define @t197 () (not (= @t111 @t101))) % 0.36/0.91 (define @t198 () (or @t105 @t104 @t103 @t197 @t196)) % 0.36/0.91 (define @t199 () (forall @t106 @t198)) % 0.36/0.91 (define @t200 () (not @t199)) % 0.36/0.91 (define @t201 () (or @t192 @t200)) % 0.36/0.91 (define @t202 () (not @t201)) % 0.36/0.91 (define @t203 () (@list true)) % 0.36/0.91 (define @t204 () (@list @t193)) % 0.36/0.91 (define @t205 () (tptp.app tptp.nil @t111)) % 0.36/0.91 (define @t206 () (= @t111 @t205)) % 0.36/0.91 (define @t207 () (or @t192 @t206)) % 0.36/0.91 (define @t208 () (@list @t191 @t207)) % 0.36/0.91 (define @t209 () (not (= @t205 @t111))) % 0.36/0.91 (define @t210 () (tptp.app @t93 @t111)) % 0.36/0.91 (define @t211 () (not (= @t210 @t111))) % 0.36/0.91 (define @t212 () (or @t95 @t95 @t192 @t211 @t209)) % 0.36/0.91 (define @t213 () (not @t206)) % 0.36/0.91 (define @t214 () (= @t111 @t210)) % 0.36/0.91 (define @t215 () (not @t214)) % 0.36/0.91 (define @t216 () (or @t95 @t95 @t192 @t215 @t213)) % 0.36/0.91 (define @t217 () (not @t94)) % 0.36/0.91 (define @t218 () (and @t215 @t214)) % 0.36/0.91 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.36/0.91 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.36/0.91 (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))))))))))) % 0.36/0.91 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.36/0.91 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.36/0.91 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.36/0.91 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.36/0.91 (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))))))))))))))))) % 0.36/0.91 (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)))))))))))))))) % 0.36/0.91 (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))))))))))))))))) % 0.36/0.91 (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))))))))))))))) % 0.36/0.91 (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))))))))))))))) % 0.36/0.91 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t37))))))))))))))) % 0.36/0.91 (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))))))))))))) % 0.36/0.91 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.36/0.91 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.36/0.91 (assume @p17 @t39) % 0.36/0.91 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.36/0.91 (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 @t41 @t40))))))))))) % 0.36/0.91 (assume @p20 (forall @t9 (=> @t17 (or @t43 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t42 @t2))))))))) % 0.36/0.91 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.36/0.91 (assume @p22 (forall @t9 (=> @t17 (=> @t45 (tptp.ssItem @t44))))) % 0.36/0.91 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.36/0.91 (assume @p24 (forall @t9 (=> @t17 (=> @t45 (tptp.ssList @t46))))) % 0.36/0.91 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.36/0.91 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t47)))))) % 0.36/0.91 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t48) (tptp.app @t42 @t2))))))))) % 0.36/0.91 (assume @p28 @t51) % 0.36/0.91 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t53 @t52) @t3)))))) % 0.36/0.91 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t53 @t26) (tptp.leq @t2 @t12))))))))) % 0.36/0.91 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.36/0.91 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t54 @t52)))))) % 0.36/0.91 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t56 (not @t55))))))) % 0.36/0.91 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t56 @t35) @t57)))))))) % 0.36/0.91 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t58 @t55)))))) % 0.36/0.91 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t59))))))))) % 0.36/0.91 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t59))))))))) % 0.36/0.91 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.36/0.91 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.36/0.91 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.36/0.91 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.36/0.91 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.36/0.91 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.36/0.91 (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)))))))))))) % 0.36/0.91 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.36/0.91 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t43)))) % 0.36/0.91 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.36/0.91 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.36/0.91 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.36/0.91 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t60 @t1))))))))) % 0.36/0.91 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.36/0.91 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t43)))) % 0.36/0.91 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.36/0.91 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.36/0.91 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.36/0.91 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t60 @t10) @t1))))))))))) % 0.36/0.91 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.36/0.91 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t43)))) % 0.36/0.91 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t61)))) % 0.36/0.91 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.36/0.91 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t61)))) % 0.36/0.91 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.36/0.91 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t61)))) % 0.36/0.91 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.36/0.91 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t61)))) % 0.36/0.91 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.36/0.91 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t65) (or @t63 (and @t64 (tptp.totalorderedP @t1) (tptp.leq @t2 @t62))))))))) % 0.36/0.91 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t61)))) % 0.36/0.91 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.36/0.91 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t65) (or @t63 (and @t64 (tptp.strictorderedP @t1) (tptp.lt @t2 @t62))))))))) % 0.36/0.91 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t61)))) % 0.36/0.91 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.36/0.91 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t61)))) % 0.36/0.91 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.36/0.91 (assume @p75 (forall @t9 (=> @t17 (=> @t45 (exists @t7 (and @t6 (= @t44 @t1))))))) % 0.36/0.91 (assume @p76 (forall @t9 (=> @t17 (=> @t45 (exists @t7 (and @t21 (= @t46 @t1))))))) % 0.36/0.91 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t64 @t45 (= @t62 @t44) (= (tptp.tl @t1) @t46)) @t40)))))) % 0.36/0.91 (assume @p78 (forall @t9 (=> @t17 (=> @t45 (= (tptp.cons @t44 @t46) @t2))))) % 0.36/0.91 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t47) @t66)))))))) % 0.36/0.91 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t48) @t66)))))))) % 0.36/0.91 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t38 (tptp.app @t18 @t2))))))) % 0.36/0.91 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t47 @t12) (tptp.app @t2 @t19))))))))) % 0.36/0.91 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t47) (and @t63 @t43))))))) % 0.36/0.91 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.36/0.91 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t45 (= (tptp.hd @t47) @t44))))))) % 0.36/0.91 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t45 (= (tptp.tl @t47) (tptp.app @t46 @t1)))))))) % 0.36/0.91 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t54 (tptp.geq @t1 @t2)) @t3)))))) % 0.36/0.91 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t54 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.36/0.91 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.36/0.91 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.36/0.91 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t53 @t35) @t57)))))))) % 0.36/0.91 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (or @t3 @t56))))))) % 0.36/0.91 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t56 (and @t4 @t53))))))) % 0.36/0.91 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t58 (not (tptp.gt @t1 @t2)))))))) % 0.36/0.91 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t58 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.36/0.91 (assume @p96 @t91) % 0.36/0.91 (assume @p97 true) % 0.36/0.91 (step @p98 :rule bool-impl-elim :args (@t17 @t92)) % 0.36/0.91 (step @p99 :rule cong :premises (@p98) :args ((forall @t9 (=> @t17 @t92)))) % 0.36/0.91 (step @p100 :rule eq-symm :args (@t49 @t2)) % 0.36/0.91 (step @p101 :rule refl :args (@t17)) % 0.36/0.91 (step @p102 :rule cong :premises (@p101 @p100) :args (@t50)) % 0.36/0.91 (step @p103 :rule cong :premises (@p102) :args (@t51)) % 0.36/0.91 (step @p104 :rule trans :premises (@p103 @p99)) % 0.36/0.91 (step @p105 :rule eq_resolve :premises (@p28 @p104)) % 0.36/0.91 (step @p106 :rule instantiate :premises (@p105) :args ((@list tptp.nil))) % 0.36/0.91 (step @p107 :rule cnf_or_pos :args (@t96)) % 0.36/0.91 (step @p108 :rule reordering :premises (@p107) :args ((or @t95 @t94 (not @t96)))) % 0.36/0.91 (step @p109 :rule chain_m_resolution :premises (@p108 @p17 @p106) :args (@t94 @t97 (@list @t39 @t96))) % 0.36/0.91 (step @p110 :rule instantiate :premises (@p105) :args ((@list @t111))) % 0.36/0.91 (step @p111 :rule aci_norm :args ((= (or @t108 @t109) @t109))) % 0.36/0.91 (step @p112 :rule bool-impl-elim :args (@t17 @t109)) % 0.36/0.91 (step @p113 :rule trans :premises (@p112 @p111)) % 0.36/0.91 (step @p114 :rule cong :premises (@p113) :args ((forall @t9 (=> @t17 @t109)))) % 0.36/0.91 (step @p115 :rule aci_norm :args ((= (or @t108 @t107 false) @t109))) % 0.36/0.91 (step @p116 :rule evaluate :args ((not true))) % 0.36/0.91 (step @p117 :rule eq-refl :args (@t2)) % 0.36/0.91 (step @p118 :rule cong :premises (@p117) :args (@t112)) % 0.36/0.91 (step @p119 :rule trans :premises (@p118 @p116)) % 0.36/0.91 (step @p120 :rule refl :args (@t107)) % 0.36/0.91 (step @p121 :rule refl :args (@t108)) % 0.36/0.91 (step @p122 :rule nary_cong :premises (@p121 @p120 @p119) :args (@t113)) % 0.36/0.91 (step @p123 :rule trans :premises (@p122 @p115)) % 0.36/0.91 (step @p124 :rule quant-var-elim-eq :args ((= (forall @t7 (or @t118 @t117 @t116 @t4)) @t113))) % 0.36/0.91 (step @p125 :rule refl :args (@t4)) % 0.36/0.91 (step @p126 :rule refl :args (@t116)) % 0.36/0.91 (step @p127 :rule refl :args (@t117)) % 0.36/0.91 (step @p128 :rule eq-symm :args (@t2 @t1)) % 0.36/0.91 (step @p129 :rule cong :premises (@p128) :args (@t4)) % 0.36/0.91 (step @p130 :rule nary_cong :premises (@p129 @p127 @p126 @p125) :args (@t119)) % 0.36/0.91 (step @p131 :rule aci_norm :args ((= @t120 @t119))) % 0.36/0.91 (step @p132 :rule trans :premises (@p131 @p130)) % 0.36/0.91 (step @p133 :rule cong :premises (@p132) :args (@t121)) % 0.36/0.91 (step @p134 :rule trans :premises (@p133 @p124)) % 0.36/0.91 (step @p135 :rule trans :premises (@p134 @p123)) % 0.36/0.91 (step @p136 :rule nary_cong :premises (@p121 @p135) :args (@t122)) % 0.36/0.91 (step @p137 :rule trans :premises (@p136 @p111)) % 0.36/0.91 (step @p138 :rule quant-miniscope-or :args ((= (forall @t7 @t123) @t122))) % 0.36/0.91 (step @p139 :rule aci_norm :args ((= @t124 @t123))) % 0.36/0.91 (step @p140 :rule cong :premises (@p139) :args ((forall @t7 @t124))) % 0.36/0.91 (step @p141 :rule trans :premises (@p140 @p138)) % 0.36/0.91 (step @p142 :rule trans 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(step @p304 :rule nary_cong :premises (@p303 @p302) :args ((or (not @t195) @t194))) % 0.36/0.91 (step @p305 :rule eq-symm :args (@t111 @t99)) % 0.36/0.91 (step @p306 :rule cong :premises (@p305) :args (@t196)) % 0.36/0.91 (step @p307 :rule eq-symm :args (@t111 @t101)) % 0.36/0.91 (step @p308 :rule cong :premises (@p307) :args (@t197)) % 0.36/0.91 (step @p309 :rule refl :args (@t103)) % 0.36/0.91 (step @p310 :rule refl :args (@t104)) % 0.36/0.91 (step @p311 :rule refl :args (@t105)) % 0.36/0.91 (step @p312 :rule nary_cong :premises (@p311 @p310 @p309 @p308 @p306) :args (@t198)) % 0.36/0.91 (step @p313 :rule cong :premises (@p312) :args (@t199)) % 0.36/0.91 (step @p314 :rule cong :premises (@p313) :args (@t200)) % 0.36/0.91 (step @p315 :rule refl :args (@t192)) % 0.36/0.91 (step @p316 :rule nary_cong :premises (@p315 @p314) :args (@t201)) % 0.36/0.91 (step @p317 :rule cong :premises (@p316) :args (@t202)) % 0.36/0.91 (step @p318 :rule refl :args (@t195)) % 0.36/0.91 (step @p319 :rule 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0.36/0.91 (step @p374 :rule trans :premises (@p373 @p372)) % 0.36/0.91 (step @p375 :rule true_intro :premises (@p374)) % 0.36/0.91 (step @p376 :rule symm :premises (@p375)) % 0.36/0.91 (step @p377 :rule trans :premises (@p376 @p370)) % 0.36/0.91 (step @p378 false :rule eq_resolve :premises (@p377 @p369)) % 0.36/0.91 (step-pop @p402 :rule scope :premises (@p378)) % 0.36/0.91 (step-pop @p403 :rule scope :premises (@p402)) % 0.36/0.91 (step @p379 :rule process_scope :premises (@p403) :args (false)) % 0.36/0.91 (assume-push @p404 @t94) % 0.36/0.91 (assume-push @p405 @t206) % 0.36/0.91 (assume-push @p406 @t215) % 0.36/0.91 (step @p371 :rule refl :args (@t111)) % 0.36/0.91 (step @p372 :rule cong :premises (@p109 @p371) :args (@t205)) % 0.36/0.91 (step @p385 :rule trans :premises (@p337 @p372)) % 0.36/0.91 (step @p386 :rule and_intro :premises (@p362 @p385)) % 0.36/0.91 (step-pop @p407 :rule scope :premises (@p386)) % 0.36/0.91 (step-pop @p408 :rule scope :premises (@p407)) % 0.36/0.91 (step-pop @p409 :rule scope :premises (@p408)) % 0.36/0.91 (step @p387 :rule process_scope :premises (@p409) :args (@t218)) % 0.36/0.91 (step @p391 :rule implies_elim :premises (@p387)) % 0.36/0.91 (step @p392 :rule resolution :premises (@p391 @p379) :args (true @t218)) % 0.36/0.91 (step @p393 :rule not_and :premises (@p392)) % 0.36/0.91 (step @p394 :rule eq_resolve :premises (@p393 @p366)) % 0.36/0.91 (step @p395 false :rule chain_m_resolution :premises (@p394 @p362 @p337 @p109) :args (false (@list true false false) (@list @t214 @t206 @t94))) % 0.36/0.91 ) % 0.36/0.91 % SZS output end Proof % 0.36/0.91 % cvc5 exiting %------------------------------------------------------------------------------