%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC116+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 : n006.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 08:58:07 AM UTC 2026 % Result : Theorem 0.36s 0.68s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC116+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 % 0.15/0.34 % Computer : n006.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 19:16:04 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.68 % SZS status Theorem % 0.36/0.68 % SZS output start Proof % 0.36/0.68 ( % 0.36/0.68 (declare-sort $$unsorted 0) % 0.36/0.68 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.36/0.68 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.36/0.68 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.68 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.68 (declare-const tptp.nil $$unsorted) % 0.36/0.68 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.36/0.68 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.68 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.68 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.68 (define @t3 () (= @t2 @t1)) % 0.36/0.68 (define @t4 () (not @t3)) % 0.36/0.68 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.36/0.68 (define @t6 () (tptp.ssItem @t1)) % 0.36/0.68 (define @t7 () (@list @t1)) % 0.36/0.68 (define @t8 () (tptp.ssItem @t2)) % 0.36/0.68 (define @t9 () (@list @t2)) % 0.36/0.68 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.68 (define @t11 () (tptp.cons @t1 @t10)) % 0.36/0.68 (define @t12 () (@var "W" $$unsorted)) % 0.36/0.68 (define @t13 () (tptp.ssList @t10)) % 0.36/0.68 (define @t14 () (@list @t10)) % 0.36/0.68 (define @t15 () (tptp.ssList @t12)) % 0.36/0.68 (define @t16 () (@list @t12)) % 0.36/0.68 (define @t17 () (tptp.ssList @t2)) % 0.36/0.68 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.36/0.68 (define @t19 () (tptp.app @t1 @t12)) % 0.36/0.68 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.36/0.68 (define @t21 () (tptp.ssList @t1)) % 0.36/0.68 (define @t22 () (tptp.app @t12 @t1)) % 0.36/0.68 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.36/0.68 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.36/0.68 (define @t25 () (tptp.leq @t12 @t1)) % 0.36/0.68 (define @t26 () (tptp.leq @t1 @t12)) % 0.36/0.68 (define @t27 () (@var "Z" $$unsorted)) % 0.36/0.68 (define @t28 () (@var "Y" $$unsorted)) % 0.36/0.68 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.36/0.68 (define @t30 () (tptp.ssList @t27)) % 0.36/0.68 (define @t31 () (@list @t27)) % 0.36/0.68 (define @t32 () (tptp.ssList @t28)) % 0.36/0.68 (define @t33 () (@list @t28)) % 0.36/0.68 (define @t34 () (tptp.ssItem @t12)) % 0.36/0.68 (define @t35 () (tptp.lt @t1 @t12)) % 0.36/0.68 (define @t36 () (= @t1 @t12)) % 0.36/0.68 (define @t37 () (forall @t7 (=> @t21 @t5))) % 0.36/0.68 (define @t38 () (=> @t17 @t37)) % 0.36/0.68 (define @t39 () (forall @t9 @t38)) % 0.36/0.68 (define @t40 () (tptp.cons @t1 @t2)) % 0.36/0.68 (define @t41 () (tptp.ssList tptp.nil)) % 0.36/0.68 (define @t42 () (= @t1 @t2)) % 0.36/0.68 (define @t43 () (tptp.cons @t12 @t1)) % 0.36/0.68 (define @t44 () (= tptp.nil @t2)) % 0.36/0.68 (define @t45 () (tptp.hd @t2)) % 0.36/0.68 (define @t46 () (not @t44)) % 0.36/0.68 (define @t47 () (tptp.tl @t2)) % 0.36/0.68 (define @t48 () (tptp.app @t2 @t1)) % 0.36/0.68 (define @t49 () (tptp.app @t1 @t2)) % 0.36/0.68 (define @t50 () (tptp.leq @t1 @t2)) % 0.36/0.68 (define @t51 () (tptp.leq @t2 @t1)) % 0.36/0.68 (define @t52 () (tptp.geq @t2 @t1)) % 0.36/0.68 (define @t53 () (tptp.lt @t1 @t2)) % 0.36/0.68 (define @t54 () (tptp.lt @t2 @t1)) % 0.36/0.68 (define @t55 () (tptp.lt @t2 @t12)) % 0.36/0.68 (define @t56 () (tptp.gt @t2 @t1)) % 0.36/0.68 (define @t57 () (tptp.memberP @t12 @t2)) % 0.36/0.68 (define @t58 () (tptp.app @t12 @t2)) % 0.36/0.68 (define @t59 () (tptp.segmentP @t1 @t12)) % 0.36/0.68 (define @t60 () (tptp.segmentP @t1 @t2)) % 0.36/0.68 (define @t61 () (tptp.cons @t2 tptp.nil)) % 0.36/0.68 (define @t62 () (tptp.hd @t1)) % 0.36/0.68 (define @t63 () (= tptp.nil @t1)) % 0.36/0.68 (define @t64 () (not @t63)) % 0.36/0.68 (define @t65 () (tptp.cons @t2 @t1)) % 0.36/0.68 (define @t66 () (= @t12 @t2)) % 0.36/0.68 (define @t67 () (and @t63 @t44)) % 0.36/0.68 (define @t68 () (not (tptp.neq @t12 tptp.nil))) % 0.36/0.68 (define @t69 () (and (tptp.neq @t10 tptp.nil) (or @t68 (not (tptp.segmentP @t10 @t12))))) % 0.36/0.68 (define @t70 () (tptp.neq @t2 tptp.nil)) % 0.36/0.68 (define @t71 () (and @t70 @t60)) % 0.36/0.68 (define @t72 () (not (= tptp.nil @t12))) % 0.36/0.68 (define @t73 () (and @t72 (= tptp.nil @t10))) % 0.36/0.68 (define @t74 () (not (= @t2 @t12))) % 0.36/0.68 (define @t75 () (not (= @t1 @t10))) % 0.36/0.68 (define @t76 () (or @t75 @t74 @t73 @t67 @t71 @t69)) % 0.36/0.68 (define @t77 () (=> @t13 @t76)) % 0.36/0.68 (define @t78 () (forall @t14 @t77)) % 0.36/0.68 (define @t79 () (=> @t15 @t78)) % 0.36/0.68 (define @t80 () (forall @t16 @t79)) % 0.36/0.68 (define @t81 () (=> @t21 @t80)) % 0.36/0.68 (define @t82 () (forall @t7 @t81)) % 0.36/0.68 (define @t83 () (=> @t17 @t82)) % 0.36/0.68 (define @t84 () (forall @t9 @t83)) % 0.36/0.68 (define @t85 () (not @t84)) % 0.36/0.68 (define @t86 () (@var "BOUND_VARIABLE_10972" $$unsorted)) % 0.36/0.68 (define @t87 () (tptp.segmentP @t86 @t2)) % 0.36/0.68 (define @t88 () (not @t70)) % 0.36/0.68 (define @t89 () (and (tptp.neq @t86 tptp.nil) (or @t88 (not @t87)))) % 0.36/0.68 (define @t90 () (= @t2 tptp.nil)) % 0.36/0.68 (define @t91 () (not @t90)) % 0.36/0.68 (define @t92 () (= @t86 tptp.nil)) % 0.36/0.68 (define @t93 () (and @t91 @t92)) % 0.36/0.68 (define @t94 () (and @t70 @t87)) % 0.36/0.68 (define @t95 () (and @t92 @t90)) % 0.36/0.68 (define @t96 () (not (tptp.ssList @t86))) % 0.36/0.68 (define @t97 () (not @t17)) % 0.36/0.68 (define @t98 () (or @t97 @t96 @t95 @t94 @t93 @t89)) % 0.36/0.68 (define @t99 () (or @t96 @t95 @t94 @t93 @t89)) % 0.36/0.68 (define @t100 () (or @t97 @t99)) % 0.36/0.68 (define @t101 () (@list @t2 @t86)) % 0.36/0.68 (define @t102 () (forall @t101 @t100)) % 0.36/0.68 (define @t103 () (@list @t86)) % 0.36/0.68 (define @t104 () (forall @t103 @t100)) % 0.36/0.68 (define @t105 () (forall @t103 @t99)) % 0.36/0.68 (define @t106 () (@list @t1)) % 0.36/0.68 (define @t107 () (or @t97 @t105)) % 0.36/0.68 (define @t108 () (tptp.neq @t1 tptp.nil)) % 0.36/0.68 (define @t109 () (and @t108 (or @t88 (not @t60)))) % 0.36/0.68 (define @t110 () (= @t1 tptp.nil)) % 0.36/0.68 (define @t111 () (and @t91 @t110)) % 0.36/0.68 (define @t112 () (and @t110 @t90)) % 0.36/0.68 (define @t113 () (not @t21)) % 0.36/0.68 (define @t114 () (or @t113 @t112 @t71 @t111 @t109)) % 0.36/0.68 (define @t115 () (or @t97 (forall @t7 @t114))) % 0.36/0.68 (define @t116 () (or @t97 @t114)) % 0.36/0.68 (define @t117 () (or @t113 @t112 @t71 @t97 @t111 @t109)) % 0.36/0.68 (define @t118 () (or @t112 @t71 @t113 @t97 @t111 @t109)) % 0.36/0.68 (define @t119 () (or @t97 @t111 @t109)) % 0.36/0.68 (define @t120 () (not (= @t2 @t2))) % 0.36/0.68 (define @t121 () (or @t97 @t120 @t111 @t109)) % 0.36/0.68 (define @t122 () (and @t108 (or @t68 (not @t59)))) % 0.36/0.68 (define @t123 () (not (= @t12 tptp.nil))) % 0.36/0.68 (define @t124 () (and @t123 @t110)) % 0.36/0.68 (define @t125 () (not @t15)) % 0.36/0.68 (define @t126 () (or @t74 @t125 @t74 @t124 @t122)) % 0.36/0.68 (define @t127 () (or @t125 @t74 @t124 @t122)) % 0.36/0.68 (define @t128 () (forall @t16 @t127)) % 0.36/0.68 (define @t129 () (or @t112 @t71 @t113 @t128)) % 0.36/0.68 (define @t130 () (or @t112 @t71 @t113 @t127)) % 0.36/0.68 (define @t131 () (or @t125 @t74 @t112 @t71 @t113 @t124 @t122)) % 0.36/0.68 (define @t132 () (or @t74 @t112 @t71 @t113 @t124 @t122)) % 0.36/0.68 (define @t133 () (or @t113 @t124 @t122)) % 0.36/0.68 (define @t134 () (not (= @t1 @t1))) % 0.36/0.68 (define @t135 () (or @t113 @t134 @t124 @t122)) % 0.36/0.68 (define @t136 () (and @t123 (= @t10 tptp.nil))) % 0.36/0.68 (define @t137 () (not @t13)) % 0.36/0.68 (define @t138 () (or @t75 @t137 @t75 @t136 @t69)) % 0.36/0.68 (define @t139 () (or @t137 @t75 @t136 @t69)) % 0.36/0.68 (define @t140 () (forall @t14 @t139)) % 0.36/0.68 (define @t141 () (or @t74 @t112 @t71 @t140)) % 0.36/0.68 (define @t142 () (or @t74 @t112 @t71 @t139)) % 0.36/0.68 (define @t143 () (or @t137 @t75 @t74 @t136 @t112 @t71 @t69)) % 0.36/0.68 (define @t144 () (or @t75 @t74 @t136 @t112 @t71 @t69)) % 0.36/0.68 (define @t145 () (= tptp.nil @t86)) % 0.36/0.68 (define @t146 () (forall @t101 (or @t97 @t96 (and @t145 @t90) @t94 (and @t91 @t145) @t89))) % 0.36/0.68 (define @t147 () (@quantifiers_skolemize @t146 0)) % 0.36/0.68 (define @t148 () (@quantifiers_skolemize @t146 1)) % 0.36/0.68 (define @t149 () (tptp.segmentP @t148 @t147)) % 0.36/0.68 (define @t150 () (not @t149)) % 0.36/0.68 (define @t151 () (tptp.neq @t147 tptp.nil)) % 0.36/0.68 (define @t152 () (not @t151)) % 0.36/0.68 (define @t153 () (or @t152 @t150)) % 0.36/0.68 (define @t154 () (tptp.neq @t148 tptp.nil)) % 0.36/0.68 (define @t155 () (and @t154 @t153)) % 0.36/0.68 (define @t156 () (= tptp.nil @t148)) % 0.36/0.68 (define @t157 () (= tptp.nil @t147)) % 0.36/0.68 (define @t158 () (not @t157)) % 0.36/0.68 (define @t159 () (and @t158 @t156)) % 0.36/0.68 (define @t160 () (and @t151 @t149)) % 0.36/0.68 (define @t161 () (and @t156 @t157)) % 0.36/0.68 (define @t162 () (tptp.ssList @t148)) % 0.36/0.68 (define @t163 () (not @t162)) % 0.36/0.68 (define @t164 () (not (tptp.ssList @t147))) % 0.36/0.68 (define @t165 () (or @t164 @t163 @t161 @t160 @t159 @t155)) % 0.36/0.68 (define @t166 () (not @t165)) % 0.36/0.68 (define @t167 () (not @t146)) % 0.36/0.68 (define @t168 () (= @t147 tptp.nil)) % 0.36/0.68 (define @t169 () (not @t168)) % 0.36/0.68 (define @t170 () (and @t169 @t156)) % 0.36/0.68 (define @t171 () (and @t156 @t168)) % 0.36/0.68 (define @t172 () (or @t164 @t163 @t171 @t160 @t170 @t155)) % 0.36/0.68 (define @t173 () (not @t172)) % 0.36/0.68 (define @t174 () (@list true)) % 0.36/0.68 (define @t175 () (@list @t165)) % 0.36/0.68 (define @t176 () (@var "BOUND_VARIABLE_9100" $$unsorted)) % 0.36/0.68 (define @t177 () (= (tptp.neq @t2 @t176) (not (= @t2 @t176)))) % 0.36/0.68 (define @t178 () (not (tptp.ssList @t176))) % 0.36/0.68 (define @t179 () (or @t97 @t178 @t177)) % 0.36/0.68 (define @t180 () (or @t178 @t177)) % 0.36/0.68 (define @t181 () (or @t97 @t180)) % 0.36/0.68 (define @t182 () (@list @t2 @t176)) % 0.36/0.68 (define @t183 () (forall @t182 @t181)) % 0.36/0.68 (define @t184 () (@list @t176)) % 0.36/0.68 (define @t185 () (forall @t184 @t181)) % 0.36/0.68 (define @t186 () (forall @t184 @t180)) % 0.36/0.68 (define @t187 () (or @t97 @t186)) % 0.36/0.68 (define @t188 () (forall @t7 (or @t113 @t5))) % 0.36/0.68 (define @t189 () (not (= @t148 tptp.nil))) % 0.36/0.68 (define @t190 () (= @t154 @t189)) % 0.36/0.68 (define @t191 () (not @t41)) % 0.36/0.68 (define @t192 () (or @t163 @t191 @t190)) % 0.36/0.68 (define @t193 () (forall @t182 @t179)) % 0.36/0.68 (define @t194 () (not @t156)) % 0.36/0.68 (define @t195 () (= @t154 @t194)) % 0.36/0.68 (define @t196 () (or @t163 @t191 @t195)) % 0.36/0.68 (define @t197 () (@list true false)) % 0.36/0.68 (define @t198 () (not @t195)) % 0.36/0.68 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.36/0.68 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.36/0.68 (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))))))))))) % 0.36/0.68 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.36/0.68 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.36/0.68 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.36/0.68 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.36/0.68 (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))))))))))))))))) % 0.36/0.68 (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)))))))))))))))) % 0.36/0.68 (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))))))))))))))))) % 0.36/0.68 (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))))))))))))))) % 0.36/0.68 (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))))))))))))))) % 0.36/0.68 (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)))))))))))))))) % 0.36/0.68 (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))))))))))))) % 0.36/0.68 (assume @p15 @t39) % 0.36/0.68 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t40)))))) % 0.36/0.68 (assume @p17 @t41) % 0.36/0.68 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t40 @t2))))))) % 0.36/0.68 (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) @t42))))))))))) % 0.36/0.68 (assume @p20 (forall @t9 (=> @t17 (or @t44 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t43 @t2))))))))) % 0.36/0.68 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t40))))))) % 0.36/0.68 (assume @p22 (forall @t9 (=> @t17 (=> @t46 (tptp.ssItem @t45))))) % 0.36/0.68 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t40) @t1)))))) % 0.36/0.68 (assume @p24 (forall @t9 (=> @t17 (=> @t46 (tptp.ssList @t47))))) % 0.36/0.68 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t40) @t2)))))) % 0.36/0.68 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t48)))))) % 0.36/0.68 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t49) (tptp.app @t43 @t2))))))))) % 0.36/0.68 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.36/0.68 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t51 @t50) @t3)))))) % 0.36/0.68 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t26) (tptp.leq @t2 @t12))))))))) % 0.36/0.68 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.36/0.68 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t50)))))) % 0.36/0.68 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t54 (not @t53))))))) % 0.36/0.68 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t54 @t35) @t55)))))))) % 0.36/0.68 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t56 @t53)))))) % 0.36/0.68 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t57))))))))) % 0.36/0.68 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t57))))))))) % 0.36/0.68 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.36/0.68 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.36/0.68 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.36/0.68 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.36/0.68 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.36/0.68 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.36/0.68 (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)))))))))))) % 0.36/0.68 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.36/0.68 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t44)))) % 0.36/0.68 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.36/0.68 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.36/0.68 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.36/0.68 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t58 @t1))))))))) % 0.36/0.68 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.36/0.68 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t44)))) % 0.36/0.68 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 @t59) (tptp.segmentP @t2 @t12))))))))) % 0.36/0.68 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 @t60) @t3)))))) % 0.36/0.68 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.36/0.68 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t58 @t10) @t1))))))))))) % 0.36/0.68 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.36/0.68 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t44)))) % 0.36/0.68 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t61)))) % 0.36/0.68 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.36/0.68 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t61)))) % 0.36/0.68 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.36/0.68 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t61)))) % 0.36/0.68 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.36/0.68 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t61)))) % 0.36/0.68 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.36/0.68 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t65) (or @t63 (and @t64 (tptp.totalorderedP @t1) (tptp.leq @t2 @t62))))))))) % 0.36/0.68 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t61)))) % 0.36/0.68 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.36/0.68 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t65) (or @t63 (and @t64 (tptp.strictorderedP @t1) (tptp.lt @t2 @t62))))))))) % 0.36/0.68 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t61)))) % 0.36/0.68 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.36/0.68 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t61)))) % 0.36/0.68 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.36/0.68 (assume @p75 (forall @t9 (=> @t17 (=> @t46 (exists @t7 (and @t6 (= @t45 @t1))))))) % 0.36/0.68 (assume @p76 (forall @t9 (=> @t17 (=> @t46 (exists @t7 (and @t21 (= @t47 @t1))))))) % 0.36/0.68 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t64 @t46 (= @t62 @t45) (= (tptp.tl @t1) @t47)) @t42)))))) % 0.36/0.68 (assume @p78 (forall @t9 (=> @t17 (=> @t46 (= (tptp.cons @t45 @t47) @t2))))) % 0.36/0.68 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t48) @t66)))))))) % 0.36/0.68 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t49) @t66)))))))) % 0.36/0.68 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t40 (tptp.app @t18 @t2))))))) % 0.36/0.68 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t48 @t12) (tptp.app @t2 @t19))))))))) % 0.36/0.68 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t48) @t67)))))) % 0.36/0.68 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.36/0.68 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t46 (= (tptp.hd @t48) @t45))))))) % 0.36/0.68 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t46 (= (tptp.tl @t48) (tptp.app @t47 @t1)))))))) % 0.36/0.68 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t52 (tptp.geq @t1 @t2)) @t3)))))) % 0.36/0.68 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.36/0.68 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.36/0.68 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.36/0.68 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t55)))))))) % 0.36/0.68 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (or @t3 @t54))))))) % 0.36/0.68 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t54 (and @t4 @t51))))))) % 0.36/0.68 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t56 (not (tptp.gt @t1 @t2)))))))) % 0.36/0.68 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t56 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.36/0.68 (assume @p96 @t85) % 0.36/0.68 (assume @p97 true) % 0.36/0.68 (step @p98 :rule refl :args (@t89)) % 0.36/0.68 (step @p99 :rule eq-symm :args (@t86 tptp.nil)) % 0.36/0.68 (step @p100 :rule refl :args (@t91)) % 0.36/0.68 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t93)) % 0.36/0.68 (step @p102 :rule refl :args (@t94)) % 0.36/0.68 (step @p103 :rule refl :args (@t90)) % 0.36/0.68 (step @p104 :rule nary_cong :premises (@p99 @p103) :args (@t95)) % 0.36/0.68 (step @p105 :rule refl :args (@t96)) % 0.36/0.68 (step @p106 :rule refl :args (@t97)) % 0.36/0.68 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104 @p102 @p101 @p98) :args (@t98)) % 0.36/0.68 (step @p108 :rule aci_norm :args ((= @t100 @t98))) % 0.36/0.68 (step @p109 :rule trans :premises (@p108 @p107)) % 0.36/0.68 (step @p110 :rule cong :premises (@p109) :args (@t102)) % 0.36/0.68 (step @p111 :rule quant-merge-prenex :args ((= (forall @t9 @t104) @t102))) % 0.36/0.68 (step @p112 :rule alpha_equiv :args (@t105 (@list @t86) @t106)) % 0.36/0.68 (step @p113 :rule refl :args (@t97)) % 0.36/0.68 (step @p114 :rule nary_cong :premises (@p113 @p112) :args (@t107)) % 0.36/0.68 (step @p115 :rule quant-miniscope-or :args ((= @t104 @t107))) % 0.36/0.68 (step @p116 :rule trans :premises (@p115 @p114)) % 0.36/0.68 (step @p117 :rule symm :premises (@p116)) % 0.36/0.68 (step @p118 :rule cong :premises (@p117) :args ((forall @t9 @t115))) % 0.36/0.68 (step @p119 :rule trans :premises (@p118 @p111)) % 0.36/0.68 (step @p120 :rule trans :premises (@p119 @p110)) % 0.36/0.68 (step @p121 :rule aci_norm :args ((= (or @t97 @t115) @t115))) % 0.36/0.68 (step @p122 :rule bool-impl-elim :args (@t17 @t115)) % 0.36/0.68 (step @p123 :rule trans :premises (@p122 @p121)) % 0.36/0.68 (step @p124 :rule cong :premises (@p123) :args ((forall @t9 (=> @t17 @t115)))) % 0.36/0.68 (step @p125 :rule trans :premises (@p124 @p120)) % 0.36/0.68 (step @p126 :rule quant-miniscope-or :args ((= (forall @t7 @t116) @t115))) % 0.36/0.68 (step @p127 :rule aci_norm :args ((= @t117 @t116))) % 0.36/0.68 (step @p128 :rule cong :premises (@p127) :args ((forall @t7 @t117))) % 0.36/0.68 (step @p129 :rule trans :premises (@p128 @p126)) % 0.36/0.68 (step @p130 :rule aci_norm :args ((= (or @t113 @t118) @t117))) % 0.36/0.68 (step @p131 :rule bool-impl-elim :args (@t21 @t118)) % 0.36/0.68 (step @p132 :rule trans :premises (@p131 @p130)) % 0.36/0.68 (step @p133 :rule cong :premises (@p132) :args ((forall @t7 (=> @t21 @t118)))) % 0.36/0.68 (step @p134 :rule trans :premises (@p133 @p129)) % 0.36/0.68 (step @p135 :rule aci_norm :args ((= (or @t112 @t71 @t113 @t119) @t118))) % 0.36/0.68 (step @p136 :rule aci_norm :args ((= (or @t97 false @t111 @t109) @t119))) % 0.36/0.68 (step @p137 :rule refl :args (@t109)) % 0.36/0.68 (step @p138 :rule refl :args (@t111)) % 0.36/0.68 (step @p139 :rule evaluate :args ((not true))) % 0.36/0.68 (step @p140 :rule eq-refl :args (@t2)) % 0.36/0.68 (step @p141 :rule cong :premises (@p140) :args (@t120)) % 0.36/0.68 (step @p142 :rule trans :premises (@p141 @p139)) % 0.36/0.68 (step @p143 :rule nary_cong :premises (@p106 @p142 @p138 @p137) :args (@t121)) % 0.36/0.68 (step @p144 :rule trans :premises (@p143 @p136)) % 0.36/0.68 (step @p145 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t66) @t125 @t74 @t124 @t122)) @t121))) % 0.36/0.68 (step @p146 :rule refl :args (@t122)) % 0.36/0.68 (step @p147 :rule refl :args (@t124)) % 0.36/0.68 (step @p148 :rule refl :args (@t74)) % 0.36/0.68 (step @p149 :rule refl :args (@t125)) % 0.36/0.68 (step @p150 :rule eq-symm :args (@t2 @t12)) % 0.36/0.68 (step @p151 :rule cong :premises (@p150) :args (@t74)) % 0.36/0.68 (step @p152 :rule nary_cong :premises (@p151 @p149 @p148 @p147 @p146) :args (@t126)) % 0.36/0.68 (step @p153 :rule aci_norm :args ((= @t127 @t126))) % 0.36/0.68 (step @p154 :rule trans :premises (@p153 @p152)) % 0.36/0.68 (step @p155 :rule cong :premises (@p154) :args (@t128)) % 0.36/0.68 (step @p156 :rule trans :premises (@p155 @p145)) % 0.36/0.68 (step @p157 :rule trans :premises (@p156 @p144)) % 0.36/0.68 (step @p158 :rule refl :args (@t113)) % 0.36/0.68 (step @p159 :rule refl :args (@t71)) % 0.36/0.68 (step @p160 :rule refl :args (@t112)) % 0.36/0.68 (step @p161 :rule nary_cong :premises (@p160 @p159 @p158 @p157) :args (@t129)) % 0.36/0.68 (step @p162 :rule trans :premises (@p161 @p135)) % 0.36/0.68 (step @p163 :rule quant-miniscope-or :args ((= (forall @t16 @t130) @t129))) % 0.36/0.68 (step @p164 :rule aci_norm :args ((= @t131 @t130))) % 0.36/0.68 (step @p165 :rule cong :premises (@p164) :args ((forall @t16 @t131))) % 0.36/0.68 (step @p166 :rule trans :premises (@p165 @p163)) % 0.36/0.68 (step @p167 :rule trans :premises (@p166 @p162)) % 0.36/0.68 (step @p168 :rule aci_norm :args ((= (or @t125 @t132) @t131))) % 0.36/0.68 (step @p169 :rule bool-impl-elim :args (@t15 @t132)) % 0.36/0.68 (step @p170 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:args (@t157)) % 0.36/0.68 (step @p340 :rule refl :args (@t159)) % 0.36/0.68 (step @p341 :rule nary_cong :premises (@p340 @p339 @p338) :args ((or @t159 (not @t158) @t194))) % 0.36/0.68 (step @p342 :rule cnf_and_neg :args (@t159)) % 0.36/0.68 (step @p343 :rule eq_resolve :premises (@p342 @p341)) % 0.36/0.69 (step @p344 :rule reordering :premises (@p343) :args ((or @t157 @t159 @t194))) % 0.36/0.69 (step @p345 false :rule chain_m_resolution :premises (@p344 @p337 @p332 @p261) :args (false (@list true false true) (@list @t157 @t156 @t159))) % 0.36/0.69 ) % 0.36/0.69 % SZS output end Proof % 0.36/0.69 % cvc5 exiting %------------------------------------------------------------------------------