%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC254+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 : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:58:37 AM UTC 2026 % Result : Theorem 0.50s 0.76s % Output : Proof 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC254+1 : TPTP v9.2.1. Released v2.4.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n009.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 19:33:14 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.50/0.76 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.50/0.76 % SZS status Theorem % 0.50/0.76 % SZS output start Proof % 0.50/0.76 ( % 0.50/0.76 (declare-sort $$unsorted 0) % 0.50/0.76 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.50/0.76 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.50/0.76 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.76 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.50/0.76 (declare-const tptp.nil $$unsorted) % 0.50/0.76 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (define @t1 () (@var "V" $$unsorted)) % 0.50/0.76 (define @t2 () (@var "U" $$unsorted)) % 0.50/0.76 (define @t3 () (= @t2 @t1)) % 0.50/0.76 (define @t4 () (not @t3)) % 0.50/0.76 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.50/0.76 (define @t6 () (tptp.ssItem @t1)) % 0.50/0.76 (define @t7 () (@list @t1)) % 0.50/0.76 (define @t8 () (tptp.ssItem @t2)) % 0.50/0.76 (define @t9 () (@list @t2)) % 0.50/0.76 (define @t10 () (@var "X" $$unsorted)) % 0.50/0.76 (define @t11 () (tptp.cons @t1 @t10)) % 0.50/0.76 (define @t12 () (@var "W" $$unsorted)) % 0.50/0.76 (define @t13 () (tptp.ssList @t10)) % 0.50/0.76 (define @t14 () (@list @t10)) % 0.50/0.76 (define @t15 () (tptp.ssList @t12)) % 0.50/0.76 (define @t16 () (@list @t12)) % 0.50/0.76 (define @t17 () (tptp.ssList @t2)) % 0.50/0.76 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.50/0.76 (define @t19 () (and @t6 (= @t18 @t2))) % 0.50/0.76 (define @t20 () (exists @t7 @t19)) % 0.50/0.76 (define @t21 () (tptp.singletonP @t2)) % 0.50/0.76 (define @t22 () (= @t21 @t20)) % 0.50/0.76 (define @t23 () (=> @t17 @t22)) % 0.50/0.76 (define @t24 () (forall @t9 @t23)) % 0.50/0.76 (define @t25 () (tptp.app @t1 @t12)) % 0.50/0.76 (define @t26 () (tptp.frontsegP @t2 @t1)) % 0.50/0.76 (define @t27 () (tptp.ssList @t1)) % 0.50/0.76 (define @t28 () (tptp.app @t12 @t1)) % 0.50/0.76 (define @t29 () (tptp.rearsegP @t2 @t1)) % 0.50/0.76 (define @t30 () (tptp.segmentP @t2 @t1)) % 0.50/0.76 (define @t31 () (tptp.leq @t12 @t1)) % 0.50/0.76 (define @t32 () (tptp.leq @t1 @t12)) % 0.50/0.76 (define @t33 () (@var "Z" $$unsorted)) % 0.50/0.76 (define @t34 () (@var "Y" $$unsorted)) % 0.50/0.76 (define @t35 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t34)) (tptp.cons @t12 @t33)) @t2)) % 0.50/0.76 (define @t36 () (tptp.ssList @t33)) % 0.50/0.76 (define @t37 () (@list @t33)) % 0.50/0.76 (define @t38 () (tptp.ssList @t34)) % 0.50/0.76 (define @t39 () (@list @t34)) % 0.50/0.76 (define @t40 () (tptp.ssItem @t12)) % 0.50/0.76 (define @t41 () (tptp.lt @t1 @t12)) % 0.50/0.76 (define @t42 () (= @t1 @t12)) % 0.50/0.76 (define @t43 () (tptp.cons @t1 @t2)) % 0.50/0.76 (define @t44 () (= @t1 @t2)) % 0.50/0.76 (define @t45 () (tptp.cons @t12 @t1)) % 0.50/0.76 (define @t46 () (= tptp.nil @t2)) % 0.50/0.76 (define @t47 () (tptp.hd @t2)) % 0.50/0.76 (define @t48 () (not @t46)) % 0.50/0.76 (define @t49 () (tptp.tl @t2)) % 0.50/0.76 (define @t50 () (tptp.app @t2 @t1)) % 0.50/0.76 (define @t51 () (tptp.app @t1 @t2)) % 0.50/0.76 (define @t52 () (tptp.leq @t1 @t2)) % 0.50/0.76 (define @t53 () (tptp.leq @t2 @t1)) % 0.50/0.76 (define @t54 () (tptp.geq @t2 @t1)) % 0.50/0.76 (define @t55 () (tptp.lt @t1 @t2)) % 0.50/0.76 (define @t56 () (tptp.lt @t2 @t1)) % 0.50/0.76 (define @t57 () (tptp.lt @t2 @t12)) % 0.50/0.76 (define @t58 () (tptp.gt @t2 @t1)) % 0.50/0.76 (define @t59 () (tptp.memberP @t12 @t2)) % 0.50/0.76 (define @t60 () (tptp.app @t12 @t2)) % 0.50/0.76 (define @t61 () (tptp.cons @t2 tptp.nil)) % 0.50/0.76 (define @t62 () (tptp.hd @t1)) % 0.50/0.76 (define @t63 () (= tptp.nil @t1)) % 0.50/0.76 (define @t64 () (not @t63)) % 0.50/0.76 (define @t65 () (tptp.cons @t2 @t1)) % 0.50/0.76 (define @t66 () (= @t12 @t2)) % 0.50/0.76 (define @t67 () (tptp.neq @t1 tptp.nil)) % 0.50/0.76 (define @t68 () (not @t67)) % 0.50/0.76 (define @t69 () (or @t68 (tptp.neq @t10 tptp.nil))) % 0.50/0.76 (define @t70 () (tptp.cons @t34 tptp.nil)) % 0.50/0.76 (define @t71 () (tptp.app @t33 @t70)) % 0.50/0.76 (define @t72 () (not (= @t71 @t10))) % 0.50/0.76 (define @t73 () (not (= @t70 @t12))) % 0.50/0.76 (define @t74 () (or @t73 @t72)) % 0.50/0.76 (define @t75 () (=> @t36 @t74)) % 0.50/0.76 (define @t76 () (forall @t37 @t75)) % 0.50/0.76 (define @t77 () (tptp.ssItem @t34)) % 0.50/0.76 (define @t78 () (=> @t77 @t76)) % 0.50/0.76 (define @t79 () (forall @t39 @t78)) % 0.50/0.76 (define @t80 () (or @t68 @t79 @t21)) % 0.50/0.76 (define @t81 () (and @t80 @t69)) % 0.50/0.76 (define @t82 () (not (= @t2 @t12))) % 0.50/0.76 (define @t83 () (not (= @t1 @t10))) % 0.50/0.76 (define @t84 () (or @t83 @t82 @t81)) % 0.50/0.76 (define @t85 () (=> @t13 @t84)) % 0.50/0.76 (define @t86 () (forall @t14 @t85)) % 0.50/0.76 (define @t87 () (=> @t15 @t86)) % 0.50/0.76 (define @t88 () (forall @t16 @t87)) % 0.50/0.76 (define @t89 () (=> @t27 @t88)) % 0.50/0.76 (define @t90 () (forall @t7 @t89)) % 0.50/0.76 (define @t91 () (=> @t17 @t90)) % 0.50/0.76 (define @t92 () (forall @t9 @t91)) % 0.50/0.76 (define @t93 () (not @t92)) % 0.50/0.76 (define @t94 () (@var "BOUND_VARIABLE_11101" $$unsorted)) % 0.50/0.76 (define @t95 () (not (tptp.ssList @t94))) % 0.50/0.76 (define @t96 () (@var "BOUND_VARIABLE_11099" $$unsorted)) % 0.50/0.76 (define @t97 () (not (tptp.ssItem @t96))) % 0.50/0.76 (define @t98 () (tptp.cons @t96 tptp.nil)) % 0.50/0.76 (define @t99 () (tptp.app @t94 @t98)) % 0.50/0.76 (define @t100 () (not (tptp.neq @t99 tptp.nil))) % 0.50/0.76 (define @t101 () (not (tptp.ssList @t99))) % 0.50/0.76 (define @t102 () (tptp.singletonP @t98)) % 0.50/0.76 (define @t103 () (not (tptp.ssList @t98))) % 0.50/0.76 (define @t104 () (or @t103 @t102 @t101 @t100 @t97 @t95)) % 0.50/0.76 (define @t105 () (not (= @t98 @t98))) % 0.50/0.76 (define @t106 () (or @t103 @t102 @t101 @t100 @t97 @t105 @t95)) % 0.50/0.76 (define @t107 () (@list @t96 @t94)) % 0.50/0.76 (define @t108 () (not (= @t2 @t98))) % 0.50/0.76 (define @t109 () (not @t17)) % 0.50/0.76 (define @t110 () (or @t108 @t109 @t21 @t101 @t100 @t97 @t108 @t95)) % 0.50/0.76 (define @t111 () (or @t109 @t21 @t101 @t100 @t97 @t108 @t95)) % 0.50/0.76 (define @t112 () (forall @t9 @t111)) % 0.50/0.76 (define @t113 () (forall @t107 @t112)) % 0.50/0.76 (define @t114 () (forall (@list @t96 @t94 @t2) @t111)) % 0.50/0.76 (define @t115 () (@list @t2 @t96 @t94)) % 0.50/0.76 (define @t116 () (or @t101 @t100 @t97 @t108 @t95)) % 0.50/0.76 (define @t117 () (or @t109 @t21 @t116)) % 0.50/0.76 (define @t118 () (forall @t115 @t117)) % 0.50/0.76 (define @t119 () (forall @t107 @t117)) % 0.50/0.76 (define @t120 () (forall @t107 @t116)) % 0.50/0.76 (define @t121 () (@var "BOUND_VARIABLE_11064" $$unsorted)) % 0.50/0.76 (define @t122 () (@var "BOUND_VARIABLE_11062" $$unsorted)) % 0.50/0.76 (define @t123 () (@list @t122 @t121)) % 0.50/0.76 (define @t124 () (or @t109 @t21 @t120)) % 0.50/0.76 (define @t125 () (not (tptp.ssList @t121))) % 0.50/0.76 (define @t126 () (tptp.cons @t122 tptp.nil)) % 0.50/0.76 (define @t127 () (not (= @t2 @t126))) % 0.50/0.76 (define @t128 () (not (tptp.ssItem @t122))) % 0.50/0.76 (define @t129 () (tptp.app @t121 @t126)) % 0.50/0.76 (define @t130 () (not (tptp.neq @t129 tptp.nil))) % 0.50/0.76 (define @t131 () (not (tptp.ssList @t129))) % 0.50/0.76 (define @t132 () (or @t131 @t130 @t128 @t127 @t125)) % 0.50/0.76 (define @t133 () (@list @t122 @t121)) % 0.50/0.76 (define @t134 () (forall @t133 @t132)) % 0.50/0.76 (define @t135 () (or @t109 @t21 @t134)) % 0.50/0.76 (define @t136 () (or @t21 @t109 @t134)) % 0.50/0.76 (define @t137 () (not (= @t129 @t129))) % 0.50/0.76 (define @t138 () (or @t131 @t130 @t128 @t127 @t125 @t137)) % 0.50/0.76 (define @t139 () (not (= @t1 @t129))) % 0.50/0.76 (define @t140 () (not @t27)) % 0.50/0.76 (define @t141 () (or @t139 @t140 @t68 @t128 @t127 @t125 @t139)) % 0.50/0.76 (define @t142 () (or @t140 @t68 @t128 @t127 @t125 @t139)) % 0.50/0.76 (define @t143 () (forall @t7 @t142)) % 0.50/0.76 (define @t144 () (forall @t133 @t143)) % 0.50/0.76 (define @t145 () (forall (@list @t122 @t121 @t1) @t142)) % 0.50/0.76 (define @t146 () (@list @t1 @t122 @t121)) % 0.50/0.76 (define @t147 () (or @t128 @t127 @t125 @t139)) % 0.50/0.76 (define @t148 () (or @t140 @t68 @t147)) % 0.50/0.76 (define @t149 () (forall @t146 @t148)) % 0.50/0.76 (define @t150 () (forall @t133 @t148)) % 0.50/0.76 (define @t151 () (forall @t133 @t147)) % 0.50/0.76 (define @t152 () (@var "BOUND_VARIABLE_11023" $$unsorted)) % 0.50/0.76 (define @t153 () (@var "BOUND_VARIABLE_11021" $$unsorted)) % 0.50/0.76 (define @t154 () (@list @t153 @t152)) % 0.50/0.76 (define @t155 () (or @t140 @t68 @t151)) % 0.50/0.76 (define @t156 () (tptp.cons @t153 tptp.nil)) % 0.50/0.76 (define @t157 () (not (= @t1 (tptp.app @t152 @t156)))) % 0.50/0.76 (define @t158 () (not (tptp.ssList @t152))) % 0.50/0.76 (define @t159 () (not (= @t2 @t156))) % 0.50/0.76 (define @t160 () (not (tptp.ssItem @t153))) % 0.50/0.76 (define @t161 () (or @t160 @t159 @t158 @t157)) % 0.50/0.76 (define @t162 () (@list @t153 @t152)) % 0.50/0.76 (define @t163 () (forall @t162 @t161)) % 0.50/0.76 (define @t164 () (or @t140 @t68 @t163)) % 0.50/0.76 (define @t165 () (forall @t7 @t164)) % 0.50/0.76 (define @t166 () (or @t21 @t109 @t165)) % 0.50/0.76 (define @t167 () (or @t21 @t109 @t164)) % 0.50/0.76 (define @t168 () (or @t140 @t68 @t21 @t109 @t163)) % 0.50/0.76 (define @t169 () (or @t109 @t163)) % 0.50/0.76 (define @t170 () (or @t109 @t161)) % 0.50/0.76 (define @t171 () (or @t109 @t160 @t159 @t158 @t157)) % 0.50/0.76 (define @t172 () (not (= @t2 @t2))) % 0.50/0.76 (define @t173 () (or @t109 @t172 @t160 @t159 @t158 @t157)) % 0.50/0.76 (define @t174 () (not (= @t12 @t156))) % 0.50/0.76 (define @t175 () (not @t15)) % 0.50/0.76 (define @t176 () (or @t82 @t175 @t82 @t160 @t174 @t158 @t157)) % 0.50/0.76 (define @t177 () (or @t175 @t82 @t160 @t174 @t158 @t157)) % 0.50/0.76 (define @t178 () (forall @t16 @t177)) % 0.50/0.76 (define @t179 () (forall @t162 @t178)) % 0.50/0.76 (define @t180 () (forall (@list @t153 @t152 @t12) @t177)) % 0.50/0.76 (define @t181 () (@list @t12 @t153 @t152)) % 0.50/0.76 (define @t182 () (or @t160 @t174 @t158 @t157)) % 0.50/0.76 (define @t183 () (or @t175 @t82 @t182)) % 0.50/0.76 (define @t184 () (forall @t181 @t183)) % 0.50/0.76 (define @t185 () (forall @t162 @t183)) % 0.50/0.76 (define @t186 () (forall @t162 @t182)) % 0.50/0.76 (define @t187 () (@var "BOUND_VARIABLE_10970" $$unsorted)) % 0.50/0.76 (define @t188 () (@var "BOUND_VARIABLE_10968" $$unsorted)) % 0.50/0.76 (define @t189 () (@list @t188 @t187)) % 0.50/0.76 (define @t190 () (or @t175 @t82 @t186)) % 0.50/0.76 (define @t191 () (tptp.cons @t188 tptp.nil)) % 0.50/0.76 (define @t192 () (tptp.app @t187 @t191)) % 0.50/0.76 (define @t193 () (not (= @t1 @t192))) % 0.50/0.76 (define @t194 () (not (tptp.ssList @t187))) % 0.50/0.76 (define @t195 () (not (= @t12 @t191))) % 0.50/0.76 (define @t196 () (not (tptp.ssItem @t188))) % 0.50/0.76 (define @t197 () (or @t196 @t195 @t194 @t193)) % 0.50/0.76 (define @t198 () (@list @t188 @t187)) % 0.50/0.76 (define @t199 () (forall @t198 @t197)) % 0.50/0.76 (define @t200 () (or @t175 @t82 @t199)) % 0.50/0.76 (define @t201 () (forall @t16 @t200)) % 0.50/0.76 (define @t202 () (or @t140 @t68 @t21 @t201)) % 0.50/0.76 (define @t203 () (or @t140 @t68 @t21 @t200)) % 0.50/0.76 (define @t204 () (or @t175 @t82 @t140 @t68 @t21 @t199)) % 0.50/0.76 (define @t205 () (or @t82 @t140 @t68 @t21 @t199)) % 0.50/0.76 (define @t206 () (or @t140 @t68 @t21 @t199)) % 0.50/0.76 (define @t207 () (or @t140 @t68 @t21 @t197)) % 0.50/0.76 (define @t208 () (or @t140 @t68 @t21 @t196 @t195 @t194 @t193)) % 0.50/0.76 (define @t209 () (or @t68 @t21 @t196 @t195 @t194 @t193)) % 0.50/0.76 (define @t210 () (and @t209 true)) % 0.50/0.76 (define @t211 () (or @t140 @t210)) % 0.50/0.76 (define @t212 () (and @t209 (or @t68 @t67))) % 0.50/0.76 (define @t213 () (or @t140 @t212)) % 0.50/0.76 (define @t214 () (not (= @t1 @t1))) % 0.50/0.76 (define @t215 () (or @t140 @t214 @t212)) % 0.50/0.76 (define @t216 () (not (= @t10 @t192))) % 0.50/0.76 (define @t217 () (or @t68 @t21 @t196 @t195 @t194 @t216)) % 0.50/0.76 (define @t218 () (and @t217 @t69)) % 0.50/0.76 (define @t219 () (not @t13)) % 0.50/0.76 (define @t220 () (or @t83 @t219 @t83 @t218)) % 0.50/0.76 (define @t221 () (or @t219 @t83 @t218)) % 0.50/0.76 (define @t222 () (forall @t14 @t221)) % 0.50/0.76 (define @t223 () (forall @t198 @t222)) % 0.50/0.76 (define @t224 () (forall (@list @t188 @t187 @t10) @t221)) % 0.50/0.76 (define @t225 () (@list @t10 @t188 @t187)) % 0.50/0.76 (define @t226 () (or @t196 @t195 @t194 @t216)) % 0.50/0.76 (define @t227 () (or @t68 @t226 @t21)) % 0.50/0.76 (define @t228 () (and @t227 @t69)) % 0.50/0.76 (define @t229 () (or @t219 @t83 @t228)) % 0.50/0.76 (define @t230 () (forall @t225 @t229)) % 0.50/0.76 (define @t231 () (forall @t198 @t229)) % 0.50/0.76 (define @t232 () (forall @t198 @t69)) % 0.50/0.76 (define @t233 () (forall @t198 @t226)) % 0.50/0.76 (define @t234 () (@var "BOUND_VARIABLE_10945" $$unsorted)) % 0.50/0.76 (define @t235 () (or @t68 @t233 @t21)) % 0.50/0.76 (define @t236 () (forall @t198 @t227)) % 0.50/0.76 (define @t237 () (and @t236 @t232)) % 0.50/0.76 (define @t238 () (forall @t198 @t228)) % 0.50/0.76 (define @t239 () (or @t219 @t83 @t238)) % 0.50/0.76 (define @t240 () (not (= @t10 (tptp.app @t234 @t70)))) % 0.50/0.76 (define @t241 () (not (tptp.ssList @t234))) % 0.50/0.76 (define @t242 () (not (= @t12 @t70))) % 0.50/0.76 (define @t243 () (not @t77)) % 0.50/0.76 (define @t244 () (or @t243 @t242 @t241 @t240)) % 0.50/0.76 (define @t245 () (@list @t34 @t234)) % 0.50/0.76 (define @t246 () (and (or @t68 (forall @t245 @t244) @t21) @t69)) % 0.50/0.76 (define @t247 () (or @t219 @t83 @t246)) % 0.50/0.76 (define @t248 () (forall @t14 @t247)) % 0.50/0.76 (define @t249 () (or @t82 @t248)) % 0.50/0.76 (define @t250 () (or @t82 @t247)) % 0.50/0.76 (define @t251 () (or @t219 @t83 @t82 @t246)) % 0.50/0.76 (define @t252 () (or @t83 @t82 @t246)) % 0.50/0.76 (define @t253 () (or @t241 @t240)) % 0.50/0.76 (define @t254 () (or @t243 @t242 @t253)) % 0.50/0.76 (define @t255 () (forall @t245 @t254)) % 0.50/0.76 (define @t256 () (@list @t234)) % 0.50/0.76 (define @t257 () (forall @t256 @t254)) % 0.50/0.76 (define @t258 () (forall @t256 @t253)) % 0.50/0.76 (define @t259 () (or @t243 @t242 @t258)) % 0.50/0.76 (define @t260 () (not (= @t10 @t71))) % 0.50/0.76 (define @t261 () (not @t36)) % 0.50/0.76 (define @t262 () (or @t261 @t260)) % 0.50/0.76 (define @t263 () (forall @t37 @t262)) % 0.50/0.76 (define @t264 () (or @t243 @t242 @t263)) % 0.50/0.76 (define @t265 () (or @t242 @t263)) % 0.50/0.76 (define @t266 () (or @t242 @t262)) % 0.50/0.76 (define @t267 () (or @t261 @t242 @t260)) % 0.50/0.76 (define @t268 () (or @t242 @t260)) % 0.50/0.76 (define @t269 () (forall @t107 @t104)) % 0.50/0.76 (define @t270 () (@quantifiers_skolemize @t269 0)) % 0.50/0.76 (define @t271 () (tptp.ssItem @t270)) % 0.50/0.76 (define @t272 () (@quantifiers_skolemize @t269 1)) % 0.50/0.76 (define @t273 () (not @t271)) % 0.50/0.76 (define @t274 () (tptp.cons @t270 tptp.nil)) % 0.50/0.76 (define @t275 () (tptp.app @t272 @t274)) % 0.50/0.76 (define @t276 () (tptp.singletonP @t274)) % 0.50/0.76 (define @t277 () (tptp.ssList @t274)) % 0.50/0.76 (define @t278 () (not @t277)) % 0.50/0.76 (define @t279 () (or @t278 @t276 (not (tptp.ssList @t275)) (not (tptp.neq @t275 tptp.nil)) @t273 (not (tptp.ssList @t272)))) % 0.50/0.76 (define @t280 () (@list true)) % 0.50/0.76 (define @t281 () (@list @t279)) % 0.50/0.76 (define @t282 () (= @t2 @t18)) % 0.50/0.76 (define @t283 () (not @t6)) % 0.50/0.76 (define @t284 () (= @t21 (not (forall @t7 (or @t283 (not @t282)))))) % 0.50/0.76 (define @t285 () (and @t6 @t282)) % 0.50/0.76 (define @t286 () (forall @t7 (not @t285))) % 0.50/0.76 (define @t287 () (not @t286)) % 0.50/0.76 (define @t288 () (not (= @t274 @t18))) % 0.50/0.76 (define @t289 () (or @t283 @t288)) % 0.50/0.76 (define @t290 () (forall @t7 @t289)) % 0.50/0.76 (define @t291 () (not @t290)) % 0.50/0.76 (define @t292 () (= @t276 @t291)) % 0.50/0.76 (define @t293 () (or @t278 @t292)) % 0.50/0.76 (define @t294 () (forall @t9 (or @t109 @t284))) % 0.50/0.76 (define @t295 () (forall @t7 (or @t283 (not (= @t18 @t274))))) % 0.50/0.76 (define @t296 () (not @t295)) % 0.50/0.76 (define @t297 () (= @t276 @t296)) % 0.50/0.76 (define @t298 () (or @t278 @t297)) % 0.50/0.76 (define @t299 () (@list false false)) % 0.50/0.76 (define @t300 () (not @t297)) % 0.50/0.76 (define @t301 () (not (= @t274 @t274))) % 0.50/0.76 (define @t302 () (or @t273 @t301)) % 0.50/0.76 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.50/0.76 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.50/0.76 (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))))))))))) % 0.50/0.76 (assume @p4 @t24) % 0.50/0.76 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= @t26 (exists @t16 (and @t15 (= @t25 @t2))))))))) % 0.50/0.76 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= @t29 (exists @t16 (and @t15 (= @t28 @t2))))))))) % 0.50/0.76 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= @t30 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t28 @t10) @t2))))))))))) % 0.50/0.76 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (not (and @t32 @t31))))))))))))))))) % 0.50/0.76 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (or @t32 @t31)))))))))))))))) % 0.50/0.76 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (or @t41 (tptp.lt @t12 @t1))))))))))))))))) % 0.50/0.76 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 @t32))))))))))))))) % 0.50/0.76 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 @t41))))))))))))))) % 0.50/0.76 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (forall @t37 (=> @t36 (=> @t35 (not @t42)))))))))))))))) % 0.50/0.76 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t40 (forall @t14 (=> @t13 (forall @t39 (=> @t38 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t34))) @t2) @t42))))))))))))) % 0.50/0.76 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t27 @t5))))) % 0.50/0.76 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t43)))))) % 0.50/0.76 (assume @p17 (tptp.ssList tptp.nil)) % 0.50/0.76 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t43 @t2))))))) % 0.50/0.76 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t40 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t44))))))))))) % 0.50/0.76 (assume @p20 (forall @t9 (=> @t17 (or @t46 (exists @t7 (and @t27 (exists @t16 (and @t40 (= @t45 @t2))))))))) % 0.50/0.76 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t43))))))) % 0.50/0.76 (assume @p22 (forall @t9 (=> @t17 (=> @t48 (tptp.ssItem @t47))))) % 0.50/0.76 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t43) @t1)))))) % 0.50/0.76 (assume @p24 (forall @t9 (=> @t17 (=> @t48 (tptp.ssList @t49))))) % 0.50/0.76 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t43) @t2)))))) % 0.50/0.76 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (tptp.ssList @t50)))))) % 0.50/0.76 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t40 (= (tptp.cons @t12 @t51) (tptp.app @t45 @t2))))))))) % 0.50/0.76 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.50/0.76 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t53 @t52) @t3)))))) % 0.50/0.76 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t53 @t32) (tptp.leq @t2 @t12))))))))) % 0.50/0.76 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.50/0.76 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t54 @t52)))))) % 0.50/0.76 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t56 (not @t55))))))) % 0.50/0.76 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t56 @t41) @t57)))))))) % 0.50/0.76 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t58 @t55)))))) % 0.50/0.76 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (= (tptp.memberP @t25 @t2) (or (tptp.memberP @t1 @t2) @t59))))))))) % 0.50/0.76 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t59))))))))) % 0.50/0.76 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.50/0.76 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.50/0.76 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (and @t26 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.50/0.76 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t26 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.50/0.76 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.50/0.76 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> @t26 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.50/0.76 (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)))))))))))) % 0.50/0.76 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.50/0.76 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t46)))) % 0.50/0.76 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (and @t29 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.50/0.76 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t29 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.50/0.76 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.50/0.76 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> @t29 (tptp.rearsegP @t60 @t1))))))))) % 0.50/0.76 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.50/0.76 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t46)))) % 0.50/0.76 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (and @t30 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.50/0.76 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t30 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.50/0.76 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.50/0.76 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t30 (tptp.segmentP (tptp.app @t60 @t10) @t1))))))))))) % 0.50/0.76 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.50/0.76 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t46)))) % 0.50/0.76 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t61)))) % 0.50/0.76 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.50/0.76 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t61)))) % 0.50/0.76 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.50/0.76 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t61)))) % 0.50/0.76 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.50/0.76 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t61)))) % 0.50/0.76 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.50/0.76 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t27 (= (tptp.totalorderedP @t65) (or @t63 (and @t64 (tptp.totalorderedP @t1) (tptp.leq @t2 @t62))))))))) % 0.50/0.76 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t61)))) % 0.50/0.76 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.50/0.76 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t27 (= (tptp.strictorderedP @t65) (or @t63 (and @t64 (tptp.strictorderedP @t1) (tptp.lt @t2 @t62))))))))) % 0.50/0.76 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t61)))) % 0.50/0.76 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.50/0.76 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t61)))) % 0.50/0.76 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.50/0.76 (assume @p75 (forall @t9 (=> @t17 (=> @t48 (exists @t7 (and @t6 (= @t47 @t1))))))) % 0.50/0.76 (assume @p76 (forall @t9 (=> @t17 (=> @t48 (exists @t7 (and @t27 (= @t49 @t1))))))) % 0.50/0.76 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> (and @t64 @t48 (= @t62 @t47) (= (tptp.tl @t1) @t49)) @t44)))))) % 0.50/0.76 (assume @p78 (forall @t9 (=> @t17 (=> @t48 (= (tptp.cons @t47 @t49) @t2))))) % 0.50/0.76 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (= @t28 @t50) @t66)))))))) % 0.50/0.76 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (=> (= @t25 @t51) @t66)))))))) % 0.50/0.76 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t43 (tptp.app @t18 @t2))))))) % 0.50/0.76 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (forall @t16 (=> @t15 (= (tptp.app @t50 @t12) (tptp.app @t2 @t25))))))))) % 0.50/0.76 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (= (= tptp.nil @t50) (and @t63 @t46))))))) % 0.50/0.76 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.50/0.76 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> @t48 (= (tptp.hd @t50) @t47))))))) % 0.50/0.76 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t27 (=> @t48 (= (tptp.tl @t50) (tptp.app @t49 @t1)))))))) % 0.50/0.76 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t54 (tptp.geq @t1 @t2)) @t3)))))) % 0.50/0.76 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t54 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.50/0.76 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.50/0.76 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.50/0.76 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t53 @t41) @t57)))))))) % 0.50/0.76 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (or @t3 @t56))))))) % 0.50/0.76 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t56 (and @t4 @t53))))))) % 0.50/0.76 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t58 (not (tptp.gt @t1 @t2)))))))) % 0.50/0.76 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t40 (=> (and @t58 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.50/0.76 (assume @p96 @t93) % 0.50/0.76 (assume @p97 true) % 0.50/0.76 (step @p98 :rule aci_norm :args ((= (or @t103 @t102 @t101 @t100 @t97 false @t95) @t104))) % 0.50/0.76 (step @p99 :rule refl :args (@t95)) % 0.50/0.76 (step @p100 :rule evaluate :args ((not true))) % 0.50/0.76 (step @p101 :rule eq-refl :args (@t98)) % 0.50/0.76 (step @p102 :rule cong :premises (@p101) :args (@t105)) % 0.50/0.76 (step @p103 :rule trans :premises (@p102 @p100)) % 0.50/0.76 (step @p104 :rule refl :args (@t97)) % 0.50/0.76 (step @p105 :rule refl :args (@t100)) % 0.50/0.76 (step @p106 :rule refl :args (@t101)) % 0.50/0.76 (step @p107 :rule refl :args (@t102)) % 0.50/0.76 (step @p108 :rule refl :args (@t103)) % 0.50/0.76 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106 @p105 @p104 @p103 @p99) :args (@t106)) % 0.50/0.76 (step @p110 :rule trans :premises (@p109 @p98)) % 0.50/0.76 (step @p111 :rule cong :premises (@p110) :args ((forall @t107 @t106))) % 0.50/0.76 (step @p112 :rule quant-var-elim-eq :args ((= (forall @t9 @t110) @t106))) % 0.50/0.76 (step @p113 :rule aci_norm :args ((= @t111 @t110))) % 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(step @p173 :rule symm :premises (@p172)) % 0.50/0.76 (step @p174 :rule cong :premises (@p173) :args (@t165)) % 0.50/0.76 (step @p175 :rule trans :premises (@p174 @p166)) % 0.50/0.76 (step @p176 :rule trans :premises (@p175 @p165)) % 0.50/0.76 (step @p177 :rule refl :args (@t109)) % 0.50/0.76 (step @p178 :rule refl :args (@t21)) % 0.50/0.76 (step @p179 :rule nary_cong :premises (@p178 @p177 @p176) :args (@t166)) % 0.50/0.76 (step @p180 :rule quant-miniscope-or :args ((= (forall @t7 @t167) @t166))) % 0.50/0.76 (step @p181 :rule aci_norm :args ((= @t168 @t167))) % 0.50/0.76 (step @p182 :rule cong :premises (@p181) :args ((forall @t7 @t168))) % 0.50/0.76 (step @p183 :rule trans :premises (@p182 @p180)) % 0.50/0.76 (step @p184 :rule trans :premises (@p183 @p179)) % 0.50/0.76 (step @p185 :rule aci_norm :args ((= (or @t140 @t168) @t168))) % 0.50/0.76 (step @p186 :rule bool-impl-elim :args (@t27 @t168)) % 0.50/0.76 (step @p187 :rule trans :premises (@p186 @p185)) % 0.50/0.76 (step @p188 :rule 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:rule nary_cong :premises (@p213 @p212 @p231) :args (@t190)) % 0.50/0.76 (step @p233 :rule quant-miniscope-or :args ((= @t185 @t190))) % 0.50/0.76 (step @p234 :rule trans :premises (@p233 @p232)) % 0.50/0.76 (step @p235 :rule symm :premises (@p234)) % 0.50/0.76 (step @p236 :rule cong :premises (@p235) :args (@t201)) % 0.50/0.76 (step @p237 :rule trans :premises (@p236 @p230)) % 0.50/0.76 (step @p238 :rule trans :premises (@p237 @p229)) % 0.50/0.76 (step @p239 :rule refl :args (@t68)) % 0.50/0.76 (step @p240 :rule refl :args (@t140)) % 0.50/0.76 (step @p241 :rule nary_cong :premises (@p240 @p239 @p178 @p238) :args (@t202)) % 0.50/0.76 (step @p242 :rule trans :premises (@p241 @p190)) % 0.50/0.76 (step @p243 :rule quant-miniscope-or :args ((= (forall @t16 @t203) @t202))) % 0.50/0.76 (step @p244 :rule aci_norm :args ((= @t204 @t203))) % 0.50/0.76 (step @p245 :rule cong :premises (@p244) :args ((forall @t16 @t204))) % 0.50/0.76 (step @p246 :rule trans :premises (@p245 @p243)) % 0.50/0.76 (step @p247 :rule trans :premises (@p246 @p242)) % 0.50/0.76 (step @p248 :rule aci_norm :args ((= (or @t175 @t205) @t204))) % 0.50/0.76 (step @p249 :rule bool-impl-elim :args (@t15 @t205)) % 0.50/0.76 (step @p250 :rule trans :premises (@p249 @p248)) % 0.50/0.76 (step @p251 :rule cong :premises (@p250) :args ((forall @t16 (=> @t15 @t205)))) % 0.50/0.76 (step @p252 :rule trans :premises (@p251 @p247)) % 0.50/0.76 (step @p253 :rule aci_norm :args ((= (or @t82 @t206) @t205))) % 0.50/0.76 (step @p254 :rule quant-miniscope-or :args ((= (forall @t198 @t207) @t206))) % 0.50/0.76 (step @p255 :rule aci_norm :args ((= @t208 @t207))) % 0.50/0.76 (step @p256 :rule cong :premises (@p255) :args ((forall @t198 @t208))) % 0.50/0.76 (step @p257 :rule trans :premises (@p256 @p254)) % 0.50/0.76 (step @p258 :rule aci_norm :args ((= (or @t140 @t209) @t208))) % 0.50/0.76 (step @p259 :rule aci_norm :args ((= @t210 @t209))) % 0.50/0.76 (step @p260 :rule nary_cong :premises (@p240 @p259) :args (@t211)) % 0.50/0.76 (step @p261 :rule trans :premises (@p260 @p258)) % 0.50/0.76 (step @p262 :rule cong :premises (@p261) :args ((forall @t198 @t211))) % 0.50/0.76 (step @p263 :rule trans :premises (@p262 @p257)) % 0.50/0.76 (step @p264 :rule bool-or-taut2 :args (false @t67 false false)) % 0.50/0.76 (step @p265 :rule refl :args (@t209)) % 0.50/0.76 (step @p266 :rule nary_cong :premises (@p265 @p264) :args (@t212)) % 0.50/0.76 (step @p267 :rule nary_cong :premises (@p169 @p266) :args (@t213)) % 0.50/0.76 (step @p268 :rule cong :premises (@p267) :args ((forall @t198 @t213))) % 0.50/0.76 (step @p269 :rule trans :premises (@p268 @p263)) % 0.50/0.76 (step @p270 :rule aci_norm :args ((= (or @t140 false @t212) @t213))) % 0.50/0.76 (step @p271 :rule refl :args (@t212)) % 0.50/0.76 (step @p272 :rule eq-refl :args (@t1)) % 0.50/0.76 (step @p273 :rule cong :premises (@p272) :args (@t214)) % 0.50/0.76 (step @p274 :rule trans :premises (@p273 @p100)) % 0.50/0.76 (step @p275 :rule nary_cong :premises (@p240 @p274 @p271) :args (@t215)) % 0.50/0.76 (step @p276 :rule trans :premises (@p275 @p270)) % 0.50/0.76 (step @p277 :rule cong :premises (@p276) :args ((forall @t198 @t215))) % 0.50/0.76 (step @p278 :rule trans :premises (@p277 @p269)) % 0.50/0.76 (step @p279 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t219 @t83 @t218)) @t215))) % 0.50/0.76 (step @p280 :rule refl :args (@t218)) % 0.50/0.76 (step @p281 :rule refl :args (@t83)) % 0.50/0.76 (step @p282 :rule refl :args (@t219)) % 0.50/0.76 (step @p283 :rule eq-symm :args (@t1 @t10)) % 0.50/0.76 (step @p284 :rule cong :premises (@p283) :args (@t83)) % 0.50/0.76 (step @p285 :rule nary_cong :premises (@p284 @p282 @p281 @p280) :args (@t220)) % 0.50/0.76 (step @p286 :rule aci_norm :args ((= @t221 @t220))) % 0.50/0.76 (step @p287 :rule trans :premises (@p286 @p285)) % 0.50/0.76 (step @p288 :rule cong :premises (@p287) :args (@t222)) % 0.50/0.76 (step @p289 :rule trans :premises (@p288 @p279)) % 0.50/0.76 (step @p290 :rule cong :premises (@p289) :args (@t223)) % 0.50/0.76 (step @p291 :rule quant-merge-prenex :args ((= @t223 @t224))) % 0.50/0.76 (step @p292 :rule symm :premises (@p291)) % 0.50/0.76 (step @p293 :rule quant_var_reordering :args ((= (forall @t225 @t221) @t224))) % 0.50/0.76 (step @p294 :rule trans :premises (@p293 @p292 @p290)) % 0.50/0.76 (step @p295 :rule trans :premises (@p294 @p278)) % 0.50/0.76 (step @p296 :rule refl :args (@t69)) % 0.50/0.76 (step @p297 :rule aci_norm :args ((= @t227 @t217))) % 0.50/0.76 (step @p298 :rule nary_cong :premises (@p297 @p296) :args (@t228)) % 0.50/0.76 (step @p299 :rule refl :args (@t83)) % 0.50/0.76 (step @p300 :rule refl :args (@t219)) % 0.50/0.76 (step @p301 :rule nary_cong :premises (@p300 @p299 @p298) :args (@t229)) % 0.50/0.76 (step @p302 :rule cong :premises (@p301) :args (@t230)) % 0.50/0.76 (step @p303 :rule trans :premises (@p302 @p295)) % 0.50/0.76 (step @p304 :rule quant-merge-prenex :args ((= (forall @t14 @t231) @t230))) % 0.50/0.76 (step @p305 :rule quant-unused-vars :args ((= @t232 @t69))) % 0.50/0.76 (step @p306 :rule alpha_equiv :args (@t233 @t189 (@list @t34 @t234))) % 0.50/0.76 (step @p307 :rule nary_cong :premises (@p168 @p306 @p127) :args (@t235)) % 0.50/0.76 (step @p308 :rule quant-miniscope-or :args ((= @t236 @t235))) % 0.50/0.76 (step @p309 :rule trans :premises (@p308 @p307)) % 0.50/0.76 (step @p310 :rule nary_cong :premises (@p309 @p305) :args (@t237)) % 0.50/0.76 (step @p311 :rule quant-miniscope-and :args ((= @t238 @t237))) % 0.50/0.76 (step @p312 :rule trans :premises (@p311 @p310)) % 0.50/0.76 (step @p313 :rule nary_cong :premises (@p282 @p281 @p312) :args (@t239)) % 0.50/0.76 (step @p314 :rule quant-miniscope-or :args ((= @t231 @t239))) % 0.50/0.76 (step @p315 :rule trans :premises (@p314 @p313)) % 0.50/0.76 (step @p316 :rule symm :premises (@p315)) % 0.50/0.76 (step @p317 :rule cong :premises (@p316) :args (@t248)) % 0.50/0.76 (step @p318 :rule trans :premises (@p317 @p304)) % 0.50/0.76 (step @p319 :rule trans :premises (@p318 @p303)) % 0.50/0.76 (step @p320 :rule refl :args (@t82)) % 0.50/0.76 (step @p321 :rule nary_cong :premises (@p320 @p319) :args (@t249)) % 0.50/0.76 (step @p322 :rule trans :premises (@p321 @p253)) % 0.50/0.76 (step @p323 :rule quant-miniscope-or :args ((= (forall @t14 @t250) @t249))) % 0.50/0.76 (step @p324 :rule aci_norm :args ((= @t251 @t250))) % 0.50/0.76 (step @p325 :rule cong :premises (@p324) :args ((forall @t14 @t251))) % 0.50/0.76 (step @p326 :rule trans :premises (@p325 @p323)) % 0.50/0.76 (step @p327 :rule trans :premises (@p326 @p322)) % 0.50/0.76 (step @p328 :rule aci_norm :args ((= (or @t219 @t252) @t251))) % 0.50/0.76 (step @p329 :rule bool-impl-elim :args (@t13 @t252)) % 0.50/0.76 (step @p330 :rule trans :premises (@p329 @p328)) % 0.50/0.76 (step @p331 :rule cong :premises (@p330) :args ((forall @t14 (=> @t13 @t252)))) % 0.50/0.76 (step @p332 :rule trans :premises (@p331 @p327)) % 0.50/0.76 (step @p333 :rule aci_norm :args ((= @t254 @t244))) % 0.50/0.76 (step @p334 :rule cong :premises (@p333) :args (@t255)) % 0.50/0.76 (step @p335 :rule quant-merge-prenex :args ((= (forall @t39 @t257) @t255))) % 0.50/0.76 (step @p336 :rule alpha_equiv :args (@t258 (@list @t234) (@list @t33))) % 0.50/0.76 (step @p337 :rule refl :args (@t242)) % 0.50/0.76 (step @p338 :rule refl :args (@t243)) % 0.50/0.76 (step @p339 :rule nary_cong :premises (@p338 @p337 @p336) :args (@t259)) % 0.50/0.76 (step @p340 :rule quant-miniscope-or :args ((= @t257 @t259))) % 0.50/0.76 (step @p341 :rule trans :premises (@p340 @p339)) % 0.50/0.76 (step @p342 :rule symm :premises (@p341)) % 0.50/0.76 (step @p343 :rule cong :premises (@p342) :args ((forall @t39 @t264))) % 0.50/0.76 (step @p344 :rule trans :premises (@p343 @p335)) % 0.50/0.76 (step @p345 :rule trans :premises (@p344 @p334)) % 0.50/0.76 (step @p346 :rule aci_norm :args ((= (or @t243 @t265) @t264))) % 0.50/0.76 (step @p347 :rule bool-impl-elim :args (@t77 @t265)) % 0.50/0.76 (step @p348 :rule trans :premises (@p347 @p346)) % 0.50/0.76 (step @p349 :rule cong :premises (@p348) :args ((forall @t39 (=> @t77 @t265)))) % 0.50/0.76 (step @p350 :rule trans :premises (@p349 @p345)) % 0.50/0.76 (step @p351 :rule quant-miniscope-or :args ((= (forall @t37 @t266) @t265))) % 0.50/0.76 (step @p352 :rule aci_norm :args ((= @t267 @t266))) % 0.50/0.76 (step @p353 :rule cong :premises (@p352) :args ((forall @t37 @t267))) % 0.50/0.76 (step @p354 :rule trans :premises (@p353 @p351)) % 0.50/0.76 (step @p355 :rule aci_norm :args ((= (or @t261 @t268) @t267))) % 0.50/0.76 (step @p356 :rule bool-impl-elim :args (@t36 @t268)) % 0.50/0.76 (step @p357 :rule trans :premises (@p356 @p355)) % 0.50/0.76 (step @p358 :rule cong :premises (@p357) :args ((forall @t37 (=> @t36 @t268)))) % 0.50/0.76 (step @p359 :rule trans :premises (@p358 @p354)) % 0.50/0.76 (step @p360 :rule eq-symm :args (@t71 @t10)) % 0.50/0.76 (step @p361 :rule cong :premises (@p360) :args (@t72)) % 0.50/0.76 (step @p362 :rule eq-symm :args (@t70 @t12)) % 0.50/0.76 (step @p363 :rule cong :premises (@p362) :args (@t73)) % 0.50/0.76 (step @p364 :rule nary_cong :premises (@p363 @p361) :args (@t74)) % 0.50/0.76 (step @p365 :rule refl :args (@t36)) % 0.50/0.76 (step @p366 :rule cong :premises (@p365 @p364) :args (@t75)) % 0.50/0.76 (step @p367 :rule cong :premises (@p366) :args (@t76)) % 0.50/0.76 (step @p368 :rule trans :premises (@p367 @p359)) % 0.50/0.76 (step @p369 :rule refl :args (@t77)) % 0.50/0.76 (step @p370 :rule cong :premises (@p369 @p368) :args (@t78)) % 0.50/0.76 (step @p371 :rule cong :premises (@p370) :args (@t79)) % 0.50/0.76 (step @p372 :rule trans :premises (@p371 @p350)) % 0.50/0.76 (step @p373 :rule nary_cong :premises (@p239 @p372 @p178) :args (@t80)) % 0.50/0.76 (step @p374 :rule nary_cong :premises (@p373 @p296) :args (@t81)) % 0.50/0.76 (step @p375 :rule nary_cong :premises (@p299 @p320 @p374) :args (@t84)) % 0.50/0.76 (step @p376 :rule refl :args (@t13)) % 0.50/0.76 (step @p377 :rule cong :premises (@p376 @p375) :args (@t85)) % 0.50/0.76 (step @p378 :rule cong :premises (@p377) :args (@t86)) % 0.50/0.76 (step @p379 :rule trans :premises (@p378 @p332)) % 0.50/0.76 (step @p380 :rule refl :args (@t15)) % 0.50/0.76 (step @p381 :rule cong :premises (@p380 @p379) :args (@t87)) % 0.50/0.76 (step @p382 :rule cong :premises (@p381) :args (@t88)) % 0.50/0.76 (step @p383 :rule trans :premises (@p382 @p252)) % 0.50/0.76 (step @p384 :rule refl :args (@t27)) % 0.50/0.76 (step @p385 :rule cong :premises (@p384 @p383) :args (@t89)) % 0.50/0.76 (step @p386 :rule cong :premises (@p385) :args (@t90)) % 0.50/0.76 (step @p387 :rule trans :premises (@p386 @p189)) % 0.50/0.76 (step @p388 :rule refl :args (@t17)) % 0.50/0.76 (step @p389 :rule cong :premises (@p388 @p387) :args (@t91)) % 0.50/0.76 (step @p390 :rule cong :premises (@p389) :args (@t92)) % 0.50/0.76 (step @p391 :rule trans :premises (@p390 @p140)) % 0.50/0.76 (step @p392 :rule cong :premises (@p391) :args (@t93)) % 0.50/0.76 (step @p393 :rule eq_resolve :premises (@p96 @p392)) % 0.50/0.76 (step @p394 :rule skolemize :premises (@p393)) % 0.50/0.76 (step @p395 :rule bool-double-not-elim :args (@t271)) % 0.50/0.76 (step @p396 :rule refl :args (@t279)) % 0.50/0.76 (step @p397 :rule nary_cong :premises (@p396 @p395) :args ((or @t279 (not @t273)))) % 0.50/0.76 (step @p398 :rule cnf_or_neg :args (@t279 4)) % 0.50/0.76 (step @p399 :rule eq_resolve :premises (@p398 @p397)) % 0.50/0.76 (step @p400 :rule reordering :premises (@p399) :args ((or @t271 @t279))) % 0.50/0.76 (step @p401 :rule chain_m_resolution :premises (@p400 @p394) :args (@t271 @t280 @t281)) % 0.50/0.76 (step @p402 :rule bool-impl-elim :args (@t17 @t284)) % 0.50/0.76 (step @p403 :rule cong :premises (@p402) :args ((forall @t9 (=> @t17 @t284)))) % 0.50/0.76 (step @p404 :rule bool-and-de-morgan :args (@t6 @t282 true)) % 0.50/0.76 (step @p405 :rule cong :premises (@p404) :args (@t286)) % 0.50/0.76 (step @p406 :rule cong :premises (@p405) :args (@t287)) % 0.50/0.76 (step @p407 :rule exists-elim :args ((= (exists @t7 @t285) @t287))) % 0.50/0.76 (step @p408 :rule trans :premises (@p407 @p406)) % 0.50/0.76 (step @p409 :rule eq-symm :args (@t18 @t2)) % 0.50/0.76 (step @p410 :rule refl :args (@t6)) % 0.50/0.76 (step @p411 :rule nary_cong :premises (@p410 @p409) :args (@t19)) % 0.50/0.76 (step @p412 :rule cong :premises (@p411) :args (@t20)) % 0.50/0.76 (step @p413 :rule trans :premises (@p412 @p408)) % 0.50/0.76 (step @p414 :rule cong :premises (@p178 @p413) :args (@t22)) % 0.50/0.76 (step @p415 :rule cong :premises (@p388 @p414) :args (@t23)) % 0.50/0.77 (step @p416 :rule cong :premises (@p415) :args (@t24)) % 0.50/0.77 (step @p417 :rule trans :premises (@p416 @p403)) % 0.50/0.77 (step @p418 :rule eq_resolve :premises (@p4 @p417)) % 0.50/0.77 (step @p419 :rule eq-symm :args (@t274 @t18)) % 0.50/0.77 (step @p420 :rule cong :premises (@p419) :args (@t288)) % 0.50/0.77 (step @p421 :rule refl :args (@t283)) % 0.50/0.77 (step @p422 :rule nary_cong :premises (@p421 @p420) :args (@t289)) % 0.50/0.77 (step @p423 :rule cong :premises (@p422) :args (@t290)) % 0.50/0.77 (step @p424 :rule cong :premises (@p423) :args (@t291)) % 0.50/0.77 (step @p425 :rule refl :args (@t276)) % 0.50/0.77 (step @p426 :rule cong :premises (@p425 @p424) :args (@t292)) % 0.50/0.77 (step @p427 :rule refl :args (@t278)) % 0.50/0.77 (step @p428 :rule nary_cong :premises (@p427 @p426) :args (@t293)) % 0.50/0.77 (step @p429 :rule refl :args (@t294)) % 0.50/0.77 (step @p430 :rule cong :premises (@p429 @p428) :args ((=> @t294 @t293))) % 0.50/0.77 (assume-push @p473 @t294) % 0.50/0.77 (step @p432 :rule instantiate :premises (@p418) :args ((@list @t274))) % 0.50/0.77 (step-pop @p474 :rule scope :premises (@p432)) % 0.50/0.77 (step @p433 :rule process_scope :premises (@p474) :args (@t293)) % 0.50/0.77 (step @p435 :rule eq_resolve :premises (@p433 @p430)) % 0.50/0.77 (step @p436 :rule implies_elim :premises (@p435)) % 0.50/0.77 (step @p437 :rule chain_m_resolution :premises (@p436 @p418) :args (@t298 (@list false) (@list @t294))) % 0.50/0.77 (step @p438 :rule bool-double-not-elim :args (@t277)) % 0.50/0.77 (step @p439 :rule nary_cong :premises (@p396 @p438) :args ((or @t279 (not @t278)))) % 0.50/0.77 (step @p440 :rule cnf_or_neg :args (@t279 0)) % 0.50/0.77 (step @p441 :rule eq_resolve :premises (@p440 @p439)) % 0.50/0.77 (step @p442 :rule reordering :premises (@p441) :args ((or @t277 @t279))) % 0.50/0.77 (step @p443 :rule chain_m_resolution :premises (@p442 @p394) :args (@t277 @t280 @t281)) % 0.50/0.77 (step @p444 :rule cnf_or_pos :args (@t298)) % 0.50/0.77 (step @p445 :rule reordering :premises (@p444) :args ((or @t278 @t297 (not @t298)))) % 0.50/0.77 (step @p446 :rule chain_m_resolution :premises (@p445 @p443 @p437) :args (@t297 @t299 (@list @t277 @t298))) % 0.50/0.77 (step @p447 :rule cnf_or_neg :args (@t279 1)) % 0.50/0.77 (step @p448 :rule chain_m_resolution :premises (@p447 @p394) :args ((not @t276) @t280 @t281)) % 0.50/0.77 (step @p449 :rule bool-double-not-elim :args (@t295)) % 0.50/0.77 (step @p450 :rule refl :args (@t300)) % 0.50/0.77 (step @p451 :rule nary_cong :premises (@p450 @p425 @p449) :args ((or @t300 @t276 (not @t296)))) % 0.50/0.77 (step @p452 :rule cnf_equiv_pos2 :args (@t297)) % 0.50/0.77 (step @p453 :rule eq_resolve :premises (@p452 @p451)) % 0.50/0.77 (step @p454 :rule reordering :premises (@p453) :args ((or @t276 @t295 @t300))) % 0.50/0.77 (step @p455 :rule chain_m_resolution :premises (@p454 @p448 @p446) :args (@t295 (@list true false) (@list @t276 @t297))) % 0.50/0.77 (step @p456 :rule aci_norm :args ((= (or @t273 false) @t273))) % 0.50/0.77 (step @p457 :rule eq-refl :args (@t274)) % 0.50/0.77 (step @p458 :rule cong :premises (@p457) :args (@t301)) % 0.50/0.77 (step @p459 :rule trans :premises (@p458 @p100)) % 0.50/0.77 (step @p460 :rule refl :args (@t273)) % 0.50/0.77 (step @p461 :rule nary_cong :premises (@p460 @p459) :args (@t302)) % 0.50/0.77 (step @p462 :rule trans :premises (@p461 @p456)) % 0.50/0.77 (step @p463 :rule refl :args (@t295)) % 0.50/0.77 (step @p464 :rule cong :premises (@p463 @p462) :args ((=> @t295 @t302))) % 0.50/0.77 (assume-push @p475 @t295) % 0.50/0.77 (step @p466 :rule instantiate :premises (@p455) :args ((@list @t270))) % 0.50/0.77 (step-pop @p476 :rule scope :premises (@p466)) % 0.50/0.77 (step @p467 :rule process_scope :premises (@p476) :args (@t302)) % 0.50/0.77 (step @p469 :rule eq_resolve :premises (@p467 @p464)) % 0.50/0.77 (step @p470 :rule implies_elim :premises (@p469)) % 0.50/0.77 (step @p471 :rule reordering :premises (@p470) :args ((or @t273 @t296))) % 0.50/0.77 (step @p472 false :rule chain_m_resolution :premises (@p471 @p455 @p401) :args (false @t299 (@list @t295 @t271))) % 0.50/0.77 ) % 0.50/0.77 % SZS output end Proof % 0.50/0.77 % cvc5 exiting %------------------------------------------------------------------------------