%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC044+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 : n024.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 08:57:49 AM UTC 2026 % Result : Theorem 0.24s 0.43s % Output : Proof 0.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SWC044+1 : TPTP v9.2.1. Released v2.4.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 14:11:00 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.24/0.43 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.24/0.43 % SZS status Theorem % 0.24/0.43 % SZS output start Proof % 0.24/0.43 ( % 0.24/0.43 (declare-sort $$unsorted 0) % 0.24/0.43 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.24/0.43 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.24/0.43 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.43 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.43 (declare-const tptp.nil $$unsorted) % 0.24/0.43 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.24/0.43 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.24/0.43 (define @t1 () (@var "V" $$unsorted)) % 0.24/0.43 (define @t2 () (@var "U" $$unsorted)) % 0.24/0.43 (define @t3 () (= @t2 @t1)) % 0.24/0.43 (define @t4 () (not @t3)) % 0.24/0.43 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.24/0.43 (define @t6 () (tptp.ssItem @t1)) % 0.24/0.43 (define @t7 () (@list @t1)) % 0.24/0.43 (define @t8 () (tptp.ssItem @t2)) % 0.24/0.43 (define @t9 () (@list @t2)) % 0.24/0.43 (define @t10 () (@var "X" $$unsorted)) % 0.24/0.43 (define @t11 () (tptp.cons @t1 @t10)) % 0.24/0.43 (define @t12 () (@var "W" $$unsorted)) % 0.24/0.43 (define @t13 () (tptp.ssList @t10)) % 0.24/0.43 (define @t14 () (@list @t10)) % 0.24/0.43 (define @t15 () (tptp.ssList @t12)) % 0.24/0.43 (define @t16 () (@list @t12)) % 0.24/0.43 (define @t17 () (tptp.ssList @t2)) % 0.24/0.43 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.24/0.43 (define @t19 () (tptp.app @t1 @t12)) % 0.24/0.43 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.24/0.43 (define @t21 () (tptp.ssList @t1)) % 0.24/0.43 (define @t22 () (tptp.app @t12 @t1)) % 0.24/0.43 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.24/0.43 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.24/0.43 (define @t25 () (tptp.leq @t12 @t1)) % 0.24/0.43 (define @t26 () (tptp.leq @t1 @t12)) % 0.24/0.43 (define @t27 () (@var "Z" $$unsorted)) % 0.24/0.43 (define @t28 () (@var "Y" $$unsorted)) % 0.24/0.43 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.24/0.43 (define @t30 () (tptp.ssList @t27)) % 0.24/0.43 (define @t31 () (@list @t27)) % 0.24/0.43 (define @t32 () (tptp.ssList @t28)) % 0.24/0.43 (define @t33 () (@list @t28)) % 0.24/0.43 (define @t34 () (tptp.ssItem @t12)) % 0.24/0.43 (define @t35 () (tptp.lt @t1 @t12)) % 0.24/0.43 (define @t36 () (= @t1 @t12)) % 0.24/0.43 (define @t37 () (tptp.cons @t1 @t2)) % 0.24/0.43 (define @t38 () (tptp.ssList tptp.nil)) % 0.24/0.43 (define @t39 () (= @t1 @t2)) % 0.24/0.43 (define @t40 () (tptp.cons @t12 @t1)) % 0.24/0.43 (define @t41 () (= tptp.nil @t2)) % 0.24/0.43 (define @t42 () (tptp.hd @t2)) % 0.24/0.43 (define @t43 () (not @t41)) % 0.24/0.43 (define @t44 () (tptp.tl @t2)) % 0.24/0.43 (define @t45 () (tptp.app @t2 @t1)) % 0.24/0.43 (define @t46 () (tptp.app @t1 @t2)) % 0.24/0.43 (define @t47 () (tptp.leq @t1 @t2)) % 0.24/0.43 (define @t48 () (tptp.leq @t2 @t1)) % 0.24/0.43 (define @t49 () (tptp.geq @t2 @t1)) % 0.24/0.43 (define @t50 () (tptp.lt @t1 @t2)) % 0.24/0.43 (define @t51 () (tptp.lt @t2 @t1)) % 0.24/0.43 (define @t52 () (tptp.lt @t2 @t12)) % 0.24/0.43 (define @t53 () (tptp.gt @t2 @t1)) % 0.24/0.43 (define @t54 () (tptp.memberP @t12 @t2)) % 0.24/0.43 (define @t55 () (tptp.rearsegP @t1 @t12)) % 0.24/0.43 (define @t56 () (tptp.rearsegP @t1 @t2)) % 0.24/0.43 (define @t57 () (and @t23 @t56)) % 0.24/0.43 (define @t58 () (=> @t57 @t3)) % 0.24/0.43 (define @t59 () (forall @t7 (=> @t21 @t58))) % 0.24/0.43 (define @t60 () (=> @t17 @t59)) % 0.24/0.43 (define @t61 () (forall @t9 @t60)) % 0.24/0.43 (define @t62 () (tptp.app @t12 @t2)) % 0.24/0.43 (define @t63 () (tptp.rearsegP @t2 tptp.nil)) % 0.24/0.43 (define @t64 () (forall @t9 (=> @t17 @t63))) % 0.24/0.43 (define @t65 () (tptp.rearsegP tptp.nil @t2)) % 0.24/0.43 (define @t66 () (tptp.cons @t2 tptp.nil)) % 0.24/0.43 (define @t67 () (tptp.hd @t1)) % 0.24/0.43 (define @t68 () (= tptp.nil @t1)) % 0.24/0.43 (define @t69 () (not @t68)) % 0.24/0.43 (define @t70 () (tptp.cons @t2 @t1)) % 0.24/0.43 (define @t71 () (= @t12 @t2)) % 0.24/0.43 (define @t72 () (not (tptp.rearsegP @t10 @t12))) % 0.24/0.43 (define @t73 () (not (= @t2 @t12))) % 0.24/0.43 (define @t74 () (not (= @t1 @t10))) % 0.24/0.43 (define @t75 () (or @t69 @t74 @t73 @t72 @t41)) % 0.24/0.43 (define @t76 () (=> @t13 @t75)) % 0.24/0.43 (define @t77 () (forall @t14 @t76)) % 0.24/0.43 (define @t78 () (=> @t15 @t77)) % 0.24/0.43 (define @t79 () (forall @t16 @t78)) % 0.24/0.43 (define @t80 () (=> @t21 @t79)) % 0.24/0.43 (define @t81 () (forall @t7 @t80)) % 0.24/0.43 (define @t82 () (=> @t17 @t81)) % 0.24/0.43 (define @t83 () (forall @t9 @t82)) % 0.24/0.43 (define @t84 () (not @t83)) % 0.24/0.43 (define @t85 () (not @t65)) % 0.24/0.43 (define @t86 () (= @t2 tptp.nil)) % 0.24/0.43 (define @t87 () (not @t17)) % 0.24/0.43 (define @t88 () (or @t87 @t86 @t85)) % 0.24/0.43 (define @t89 () (forall @t9 @t88)) % 0.24/0.43 (define @t90 () (not @t38)) % 0.24/0.43 (define @t91 () (or @t90 @t88)) % 0.24/0.43 (define @t92 () (or @t87 @t86 @t90 @t85)) % 0.24/0.43 (define @t93 () (or @t86 @t87 @t90 @t85)) % 0.24/0.43 (define @t94 () (or @t90 @t85)) % 0.24/0.43 (define @t95 () (not (= tptp.nil tptp.nil))) % 0.24/0.43 (define @t96 () (or @t90 @t95 @t85)) % 0.24/0.43 (define @t97 () (not @t56)) % 0.24/0.43 (define @t98 () (not (= @t1 tptp.nil))) % 0.24/0.43 (define @t99 () (not @t21)) % 0.24/0.43 (define @t100 () (or @t98 @t99 @t98 @t97)) % 0.24/0.43 (define @t101 () (or @t99 @t98 @t97)) % 0.24/0.43 (define @t102 () (forall @t7 @t101)) % 0.24/0.43 (define @t103 () (or @t86 @t87 @t102)) % 0.24/0.43 (define @t104 () (or @t86 @t87 @t101)) % 0.24/0.43 (define @t105 () (or @t99 @t98 @t86 @t87 @t97)) % 0.24/0.43 (define @t106 () (or @t98 @t86 @t99 @t87 @t97)) % 0.24/0.43 (define @t107 () (or @t87 @t97)) % 0.24/0.43 (define @t108 () (not (= @t2 @t2))) % 0.24/0.43 (define @t109 () (or @t87 @t108 @t97)) % 0.24/0.43 (define @t110 () (not @t55)) % 0.24/0.43 (define @t111 () (not @t15)) % 0.24/0.43 (define @t112 () (or @t73 @t111 @t73 @t110)) % 0.24/0.43 (define @t113 () (or @t111 @t73 @t110)) % 0.24/0.43 (define @t114 () (forall @t16 @t113)) % 0.24/0.43 (define @t115 () (or @t98 @t86 @t99 @t114)) % 0.24/0.43 (define @t116 () (or @t98 @t86 @t99 @t113)) % 0.24/0.43 (define @t117 () (or @t111 @t98 @t73 @t86 @t99 @t110)) % 0.24/0.43 (define @t118 () (or @t98 @t73 @t86 @t99 @t110)) % 0.24/0.43 (define @t119 () (or @t99 @t110)) % 0.24/0.43 (define @t120 () (not (= @t1 @t1))) % 0.24/0.43 (define @t121 () (or @t99 @t120 @t110)) % 0.24/0.43 (define @t122 () (not @t13)) % 0.24/0.43 (define @t123 () (or @t74 @t122 @t74 @t72)) % 0.24/0.43 (define @t124 () (or @t122 @t74 @t72)) % 0.24/0.43 (define @t125 () (forall @t14 @t124)) % 0.24/0.43 (define @t126 () (or @t98 @t73 @t86 @t125)) % 0.24/0.43 (define @t127 () (or @t98 @t73 @t86 @t124)) % 0.24/0.43 (define @t128 () (or @t122 @t98 @t74 @t73 @t72 @t86)) % 0.24/0.43 (define @t129 () (or @t98 @t74 @t73 @t72 @t86)) % 0.24/0.43 (define @t130 () (@quantifiers_skolemize @t89 0)) % 0.24/0.43 (define @t131 () (tptp.rearsegP tptp.nil @t130)) % 0.24/0.43 (define @t132 () (not @t131)) % 0.24/0.43 (define @t133 () (= tptp.nil @t130)) % 0.24/0.43 (define @t134 () (tptp.ssList @t130)) % 0.24/0.43 (define @t135 () (not @t134)) % 0.24/0.43 (define @t136 () (or @t135 @t133 @t132)) % 0.24/0.43 (define @t137 () (not @t136)) % 0.24/0.43 (define @t138 () (not @t89)) % 0.24/0.43 (define @t139 () (or @t135 (= @t130 tptp.nil) @t132)) % 0.24/0.43 (define @t140 () (not @t139)) % 0.24/0.43 (define @t141 () (@list true)) % 0.24/0.43 (define @t142 () (@list @t136)) % 0.24/0.43 (define @t143 () (@var "BOUND_VARIABLE_9982" $$unsorted)) % 0.24/0.43 (define @t144 () (= @t2 @t143)) % 0.24/0.43 (define @t145 () (not (tptp.rearsegP @t143 @t2))) % 0.24/0.43 (define @t146 () (not (tptp.rearsegP @t2 @t143))) % 0.24/0.43 (define @t147 () (not (tptp.ssList @t143))) % 0.24/0.43 (define @t148 () (or @t147 @t146 @t145 @t144)) % 0.24/0.43 (define @t149 () (or @t87 @t148)) % 0.24/0.43 (define @t150 () (forall (@list @t2 @t143) @t149)) % 0.24/0.43 (define @t151 () (@list @t143)) % 0.24/0.43 (define @t152 () (forall @t151 @t149)) % 0.24/0.43 (define @t153 () (forall @t151 @t148)) % 0.24/0.43 (define @t154 () (or @t87 @t153)) % 0.24/0.43 (define @t155 () (not @t23)) % 0.24/0.43 (define @t156 () (or @t99 @t155 @t97 @t3)) % 0.24/0.43 (define @t157 () (forall @t7 @t156)) % 0.24/0.43 (define @t158 () (or @t155 @t97 @t3)) % 0.24/0.43 (define @t159 () (tptp.rearsegP @t130 tptp.nil)) % 0.24/0.43 (define @t160 () (not @t159)) % 0.24/0.43 (define @t161 () (or @t90 @t135 @t132 @t160 @t133)) % 0.24/0.43 (define @t162 () (or @t135 @t159)) % 0.24/0.43 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.24/0.43 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.24/0.43 (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))))))))))) % 0.24/0.43 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.24/0.43 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.24/0.43 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.24/0.43 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.24/0.43 (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))))))))))))))))) % 0.24/0.43 (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)))))))))))))))) % 0.24/0.43 (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))))))))))))))))) % 0.24/0.43 (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))))))))))))))) % 0.24/0.43 (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))))))))))))))) % 0.24/0.43 (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)))))))))))))))) % 0.24/0.43 (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))))))))))))) % 0.24/0.43 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.24/0.43 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.24/0.43 (assume @p17 @t38) % 0.24/0.43 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.24/0.43 (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) @t39))))))))))) % 0.24/0.43 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t40 @t2))))))))) % 0.24/0.43 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.24/0.43 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.24/0.43 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.24/0.43 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.24/0.43 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.24/0.43 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t45)))))) % 0.24/0.43 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.24/0.43 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.24/0.43 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.24/0.43 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t26) (tptp.leq @t2 @t12))))))))) % 0.24/0.43 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.24/0.43 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.24/0.43 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.24/0.43 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t52)))))))) % 0.24/0.43 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.24/0.43 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 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(assume @p78 (forall @t9 (=> @t17 (=> @t43 (= (tptp.cons @t42 @t44) @t2))))) % 0.24/0.43 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t45) @t71)))))))) % 0.24/0.43 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t46) @t71)))))))) % 0.24/0.43 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.24/0.43 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t45 @t12) (tptp.app @t2 @t19))))))))) % 0.24/0.43 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t45) (and @t68 @t41))))))) % 0.24/0.43 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.24/0.43 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.hd @t45) @t42))))))) % 0.24/0.43 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.tl @t45) (tptp.app @t44 @t1)))))))) % 0.24/0.43 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 (tptp.geq @t1 @t2)) @t3)))))) % 0.24/0.43 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t49 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.24/0.43 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.24/0.43 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.24/0.43 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t35) @t52)))))))) % 0.24/0.43 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t48 (or @t3 @t51))))))) % 0.24/0.43 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t51 (and @t4 @t48))))))) % 0.24/0.43 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (not (tptp.gt @t1 @t2)))))))) % 0.24/0.43 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t53 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.24/0.43 (assume @p96 @t84) % 0.24/0.43 (assume @p97 true) % 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:premises (@p185 @p184)) % 0.24/0.43 (step @p187 :rule cong :premises (@p186) :args (@t125)) % 0.24/0.43 (step @p188 :rule trans :premises (@p187 @p178)) % 0.24/0.43 (step @p189 :rule trans :premises (@p188 @p177)) % 0.24/0.43 (step @p190 :rule refl :args (@t73)) % 0.24/0.43 (step @p191 :rule nary_cong :premises (@p157 @p190 @p123 @p189) :args (@t126)) % 0.24/0.43 (step @p192 :rule trans :premises (@p191 @p170)) % 0.24/0.43 (step @p193 :rule quant-miniscope-or :args ((= (forall @t14 @t127) @t126))) % 0.24/0.43 (step @p194 :rule aci_norm :args ((= @t128 @t127))) % 0.24/0.43 (step @p195 :rule cong :premises (@p194) :args ((forall @t14 @t128))) % 0.24/0.43 (step @p196 :rule trans :premises (@p195 @p193)) % 0.24/0.43 (step @p197 :rule trans :premises (@p196 @p192)) % 0.24/0.43 (step @p198 :rule aci_norm :args ((= (or @t122 @t129) @t128))) % 0.24/0.43 (step @p199 :rule bool-impl-elim :args (@t13 @t129)) % 0.24/0.43 (step @p200 :rule trans :premises (@p199 @p198)) % 0.24/0.43 (step @p201 :rule cong :premises (@p200) :args ((forall @t14 (=> @t13 @t129)))) % 0.24/0.43 (step @p202 :rule trans :premises (@p201 @p197)) % 0.24/0.43 (step @p203 :rule eq-symm :args (tptp.nil @t2)) % 0.24/0.43 (step @p204 :rule refl :args (@t72)) % 0.24/0.43 (step @p205 :rule refl :args (@t74)) % 0.24/0.43 (step @p206 :rule eq-symm :args (tptp.nil @t1)) % 0.24/0.43 (step @p207 :rule cong :premises (@p206) :args (@t69)) % 0.24/0.43 (step @p208 :rule nary_cong :premises (@p207 @p205 @p190 @p204 @p203) :args (@t75)) % 0.24/0.43 (step @p209 :rule refl :args (@t13)) % 0.24/0.43 (step @p210 :rule cong :premises (@p209 @p208) :args (@t76)) % 0.24/0.43 (step @p211 :rule cong :premises (@p210) :args (@t77)) % 0.24/0.43 (step @p212 :rule trans :premises (@p211 @p202)) % 0.24/0.43 (step @p213 :rule refl :args (@t15)) % 0.24/0.43 (step @p214 :rule cong :premises (@p213 @p212) :args (@t78)) % 0.24/0.43 (step @p215 :rule cong :premises (@p214) :args (@t79)) % 0.24/0.43 (step @p216 :rule trans :premises (@p215 @p169)) % 0.24/0.43 (step @p217 :rule refl :args (@t21)) % 0.24/0.43 (step @p218 :rule cong :premises (@p217 @p216) :args (@t80)) % 0.24/0.43 (step @p219 :rule cong :premises (@p218) :args (@t81)) % 0.24/0.43 (step @p220 :rule trans :premises (@p219 @p135)) % 0.24/0.43 (step @p221 :rule refl :args (@t17)) % 0.24/0.43 (step @p222 :rule cong :premises (@p221 @p220) :args (@t82)) % 0.24/0.43 (step @p223 :rule cong :premises (@p222) :args (@t83)) % 0.24/0.43 (step @p224 :rule trans :premises (@p223 @p106)) % 0.24/0.43 (step @p225 :rule cong :premises (@p224) :args (@t84)) % 0.24/0.43 (step @p226 :rule eq_resolve :premises (@p96 @p225)) % 0.24/0.43 (step @p227 :rule not_or_elim :premises (@p226) :args (1)) % 0.24/0.43 (step @p228 :rule refl :args (@t137)) % 0.24/0.43 (step @p229 :rule bool-double-not-elim :args (@t89)) % 0.24/0.43 (step @p230 :rule nary_cong :premises (@p229 @p228) :args ((or (not @t138) @t137))) % 0.24/0.43 (step @p231 :rule refl :args (@t132)) % 0.24/0.43 (step @p232 :rule eq-symm :args (@t130 tptp.nil)) % 0.24/0.43 (step @p233 :rule refl :args (@t135)) % 0.24/0.43 (step @p234 :rule nary_cong :premises (@p233 @p232 @p231) :args (@t139)) % 0.24/0.43 (step @p235 :rule cong :premises (@p234) :args (@t140)) % 0.24/0.43 (step @p236 :rule refl :args (@t138)) % 0.24/0.43 (step @p237 :rule cong :premises (@p236 @p235) :args ((=> @t138 @t140))) % 0.24/0.43 (assume-push @p307 @t138) % 0.24/0.43 (step @p239 :rule skolemize :premises (@p227)) % 0.24/0.43 (step-pop @p308 :rule scope :premises (@p239)) % 0.24/0.43 (step @p240 :rule process_scope :premises (@p308) :args (@t140)) % 0.24/0.43 (step @p242 :rule eq_resolve :premises (@p240 @p237)) % 0.24/0.43 (step @p243 :rule implies_elim :premises (@p242)) % 0.24/0.43 (step @p244 :rule eq_resolve :premises (@p243 @p230)) % 0.24/0.43 (step @p245 :rule chain_m_resolution :premises (@p244 @p227) :args (@t137 @t141 (@list @t89))) % 0.24/0.43 (step @p246 :rule bool-double-not-elim :args (@t134)) % 0.24/0.43 (step @p247 :rule refl :args (@t136)) % 0.24/0.43 (step @p248 :rule nary_cong :premises (@p247 @p246) :args ((or @t136 (not @t135)))) % 0.24/0.43 (step @p249 :rule cnf_or_neg :args (@t136 0)) % 0.24/0.43 (step @p250 :rule eq_resolve :premises (@p249 @p248)) % 0.24/0.43 (step @p251 :rule reordering :premises (@p250) :args ((or @t134 @t136))) % 0.24/0.43 (step @p252 :rule chain_m_resolution :premises (@p251 @p245) :args (@t134 @t141 @t142)) % 0.24/0.43 (step @p253 :rule bool-impl-elim :args (@t17 @t63)) % 0.24/0.43 (step @p254 :rule cong :premises (@p253) :args (@t64)) % 0.24/0.43 (step @p255 :rule eq_resolve :premises (@p51 @p254)) % 0.24/0.43 (step @p256 :rule instantiate :premises (@p255) :args ((@list @t130))) % 0.24/0.43 (step @p257 :rule aci_norm :args ((= @t149 (or @t87 @t147 @t146 @t145 @t144)))) % 0.24/0.43 (step @p258 :rule cong :premises (@p257) :args (@t150)) % 0.24/0.43 (step @p259 :rule quant-merge-prenex :args ((= (forall @t9 @t152) @t150))) % 0.24/0.43 (step @p260 :rule alpha_equiv :args (@t153 (@list @t143) (@list @t1))) % 0.24/0.43 (step @p261 :rule refl :args (@t87)) % 0.24/0.43 (step @p262 :rule nary_cong :premises (@p261 @p260) :args (@t154)) % 0.24/0.43 (step @p263 :rule quant-miniscope-or :args ((= @t152 @t154))) % 0.24/0.43 (step @p264 :rule trans :premises (@p263 @p262)) % 0.24/0.43 (step @p265 :rule symm :premises (@p264)) % 0.24/0.43 (step @p266 :rule cong :premises (@p265) :args ((forall @t9 (or @t87 @t157)))) % 0.24/0.43 (step @p267 :rule trans :premises (@p266 @p259)) % 0.24/0.43 (step @p268 :rule trans :premises (@p267 @p258)) % 0.24/0.43 (step @p269 :rule bool-impl-elim :args (@t17 @t157)) % 0.24/0.43 (step @p270 :rule cong :premises (@p269) :args ((forall @t9 (=> @t17 @t157)))) % 0.24/0.43 (step @p271 :rule trans :premises (@p270 @p268)) % 0.24/0.43 (step @p272 :rule aci_norm :args ((= (or @t99 @t158) @t156))) % 0.24/0.43 (step @p273 :rule aci_norm :args ((= (or (or @t155 @t97) @t3) @t158))) % 0.24/0.43 (step @p274 :rule refl :args (@t3)) % 0.24/0.43 (step @p275 :rule bool-and-de-morgan :args (@t23 @t56 true)) % 0.24/0.43 (step @p276 :rule nary_cong :premises (@p275 @p274) :args ((or (not @t57) @t3))) % 0.24/0.43 (step @p277 :rule trans :premises (@p276 @p273)) % 0.24/0.43 (step @p278 :rule bool-impl-elim :args (@t57 @t3)) % 0.24/0.43 (step @p279 :rule trans :premises (@p278 @p277)) % 0.24/0.43 (step @p280 :rule refl :args (@t99)) % 0.24/0.43 (step @p281 :rule nary_cong :premises (@p280 @p279) :args ((or @t99 @t58))) % 0.24/0.43 (step @p282 :rule trans :premises (@p281 @p272)) % 0.24/0.43 (step @p283 :rule bool-impl-elim :args (@t21 @t58)) % 0.24/0.43 (step @p284 :rule trans :premises (@p283 @p282)) % 0.24/0.43 (step @p285 :rule cong :premises (@p284) :args (@t59)) % 0.24/0.43 (step @p286 :rule cong :premises (@p221 @p285) :args (@t60)) % 0.24/0.43 (step @p287 :rule cong :premises (@p286) :args (@t61)) % 0.24/0.43 (step @p288 :rule trans :premises (@p287 @p271)) % 0.24/0.43 (step @p289 :rule eq_resolve :premises (@p48 @p288)) % 0.24/0.43 (step @p290 :rule instantiate :premises (@p289) :args ((@list tptp.nil @t130))) % 0.24/0.43 (step @p291 :rule cnf_or_neg :args (@t136 1)) % 0.24/0.43 (step @p292 :rule chain_m_resolution :premises (@p291 @p245) :args ((not @t133) @t141 @t142)) % 0.24/0.43 (step @p293 :rule bool-double-not-elim :args (@t131)) % 0.24/0.43 (step @p294 :rule nary_cong :premises (@p247 @p293) :args ((or @t136 (not @t132)))) % 0.24/0.43 (step @p295 :rule cnf_or_neg :args (@t136 2)) % 0.24/0.43 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 0.24/0.43 (step @p297 :rule reordering :premises (@p296) :args ((or @t131 @t136))) % 0.24/0.43 (step @p298 :rule chain_m_resolution :premises (@p297 @p245) :args (@t131 @t141 @t142)) % 0.24/0.43 (step @p299 :rule not_or_elim :premises (@p226) :args (0)) % 0.24/0.43 (step @p300 :rule not_not_elim :premises (@p299)) % 0.24/0.43 (step @p301 :rule cnf_or_pos :args (@t161)) % 0.24/0.43 (step @p302 :rule reordering :premises (@p301) :args ((or @t90 @t135 @t132 @t133 @t160 (not @t161)))) % 0.24/0.43 (step @p303 :rule chain_m_resolution :premises (@p302 @p300 @p252 @p298 @p292 @p290) :args (@t160 (@list false false false true false) (@list @t38 @t134 @t131 @t133 @t161))) % 0.24/0.43 (step @p304 :rule cnf_or_pos :args (@t162)) % 0.24/0.43 (step @p305 :rule reordering :premises (@p304) :args ((or @t135 @t159 (not @t162)))) % 0.24/0.43 (step @p306 false :rule chain_m_resolution :premises (@p305 @p303 @p256 @p252) :args (false (@list true false false) (@list @t159 @t162 @t134))) % 0.24/0.43 ) % 0.24/0.43 % SZS output end Proof % 0.24/0.43 % cvc5 exiting %------------------------------------------------------------------------------