%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC016+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:57:42 AM UTC 2026 % Result : Theorem 0.37s 0.72s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC016+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n005.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 19:09:33 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.72 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.72 % SZS status Theorem % 0.37/0.72 % SZS output start Proof % 0.37/0.72 ( % 0.37/0.72 (declare-sort $$unsorted 0) % 0.37/0.72 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.37/0.72 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.37/0.72 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.72 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.72 (declare-const tptp.nil $$unsorted) % 0.37/0.72 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.37/0.72 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.72 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.72 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.72 (define @t3 () (= @t2 @t1)) % 0.37/0.72 (define @t4 () (not @t3)) % 0.37/0.72 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.37/0.72 (define @t6 () (tptp.ssItem @t1)) % 0.37/0.72 (define @t7 () (@list @t1)) % 0.37/0.72 (define @t8 () (tptp.ssItem @t2)) % 0.37/0.72 (define @t9 () (@list @t2)) % 0.37/0.72 (define @t10 () (@var "X" $$unsorted)) % 0.37/0.72 (define @t11 () (tptp.cons @t1 @t10)) % 0.37/0.72 (define @t12 () (@var "W" $$unsorted)) % 0.37/0.72 (define @t13 () (tptp.ssList @t10)) % 0.37/0.72 (define @t14 () (@list @t10)) % 0.37/0.72 (define @t15 () (tptp.ssList @t12)) % 0.37/0.72 (define @t16 () (@list @t12)) % 0.37/0.72 (define @t17 () (tptp.ssList @t2)) % 0.37/0.72 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.37/0.72 (define @t19 () (tptp.app @t1 @t12)) % 0.37/0.72 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.37/0.72 (define @t21 () (tptp.ssList @t1)) % 0.37/0.72 (define @t22 () (tptp.app @t12 @t1)) % 0.37/0.72 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.37/0.72 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.37/0.72 (define @t25 () (tptp.leq @t12 @t1)) % 0.37/0.72 (define @t26 () (tptp.leq @t1 @t12)) % 0.37/0.72 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.72 (define @t28 () (@var "Y" $$unsorted)) % 0.37/0.72 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.37/0.72 (define @t30 () (tptp.ssList @t27)) % 0.37/0.72 (define @t31 () (@list @t27)) % 0.37/0.72 (define @t32 () (tptp.ssList @t28)) % 0.37/0.72 (define @t33 () (@list @t28)) % 0.37/0.72 (define @t34 () (tptp.ssItem @t12)) % 0.37/0.72 (define @t35 () (tptp.lt @t1 @t12)) % 0.37/0.72 (define @t36 () (= @t1 @t12)) % 0.37/0.72 (define @t37 () (tptp.cons @t1 @t2)) % 0.37/0.72 (define @t38 () (= @t1 @t2)) % 0.37/0.72 (define @t39 () (tptp.cons @t12 @t1)) % 0.37/0.72 (define @t40 () (= tptp.nil @t2)) % 0.37/0.72 (define @t41 () (tptp.hd @t2)) % 0.37/0.72 (define @t42 () (not @t40)) % 0.37/0.72 (define @t43 () (tptp.tl @t2)) % 0.37/0.72 (define @t44 () (tptp.app @t2 @t1)) % 0.37/0.72 (define @t45 () (tptp.app @t1 @t2)) % 0.37/0.72 (define @t46 () (tptp.leq @t1 @t2)) % 0.37/0.72 (define @t47 () (tptp.leq @t2 @t1)) % 0.37/0.72 (define @t48 () (tptp.geq @t2 @t1)) % 0.37/0.72 (define @t49 () (tptp.lt @t1 @t2)) % 0.37/0.72 (define @t50 () (tptp.lt @t2 @t1)) % 0.37/0.72 (define @t51 () (tptp.lt @t2 @t12)) % 0.37/0.72 (define @t52 () (tptp.gt @t2 @t1)) % 0.37/0.72 (define @t53 () (tptp.memberP @t12 @t2)) % 0.37/0.72 (define @t54 () (tptp.app @t12 @t2)) % 0.37/0.72 (define @t55 () (tptp.cons @t2 tptp.nil)) % 0.37/0.72 (define @t56 () (tptp.hd @t1)) % 0.37/0.72 (define @t57 () (= tptp.nil @t1)) % 0.37/0.72 (define @t58 () (not @t57)) % 0.37/0.72 (define @t59 () (tptp.cons @t2 @t1)) % 0.37/0.72 (define @t60 () (= @t12 @t2)) % 0.37/0.72 (define @t61 () (tptp.frontsegP @t2 @t27)) % 0.37/0.72 (define @t62 () (tptp.frontsegP @t1 @t27)) % 0.37/0.72 (define @t63 () (tptp.neq @t27 tptp.nil)) % 0.37/0.72 (define @t64 () (and @t30 @t63 @t62 @t61)) % 0.37/0.72 (define @t65 () (exists @t31 @t64)) % 0.37/0.72 (define @t66 () (tptp.neq @t1 tptp.nil)) % 0.37/0.72 (define @t67 () (not @t66)) % 0.37/0.72 (define @t68 () (or @t67 @t65)) % 0.37/0.72 (define @t69 () (or @t58 @t40)) % 0.37/0.72 (define @t70 () (and @t69 @t68)) % 0.37/0.72 (define @t71 () (tptp.neq @t10 tptp.nil)) % 0.37/0.72 (define @t72 () (not (tptp.frontsegP @t12 @t28))) % 0.37/0.72 (define @t73 () (not (tptp.frontsegP @t10 @t28))) % 0.37/0.72 (define @t74 () (not (tptp.neq @t28 tptp.nil))) % 0.37/0.72 (define @t75 () (or @t74 @t73 @t72)) % 0.37/0.72 (define @t76 () (forall @t33 (=> @t32 @t75))) % 0.37/0.72 (define @t77 () (and @t76 @t71)) % 0.37/0.72 (define @t78 () (not (= tptp.nil @t12))) % 0.37/0.72 (define @t79 () (and @t78 (= tptp.nil @t10))) % 0.37/0.72 (define @t80 () (not (= @t2 @t12))) % 0.37/0.72 (define @t81 () (not (= @t1 @t10))) % 0.37/0.72 (define @t82 () (or @t81 @t80 @t79 @t77 @t70)) % 0.37/0.72 (define @t83 () (=> @t13 @t82)) % 0.37/0.72 (define @t84 () (forall @t14 @t83)) % 0.37/0.72 (define @t85 () (=> @t15 @t84)) % 0.37/0.72 (define @t86 () (forall @t16 @t85)) % 0.37/0.72 (define @t87 () (=> @t21 @t86)) % 0.37/0.72 (define @t88 () (forall @t7 @t87)) % 0.37/0.72 (define @t89 () (=> @t17 @t88)) % 0.37/0.72 (define @t90 () (forall @t9 @t89)) % 0.37/0.72 (define @t91 () (not @t90)) % 0.37/0.72 (define @t92 () (@var "BOUND_VARIABLE_11091" $$unsorted)) % 0.37/0.72 (define @t93 () (tptp.neq @t92 tptp.nil)) % 0.37/0.72 (define @t94 () (@var "BOUND_VARIABLE_11093" $$unsorted)) % 0.37/0.72 (define @t95 () (and (or (not (tptp.ssList @t94)) (not (tptp.neq @t94 tptp.nil)) (not (tptp.frontsegP @t92 @t94)) (not (tptp.frontsegP @t2 @t94))) @t93)) % 0.37/0.72 (define @t96 () (= @t2 tptp.nil)) % 0.37/0.72 (define @t97 () (not @t96)) % 0.37/0.72 (define @t98 () (= @t92 tptp.nil)) % 0.37/0.72 (define @t99 () (and @t97 @t98)) % 0.37/0.72 (define @t100 () (not @t61)) % 0.37/0.72 (define @t101 () (not @t63)) % 0.37/0.72 (define @t102 () (not @t30)) % 0.37/0.72 (define @t103 () (or (not @t93) (not (forall @t31 (or @t102 @t101 (not (tptp.frontsegP @t92 @t27)) @t100))))) % 0.37/0.72 (define @t104 () (not @t98)) % 0.37/0.72 (define @t105 () (or @t104 @t96)) % 0.37/0.72 (define @t106 () (and @t105 @t103)) % 0.37/0.72 (define @t107 () (not (tptp.ssList @t92))) % 0.37/0.72 (define @t108 () (not @t17)) % 0.37/0.72 (define @t109 () (or @t108 @t107 @t106 @t99 @t95)) % 0.37/0.72 (define @t110 () (or @t107 @t106 @t99 @t95)) % 0.37/0.72 (define @t111 () (or @t108 @t110)) % 0.37/0.72 (define @t112 () (@list @t2 @t92 @t94)) % 0.37/0.72 (define @t113 () (forall @t112 @t111)) % 0.37/0.72 (define @t114 () (@list @t92 @t94)) % 0.37/0.72 (define @t115 () (forall @t114 @t111)) % 0.37/0.72 (define @t116 () (forall @t114 @t110)) % 0.37/0.72 (define @t117 () (@var "BOUND_VARIABLE_11072" $$unsorted)) % 0.37/0.72 (define @t118 () (or @t108 @t116)) % 0.37/0.72 (define @t119 () (or (not (tptp.ssList @t117)) (not (tptp.neq @t117 tptp.nil)) (not (tptp.frontsegP @t1 @t117)) (not (tptp.frontsegP @t2 @t117)))) % 0.37/0.72 (define @t120 () (and @t119 @t66)) % 0.37/0.72 (define @t121 () (= @t1 tptp.nil)) % 0.37/0.72 (define @t122 () (and @t97 @t121)) % 0.37/0.72 (define @t123 () (not @t62)) % 0.37/0.72 (define @t124 () (or @t102 @t101 @t123 @t100)) % 0.37/0.72 (define @t125 () (and (or (not @t121) @t96) (or @t67 (not (forall @t31 @t124))))) % 0.37/0.72 (define @t126 () (not @t21)) % 0.37/0.72 (define @t127 () (or @t126 @t125 @t122 @t120)) % 0.37/0.72 (define @t128 () (forall (@list @t1 @t117) @t127)) % 0.37/0.72 (define @t129 () (or @t108 @t128)) % 0.37/0.72 (define @t130 () (@list @t117)) % 0.37/0.72 (define @t131 () (forall @t130 @t127)) % 0.37/0.72 (define @t132 () (forall @t130 @t66)) % 0.37/0.72 (define @t133 () (forall @t130 @t119)) % 0.37/0.72 (define @t134 () (@var "BOUND_VARIABLE_11046" $$unsorted)) % 0.37/0.72 (define @t135 () (@list @t134)) % 0.37/0.72 (define @t136 () (and @t133 @t132)) % 0.37/0.72 (define @t137 () (forall @t130 @t120)) % 0.37/0.72 (define @t138 () (or @t126 @t125 @t122 @t137)) % 0.37/0.72 (define @t139 () (and (forall (@list @t134) (or (not (tptp.ssList @t134)) (not (tptp.neq @t134 tptp.nil)) (not (tptp.frontsegP @t1 @t134)) (not (tptp.frontsegP @t2 @t134)))) @t66)) % 0.37/0.72 (define @t140 () (or @t126 @t125 @t122 @t139)) % 0.37/0.72 (define @t141 () (forall @t7 @t140)) % 0.37/0.72 (define @t142 () (or @t108 @t141)) % 0.37/0.72 (define @t143 () (or @t108 @t140)) % 0.37/0.72 (define @t144 () (or @t126 @t125 @t108 @t122 @t139)) % 0.37/0.72 (define @t145 () (or @t125 @t126 @t108 @t122 @t139)) % 0.37/0.72 (define @t146 () (@var "BOUND_VARIABLE_11016" $$unsorted)) % 0.37/0.72 (define @t147 () (@list @t146)) % 0.37/0.72 (define @t148 () (forall @t147 @t66)) % 0.37/0.72 (define @t149 () (not (tptp.frontsegP @t1 @t146))) % 0.37/0.72 (define @t150 () (not (tptp.neq @t146 tptp.nil))) % 0.37/0.72 (define @t151 () (not (tptp.ssList @t146))) % 0.37/0.72 (define @t152 () (or @t151 @t150 @t149 (not (tptp.frontsegP @t2 @t146)))) % 0.37/0.72 (define @t153 () (forall @t147 @t152)) % 0.37/0.72 (define @t154 () (@list @t146)) % 0.37/0.72 (define @t155 () (and @t153 @t148)) % 0.37/0.72 (define @t156 () (and @t152 @t66)) % 0.37/0.72 (define @t157 () (forall @t147 @t156)) % 0.37/0.72 (define @t158 () (or @t108 @t122 @t157)) % 0.37/0.72 (define @t159 () (or @t108 @t122 @t156)) % 0.37/0.72 (define @t160 () (not (= @t2 @t2))) % 0.37/0.72 (define @t161 () (or @t108 @t160 @t122 @t156)) % 0.37/0.72 (define @t162 () (or @t151 @t150 @t149 (not (tptp.frontsegP @t12 @t146)))) % 0.37/0.72 (define @t163 () (and @t162 @t66)) % 0.37/0.72 (define @t164 () (not (= @t12 tptp.nil))) % 0.37/0.72 (define @t165 () (and @t164 @t121)) % 0.37/0.72 (define @t166 () (not @t15)) % 0.37/0.72 (define @t167 () (or @t80 @t166 @t80 @t165 @t163)) % 0.37/0.72 (define @t168 () (or @t166 @t80 @t165 @t163)) % 0.37/0.72 (define @t169 () (forall @t16 @t168)) % 0.37/0.72 (define @t170 () (forall @t147 @t169)) % 0.37/0.72 (define @t171 () (forall (@list @t146 @t12) @t168)) % 0.37/0.72 (define @t172 () (forall (@list @t12 @t146) @t168)) % 0.37/0.72 (define @t173 () (forall @t147 @t168)) % 0.37/0.72 (define @t174 () (forall @t147 @t162)) % 0.37/0.72 (define @t175 () (@var "BOUND_VARIABLE_10990" $$unsorted)) % 0.37/0.72 (define @t176 () (@list @t175)) % 0.37/0.72 (define @t177 () (and @t174 @t148)) % 0.37/0.72 (define @t178 () (forall @t147 @t163)) % 0.37/0.72 (define @t179 () (or @t166 @t80 @t165 @t178)) % 0.37/0.72 (define @t180 () (and (forall (@list @t175) (or (not (tptp.ssList @t175)) (not (tptp.neq @t175 tptp.nil)) (not (tptp.frontsegP @t1 @t175)) (not (tptp.frontsegP @t12 @t175)))) @t66)) % 0.37/0.72 (define @t181 () (or @t166 @t80 @t165 @t180)) % 0.37/0.72 (define @t182 () (forall @t16 @t181)) % 0.37/0.72 (define @t183 () (or @t125 @t126 @t182)) % 0.37/0.72 (define @t184 () (or @t125 @t126 @t181)) % 0.37/0.72 (define @t185 () (or @t166 @t80 @t125 @t126 @t165 @t180)) % 0.37/0.72 (define @t186 () (or @t80 @t125 @t126 @t165 @t180)) % 0.37/0.72 (define @t187 () (@var "BOUND_VARIABLE_10962" $$unsorted)) % 0.37/0.72 (define @t188 () (@list @t187)) % 0.37/0.72 (define @t189 () (forall @t188 @t66)) % 0.37/0.72 (define @t190 () (not (tptp.frontsegP @t12 @t187))) % 0.37/0.72 (define @t191 () (not (tptp.neq @t187 tptp.nil))) % 0.37/0.72 (define @t192 () (not (tptp.ssList @t187))) % 0.37/0.72 (define @t193 () (or @t192 @t191 (not (tptp.frontsegP @t1 @t187)) @t190)) % 0.37/0.72 (define @t194 () (forall @t188 @t193)) % 0.37/0.72 (define @t195 () (@list @t187)) % 0.37/0.72 (define @t196 () (and @t194 @t189)) % 0.37/0.72 (define @t197 () (and @t193 @t66)) % 0.37/0.72 (define @t198 () (forall @t188 @t197)) % 0.37/0.72 (define @t199 () (or @t126 @t165 @t198)) % 0.37/0.72 (define @t200 () (or @t126 @t165 @t197)) % 0.37/0.72 (define @t201 () (not (= @t1 @t1))) % 0.37/0.72 (define @t202 () (or @t126 @t201 @t165 @t197)) % 0.37/0.72 (define @t203 () (or @t192 @t191 (not (tptp.frontsegP @t10 @t187)) @t190)) % 0.37/0.72 (define @t204 () (and @t203 @t71)) % 0.37/0.72 (define @t205 () (and @t164 (= @t10 tptp.nil))) % 0.37/0.72 (define @t206 () (not @t13)) % 0.37/0.72 (define @t207 () (or @t81 @t206 @t81 @t205 @t204)) % 0.37/0.72 (define @t208 () (or @t206 @t81 @t205 @t204)) % 0.37/0.72 (define @t209 () (forall @t14 @t208)) % 0.37/0.72 (define @t210 () (forall @t188 @t209)) % 0.37/0.72 (define @t211 () (forall (@list @t187 @t10) @t208)) % 0.37/0.72 (define @t212 () (forall (@list @t10 @t187) @t208)) % 0.37/0.72 (define @t213 () (forall @t188 @t208)) % 0.37/0.72 (define @t214 () (forall @t188 @t71)) % 0.37/0.72 (define @t215 () (forall @t188 @t203)) % 0.37/0.72 (define @t216 () (and @t215 @t214)) % 0.37/0.72 (define @t217 () (forall @t188 @t204)) % 0.37/0.72 (define @t218 () (or @t206 @t81 @t205 @t217)) % 0.37/0.72 (define @t219 () (not @t32)) % 0.37/0.72 (define @t220 () (or @t219 @t74 @t73 @t72)) % 0.37/0.72 (define @t221 () (and (forall @t33 @t220) @t71)) % 0.37/0.72 (define @t222 () (or @t206 @t81 @t205 @t221)) % 0.37/0.72 (define @t223 () (forall @t14 @t222)) % 0.37/0.72 (define @t224 () (or @t80 @t125 @t223)) % 0.37/0.72 (define @t225 () (or @t80 @t125 @t222)) % 0.37/0.72 (define @t226 () (or @t206 @t81 @t80 @t205 @t221 @t125)) % 0.37/0.72 (define @t227 () (or @t81 @t80 @t205 @t221 @t125)) % 0.37/0.72 (define @t228 () (forall @t31 (not @t64))) % 0.37/0.72 (define @t229 () (not @t228)) % 0.37/0.72 (define @t230 () (= tptp.nil @t92)) % 0.37/0.72 (define @t231 () (forall @t112 (or @t108 @t107 (and (or (not @t230) @t96) @t103) (and @t97 @t230) @t95))) % 0.37/0.72 (define @t232 () (@quantifiers_skolemize @t231 1)) % 0.37/0.72 (define @t233 () (tptp.neq @t232 tptp.nil)) % 0.37/0.72 (define @t234 () (@quantifiers_skolemize @t231 2)) % 0.37/0.72 (define @t235 () (@quantifiers_skolemize @t231 0)) % 0.37/0.72 (define @t236 () (or (not (tptp.ssList @t234)) (not (tptp.neq @t234 tptp.nil)) (not (tptp.frontsegP @t232 @t234)) (not (tptp.frontsegP @t235 @t234)))) % 0.37/0.72 (define @t237 () (and @t236 @t233)) % 0.37/0.72 (define @t238 () (= tptp.nil @t232)) % 0.37/0.72 (define @t239 () (= tptp.nil @t235)) % 0.37/0.72 (define @t240 () (not @t239)) % 0.37/0.72 (define @t241 () (and @t240 @t238)) % 0.37/0.72 (define @t242 () (forall @t31 (or @t102 @t101 (not (tptp.frontsegP @t232 @t27)) (not (tptp.frontsegP @t235 @t27))))) % 0.37/0.72 (define @t243 () (not @t242)) % 0.37/0.72 (define @t244 () (not @t233)) % 0.37/0.72 (define @t245 () (or @t244 @t243)) % 0.37/0.72 (define @t246 () (not @t238)) % 0.37/0.72 (define @t247 () (or @t246 @t239)) % 0.37/0.72 (define @t248 () (and @t247 @t245)) % 0.37/0.72 (define @t249 () (not (tptp.ssList @t232))) % 0.37/0.72 (define @t250 () (not (tptp.ssList @t235))) % 0.37/0.72 (define @t251 () (or @t250 @t249 @t248 @t241 @t237)) % 0.37/0.72 (define @t252 () (not @t251)) % 0.37/0.72 (define @t253 () (not @t231)) % 0.37/0.72 (define @t254 () (= @t235 tptp.nil)) % 0.37/0.72 (define @t255 () (not @t254)) % 0.37/0.72 (define @t256 () (and @t255 @t238)) % 0.37/0.72 (define @t257 () (or @t246 @t254)) % 0.37/0.72 (define @t258 () (and @t257 @t245)) % 0.37/0.72 (define @t259 () (or @t250 @t249 @t258 @t256 @t237)) % 0.37/0.72 (define @t260 () (not @t259)) % 0.37/0.72 (define @t261 () (@list true)) % 0.37/0.72 (define @t262 () (@list @t251)) % 0.37/0.72 (define @t263 () (@list @t247)) % 0.37/0.72 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.72 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.37/0.72 (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))))))))))) % 0.37/0.72 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.37/0.72 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.37/0.72 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.37/0.72 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.37/0.72 (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))))))))))))))))) % 0.37/0.72 (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)))))))))))))))) % 0.37/0.72 (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))))))))))))))))) % 0.37/0.72 (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))))))))))))))) % 0.37/0.72 (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))))))))))))))) % 0.37/0.72 (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)))))))))))))))) % 0.37/0.72 (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))))))))))))) % 0.37/0.72 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.37/0.72 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.37/0.72 (assume @p17 (tptp.ssList tptp.nil)) % 0.37/0.72 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.37/0.72 (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))))))))))) % 0.37/0.72 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.37/0.72 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.37/0.72 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.37/0.72 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.37/0.72 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.37/0.72 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.37/0.72 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.37/0.72 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.37/0.72 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.37/0.72 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.37/0.72 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.37/0.72 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.37/0.72 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.37/0.72 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 0.37/0.72 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 @t35) @t51)))))))) % 0.37/0.72 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t49)))))) % 0.37/0.72 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t53))))))))) % 0.37/0.72 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t53))))))))) % 0.37/0.72 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.37/0.72 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.37/0.72 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.37/0.72 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.37/0.72 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.37/0.72 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.37/0.72 (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)))))))))))) % 0.37/0.72 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.37/0.72 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t40)))) % 0.37/0.72 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.37/0.72 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.37/0.72 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.37/0.72 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t54 @t1))))))))) % 0.37/0.72 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.37/0.72 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.37/0.72 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.37/0.72 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.37/0.72 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.37/0.72 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t54 @t10) @t1))))))))))) % 0.37/0.72 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.37/0.72 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t40)))) % 0.37/0.72 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t55)))) % 0.37/0.72 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.37/0.72 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t55)))) % 0.37/0.72 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.37/0.72 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t55)))) % 0.37/0.72 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.37/0.72 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t55)))) % 0.37/0.72 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.37/0.72 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t59) (or @t57 (and @t58 (tptp.totalorderedP @t1) (tptp.leq @t2 @t56))))))))) % 0.37/0.72 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t55)))) % 0.37/0.72 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.37/0.72 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t59) (or @t57 (and @t58 (tptp.strictorderedP @t1) (tptp.lt @t2 @t56))))))))) % 0.37/0.72 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t55)))) % 0.37/0.72 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.37/0.72 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t55)))) % 0.37/0.72 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.37/0.72 (assume @p75 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t6 (= @t41 @t1))))))) % 0.37/0.72 (assume @p76 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t21 (= @t43 @t1))))))) % 0.37/0.72 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t58 @t42 (= @t56 @t41) (= (tptp.tl @t1) @t43)) @t38)))))) % 0.37/0.72 (assume @p78 (forall @t9 (=> @t17 (=> @t42 (= (tptp.cons @t41 @t43) @t2))))) % 0.37/0.72 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t44) @t60)))))))) % 0.37/0.72 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t45) @t60)))))))) % 0.37/0.72 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.37/0.72 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.37/0.72 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) (and @t57 @t40))))))) % 0.37/0.72 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.37/0.72 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.hd @t44) @t41))))))) % 0.37/0.72 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.tl @t44) (tptp.app @t43 @t1)))))))) % 0.37/0.72 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 (tptp.geq @t1 @t2)) @t3)))))) % 0.37/0.72 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.37/0.72 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.37/0.72 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.37/0.72 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t35) @t51)))))))) % 0.37/0.72 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t47 (or @t3 @t50))))))) % 0.37/0.72 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 (and @t4 @t47))))))) % 0.37/0.72 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not (tptp.gt @t1 @t2)))))))) % 0.37/0.72 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.37/0.72 (assume @p96 @t91) % 0.37/0.72 (assume @p97 true) % 0.37/0.72 (step @p98 :rule refl :args (@t95)) % 0.37/0.72 (step @p99 :rule eq-symm :args (@t92 tptp.nil)) % 0.37/0.72 (step @p100 :rule refl :args (@t97)) % 0.37/0.72 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t99)) % 0.37/0.72 (step @p102 :rule refl :args (@t103)) % 0.37/0.72 (step @p103 :rule refl :args (@t96)) % 0.37/0.72 (step @p104 :rule cong :premises (@p99) :args (@t104)) % 0.37/0.72 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t105)) % 0.37/0.72 (step @p106 :rule nary_cong :premises (@p105 @p102) :args (@t106)) % 0.37/0.72 (step @p107 :rule refl :args (@t107)) % 0.37/0.72 (step @p108 :rule refl :args (@t108)) % 0.37/0.72 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106 @p101 @p98) :args (@t109)) % 0.37/0.72 (step @p110 :rule aci_norm :args ((= @t111 @t109))) % 0.37/0.72 (step @p111 :rule trans :premises (@p110 @p109)) % 0.37/0.72 (step @p112 :rule cong :premises (@p111) :args (@t113)) % 0.37/0.72 (step @p113 :rule quant-merge-prenex :args ((= (forall @t9 @t115) @t113))) % 0.37/0.72 (step @p114 :rule alpha_equiv :args (@t116 (@list @t92 @t94) (@list @t1 @t117))) % 0.37/0.72 (step @p115 :rule refl :args (@t108)) % 0.37/0.72 (step @p116 :rule nary_cong :premises (@p115 @p114) :args (@t118)) % 0.37/0.72 (step @p117 :rule quant-miniscope-or :args ((= @t115 @t118))) % 0.37/0.72 (step @p118 :rule trans :premises (@p117 @p116)) % 0.37/0.72 (step @p119 :rule symm :premises (@p118)) % 0.37/0.72 (step @p120 :rule cong :premises (@p119) :args ((forall @t9 @t129))) % 0.37/0.72 (step @p121 :rule trans :premises (@p120 @p113)) % 0.37/0.72 (step @p122 :rule trans :premises (@p121 @p112)) % 0.37/0.72 (step @p123 :rule aci_norm :args ((= (or @t108 @t129) @t129))) % 0.37/0.72 (step @p124 :rule bool-impl-elim :args (@t17 @t129)) % 0.37/0.72 (step @p125 :rule trans :premises (@p124 @p123)) % 0.37/0.72 (step @p126 :rule cong :premises (@p125) :args ((forall @t9 (=> @t17 @t129)))) % 0.37/0.72 (step @p127 :rule trans :premises (@p126 @p122)) % 0.37/0.72 (step @p128 :rule quant-merge-prenex :args ((= (forall @t7 @t131) @t128))) % 0.37/0.72 (step @p129 :rule quant-unused-vars :args ((= @t132 @t66))) % 0.37/0.72 (step @p130 :rule alpha_equiv :args (@t133 (@list @t117) @t135)) % 0.37/0.72 (step @p131 :rule nary_cong :premises (@p130 @p129) :args (@t136)) % 0.37/0.72 (step @p132 :rule quant-miniscope-and :args ((= @t137 @t136))) % 0.37/0.72 (step @p133 :rule trans :premises (@p132 @p131)) % 0.37/0.72 (step @p134 :rule refl :args (@t122)) % 0.37/0.72 (step @p135 :rule refl :args (@t125)) % 0.37/0.72 (step @p136 :rule refl :args (@t126)) % 0.37/0.72 (step @p137 :rule nary_cong :premises (@p136 @p135 @p134 @p133) :args (@t138)) % 0.37/0.72 (step @p138 :rule quant-miniscope-or :args ((= @t131 @t138))) % 0.37/0.72 (step @p139 :rule trans :premises (@p138 @p137)) % 0.37/0.72 (step @p140 :rule symm :premises (@p139)) % 0.37/0.72 (step @p141 :rule cong :premises (@p140) :args (@t141)) % 0.37/0.72 (step @p142 :rule trans :premises (@p141 @p128)) % 0.37/0.72 (step @p143 :rule nary_cong :premises (@p108 @p142) :args (@t142)) % 0.37/0.72 (step @p144 :rule quant-miniscope-or :args ((= (forall @t7 @t143) @t142))) % 0.37/0.72 (step @p145 :rule aci_norm :args ((= @t144 @t143))) % 0.37/0.72 (step @p146 :rule cong :premises (@p145) :args ((forall @t7 @t144))) % 0.37/0.72 (step @p147 :rule trans :premises (@p146 @p144)) % 0.37/0.72 (step @p148 :rule trans :premises (@p147 @p143)) % 0.37/0.72 (step @p149 :rule aci_norm :args ((= (or @t126 @t145) @t144))) % 0.37/0.72 (step @p150 :rule bool-impl-elim :args (@t21 @t145)) % 0.37/0.72 (step @p151 :rule trans :premises (@p150 @p149)) % 0.37/0.72 (step @p152 :rule cong :premises (@p151) :args ((forall @t7 (=> @t21 @t145)))) % 0.37/0.72 (step @p153 :rule trans :premises (@p152 @p148)) % 0.37/0.72 (step @p154 :rule aci_norm :args ((= (or @t125 @t126 (or @t108 @t122 @t139)) @t145))) % 0.37/0.72 (step @p155 :rule quant-unused-vars :args ((= @t148 @t66))) % 0.37/0.72 (step @p156 :rule alpha_equiv :args (@t153 @t154 @t135)) % 0.37/0.72 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t155)) % 0.37/0.72 (step @p158 :rule quant-miniscope-and :args ((= @t157 @t155))) % 0.37/0.72 (step @p159 :rule trans :premises (@p158 @p157)) % 0.37/0.72 (step @p160 :rule refl :args (@t122)) % 0.37/0.72 (step @p161 :rule nary_cong :premises (@p108 @p160 @p159) :args (@t158)) % 0.37/0.72 (step @p162 :rule quant-miniscope-or :args ((= (forall @t147 @t159) @t158))) % 0.37/0.72 (step @p163 :rule trans :premises (@p162 @p161)) % 0.37/0.72 (step @p164 :rule aci_norm :args ((= (or @t108 false @t122 @t156) @t159))) % 0.37/0.72 (step @p165 :rule refl :args (@t156)) % 0.37/0.72 (step @p166 :rule evaluate :args ((not true))) % 0.37/0.72 (step @p167 :rule eq-refl :args (@t2)) % 0.37/0.72 (step @p168 :rule cong :premises (@p167) :args (@t160)) % 0.37/0.72 (step @p169 :rule trans :premises (@p168 @p166)) % 0.37/0.72 (step @p170 :rule nary_cong :premises (@p108 @p169 @p160 @p165) :args (@t161)) % 0.37/0.72 (step @p171 :rule trans :premises (@p170 @p164)) % 0.37/0.72 (step @p172 :rule cong :premises (@p171) :args ((forall @t147 @t161))) % 0.37/0.72 (step @p173 :rule trans :premises (@p172 @p163)) % 0.37/0.72 (step @p174 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t60) @t166 @t80 @t165 @t163)) @t161))) % 0.37/0.72 (step @p175 :rule refl :args (@t163)) % 0.37/0.72 (step @p176 :rule refl :args (@t165)) % 0.37/0.72 (step @p177 :rule refl :args (@t80)) % 0.37/0.72 (step @p178 :rule refl :args (@t166)) % 0.37/0.72 (step @p179 :rule eq-symm :args (@t2 @t12)) % 0.37/0.72 (step @p180 :rule cong :premises (@p179) :args (@t80)) % 0.37/0.72 (step @p181 :rule nary_cong :premises (@p180 @p178 @p177 @p176 @p175) :args (@t167)) % 0.37/0.72 (step @p182 :rule aci_norm :args ((= @t168 @t167))) % 0.37/0.72 (step @p183 :rule trans :premises (@p182 @p181)) % 0.37/0.72 (step @p184 :rule cong :premises (@p183) :args (@t169)) % 0.37/0.72 (step @p185 :rule trans :premises (@p184 @p174)) % 0.37/0.72 (step @p186 :rule cong :premises (@p185) :args (@t170)) % 0.37/0.72 (step @p187 :rule quant-merge-prenex :args ((= @t170 @t171))) % 0.37/0.72 (step @p188 :rule symm :premises (@p187)) % 0.37/0.72 (step @p189 :rule quant_var_reordering :args ((= @t172 @t171))) % 0.37/0.72 (step @p190 :rule trans :premises (@p189 @p188 @p186)) % 0.37/0.72 (step @p191 :rule trans :premises (@p190 @p173)) % 0.37/0.72 (step @p192 :rule quant-merge-prenex :args ((= (forall @t16 @t173) @t172))) % 0.37/0.72 (step @p193 :rule alpha_equiv :args (@t174 @t154 @t176)) % 0.37/0.72 (step @p194 :rule nary_cong :premises (@p193 @p155) :args (@t177)) % 0.37/0.72 (step @p195 :rule quant-miniscope-and :args ((= @t178 @t177))) % 0.37/0.72 (step @p196 :rule trans :premises (@p195 @p194)) % 0.37/0.72 (step @p197 :rule nary_cong :premises (@p178 @p177 @p176 @p196) :args (@t179)) % 0.37/0.72 (step @p198 :rule quant-miniscope-or :args ((= @t173 @t179))) % 0.37/0.72 (step @p199 :rule trans :premises (@p198 @p197)) % 0.37/0.72 (step @p200 :rule symm :premises (@p199)) % 0.37/0.72 (step @p201 :rule cong :premises (@p200) :args (@t182)) % 0.37/0.72 (step @p202 :rule trans :premises (@p201 @p192)) % 0.37/0.72 (step @p203 :rule trans :premises (@p202 @p191)) % 0.37/0.72 (step @p204 :rule refl :args (@t126)) % 0.37/0.72 (step @p205 :rule refl :args (@t125)) % 0.37/0.72 (step @p206 :rule nary_cong :premises (@p205 @p204 @p203) :args (@t183)) % 0.37/0.72 (step @p207 :rule trans :premises (@p206 @p154)) % 0.37/0.72 (step @p208 :rule quant-miniscope-or :args ((= (forall @t16 @t184) @t183))) % 0.37/0.72 (step @p209 :rule aci_norm :args ((= @t185 @t184))) % 0.37/0.72 (step @p210 :rule cong :premises (@p209) :args ((forall @t16 @t185))) % 0.37/0.72 (step @p211 :rule trans :premises (@p210 @p208)) % 0.37/0.72 (step @p212 :rule trans :premises (@p211 @p207)) % 0.37/0.72 (step @p213 :rule aci_norm :args ((= (or @t166 @t186) @t185))) % 0.37/0.72 (step @p214 :rule bool-impl-elim :args (@t15 @t186)) % 0.37/0.72 (step @p215 :rule trans :premises (@p214 @p213)) % 0.37/0.72 (step @p216 :rule cong :premises (@p215) :args ((forall @t16 (=> @t15 @t186)))) % 0.37/0.72 (step @p217 :rule trans :premises (@p216 @p212)) % 0.37/0.72 (step @p218 :rule aci_norm :args ((= (or @t80 @t125 (or @t126 @t165 @t180)) @t186))) % 0.37/0.72 (step @p219 :rule quant-unused-vars :args ((= @t189 @t66))) % 0.37/0.72 (step @p220 :rule alpha_equiv :args (@t194 @t195 @t176)) % 0.37/0.72 (step @p221 :rule nary_cong :premises (@p220 @p219) :args (@t196)) % 0.37/0.72 (step @p222 :rule quant-miniscope-and :args ((= @t198 @t196))) % 0.37/0.72 (step @p223 :rule trans :premises (@p222 @p221)) % 0.37/0.72 (step @p224 :rule refl :args (@t165)) % 0.37/0.72 (step @p225 :rule nary_cong :premises (@p204 @p224 @p223) :args (@t199)) % 0.37/0.72 (step @p226 :rule quant-miniscope-or :args ((= (forall @t188 @t200) @t199))) % 0.37/0.72 (step @p227 :rule trans :premises (@p226 @p225)) % 0.37/0.72 (step @p228 :rule aci_norm :args ((= (or @t126 false @t165 @t197) @t200))) % 0.37/0.72 (step @p229 :rule refl :args (@t197)) % 0.37/0.72 (step @p230 :rule eq-refl :args (@t1)) % 0.37/0.72 (step @p231 :rule cong :premises (@p230) :args (@t201)) % 0.37/0.72 (step @p232 :rule trans :premises (@p231 @p166)) % 0.37/0.72 (step @p233 :rule nary_cong :premises (@p204 @p232 @p224 @p229) :args (@t202)) % 0.37/0.72 (step @p234 :rule trans :premises (@p233 @p228)) % 0.37/0.72 (step @p235 :rule cong :premises (@p234) :args ((forall @t188 @t202))) % 0.37/0.72 (step @p236 :rule trans :premises (@p235 @p227)) % 0.37/0.72 (step @p237 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t206 @t81 @t205 @t204)) @t202))) % 0.37/0.72 (step @p238 :rule refl :args (@t204)) % 0.37/0.72 (step @p239 :rule refl :args (@t205)) % 0.37/0.72 (step @p240 :rule refl :args (@t81)) % 0.37/0.72 (step @p241 :rule refl :args (@t206)) % 0.37/0.72 (step @p242 :rule eq-symm :args (@t1 @t10)) % 0.37/0.72 (step @p243 :rule cong :premises (@p242) :args (@t81)) % 0.37/0.72 (step @p244 :rule nary_cong :premises (@p243 @p241 @p240 @p239 @p238) :args (@t207)) % 0.37/0.72 (step @p245 :rule aci_norm :args ((= @t208 @t207))) % 0.37/0.72 (step @p246 :rule trans :premises (@p245 @p244)) % 0.37/0.72 (step @p247 :rule cong :premises (@p246) :args (@t209)) % 0.37/0.72 (step @p248 :rule trans :premises (@p247 @p237)) % 0.37/0.72 (step @p249 :rule cong :premises (@p248) :args (@t210)) % 0.37/0.72 (step @p250 :rule quant-merge-prenex :args ((= @t210 @t211))) % 0.37/0.72 (step @p251 :rule symm :premises (@p250)) % 0.37/0.72 (step @p252 :rule quant_var_reordering :args ((= @t212 @t211))) % 0.37/0.72 (step @p253 :rule trans :premises (@p252 @p251 @p249)) % 0.37/0.72 (step @p254 :rule trans :premises (@p253 @p236)) % 0.37/0.72 (step @p255 :rule quant-merge-prenex :args ((= (forall @t14 @t213) @t212))) % 0.37/0.72 (step @p256 :rule quant-unused-vars :args ((= @t214 @t71))) % 0.37/0.72 (step @p257 :rule alpha_equiv :args (@t215 @t195 (@list @t28))) % 0.37/0.72 (step @p258 :rule nary_cong :premises (@p257 @p256) :args (@t216)) % 0.37/0.72 (step @p259 :rule quant-miniscope-and :args ((= @t217 @t216))) % 0.37/0.72 (step @p260 :rule trans :premises (@p259 @p258)) % 0.37/0.72 (step @p261 :rule nary_cong :premises (@p241 @p240 @p239 @p260) :args (@t218)) % 0.37/0.72 (step @p262 :rule quant-miniscope-or :args ((= @t213 @t218))) % 0.37/0.72 (step @p263 :rule trans :premises (@p262 @p261)) % 0.37/0.72 (step @p264 :rule symm :premises (@p263)) % 0.37/0.72 (step @p265 :rule cong :premises (@p264) :args (@t223)) % 0.37/0.72 (step @p266 :rule trans :premises (@p265 @p255)) % 0.37/0.72 (step @p267 :rule trans :premises (@p266 @p254)) % 0.37/0.72 (step @p268 :rule refl :args (@t80)) % 0.37/0.72 (step @p269 :rule nary_cong :premises (@p268 @p205 @p267) :args (@t224)) % 0.37/0.72 (step @p270 :rule trans :premises (@p269 @p218)) % 0.37/0.72 (step @p271 :rule quant-miniscope-or :args ((= (forall @t14 @t225) @t224))) % 0.37/0.72 (step @p272 :rule aci_norm :args ((= @t226 @t225))) % 0.37/0.72 (step @p273 :rule cong :premises (@p272) :args ((forall @t14 @t226))) % 0.37/0.72 (step @p274 :rule trans :premises (@p273 @p271)) % 0.37/0.72 (step @p275 :rule trans :premises (@p274 @p270)) % 0.37/0.72 (step @p276 :rule aci_norm :args ((= (or @t206 @t227) @t226))) % 0.37/0.72 (step @p277 :rule bool-impl-elim :args (@t13 @t227)) % 0.37/0.72 (step @p278 :rule trans :premises (@p277 @p276)) % 0.37/0.72 (step @p279 :rule cong :premises (@p278) :args ((forall @t14 (=> @t13 @t227)))) % 0.37/0.72 (step @p280 :rule trans :premises (@p279 @p275)) % 0.37/0.72 (step @p281 :rule aci_norm :args ((= (or @t102 (or @t101 (or @t123 @t100))) @t124))) % 0.37/0.72 (step @p282 :rule bool-and-de-morgan :args (@t62 @t61 true)) % 0.37/0.72 (step @p283 :rule refl :args (@t101)) % 0.37/0.72 (step @p284 :rule nary_cong :premises (@p283 @p282) :args ((or @t101 (not (and @t62 @t61))))) % 0.37/0.72 (step @p285 :rule bool-and-de-morgan :args (@t63 @t62 (and @t61))) % 0.37/0.72 (step @p286 :rule trans :premises (@p285 @p284)) % 0.37/0.72 (step @p287 :rule refl :args (@t102)) % 0.37/0.72 (step @p288 :rule nary_cong :premises (@p287 @p286) :args ((or @t102 (not (and @t63 @t62 @t61))))) % 0.37/0.72 (step @p289 :rule bool-and-de-morgan :args (@t30 @t63 (and @t62 @t61))) % 0.37/0.72 (step @p290 :rule trans :premises (@p289 @p288)) % 0.37/0.72 (step @p291 :rule trans :premises (@p290 @p281)) % 0.37/0.72 (step @p292 :rule cong :premises (@p291) :args (@t228)) % 0.37/0.72 (step @p293 :rule cong :premises (@p292) :args (@t229)) % 0.37/0.72 (step @p294 :rule exists-elim :args ((= @t65 @t229))) % 0.37/0.72 (step @p295 :rule trans :premises (@p294 @p293)) % 0.37/0.72 (step @p296 :rule refl :args (@t67)) % 0.37/0.72 (step @p297 :rule nary_cong :premises (@p296 @p295) :args (@t68)) % 0.37/0.72 (step @p298 :rule eq-symm :args (tptp.nil @t2)) % 0.37/0.72 (step @p299 :rule eq-symm :args (tptp.nil @t1)) % 0.37/0.72 (step @p300 :rule cong :premises (@p299) :args (@t58)) % 0.37/0.72 (step @p301 :rule nary_cong :premises (@p300 @p298) :args (@t69)) % 0.37/0.72 (step @p302 :rule nary_cong :premises (@p301 @p297) :args (@t70)) % 0.37/0.72 (step @p303 :rule refl :args (@t71)) % 0.37/0.72 (step @p304 :rule aci_norm :args ((= (or @t219 @t75) @t220))) % 0.37/0.72 (step @p305 :rule bool-impl-elim :args (@t32 @t75)) % 0.37/0.72 (step @p306 :rule trans :premises (@p305 @p304)) % 0.37/0.72 (step @p307 :rule cong :premises (@p306) :args (@t76)) % 0.37/0.72 (step @p308 :rule nary_cong :premises (@p307 @p303) :args (@t77)) % 0.37/0.72 (step @p309 :rule eq-symm :args (tptp.nil @t10)) % 0.37/0.72 (step @p310 :rule eq-symm :args (tptp.nil @t12)) % 0.37/0.72 (step @p311 :rule cong :premises (@p310) :args (@t78)) % 0.37/0.72 (step @p312 :rule nary_cong :premises (@p311 @p309) :args (@t79)) % 0.37/0.72 (step @p313 :rule refl :args (@t81)) % 0.37/0.72 (step @p314 :rule nary_cong :premises (@p313 @p268 @p312 @p308 @p302) :args (@t82)) % 0.37/0.72 (step @p315 :rule refl :args (@t13)) % 0.37/0.72 (step @p316 :rule cong :premises (@p315 @p314) :args (@t83)) % 0.37/0.72 (step @p317 :rule cong :premises (@p316) :args (@t84)) % 0.37/0.72 (step @p318 :rule trans :premises (@p317 @p280)) % 0.37/0.72 (step @p319 :rule refl :args (@t15)) % 0.37/0.72 (step @p320 :rule cong :premises (@p319 @p318) :args (@t85)) % 0.37/0.72 (step @p321 :rule cong :premises (@p320) :args (@t86)) % 0.37/0.72 (step @p322 :rule trans :premises (@p321 @p217)) % 0.37/0.72 (step @p323 :rule refl :args (@t21)) % 0.37/0.72 (step @p324 :rule cong :premises (@p323 @p322) :args (@t87)) % 0.37/0.72 (step @p325 :rule cong :premises (@p324) :args (@t88)) % 0.37/0.72 (step @p326 :rule trans :premises (@p325 @p153)) % 0.37/0.72 (step @p327 :rule refl :args (@t17)) % 0.37/0.72 (step @p328 :rule cong :premises (@p327 @p326) :args (@t89)) % 0.37/0.72 (step @p329 :rule cong :premises (@p328) :args (@t90)) % 0.37/0.72 (step @p330 :rule trans :premises (@p329 @p127)) % 0.37/0.72 (step @p331 :rule cong :premises (@p330) :args (@t91)) % 0.37/0.72 (step @p332 :rule eq_resolve :premises (@p96 @p331)) % 0.37/0.72 (step @p333 :rule refl :args (@t252)) % 0.37/0.72 (step @p334 :rule bool-double-not-elim :args (@t231)) % 0.37/0.72 (step @p335 :rule nary_cong :premises (@p334 @p333) :args ((or (not @t253) @t252))) % 0.37/0.72 (step @p336 :rule refl :args (@t237)) % 0.37/0.72 (step @p337 :rule refl :args (@t238)) % 0.37/0.72 (step @p338 :rule eq-symm :args (@t235 tptp.nil)) % 0.37/0.72 (step @p339 :rule cong :premises (@p338) :args (@t255)) % 0.37/0.72 (step @p340 :rule nary_cong :premises (@p339 @p337) :args (@t256)) % 0.37/0.72 (step @p341 :rule refl :args (@t245)) % 0.37/0.72 (step @p342 :rule refl :args (@t246)) % 0.37/0.72 (step @p343 :rule nary_cong :premises (@p342 @p338) :args (@t257)) % 0.37/0.72 (step @p344 :rule nary_cong :premises (@p343 @p341) :args (@t258)) % 0.37/0.72 (step @p345 :rule refl :args (@t249)) % 0.37/0.72 (step @p346 :rule refl :args (@t250)) % 0.37/0.72 (step @p347 :rule nary_cong :premises (@p346 @p345 @p344 @p340 @p336) :args (@t259)) % 0.37/0.72 (step @p348 :rule cong :premises (@p347) :args (@t260)) % 0.37/0.72 (step @p349 :rule refl :args (@t253)) % 0.37/0.72 (step @p350 :rule cong :premises (@p349 @p348) :args ((=> @t253 @t260))) % 0.37/0.72 (assume-push @p401 @t253) % 0.37/0.72 (step @p352 :rule skolemize :premises (@p332)) % 0.37/0.72 (step-pop @p402 :rule scope :premises (@p352)) % 0.37/0.72 (step @p353 :rule process_scope :premises (@p402) :args (@t260)) % 0.37/0.72 (step @p355 :rule eq_resolve :premises (@p353 @p350)) % 0.37/0.72 (step @p356 :rule implies_elim :premises (@p355)) % 0.37/0.72 (step @p357 :rule eq_resolve :premises (@p356 @p335)) % 0.37/0.72 (step @p358 :rule chain_m_resolution :premises (@p357 @p332) :args (@t252 @t261 (@list @t231))) % 0.37/0.72 (step @p359 :rule cnf_or_neg :args (@t251 3)) % 0.37/0.72 (step @p360 :rule chain_m_resolution :premises (@p359 @p358) :args ((not @t241) @t261 @t262)) % 0.37/0.72 (step @p361 :rule bool-double-not-elim :args (@t233)) % 0.37/0.72 (step @p362 :rule nary_cong :premises (@p341 @p361) :args ((or @t245 (not @t244)))) % 0.37/0.72 (step @p363 :rule cnf_or_neg :args (@t245 0)) % 0.37/0.72 (step @p364 :rule eq_resolve :premises (@p363 @p362)) % 0.37/0.72 (step @p365 :rule reordering :premises (@p364) :args ((or @t233 @t245))) % 0.37/0.72 (step @p366 :rule bool-double-not-elim :args (@t242)) % 0.37/0.72 (step @p367 :rule nary_cong :premises (@p341 @p366) :args ((or @t245 (not @t243)))) % 0.37/0.72 (step @p368 :rule cnf_or_neg :args (@t245 1)) % 0.37/0.72 (step @p369 :rule eq_resolve :premises (@p368 @p367)) % 0.37/0.72 (step @p370 :rule reordering :premises (@p369) :args ((or @t242 @t245))) % 0.37/0.72 (step @p371 :rule cnf_or_neg :args (@t251 4)) % 0.37/0.72 (step @p372 :rule chain_m_resolution :premises (@p371 @p358) :args ((not @t237) @t261 @t262)) % 0.37/0.72 (step @p373 :rule cnf_and_neg :args (@t237)) % 0.37/0.72 (step @p374 :rule reordering :premises (@p373) :args ((or @t244 @t237 (not @t236)))) % 0.37/0.72 (assume-push @p403 @t242) % 0.37/0.72 (step @p376 :rule instantiate :premises (@p403) :args ((@list @t234))) % 0.37/0.72 (step-pop @p404 :rule scope :premises (@p376)) % 0.37/0.72 (step @p377 :rule process_scope :premises (@p404) :args (@t236)) % 0.37/0.72 (step @p379 :rule implies_elim :premises (@p377)) % 0.37/0.72 (step @p380 :rule chain_m_resolution :premises (@p379 @p374 @p372 @p370 @p365) :args (@t245 (@list true true false false) (@list @t236 @t237 @t242 @t233))) % 0.37/0.72 (step @p381 :rule cnf_or_neg :args (@t251 2)) % 0.37/0.72 (step @p382 :rule chain_m_resolution :premises (@p381 @p358) :args ((not @t248) @t261 @t262)) % 0.37/0.72 (step @p383 :rule cnf_and_neg :args (@t248)) % 0.37/0.72 (step @p384 :rule chain_m_resolution :premises (@p383 @p382 @p380) :args ((not @t247) (@list true false) (@list @t248 @t245))) % 0.37/0.72 (step @p385 :rule bool-double-not-elim :args (@t238)) % 0.37/0.72 (step @p386 :rule refl :args (@t247)) % 0.37/0.72 (step @p387 :rule nary_cong :premises (@p386 @p385) :args ((or @t247 (not @t246)))) % 0.37/0.72 (step @p388 :rule cnf_or_neg :args (@t247 0)) % 0.37/0.72 (step @p389 :rule eq_resolve :premises (@p388 @p387)) % 0.37/0.72 (step @p390 :rule reordering :premises (@p389) :args ((or @t238 @t247))) % 0.37/0.72 (step @p391 :rule chain_m_resolution :premises (@p390 @p384) :args (@t238 @t261 @t263)) % 0.37/0.72 (step @p392 :rule cnf_or_neg :args (@t247 1)) % 0.37/0.72 (step @p393 :rule chain_m_resolution :premises (@p392 @p384) :args (@t240 @t261 @t263)) % 0.37/0.72 (step @p394 :rule bool-double-not-elim :args (@t239)) % 0.37/0.72 (step @p395 :rule refl :args (@t241)) % 0.37/0.72 (step @p396 :rule nary_cong :premises (@p395 @p394 @p342) :args ((or @t241 (not @t240) @t246))) % 0.37/0.72 (step @p397 :rule cnf_and_neg :args (@t241)) % 0.37/0.72 (step @p398 :rule eq_resolve :premises (@p397 @p396)) % 0.37/0.72 (step @p399 :rule reordering :premises (@p398) :args ((or @t246 @t239 @t241))) % 0.37/0.72 (step @p400 false :rule chain_m_resolution :premises (@p399 @p393 @p391 @p360) :args (false (@list true false true) (@list @t239 @t238 @t241))) % 0.37/0.72 ) % 0.37/0.72 % SZS output end Proof % 0.37/0.72 % cvc5 exiting %------------------------------------------------------------------------------