%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC038+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 : n002.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 08:57:48 AM UTC 2026 % Result : Theorem 0.37s 0.68s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC038+1 : TPTP v9.2.1. Released v2.4.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n002.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 19:11:03 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.68 % SZS status Theorem % 0.37/0.68 % SZS output start Proof % 0.37/0.68 ( % 0.37/0.68 (declare-sort $$unsorted 0) % 0.37/0.68 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.nil $$unsorted) % 0.37/0.68 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.37/0.69 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.69 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.69 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.69 (define @t3 () (= @t2 @t1)) % 0.37/0.69 (define @t4 () (not @t3)) % 0.37/0.69 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.37/0.69 (define @t6 () (tptp.ssItem @t1)) % 0.37/0.69 (define @t7 () (@list @t1)) % 0.37/0.69 (define @t8 () (tptp.ssItem @t2)) % 0.37/0.69 (define @t9 () (@list @t2)) % 0.37/0.69 (define @t10 () (@var "X" $$unsorted)) % 0.37/0.69 (define @t11 () (tptp.cons @t1 @t10)) % 0.37/0.69 (define @t12 () (@var "W" $$unsorted)) % 0.37/0.69 (define @t13 () (tptp.ssList @t10)) % 0.37/0.69 (define @t14 () (@list @t10)) % 0.37/0.69 (define @t15 () (tptp.ssList @t12)) % 0.37/0.69 (define @t16 () (@list @t12)) % 0.37/0.69 (define @t17 () (tptp.ssList @t2)) % 0.37/0.69 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.37/0.69 (define @t19 () (tptp.app @t1 @t12)) % 0.37/0.69 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.37/0.69 (define @t21 () (tptp.ssList @t1)) % 0.37/0.69 (define @t22 () (tptp.app @t12 @t1)) % 0.37/0.69 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.37/0.69 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.37/0.69 (define @t25 () (tptp.leq @t12 @t1)) % 0.37/0.69 (define @t26 () (tptp.leq @t1 @t12)) % 0.37/0.69 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.69 (define @t28 () (@var "Y" $$unsorted)) % 0.37/0.69 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.37/0.69 (define @t30 () (tptp.ssList @t27)) % 0.37/0.69 (define @t31 () (@list @t27)) % 0.37/0.69 (define @t32 () (tptp.ssList @t28)) % 0.37/0.69 (define @t33 () (@list @t28)) % 0.37/0.69 (define @t34 () (tptp.ssItem @t12)) % 0.37/0.69 (define @t35 () (tptp.lt @t1 @t12)) % 0.37/0.69 (define @t36 () (= @t1 @t12)) % 0.37/0.69 (define @t37 () (tptp.cons @t1 @t2)) % 0.37/0.69 (define @t38 () (tptp.ssList tptp.nil)) % 0.37/0.69 (define @t39 () (= @t1 @t2)) % 0.37/0.69 (define @t40 () (tptp.cons @t12 @t1)) % 0.37/0.69 (define @t41 () (= tptp.nil @t2)) % 0.37/0.69 (define @t42 () (tptp.hd @t2)) % 0.37/0.69 (define @t43 () (not @t41)) % 0.37/0.69 (define @t44 () (tptp.tl @t2)) % 0.37/0.69 (define @t45 () (tptp.app @t2 @t1)) % 0.37/0.69 (define @t46 () (tptp.app @t1 @t2)) % 0.37/0.69 (define @t47 () (tptp.leq @t1 @t2)) % 0.37/0.69 (define @t48 () (tptp.leq @t2 @t1)) % 0.37/0.69 (define @t49 () (tptp.geq @t2 @t1)) % 0.37/0.69 (define @t50 () (tptp.lt @t1 @t2)) % 0.37/0.69 (define @t51 () (tptp.lt @t2 @t1)) % 0.37/0.69 (define @t52 () (tptp.lt @t2 @t12)) % 0.37/0.69 (define @t53 () (tptp.gt @t2 @t1)) % 0.37/0.69 (define @t54 () (tptp.memberP @t12 @t2)) % 0.37/0.69 (define @t55 () (tptp.frontsegP @t1 @t12)) % 0.37/0.69 (define @t56 () (tptp.frontsegP @t1 @t2)) % 0.37/0.69 (define @t57 () (and @t20 @t56)) % 0.37/0.69 (define @t58 () (=> @t57 @t3)) % 0.37/0.69 (define @t59 () (forall @t7 (=> @t21 @t58))) % 0.37/0.69 (define @t60 () (=> @t17 @t59)) % 0.37/0.69 (define @t61 () (forall @t9 @t60)) % 0.37/0.69 (define @t62 () (tptp.frontsegP @t2 tptp.nil)) % 0.37/0.69 (define @t63 () (forall @t9 (=> @t17 @t62))) % 0.37/0.69 (define @t64 () (tptp.frontsegP tptp.nil @t2)) % 0.37/0.69 (define @t65 () (tptp.app @t12 @t2)) % 0.37/0.69 (define @t66 () (tptp.cons @t2 tptp.nil)) % 0.37/0.69 (define @t67 () (tptp.hd @t1)) % 0.37/0.69 (define @t68 () (= tptp.nil @t1)) % 0.37/0.69 (define @t69 () (not @t68)) % 0.37/0.69 (define @t70 () (tptp.cons @t2 @t1)) % 0.37/0.69 (define @t71 () (= @t12 @t2)) % 0.37/0.69 (define @t72 () (not (tptp.neq @t12 tptp.nil))) % 0.37/0.69 (define @t73 () (or @t72 (not (tptp.frontsegP @t10 @t12)))) % 0.37/0.69 (define @t74 () (not (= tptp.nil @t12))) % 0.37/0.69 (define @t75 () (not (= tptp.nil @t10))) % 0.37/0.69 (define @t76 () (or @t75 @t74)) % 0.37/0.69 (define @t77 () (and @t76 @t73)) % 0.37/0.69 (define @t78 () (not (= @t2 @t12))) % 0.37/0.69 (define @t79 () (not (= @t1 @t10))) % 0.37/0.69 (define @t80 () (or @t69 @t79 @t78 @t41 @t77)) % 0.37/0.69 (define @t81 () (=> @t13 @t80)) % 0.37/0.69 (define @t82 () (forall @t14 @t81)) % 0.37/0.69 (define @t83 () (=> @t15 @t82)) % 0.37/0.69 (define @t84 () (forall @t16 @t83)) % 0.37/0.69 (define @t85 () (=> @t21 @t84)) % 0.37/0.69 (define @t86 () (forall @t7 @t85)) % 0.37/0.69 (define @t87 () (=> @t17 @t86)) % 0.37/0.69 (define @t88 () (forall @t9 @t87)) % 0.37/0.69 (define @t89 () (not @t88)) % 0.37/0.69 (define @t90 () (not (tptp.neq @t2 tptp.nil))) % 0.37/0.69 (define @t91 () (or @t90 (not @t64))) % 0.37/0.69 (define @t92 () (= @t2 tptp.nil)) % 0.37/0.69 (define @t93 () (not @t92)) % 0.37/0.69 (define @t94 () (and @t93 @t91)) % 0.37/0.69 (define @t95 () (not @t17)) % 0.37/0.69 (define @t96 () (or @t95 @t92 @t94)) % 0.37/0.69 (define @t97 () (forall @t9 @t96)) % 0.37/0.69 (define @t98 () (not @t38)) % 0.37/0.69 (define @t99 () (or @t98 @t96)) % 0.37/0.69 (define @t100 () (or @t95 @t92 @t98 @t94)) % 0.37/0.69 (define @t101 () (or @t92 @t95 @t98 @t94)) % 0.37/0.69 (define @t102 () (or @t98 @t94)) % 0.37/0.69 (define @t103 () (not (= tptp.nil tptp.nil))) % 0.37/0.69 (define @t104 () (or @t103 @t93)) % 0.37/0.69 (define @t105 () (and @t104 @t91)) % 0.37/0.69 (define @t106 () (or @t98 @t103 @t105)) % 0.37/0.69 (define @t107 () (not @t56)) % 0.37/0.69 (define @t108 () (not (= @t1 tptp.nil))) % 0.37/0.69 (define @t109 () (and (or @t108 @t93) (or @t90 @t107))) % 0.37/0.69 (define @t110 () (not @t21)) % 0.37/0.69 (define @t111 () (or @t108 @t110 @t108 @t109)) % 0.37/0.69 (define @t112 () (or @t110 @t108 @t109)) % 0.37/0.69 (define @t113 () (forall @t7 @t112)) % 0.37/0.69 (define @t114 () (or @t92 @t95 @t113)) % 0.37/0.69 (define @t115 () (or @t92 @t95 @t112)) % 0.37/0.69 (define @t116 () (or @t110 @t108 @t92 @t95 @t109)) % 0.37/0.69 (define @t117 () (or @t108 @t92 @t110 @t95 @t109)) % 0.37/0.69 (define @t118 () (or @t95 @t109)) % 0.37/0.69 (define @t119 () (not (= @t2 @t2))) % 0.37/0.69 (define @t120 () (or @t95 @t119 @t109)) % 0.37/0.69 (define @t121 () (not (= @t12 tptp.nil))) % 0.37/0.69 (define @t122 () (and (or @t108 @t121) (or @t72 (not @t55)))) % 0.37/0.69 (define @t123 () (not @t15)) % 0.37/0.69 (define @t124 () (or @t78 @t123 @t78 @t122)) % 0.37/0.69 (define @t125 () (or @t123 @t78 @t122)) % 0.37/0.69 (define @t126 () (forall @t16 @t125)) % 0.37/0.69 (define @t127 () (or @t108 @t92 @t110 @t126)) % 0.37/0.69 (define @t128 () (or @t108 @t92 @t110 @t125)) % 0.37/0.69 (define @t129 () (or @t123 @t108 @t78 @t92 @t110 @t122)) % 0.37/0.69 (define @t130 () (or @t108 @t78 @t92 @t110 @t122)) % 0.37/0.69 (define @t131 () (or @t110 @t122)) % 0.37/0.69 (define @t132 () (not (= @t1 @t1))) % 0.37/0.69 (define @t133 () (or @t110 @t132 @t122)) % 0.37/0.69 (define @t134 () (and (or (not (= @t10 tptp.nil)) @t121) @t73)) % 0.37/0.69 (define @t135 () (not @t13)) % 0.37/0.69 (define @t136 () (or @t79 @t135 @t79 @t134)) % 0.37/0.69 (define @t137 () (or @t135 @t79 @t134)) % 0.37/0.69 (define @t138 () (forall @t14 @t137)) % 0.37/0.69 (define @t139 () (or @t108 @t78 @t92 @t138)) % 0.37/0.69 (define @t140 () (or @t108 @t78 @t92 @t137)) % 0.37/0.69 (define @t141 () (or @t135 @t108 @t79 @t78 @t92 @t134)) % 0.37/0.69 (define @t142 () (or @t108 @t79 @t78 @t92 @t134)) % 0.37/0.69 (define @t143 () (@quantifiers_skolemize @t97 0)) % 0.37/0.69 (define @t144 () (tptp.frontsegP tptp.nil @t143)) % 0.37/0.69 (define @t145 () (not @t144)) % 0.37/0.69 (define @t146 () (or (not (tptp.neq @t143 tptp.nil)) @t145)) % 0.37/0.69 (define @t147 () (= tptp.nil @t143)) % 0.37/0.69 (define @t148 () (not @t147)) % 0.37/0.69 (define @t149 () (and @t148 @t146)) % 0.37/0.69 (define @t150 () (tptp.ssList @t143)) % 0.37/0.69 (define @t151 () (not @t150)) % 0.37/0.69 (define @t152 () (or @t151 @t147 @t149)) % 0.37/0.69 (define @t153 () (not @t152)) % 0.37/0.69 (define @t154 () (not @t97)) % 0.37/0.69 (define @t155 () (= @t143 tptp.nil)) % 0.37/0.69 (define @t156 () (not @t155)) % 0.37/0.69 (define @t157 () (and @t156 @t146)) % 0.37/0.69 (define @t158 () (or @t151 @t155 @t157)) % 0.37/0.69 (define @t159 () (not @t158)) % 0.37/0.69 (define @t160 () (@list true)) % 0.37/0.69 (define @t161 () (@list @t152)) % 0.37/0.69 (define @t162 () (@var "BOUND_VARIABLE_9780" $$unsorted)) % 0.37/0.69 (define @t163 () (= @t2 @t162)) % 0.37/0.69 (define @t164 () (not (tptp.frontsegP @t162 @t2))) % 0.37/0.69 (define @t165 () (not (tptp.frontsegP @t2 @t162))) % 0.37/0.69 (define @t166 () (not (tptp.ssList @t162))) % 0.37/0.69 (define @t167 () (or @t166 @t165 @t164 @t163)) % 0.37/0.69 (define @t168 () (or @t95 @t167)) % 0.37/0.69 (define @t169 () (forall (@list @t2 @t162) @t168)) % 0.37/0.69 (define @t170 () (@list @t162)) % 0.37/0.69 (define @t171 () (forall @t170 @t168)) % 0.37/0.69 (define @t172 () (forall @t170 @t167)) % 0.37/0.69 (define @t173 () (or @t95 @t172)) % 0.37/0.69 (define @t174 () (not @t20)) % 0.37/0.69 (define @t175 () (or @t110 @t174 @t107 @t3)) % 0.37/0.69 (define @t176 () (forall @t7 @t175)) % 0.37/0.69 (define @t177 () (or @t174 @t107 @t3)) % 0.37/0.69 (define @t178 () (not @t146)) % 0.37/0.69 (define @t179 () (tptp.frontsegP @t143 tptp.nil)) % 0.37/0.69 (define @t180 () (not @t179)) % 0.37/0.69 (define @t181 () (or @t98 @t151 @t145 @t180 @t147)) % 0.37/0.69 (define @t182 () (or @t151 @t179)) % 0.37/0.69 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.69 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.37/0.69 (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))))))))))) % 0.37/0.69 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.37/0.69 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.37/0.69 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.37/0.69 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.37/0.69 (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))))))))))))))))) % 0.37/0.69 (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)))))))))))))))) % 0.37/0.69 (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))))))))))))))))) % 0.37/0.69 (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))))))))))))))) % 0.37/0.69 (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))))))))))))))) % 0.37/0.69 (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)))))))))))))))) % 0.37/0.69 (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))))))))))))) % 0.37/0.69 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.37/0.69 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.37/0.69 (assume @p17 @t38) % 0.37/0.69 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.37/0.69 (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))))))))))) % 0.37/0.69 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t40 @t2))))))))) % 0.37/0.69 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.37/0.69 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.37/0.69 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.37/0.69 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.37/0.69 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.37/0.69 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t45)))))) % 0.37/0.69 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.37/0.69 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.37/0.69 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.37/0.69 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t26) (tptp.leq @t2 @t12))))))))) % 0.37/0.69 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.37/0.69 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.37/0.69 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.37/0.69 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t52)))))))) % 0.37/0.69 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.37/0.69 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t54))))))))) % 0.37/0.69 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t54))))))))) % 0.37/0.69 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.37/0.69 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.37/0.69 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 @t55) (tptp.frontsegP @t2 @t12))))))))) % 0.37/0.69 (assume @p41 @t61) % 0.37/0.69 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.37/0.69 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.37/0.69 (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)))))))))))) % 0.37/0.69 (assume @p45 @t63) % 0.37/0.69 (assume @p46 (forall @t9 (=> @t17 (= @t64 @t41)))) % 0.37/0.69 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.37/0.69 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.37/0.69 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.37/0.69 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t65 @t1))))))))) % 0.37/0.69 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.37/0.69 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t41)))) % 0.37/0.69 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.37/0.69 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.37/0.69 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.37/0.69 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t65 @t10) @t1))))))))))) % 0.37/0.69 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.37/0.69 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t41)))) % 0.37/0.69 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t66)))) % 0.37/0.69 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.37/0.69 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t66)))) % 0.37/0.69 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.37/0.69 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t66)))) % 0.37/0.69 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.37/0.69 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t66)))) % 0.37/0.69 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.37/0.69 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t70) (or @t68 (and @t69 (tptp.totalorderedP @t1) (tptp.leq @t2 @t67))))))))) % 0.37/0.69 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t66)))) % 0.37/0.69 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.37/0.69 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t70) (or @t68 (and @t69 (tptp.strictorderedP @t1) (tptp.lt @t2 @t67))))))))) % 0.37/0.69 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t66)))) % 0.37/0.69 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.37/0.69 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t66)))) % 0.37/0.69 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.37/0.69 (assume @p75 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t6 (= @t42 @t1))))))) % 0.37/0.69 (assume @p76 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t21 (= @t44 @t1))))))) % 0.37/0.69 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t69 @t43 (= @t67 @t42) (= (tptp.tl @t1) @t44)) @t39)))))) % 0.37/0.69 (assume @p78 (forall @t9 (=> @t17 (=> @t43 (= (tptp.cons @t42 @t44) @t2))))) % 0.37/0.69 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t45) @t71)))))))) % 0.37/0.69 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t46) @t71)))))))) % 0.37/0.69 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.37/0.69 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t45 @t12) (tptp.app @t2 @t19))))))))) % 0.37/0.69 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t45) (and @t68 @t41))))))) % 0.37/0.69 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.37/0.69 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.hd @t45) @t42))))))) % 0.37/0.69 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t43 (= (tptp.tl @t45) (tptp.app @t44 @t1)))))))) % 0.37/0.69 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 (tptp.geq @t1 @t2)) @t3)))))) % 0.37/0.69 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t49 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.37/0.69 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.37/0.69 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.37/0.69 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t35) @t52)))))))) % 0.37/0.69 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t48 (or @t3 @t51))))))) % 0.37/0.69 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t51 (and @t4 @t48))))))) % 0.37/0.69 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (not (tptp.gt @t1 @t2)))))))) % 0.37/0.69 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t53 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.37/0.69 (assume @p96 @t89) % 0.37/0.69 (assume @p97 true) % 0.37/0.69 (step @p98 :rule quant-miniscope-or :args ((= (forall @t9 @t99) (or @t98 @t97)))) % 0.37/0.69 (step @p99 :rule aci_norm :args ((= @t100 @t99))) % 0.37/0.69 (step @p100 :rule cong :premises (@p99) :args ((forall @t9 @t100))) % 0.37/0.69 (step @p101 :rule trans :premises (@p100 @p98)) % 0.37/0.69 (step @p102 :rule aci_norm :args ((= (or @t95 @t101) @t100))) % 0.37/0.69 (step @p103 :rule bool-impl-elim :args (@t17 @t101)) % 0.37/0.69 (step @p104 :rule trans :premises (@p103 @p102)) % 0.37/0.69 (step @p105 :rule cong :premises (@p104) :args ((forall @t9 (=> @t17 @t101)))) % 0.37/0.69 (step @p106 :rule trans :premises (@p105 @p101)) % 0.37/0.69 (step @p107 :rule aci_norm :args ((= (or @t92 @t95 @t102) @t101))) % 0.37/0.69 (step @p108 :rule aci_norm :args ((= (or @t98 false @t94) @t102))) % 0.37/0.69 (step @p109 :rule refl :args (@t91)) % 0.37/0.69 (step @p110 :rule aci_norm :args ((= (or false @t93) @t93))) % 0.37/0.69 (step @p111 :rule refl :args (@t93)) % 0.37/0.69 (step @p112 :rule evaluate :args ((not true))) % 0.37/0.69 (step @p113 :rule eq-refl :args (tptp.nil)) % 0.37/0.69 (step @p114 :rule cong :premises (@p113) :args (@t103)) % 0.37/0.69 (step @p115 :rule trans :premises (@p114 @p112)) % 0.37/0.69 (step @p116 :rule nary_cong :premises (@p115 @p111) :args (@t104)) % 0.37/0.69 (step @p117 :rule trans :premises (@p116 @p110)) % 0.37/0.69 (step @p118 :rule nary_cong :premises (@p117 @p109) :args (@t105)) % 0.37/0.69 (step @p119 :rule refl :args (@t98)) % 0.37/0.69 (step @p120 :rule nary_cong :premises (@p119 @p115 @p118) :args (@t106)) % 0.37/0.69 (step @p121 :rule trans :premises (@p120 @p108)) % 0.37/0.69 (step @p122 :rule quant-var-elim-eq :args ((= (forall @t7 @t111) @t106))) % 0.37/0.69 (step @p123 :rule aci_norm :args ((= @t112 @t111))) % 0.37/0.69 (step @p124 :rule cong :premises (@p123) :args (@t113)) % 0.37/0.69 (step @p125 :rule trans :premises (@p124 @p122)) % 0.37/0.69 (step @p126 :rule trans :premises (@p125 @p121)) % 0.37/0.69 (step @p127 :rule refl :args (@t95)) % 0.37/0.69 (step @p128 :rule refl :args (@t92)) % 0.37/0.69 (step @p129 :rule nary_cong :premises (@p128 @p127 @p126) :args (@t114)) % 0.37/0.69 (step @p130 :rule trans :premises (@p129 @p107)) % 0.37/0.69 (step @p131 :rule quant-miniscope-or :args ((= (forall @t7 @t115) @t114))) % 0.37/0.69 (step @p132 :rule aci_norm :args ((= @t116 @t115))) % 0.37/0.69 (step @p133 :rule cong :premises (@p132) :args ((forall @t7 @t116))) % 0.37/0.69 (step @p134 :rule trans :premises (@p133 @p131)) % 0.37/0.69 (step @p135 :rule trans :premises (@p134 @p130)) % 0.37/0.69 (step @p136 :rule aci_norm :args ((= (or @t110 @t117) @t116))) % 0.37/0.69 (step @p137 :rule bool-impl-elim :args (@t21 @t117)) % 0.37/0.69 (step @p138 :rule trans :premises (@p137 @p136)) % 0.37/0.69 (step @p139 :rule cong :premises (@p138) :args ((forall @t7 (=> @t21 @t117)))) % 0.37/0.69 (step @p140 :rule trans :premises (@p139 @p135)) % 0.37/0.69 (step @p141 :rule aci_norm :args ((= (or @t108 @t92 @t110 @t118) @t117))) % 0.37/0.69 (step @p142 :rule aci_norm :args ((= (or @t95 false @t109) @t118))) % 0.37/0.69 (step @p143 :rule refl :args (@t109)) % 0.37/0.69 (step @p144 :rule eq-refl :args (@t2)) % 0.37/0.69 (step @p145 :rule cong :premises (@p144) :args (@t119)) % 0.37/0.69 (step @p146 :rule trans :premises (@p145 @p112)) % 0.37/0.69 (step @p147 :rule nary_cong :premises (@p127 @p146 @p143) :args (@t120)) % 0.37/0.69 (step @p148 :rule trans :premises (@p147 @p142)) % 0.37/0.69 (step @p149 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t71) @t123 @t78 @t122)) @t120))) % 0.37/0.69 (step @p150 :rule refl :args (@t122)) % 0.37/0.69 (step @p151 :rule refl :args (@t78)) % 0.37/0.69 (step @p152 :rule refl :args (@t123)) % 0.37/0.69 (step @p153 :rule eq-symm :args (@t2 @t12)) % 0.37/0.69 (step @p154 :rule cong :premises (@p153) :args (@t78)) % 0.37/0.69 (step @p155 :rule nary_cong :premises (@p154 @p152 @p151 @p150) :args (@t124)) % 0.37/0.69 (step @p156 :rule aci_norm :args ((= @t125 @t124))) % 0.37/0.69 (step @p157 :rule trans :premises (@p156 @p155)) % 0.37/0.69 (step @p158 :rule cong :premises (@p157) :args (@t126)) % 0.37/0.69 (step @p159 :rule trans :premises (@p158 @p149)) % 0.37/0.69 (step @p160 :rule trans :premises (@p159 @p148)) % 0.37/0.69 (step @p161 :rule refl :args (@t110)) % 0.37/0.69 (step @p162 :rule refl :args (@t108)) % 0.37/0.69 (step @p163 :rule nary_cong :premises (@p162 @p128 @p161 @p160) :args (@t127)) % 0.37/0.69 (step @p164 :rule trans :premises (@p163 @p141)) % 0.37/0.69 (step @p165 :rule quant-miniscope-or :args ((= (forall @t16 @t128) @t127))) % 0.37/0.69 (step @p166 :rule aci_norm :args ((= @t129 @t128))) % 0.37/0.69 (step @p167 :rule cong :premises (@p166) :args ((forall @t16 @t129))) % 0.37/0.69 (step @p168 :rule trans :premises (@p167 @p165)) % 0.37/0.69 (step @p169 :rule trans :premises (@p168 @p164)) % 0.37/0.69 (step @p170 :rule aci_norm :args ((= (or @t123 @t130) @t129))) % 0.37/0.69 (step @p171 :rule bool-impl-elim :args (@t15 @t130)) % 0.37/0.69 (step @p172 :rule trans :premises (@p171 @p170)) % 0.37/0.69 (step @p173 :rule cong :premises (@p172) :args ((forall @t16 (=> @t15 @t130)))) % 0.37/0.69 (step @p174 :rule trans :premises (@p173 @p169)) % 0.37/0.69 (step @p175 :rule aci_norm :args ((= (or @t108 @t78 @t92 @t131) @t130))) % 0.37/0.69 (step @p176 :rule aci_norm :args ((= (or @t110 false @t122) @t131))) % 0.37/0.69 (step @p177 :rule refl :args (@t122)) % 0.37/0.69 (step @p178 :rule eq-refl :args (@t1)) % 0.37/0.69 (step @p179 :rule cong :premises (@p178) :args (@t132)) % 0.37/0.69 (step @p180 :rule trans :premises (@p179 @p112)) % 0.37/0.69 (step @p181 :rule nary_cong :premises (@p161 @p180 @p177) :args (@t133)) % 0.37/0.69 (step @p182 :rule trans :premises (@p181 @p176)) % 0.37/0.69 (step @p183 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t135 @t79 @t134)) @t133))) % 0.37/0.69 (step @p184 :rule refl :args (@t134)) % 0.37/0.69 (step @p185 :rule refl :args (@t79)) % 0.37/0.69 (step @p186 :rule refl :args (@t135)) % 0.37/0.69 (step @p187 :rule eq-symm :args (@t1 @t10)) % 0.37/0.69 (step @p188 :rule cong :premises (@p187) :args (@t79)) % 0.37/0.69 (step @p189 :rule nary_cong :premises (@p188 @p186 @p185 @p184) :args (@t136)) % 0.37/0.69 (step @p190 :rule aci_norm :args ((= @t137 @t136))) % 0.37/0.69 (step @p191 :rule trans :premises (@p190 @p189)) % 0.37/0.69 (step @p192 :rule cong :premises (@p191) :args (@t138)) % 0.37/0.69 (step @p193 :rule trans :premises (@p192 @p183)) % 0.37/0.69 (step @p194 :rule trans :premises (@p193 @p182)) % 0.37/0.69 (step @p195 :rule refl :args (@t78)) % 0.37/0.69 (step @p196 :rule nary_cong :premises (@p162 @p195 @p128 @p194) :args (@t139)) % 0.37/0.69 (step @p197 :rule trans :premises (@p196 @p175)) % 0.37/0.69 (step @p198 :rule quant-miniscope-or :args ((= (forall @t14 @t140) @t139))) % 0.37/0.69 (step @p199 :rule aci_norm :args ((= @t141 @t140))) % 0.37/0.69 (step @p200 :rule cong :premises (@p199) :args ((forall @t14 @t141))) % 0.37/0.69 (step @p201 :rule trans :premises (@p200 @p198)) % 0.37/0.69 (step @p202 :rule trans :premises (@p201 @p197)) % 0.37/0.69 (step @p203 :rule aci_norm :args ((= (or @t135 @t142) @t141))) % 0.37/0.69 (step @p204 :rule bool-impl-elim :args (@t13 @t142)) % 0.37/0.69 (step @p205 :rule trans :premises (@p204 @p203)) % 0.37/0.69 (step @p206 :rule cong :premises (@p205) :args ((forall @t14 (=> @t13 @t142)))) % 0.37/0.69 (step @p207 :rule trans :premises (@p206 @p202)) % 0.37/0.69 (step @p208 :rule refl :args (@t73)) % 0.37/0.69 (step @p209 :rule eq-symm :args (tptp.nil @t12)) % 0.37/0.69 (step @p210 :rule cong :premises (@p209) :args (@t74)) % 0.37/0.69 (step @p211 :rule eq-symm :args (tptp.nil @t10)) % 0.37/0.69 (step @p212 :rule cong :premises (@p211) :args (@t75)) % 0.37/0.69 (step @p213 :rule nary_cong :premises (@p212 @p210) :args (@t76)) % 0.37/0.69 (step @p214 :rule nary_cong :premises (@p213 @p208) :args (@t77)) % 0.37/0.69 (step @p215 :rule eq-symm :args (tptp.nil @t2)) % 0.37/0.69 (step @p216 :rule refl :args (@t79)) % 0.37/0.69 (step @p217 :rule eq-symm :args (tptp.nil @t1)) % 0.37/0.69 (step @p218 :rule cong :premises (@p217) :args (@t69)) % 0.37/0.69 (step @p219 :rule nary_cong :premises (@p218 @p216 @p195 @p215 @p214) :args (@t80)) % 0.37/0.69 (step @p220 :rule refl :args (@t13)) % 0.37/0.69 (step @p221 :rule cong :premises (@p220 @p219) :args (@t81)) % 0.37/0.69 (step @p222 :rule cong :premises (@p221) :args (@t82)) % 0.37/0.69 (step @p223 :rule trans :premises (@p222 @p207)) % 0.37/0.69 (step @p224 :rule refl :args (@t15)) % 0.37/0.69 (step @p225 :rule cong :premises (@p224 @p223) :args (@t83)) % 0.37/0.69 (step @p226 :rule cong :premises (@p225) :args (@t84)) % 0.37/0.69 (step @p227 :rule trans :premises (@p226 @p174)) % 0.37/0.69 (step @p228 :rule refl :args (@t21)) % 0.37/0.69 (step @p229 :rule cong :premises (@p228 @p227) :args (@t85)) % 0.37/0.69 (step @p230 :rule cong :premises (@p229) :args (@t86)) % 0.37/0.69 (step @p231 :rule trans :premises (@p230 @p140)) % 0.37/0.69 (step @p232 :rule refl :args (@t17)) % 0.37/0.69 (step @p233 :rule cong :premises (@p232 @p231) :args (@t87)) % 0.37/0.69 (step @p234 :rule cong :premises (@p233) :args (@t88)) % 0.37/0.69 (step @p235 :rule trans :premises (@p234 @p106)) % 0.37/0.69 (step @p236 :rule cong :premises (@p235) :args (@t89)) % 0.37/0.69 (step @p237 :rule eq_resolve :premises (@p96 @p236)) % 0.37/0.69 (step @p238 :rule not_or_elim :premises (@p237) :args (1)) % 0.37/0.69 (step @p239 :rule refl :args (@t153)) % 0.37/0.69 (step @p240 :rule bool-double-not-elim :args (@t97)) % 0.37/0.69 (step @p241 :rule nary_cong :premises (@p240 @p239) :args ((or (not @t154) @t153))) % 0.37/0.69 (step @p242 :rule refl :args (@t146)) % 0.37/0.69 (step @p243 :rule eq-symm :args (@t143 tptp.nil)) % 0.37/0.69 (step @p244 :rule cong :premises (@p243) :args (@t156)) % 0.37/0.69 (step @p245 :rule nary_cong :premises (@p244 @p242) :args (@t157)) % 0.37/0.69 (step @p246 :rule refl :args (@t151)) % 0.37/0.69 (step @p247 :rule nary_cong :premises (@p246 @p243 @p245) :args (@t158)) % 0.37/0.69 (step @p248 :rule cong :premises (@p247) :args (@t159)) % 0.37/0.69 (step @p249 :rule refl :args (@t154)) % 0.37/0.69 (step @p250 :rule cong :premises (@p249 @p248) :args ((=> @t154 @t159))) % 0.37/0.69 (assume-push @p331 @t154) % 0.37/0.69 (step @p252 :rule skolemize :premises (@p238)) % 0.37/0.69 (step-pop @p332 :rule scope :premises (@p252)) % 0.37/0.69 (step @p253 :rule process_scope :premises (@p332) :args (@t159)) % 0.37/0.69 (step @p255 :rule eq_resolve :premises (@p253 @p250)) % 0.37/0.69 (step @p256 :rule implies_elim :premises (@p255)) % 0.37/0.69 (step @p257 :rule eq_resolve :premises (@p256 @p241)) % 0.37/0.69 (step @p258 :rule chain_m_resolution :premises (@p257 @p238) :args (@t153 @t160 (@list @t97))) % 0.37/0.69 (step @p259 :rule bool-double-not-elim :args (@t150)) % 0.37/0.69 (step @p260 :rule refl :args (@t152)) % 0.37/0.69 (step @p261 :rule nary_cong :premises (@p260 @p259) :args ((or @t152 (not @t151)))) % 0.37/0.69 (step @p262 :rule cnf_or_neg :args (@t152 0)) % 0.37/0.69 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.37/0.69 (step @p264 :rule reordering :premises (@p263) :args ((or @t150 @t152))) % 0.37/0.69 (step @p265 :rule chain_m_resolution :premises (@p264 @p258) :args (@t150 @t160 @t161)) % 0.37/0.69 (step @p266 :rule bool-impl-elim :args (@t17 @t62)) % 0.37/0.69 (step @p267 :rule cong :premises (@p266) :args (@t63)) % 0.37/0.69 (step @p268 :rule eq_resolve :premises (@p45 @p267)) % 0.37/0.69 (step @p269 :rule instantiate :premises (@p268) :args ((@list @t143))) % 0.37/0.69 (step @p270 :rule aci_norm :args ((= @t168 (or @t95 @t166 @t165 @t164 @t163)))) % 0.37/0.69 (step @p271 :rule cong :premises (@p270) :args (@t169)) % 0.37/0.69 (step @p272 :rule quant-merge-prenex :args ((= (forall @t9 @t171) @t169))) % 0.37/0.69 (step @p273 :rule alpha_equiv :args (@t172 (@list @t162) (@list @t1))) % 0.37/0.69 (step @p274 :rule refl :args (@t95)) % 0.37/0.69 (step @p275 :rule nary_cong :premises (@p274 @p273) :args (@t173)) % 0.37/0.69 (step @p276 :rule quant-miniscope-or :args ((= @t171 @t173))) % 0.37/0.69 (step @p277 :rule trans :premises (@p276 @p275)) % 0.37/0.69 (step @p278 :rule symm :premises (@p277)) % 0.37/0.69 (step @p279 :rule cong :premises (@p278) :args ((forall @t9 (or @t95 @t176)))) % 0.37/0.69 (step @p280 :rule trans :premises (@p279 @p272)) % 0.37/0.69 (step @p281 :rule trans :premises (@p280 @p271)) % 0.37/0.69 (step @p282 :rule bool-impl-elim :args (@t17 @t176)) % 0.37/0.69 (step @p283 :rule cong :premises (@p282) :args ((forall @t9 (=> @t17 @t176)))) % 0.37/0.69 (step @p284 :rule trans :premises (@p283 @p281)) % 0.37/0.69 (step @p285 :rule aci_norm :args ((= (or @t110 @t177) @t175))) % 0.37/0.69 (step @p286 :rule aci_norm :args ((= (or (or @t174 @t107) @t3) @t177))) % 0.37/0.69 (step @p287 :rule refl :args (@t3)) % 0.37/0.69 (step @p288 :rule bool-and-de-morgan :args (@t20 @t56 true)) % 0.37/0.69 (step @p289 :rule nary_cong :premises (@p288 @p287) :args ((or (not @t57) @t3))) % 0.37/0.69 (step @p290 :rule trans :premises (@p289 @p286)) % 0.37/0.69 (step @p291 :rule bool-impl-elim :args (@t57 @t3)) % 0.37/0.69 (step @p292 :rule trans :premises (@p291 @p290)) % 0.37/0.69 (step @p293 :rule refl :args (@t110)) % 0.37/0.69 (step @p294 :rule nary_cong :premises (@p293 @p292) :args ((or @t110 @t58))) % 0.37/0.69 (step @p295 :rule trans :premises (@p294 @p285)) % 0.37/0.69 (step @p296 :rule bool-impl-elim :args (@t21 @t58)) % 0.37/0.69 (step @p297 :rule trans :premises (@p296 @p295)) % 0.37/0.69 (step @p298 :rule cong :premises (@p297) :args (@t59)) % 0.37/0.69 (step @p299 :rule cong :premises (@p232 @p298) :args (@t60)) % 0.37/0.69 (step @p300 :rule cong :premises (@p299) :args (@t61)) % 0.37/0.69 (step @p301 :rule trans :premises (@p300 @p284)) % 0.37/0.69 (step @p302 :rule eq_resolve :premises (@p41 @p301)) % 0.37/0.69 (step @p303 :rule instantiate :premises (@p302) :args ((@list tptp.nil @t143))) % 0.37/0.69 (step @p304 :rule cnf_or_neg :args (@t152 1)) % 0.37/0.69 (step @p305 :rule reordering :premises (@p304) :args ((or @t148 @t152))) % 0.37/0.69 (step @p306 :rule chain_m_resolution :premises (@p305 @p258) :args (@t148 @t160 @t161)) % 0.37/0.69 (step @p307 :rule cnf_or_neg :args (@t152 2)) % 0.37/0.69 (step @p308 :rule chain_m_resolution :premises (@p307 @p258) :args ((not @t149) @t160 @t161)) % 0.37/0.69 (step @p309 :rule refl :args (@t178)) % 0.37/0.69 (step @p310 :rule bool-double-not-elim :args (@t147)) % 0.37/0.69 (step @p311 :rule refl :args (@t149)) % 0.37/0.69 (step @p312 :rule nary_cong :premises (@p311 @p310 @p309) :args ((or @t149 (not @t148) @t178))) % 0.37/0.69 (step @p313 :rule cnf_and_neg :args (@t149)) % 0.37/0.69 (step @p314 :rule eq_resolve :premises (@p313 @p312)) % 0.37/0.69 (step @p315 :rule reordering :premises (@p314) :args ((or @t147 @t149 @t178))) % 0.37/0.69 (step @p316 :rule chain_m_resolution :premises (@p315 @p306 @p308) :args (@t178 (@list true true) (@list @t147 @t149))) % 0.37/0.69 (step @p317 :rule bool-double-not-elim :args (@t144)) % 0.37/0.69 (step @p318 :rule nary_cong :premises (@p242 @p317) :args ((or @t146 (not @t145)))) % 0.37/0.69 (step @p319 :rule cnf_or_neg :args (@t146 1)) % 0.37/0.69 (step @p320 :rule eq_resolve :premises (@p319 @p318)) % 0.37/0.69 (step @p321 :rule reordering :premises (@p320) :args ((or @t144 @t146))) % 0.37/0.69 (step @p322 :rule chain_m_resolution :premises (@p321 @p316) :args (@t144 @t160 (@list @t146))) % 0.37/0.69 (step @p323 :rule not_or_elim :premises (@p237) :args (0)) % 0.37/0.69 (step @p324 :rule not_not_elim :premises (@p323)) % 0.37/0.69 (step @p325 :rule cnf_or_pos :args (@t181)) % 0.37/0.69 (step @p326 :rule reordering :premises (@p325) :args ((or @t98 @t151 @t145 @t147 @t180 (not @t181)))) % 0.37/0.69 (step @p327 :rule chain_m_resolution :premises (@p326 @p324 @p265 @p322 @p306 @p303) :args (@t180 (@list false false false true false) (@list @t38 @t150 @t144 @t147 @t181))) % 0.37/0.69 (step @p328 :rule cnf_or_pos :args (@t182)) % 0.37/0.69 (step @p329 :rule reordering :premises (@p328) :args ((or @t151 @t179 (not @t182)))) % 0.37/0.69 (step @p330 false :rule chain_m_resolution :premises (@p329 @p327 @p269 @p265) :args (false (@list true false false) (@list @t179 @t182 @t150))) % 0.37/0.69 ) % 0.37/0.69 % SZS output end Proof % 0.37/0.69 % cvc5 exiting %------------------------------------------------------------------------------