%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC051+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 : n008.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 08:57:51 AM UTC 2026 % Result : Theorem 0.43s 0.68s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC051+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 % 0.17/0.34 % Computer : n008.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 19:11:33 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.43/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.68 % SZS status Theorem % 0.43/0.68 % SZS output start Proof % 0.43/0.68 ( % 0.43/0.68 (declare-sort $$unsorted 0) % 0.43/0.68 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.nil $$unsorted) % 0.43/0.68 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (define @t1 () (@var "V" $$unsorted)) % 0.43/0.68 (define @t2 () (@var "U" $$unsorted)) % 0.43/0.68 (define @t3 () (= @t2 @t1)) % 0.43/0.68 (define @t4 () (not @t3)) % 0.43/0.68 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.43/0.68 (define @t6 () (tptp.ssItem @t1)) % 0.43/0.68 (define @t7 () (@list @t1)) % 0.43/0.68 (define @t8 () (tptp.ssItem @t2)) % 0.43/0.68 (define @t9 () (@list @t2)) % 0.43/0.68 (define @t10 () (@var "X" $$unsorted)) % 0.43/0.68 (define @t11 () (tptp.cons @t1 @t10)) % 0.43/0.68 (define @t12 () (@var "W" $$unsorted)) % 0.43/0.68 (define @t13 () (tptp.ssList @t10)) % 0.43/0.68 (define @t14 () (@list @t10)) % 0.43/0.68 (define @t15 () (tptp.ssList @t12)) % 0.43/0.68 (define @t16 () (@list @t12)) % 0.43/0.68 (define @t17 () (tptp.ssList @t2)) % 0.43/0.68 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.43/0.68 (define @t19 () (tptp.app @t1 @t12)) % 0.43/0.68 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.43/0.68 (define @t21 () (tptp.ssList @t1)) % 0.43/0.68 (define @t22 () (tptp.app @t12 @t1)) % 0.43/0.68 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.43/0.68 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.43/0.68 (define @t25 () (tptp.leq @t12 @t1)) % 0.43/0.68 (define @t26 () (tptp.leq @t1 @t12)) % 0.43/0.68 (define @t27 () (@var "Z" $$unsorted)) % 0.43/0.68 (define @t28 () (@var "Y" $$unsorted)) % 0.43/0.68 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.43/0.68 (define @t30 () (tptp.ssList @t27)) % 0.43/0.68 (define @t31 () (@list @t27)) % 0.43/0.68 (define @t32 () (tptp.ssList @t28)) % 0.43/0.68 (define @t33 () (@list @t28)) % 0.43/0.68 (define @t34 () (tptp.ssItem @t12)) % 0.43/0.68 (define @t35 () (tptp.lt @t1 @t12)) % 0.43/0.68 (define @t36 () (= @t1 @t12)) % 0.43/0.68 (define @t37 () (tptp.cons @t1 @t2)) % 0.43/0.68 (define @t38 () (= @t1 @t2)) % 0.43/0.68 (define @t39 () (tptp.cons @t12 @t1)) % 0.43/0.68 (define @t40 () (= tptp.nil @t2)) % 0.43/0.68 (define @t41 () (tptp.hd @t2)) % 0.43/0.68 (define @t42 () (not @t40)) % 0.43/0.68 (define @t43 () (tptp.tl @t2)) % 0.43/0.68 (define @t44 () (tptp.app @t2 @t1)) % 0.43/0.68 (define @t45 () (tptp.app @t1 @t2)) % 0.43/0.68 (define @t46 () (tptp.leq @t1 @t2)) % 0.43/0.68 (define @t47 () (tptp.leq @t2 @t1)) % 0.43/0.68 (define @t48 () (tptp.geq @t2 @t1)) % 0.43/0.68 (define @t49 () (tptp.lt @t1 @t2)) % 0.43/0.68 (define @t50 () (tptp.lt @t2 @t1)) % 0.43/0.68 (define @t51 () (tptp.lt @t2 @t12)) % 0.43/0.68 (define @t52 () (tptp.gt @t2 @t1)) % 0.43/0.68 (define @t53 () (tptp.memberP @t12 @t2)) % 0.43/0.68 (define @t54 () (tptp.rearsegP @t1 @t12)) % 0.43/0.68 (define @t55 () (tptp.rearsegP @t1 @t2)) % 0.43/0.68 (define @t56 () (tptp.rearsegP @t2 @t2)) % 0.43/0.68 (define @t57 () (forall @t9 (=> @t17 @t56))) % 0.43/0.68 (define @t58 () (tptp.app @t12 @t2)) % 0.43/0.68 (define @t59 () (tptp.cons @t2 tptp.nil)) % 0.43/0.68 (define @t60 () (tptp.hd @t1)) % 0.43/0.68 (define @t61 () (= tptp.nil @t1)) % 0.43/0.68 (define @t62 () (not @t61)) % 0.43/0.68 (define @t63 () (tptp.cons @t2 @t1)) % 0.43/0.68 (define @t64 () (= @t12 @t2)) % 0.43/0.68 (define @t65 () (not (tptp.neq @t12 tptp.nil))) % 0.43/0.68 (define @t66 () (and (tptp.neq @t10 tptp.nil) (or @t65 (not (tptp.rearsegP @t10 @t12))))) % 0.43/0.68 (define @t67 () (not (= tptp.nil @t12))) % 0.43/0.68 (define @t68 () (and @t67 (= tptp.nil @t10))) % 0.43/0.68 (define @t69 () (tptp.rearsegP @t2 @t28)) % 0.43/0.68 (define @t70 () (tptp.rearsegP @t1 @t28)) % 0.43/0.68 (define @t71 () (tptp.neq @t28 tptp.nil)) % 0.43/0.68 (define @t72 () (and @t32 @t71 @t70 @t69)) % 0.43/0.68 (define @t73 () (exists @t33 @t72)) % 0.43/0.68 (define @t74 () (tptp.neq @t1 tptp.nil)) % 0.43/0.68 (define @t75 () (not @t74)) % 0.43/0.68 (define @t76 () (not (= @t2 @t12))) % 0.43/0.68 (define @t77 () (not (= @t1 @t10))) % 0.43/0.68 (define @t78 () (or @t77 @t76 @t75 @t73 @t68 @t66)) % 0.43/0.68 (define @t79 () (=> @t13 @t78)) % 0.43/0.68 (define @t80 () (forall @t14 @t79)) % 0.43/0.68 (define @t81 () (=> @t15 @t80)) % 0.43/0.68 (define @t82 () (forall @t16 @t81)) % 0.43/0.68 (define @t83 () (=> @t21 @t82)) % 0.43/0.68 (define @t84 () (forall @t7 @t83)) % 0.43/0.68 (define @t85 () (=> @t17 @t84)) % 0.43/0.68 (define @t86 () (forall @t9 @t85)) % 0.43/0.68 (define @t87 () (not @t86)) % 0.43/0.68 (define @t88 () (@var "BOUND_VARIABLE_10986" $$unsorted)) % 0.43/0.68 (define @t89 () (not (tptp.neq @t2 tptp.nil))) % 0.43/0.68 (define @t90 () (tptp.neq @t88 tptp.nil)) % 0.43/0.68 (define @t91 () (and @t90 (or @t89 (not (tptp.rearsegP @t88 @t2))))) % 0.43/0.68 (define @t92 () (not (= @t2 tptp.nil))) % 0.43/0.68 (define @t93 () (and @t92 (= @t88 tptp.nil))) % 0.43/0.68 (define @t94 () (not @t69)) % 0.43/0.68 (define @t95 () (not @t71)) % 0.43/0.68 (define @t96 () (not @t32)) % 0.43/0.68 (define @t97 () (not (forall @t33 (or @t96 @t95 (not (tptp.rearsegP @t88 @t28)) @t94)))) % 0.43/0.68 (define @t98 () (not @t90)) % 0.43/0.68 (define @t99 () (not (tptp.ssList @t88))) % 0.43/0.68 (define @t100 () (not @t17)) % 0.43/0.68 (define @t101 () (or @t100 @t99 @t98 @t97 @t93 @t91)) % 0.43/0.68 (define @t102 () (or @t99 @t98 @t97 @t93 @t91)) % 0.43/0.68 (define @t103 () (or @t100 @t102)) % 0.43/0.68 (define @t104 () (@list @t2 @t88)) % 0.43/0.68 (define @t105 () (forall @t104 @t103)) % 0.43/0.68 (define @t106 () (@list @t88)) % 0.43/0.68 (define @t107 () (forall @t106 @t103)) % 0.43/0.68 (define @t108 () (forall @t106 @t102)) % 0.43/0.68 (define @t109 () (or @t100 @t108)) % 0.43/0.68 (define @t110 () (and @t74 (or @t89 (not @t55)))) % 0.43/0.68 (define @t111 () (= @t1 tptp.nil)) % 0.43/0.68 (define @t112 () (and @t92 @t111)) % 0.43/0.68 (define @t113 () (not @t70)) % 0.43/0.68 (define @t114 () (or @t96 @t95 @t113 @t94)) % 0.43/0.68 (define @t115 () (not (forall @t33 @t114))) % 0.43/0.68 (define @t116 () (not @t21)) % 0.43/0.68 (define @t117 () (or @t116 @t75 @t115 @t112 @t110)) % 0.43/0.68 (define @t118 () (or @t100 (forall @t7 @t117))) % 0.43/0.68 (define @t119 () (or @t100 @t117)) % 0.43/0.68 (define @t120 () (or @t116 @t75 @t115 @t100 @t112 @t110)) % 0.43/0.68 (define @t121 () (or @t75 @t115 @t116 @t100 @t112 @t110)) % 0.43/0.68 (define @t122 () (or @t100 @t112 @t110)) % 0.43/0.68 (define @t123 () (not (= @t2 @t2))) % 0.43/0.68 (define @t124 () (or @t100 @t123 @t112 @t110)) % 0.43/0.68 (define @t125 () (and @t74 (or @t65 (not @t54)))) % 0.43/0.68 (define @t126 () (not (= @t12 tptp.nil))) % 0.43/0.68 (define @t127 () (and @t126 @t111)) % 0.43/0.68 (define @t128 () (not @t15)) % 0.43/0.68 (define @t129 () (or @t76 @t128 @t76 @t127 @t125)) % 0.43/0.68 (define @t130 () (or @t128 @t76 @t127 @t125)) % 0.43/0.68 (define @t131 () (forall @t16 @t130)) % 0.43/0.68 (define @t132 () (or @t75 @t115 @t116 @t131)) % 0.43/0.68 (define @t133 () (or @t75 @t115 @t116 @t130)) % 0.43/0.68 (define @t134 () (or @t128 @t76 @t75 @t115 @t116 @t127 @t125)) % 0.43/0.68 (define @t135 () (or @t76 @t75 @t115 @t116 @t127 @t125)) % 0.43/0.68 (define @t136 () (or @t116 @t127 @t125)) % 0.43/0.68 (define @t137 () (not (= @t1 @t1))) % 0.43/0.68 (define @t138 () (or @t116 @t137 @t127 @t125)) % 0.43/0.68 (define @t139 () (and @t126 (= @t10 tptp.nil))) % 0.43/0.68 (define @t140 () (not @t13)) % 0.43/0.68 (define @t141 () (or @t77 @t140 @t77 @t139 @t66)) % 0.43/0.68 (define @t142 () (or @t140 @t77 @t139 @t66)) % 0.43/0.68 (define @t143 () (forall @t14 @t142)) % 0.43/0.68 (define @t144 () (or @t76 @t75 @t115 @t143)) % 0.43/0.68 (define @t145 () (or @t76 @t75 @t115 @t142)) % 0.43/0.68 (define @t146 () (or @t140 @t77 @t76 @t75 @t115 @t139 @t66)) % 0.43/0.68 (define @t147 () (or @t77 @t76 @t75 @t115 @t139 @t66)) % 0.43/0.68 (define @t148 () (forall @t33 (not @t72))) % 0.43/0.68 (define @t149 () (not @t148)) % 0.43/0.68 (define @t150 () (forall @t104 (or @t100 @t99 @t98 @t97 (and @t92 (= tptp.nil @t88)) @t91))) % 0.43/0.68 (define @t151 () (@quantifiers_skolemize @t150 0)) % 0.43/0.68 (define @t152 () (@quantifiers_skolemize @t150 1)) % 0.43/0.68 (define @t153 () (tptp.rearsegP @t152 @t151)) % 0.43/0.68 (define @t154 () (not @t153)) % 0.43/0.68 (define @t155 () (tptp.neq @t151 tptp.nil)) % 0.43/0.68 (define @t156 () (not @t155)) % 0.43/0.68 (define @t157 () (or @t156 @t154)) % 0.43/0.68 (define @t158 () (tptp.neq @t152 tptp.nil)) % 0.43/0.68 (define @t159 () (and @t158 @t157)) % 0.43/0.68 (define @t160 () (= tptp.nil @t152)) % 0.43/0.68 (define @t161 () (forall @t33 (or @t96 @t95 (not (tptp.rearsegP @t152 @t28)) (not (tptp.rearsegP @t151 @t28))))) % 0.43/0.68 (define @t162 () (not @t161)) % 0.43/0.68 (define @t163 () (not @t158)) % 0.43/0.68 (define @t164 () (not (tptp.ssList @t152))) % 0.43/0.68 (define @t165 () (tptp.ssList @t151)) % 0.43/0.68 (define @t166 () (not @t165)) % 0.43/0.68 (define @t167 () (or @t166 @t164 @t163 @t162 (and (not (= tptp.nil @t151)) @t160) @t159)) % 0.43/0.68 (define @t168 () (not @t167)) % 0.43/0.68 (define @t169 () (not @t150)) % 0.43/0.68 (define @t170 () (not (= @t151 tptp.nil))) % 0.43/0.68 (define @t171 () (and @t170 @t160)) % 0.43/0.68 (define @t172 () (or @t166 @t164 @t163 @t162 @t171 @t159)) % 0.43/0.68 (define @t173 () (not @t172)) % 0.43/0.68 (define @t174 () (@list true)) % 0.43/0.68 (define @t175 () (@list @t167)) % 0.43/0.68 (define @t176 () (not @t157)) % 0.43/0.68 (define @t177 () (@list @t157)) % 0.43/0.68 (define @t178 () (@list @t151)) % 0.43/0.68 (define @t179 () (tptp.rearsegP @t151 @t151)) % 0.43/0.68 (define @t180 () (or @t166 @t179)) % 0.43/0.68 (define @t181 () (not @t179)) % 0.43/0.68 (define @t182 () (or @t166 @t156 @t154 @t181)) % 0.43/0.68 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.43/0.68 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.43/0.68 (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))))))))))) % 0.43/0.68 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.43/0.68 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.43/0.68 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.43/0.68 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.43/0.68 (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))))))))))))))))) % 0.43/0.68 (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)))))))))))))))) % 0.43/0.68 (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))))))))))))))))) % 0.43/0.68 (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))))))))))))))) % 0.43/0.68 (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))))))))))))))) % 0.43/0.68 (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)))))))))))))))) % 0.43/0.68 (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))))))))))))) % 0.43/0.68 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.43/0.68 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.43/0.68 (assume @p17 (tptp.ssList tptp.nil)) % 0.43/0.68 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.43/0.68 (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) @t38))))))))))) % 0.43/0.68 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.43/0.68 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.43/0.68 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.43/0.68 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.43/0.68 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.43/0.68 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.43/0.68 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.43/0.68 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.43/0.68 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.43/0.68 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.43/0.68 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 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@t3)))))) % 0.43/0.68 (assume @p49 @t57) % 0.43/0.68 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t58 @t1))))))))) % 0.43/0.68 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.43/0.68 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.43/0.68 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.43/0.68 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.43/0.68 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.43/0.68 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t58 @t10) @t1))))))))))) % 0.43/0.68 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.43/0.68 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP 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@t2))))))) % 0.43/0.68 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.43/0.68 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) (and @t61 @t40))))))) % 0.43/0.68 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.43/0.68 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.hd @t44) @t41))))))) % 0.43/0.68 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.tl @t44) (tptp.app @t43 @t1)))))))) % 0.43/0.68 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 (tptp.geq @t1 @t2)) @t3)))))) % 0.43/0.68 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.43/0.68 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.43/0.68 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.43/0.68 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t35) @t51)))))))) % 0.43/0.68 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t47 (or @t3 @t50))))))) % 0.43/0.68 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 (and @t4 @t47))))))) % 0.43/0.68 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not (tptp.gt @t1 @t2)))))))) % 0.43/0.68 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.43/0.68 (assume @p96 @t87) % 0.43/0.68 (assume @p97 true) % 0.43/0.68 (step @p98 :rule refl :args (@t91)) % 0.43/0.68 (step @p99 :rule eq-symm :args (@t88 tptp.nil)) % 0.43/0.68 (step @p100 :rule refl :args (@t92)) % 0.43/0.68 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t93)) % 0.43/0.68 (step @p102 :rule refl :args (@t97)) % 0.43/0.68 (step @p103 :rule refl :args (@t98)) % 0.43/0.68 (step @p104 :rule refl :args (@t99)) % 0.43/0.68 (step @p105 :rule 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0.43/0.68 (step @p179 :rule nary_cong :premises (@p157 @p178 @p175 @p174) :args (@t138)) % 0.43/0.68 (step @p180 :rule trans :premises (@p179 @p173)) % 0.43/0.68 (step @p181 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t140 @t77 @t139 @t66)) @t138))) % 0.43/0.68 (step @p182 :rule refl :args (@t66)) % 0.43/0.68 (step @p183 :rule refl :args (@t139)) % 0.43/0.68 (step @p184 :rule refl :args (@t77)) % 0.43/0.68 (step @p185 :rule refl :args (@t140)) % 0.43/0.68 (step @p186 :rule eq-symm :args (@t1 @t10)) % 0.43/0.68 (step @p187 :rule cong :premises (@p186) :args (@t77)) % 0.43/0.68 (step @p188 :rule nary_cong :premises (@p187 @p185 @p184 @p183 @p182) :args (@t141)) % 0.43/0.68 (step @p189 :rule aci_norm :args ((= @t142 @t141))) % 0.43/0.68 (step @p190 :rule trans :premises (@p189 @p188)) % 0.43/0.68 (step @p191 :rule cong :premises (@p190) :args (@t143)) % 0.43/0.68 (step @p192 :rule trans :premises (@p191 @p181)) % 0.43/0.68 (step @p193 :rule trans :premises (@p192 @p180)) % 0.43/0.68 (step @p194 :rule refl :args (@t76)) % 0.43/0.68 (step @p195 :rule nary_cong :premises (@p194 @p159 @p158 @p193) :args (@t144)) % 0.43/0.68 (step @p196 :rule trans :premises (@p195 @p172)) % 0.43/0.68 (step @p197 :rule quant-miniscope-or :args ((= (forall @t14 @t145) @t144))) % 0.43/0.68 (step @p198 :rule aci_norm :args ((= @t146 @t145))) % 0.43/0.68 (step @p199 :rule cong :premises (@p198) :args ((forall @t14 @t146))) % 0.43/0.68 (step @p200 :rule trans :premises (@p199 @p197)) % 0.43/0.68 (step @p201 :rule trans :premises (@p200 @p196)) % 0.43/0.68 (step @p202 :rule aci_norm :args ((= (or @t140 @t147) @t146))) % 0.43/0.68 (step @p203 :rule bool-impl-elim :args (@t13 @t147)) % 0.43/0.68 (step @p204 :rule trans :premises (@p203 @p202)) % 0.43/0.68 (step @p205 :rule cong :premises (@p204) :args ((forall @t14 (=> @t13 @t147)))) % 0.43/0.68 (step @p206 :rule trans :premises (@p205 @p201)) % 0.43/0.68 (step @p207 :rule refl :args (@t66)) % 0.43/0.68 (step @p208 :rule eq-symm :args (tptp.nil @t10)) % 0.43/0.68 (step @p209 :rule eq-symm :args (tptp.nil @t12)) % 0.43/0.68 (step @p210 :rule cong :premises (@p209) :args (@t67)) % 0.43/0.68 (step @p211 :rule nary_cong :premises (@p210 @p208) :args (@t68)) % 0.43/0.68 (step @p212 :rule aci_norm :args ((= (or @t96 (or @t95 (or @t113 @t94))) @t114))) % 0.43/0.68 (step @p213 :rule bool-and-de-morgan :args (@t70 @t69 true)) % 0.43/0.68 (step @p214 :rule refl :args (@t95)) % 0.43/0.68 (step @p215 :rule nary_cong :premises (@p214 @p213) :args ((or @t95 (not (and @t70 @t69))))) % 0.43/0.68 (step @p216 :rule bool-and-de-morgan :args (@t71 @t70 (and @t69))) % 0.43/0.68 (step @p217 :rule trans :premises (@p216 @p215)) % 0.43/0.68 (step @p218 :rule refl :args (@t96)) % 0.43/0.68 (step @p219 :rule nary_cong :premises (@p218 @p217) :args ((or @t96 (not (and @t71 @t70 @t69))))) % 0.43/0.68 (step @p220 :rule bool-and-de-morgan :args (@t32 @t71 (and @t70 @t69))) % 0.43/0.68 (step @p221 :rule trans :premises (@p220 @p219)) % 0.43/0.68 (step @p222 :rule trans :premises (@p221 @p212)) % 0.43/0.68 (step @p223 :rule cong :premises (@p222) :args (@t148)) % 0.43/0.68 (step @p224 :rule cong :premises (@p223) :args (@t149)) % 0.43/0.68 (step @p225 :rule exists-elim :args ((= @t73 @t149))) % 0.43/0.68 (step @p226 :rule trans :premises (@p225 @p224)) % 0.43/0.68 (step @p227 :rule refl :args (@t77)) % 0.43/0.68 (step @p228 :rule nary_cong :premises (@p227 @p194 @p159 @p226 @p211 @p207) :args (@t78)) % 0.43/0.68 (step @p229 :rule refl :args (@t13)) % 0.43/0.68 (step @p230 :rule cong :premises (@p229 @p228) :args (@t79)) % 0.43/0.68 (step @p231 :rule cong :premises (@p230) :args (@t80)) % 0.43/0.68 (step @p232 :rule trans :premises (@p231 @p206)) % 0.43/0.68 (step @p233 :rule refl :args (@t15)) % 0.43/0.68 (step @p234 :rule cong :premises (@p233 @p232) :args (@t81)) % 0.43/0.68 (step @p235 :rule cong :premises (@p234) :args (@t82)) % 0.43/0.68 (step @p236 :rule trans :premises (@p235 @p171)) % 0.43/0.68 (step @p237 :rule refl :args (@t21)) % 0.43/0.68 (step @p238 :rule cong :premises (@p237 @p236) :args (@t83)) % 0.43/0.68 (step @p239 :rule cong :premises (@p238) :args (@t84)) % 0.43/0.68 (step @p240 :rule trans :premises (@p239 @p133)) % 0.43/0.68 (step @p241 :rule refl :args (@t17)) % 0.43/0.68 (step @p242 :rule cong :premises (@p241 @p240) :args (@t85)) % 0.43/0.68 (step @p243 :rule cong :premises (@p242) :args (@t86)) % 0.43/0.68 (step @p244 :rule trans :premises (@p243 @p124)) % 0.43/0.68 (step @p245 :rule cong :premises (@p244) :args (@t87)) % 0.43/0.68 (step @p246 :rule eq_resolve :premises (@p96 @p245)) % 0.43/0.68 (step @p247 :rule refl :args (@t168)) % 0.43/0.68 (step @p248 :rule bool-double-not-elim :args (@t150)) % 0.43/0.68 (step @p249 :rule nary_cong :premises (@p248 @p247) :args ((or (not @t169) @t168))) % 0.43/0.68 (step @p250 :rule refl :args (@t159)) % 0.43/0.68 (step @p251 :rule refl :args (@t160)) % 0.43/0.68 (step @p252 :rule eq-symm :args (@t151 tptp.nil)) % 0.43/0.68 (step @p253 :rule cong :premises (@p252) :args (@t170)) % 0.43/0.68 (step @p254 :rule nary_cong :premises (@p253 @p251) :args (@t171)) % 0.43/0.68 (step @p255 :rule refl :args (@t162)) % 0.43/0.68 (step @p256 :rule refl :args (@t163)) % 0.43/0.68 (step @p257 :rule refl :args (@t164)) % 0.43/0.68 (step @p258 :rule refl :args (@t166)) % 0.43/0.68 (step @p259 :rule nary_cong :premises (@p258 @p257 @p256 @p255 @p254 @p250) :args (@t172)) % 0.43/0.68 (step @p260 :rule cong :premises (@p259) :args (@t173)) % 0.43/0.68 (step @p261 :rule refl :args (@t169)) % 0.43/0.68 (step @p262 :rule cong :premises (@p261 @p260) :args ((=> @t169 @t173))) % 0.43/0.68 (assume-push @p319 @t169) % 0.43/0.68 (step @p264 :rule skolemize :premises (@p246)) % 0.43/0.68 (step-pop @p320 :rule scope :premises (@p264)) % 0.43/0.68 (step @p265 :rule process_scope :premises (@p320) :args (@t173)) % 0.43/0.68 (step @p267 :rule eq_resolve :premises (@p265 @p262)) % 0.43/0.68 (step @p268 :rule implies_elim :premises (@p267)) % 0.43/0.68 (step @p269 :rule eq_resolve :premises (@p268 @p249)) % 0.43/0.68 (step @p270 :rule chain_m_resolution :premises (@p269 @p246) :args (@t168 @t174 (@list @t150))) % 0.43/0.68 (step @p271 :rule bool-double-not-elim :args (@t165)) % 0.43/0.68 (step @p272 :rule refl :args (@t167)) % 0.43/0.68 (step @p273 :rule nary_cong :premises (@p272 @p271) :args ((or @t167 (not @t166)))) % 0.43/0.68 (step @p274 :rule cnf_or_neg :args (@t167 0)) % 0.43/0.68 (step @p275 :rule eq_resolve :premises (@p274 @p273)) % 0.43/0.68 (step @p276 :rule reordering :premises (@p275) :args ((or @t165 @t167))) % 0.43/0.68 (step @p277 :rule chain_m_resolution :premises (@p276 @p270) :args (@t165 @t174 @t175)) % 0.43/0.68 (step @p278 :rule cnf_or_neg :args (@t167 5)) % 0.43/0.68 (step @p279 :rule chain_m_resolution :premises (@p278 @p270) :args ((not @t159) @t174 @t175)) % 0.43/0.68 (step @p280 :rule bool-double-not-elim :args (@t158)) % 0.43/0.68 (step @p281 :rule nary_cong :premises (@p272 @p280) :args ((or @t167 (not @t163)))) % 0.43/0.68 (step @p282 :rule cnf_or_neg :args (@t167 2)) % 0.43/0.68 (step @p283 :rule eq_resolve :premises (@p282 @p281)) % 0.43/0.68 (step @p284 :rule reordering :premises (@p283) :args ((or @t158 @t167))) % 0.43/0.69 (step @p285 :rule chain_m_resolution :premises (@p284 @p270) :args (@t158 @t174 @t175)) % 0.43/0.69 (step @p286 :rule cnf_and_neg :args (@t159)) % 0.43/0.69 (step @p287 :rule reordering :premises (@p286) :args ((or @t163 @t159 @t176))) % 0.43/0.69 (step @p288 :rule chain_m_resolution :premises (@p287 @p285 @p279) :args (@t176 (@list false true) (@list @t158 @t159))) % 0.43/0.69 (step @p289 :rule bool-double-not-elim :args (@t155)) % 0.43/0.69 (step @p290 :rule refl :args (@t157)) % 0.43/0.69 (step @p291 :rule nary_cong :premises (@p290 @p289) :args ((or @t157 (not @t156)))) % 0.43/0.69 (step @p292 :rule cnf_or_neg :args (@t157 0)) % 0.43/0.69 (step @p293 :rule eq_resolve :premises (@p292 @p291)) % 0.43/0.69 (step @p294 :rule reordering :premises (@p293) :args ((or @t155 @t157))) % 0.43/0.69 (step @p295 :rule chain_m_resolution :premises (@p294 @p288) :args (@t155 @t174 @t177)) % 0.43/0.69 (step @p296 :rule bool-double-not-elim :args (@t153)) % 0.43/0.69 (step @p297 :rule nary_cong :premises (@p290 @p296) :args ((or @t157 (not @t154)))) % 0.43/0.69 (step @p298 :rule cnf_or_neg :args (@t157 1)) % 0.43/0.69 (step @p299 :rule eq_resolve :premises (@p298 @p297)) % 0.43/0.69 (step @p300 :rule reordering :premises (@p299) :args ((or @t153 @t157))) % 0.43/0.69 (step @p301 :rule chain_m_resolution :premises (@p300 @p288) :args (@t153 @t174 @t177)) % 0.43/0.69 (step @p302 :rule bool-double-not-elim :args (@t161)) % 0.43/0.69 (step @p303 :rule nary_cong :premises (@p272 @p302) :args ((or @t167 (not @t162)))) % 0.43/0.69 (step @p304 :rule cnf_or_neg :args (@t167 3)) % 0.43/0.69 (step @p305 :rule eq_resolve :premises (@p304 @p303)) % 0.43/0.69 (step @p306 :rule reordering :premises (@p305) :args ((or @t161 @t167))) % 0.43/0.69 (step @p307 :rule chain_m_resolution :premises (@p306 @p270) :args (@t161 @t174 @t175)) % 0.43/0.69 (step @p308 :rule instantiate :premises (@p307) :args (@t178)) % 0.43/0.69 (step @p309 :rule bool-impl-elim :args (@t17 @t56)) % 0.43/0.69 (step @p310 :rule cong :premises (@p309) :args (@t57)) % 0.43/0.69 (step @p311 :rule eq_resolve :premises (@p49 @p310)) % 0.43/0.69 (step @p312 :rule instantiate :premises (@p311) :args (@t178)) % 0.43/0.69 (step @p313 :rule cnf_or_pos :args (@t180)) % 0.43/0.69 (step @p314 :rule reordering :premises (@p313) :args ((or @t166 @t179 (not @t180)))) % 0.43/0.69 (step @p315 :rule chain_m_resolution :premises (@p314 @p277 @p312) :args (@t179 (@list false false) (@list @t165 @t180))) % 0.43/0.69 (step @p316 :rule cnf_or_pos :args (@t182)) % 0.43/0.69 (step @p317 :rule reordering :premises (@p316) :args ((or @t166 @t156 @t154 @t181 (not @t182)))) % 0.43/0.69 (step @p318 false :rule chain_m_resolution :premises (@p317 @p315 @p308 @p301 @p295 @p277) :args (false (@list false false false false false) (@list @t179 @t182 @t153 @t155 @t165))) % 0.43/0.69 ) % 0.43/0.69 % SZS output end Proof % 0.43/0.69 % cvc5 exiting %------------------------------------------------------------------------------