%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC120+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 : n028.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 08:58:08 AM UTC 2026 % Result : Theorem 7.73s 7.92s % Output : Proof 7.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC120+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 % 0.16/0.34 % Computer : n028.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 19:15:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 7.73/7.92 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 7.73/7.92 % SZS status Theorem % 7.73/7.92 % SZS output start Proof % 7.73/7.92 ( % 7.73/7.92 (declare-sort $$unsorted 0) % 7.73/7.92 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 7.73/7.92 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 7.73/7.92 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 7.73/7.92 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 7.73/7.92 (declare-const tptp.nil $$unsorted) % 7.73/7.92 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.ssList (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 7.73/7.92 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 7.73/7.92 (define @t1 () (@var "V" $$unsorted)) % 7.73/7.92 (define @t2 () (@var "U" $$unsorted)) % 7.73/7.92 (define @t3 () (= @t2 @t1)) % 7.73/7.92 (define @t4 () (not @t3)) % 7.73/7.92 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 7.73/7.92 (define @t6 () (tptp.ssItem @t1)) % 7.73/7.92 (define @t7 () (@list @t1)) % 7.73/7.92 (define @t8 () (tptp.ssItem @t2)) % 7.73/7.92 (define @t9 () (@list @t2)) % 7.73/7.92 (define @t10 () (@var "X" $$unsorted)) % 7.73/7.92 (define @t11 () (tptp.cons @t1 @t10)) % 7.73/7.92 (define @t12 () (@var "W" $$unsorted)) % 7.73/7.92 (define @t13 () (tptp.ssList @t10)) % 7.73/7.92 (define @t14 () (@list @t10)) % 7.73/7.92 (define @t15 () (tptp.ssList @t12)) % 7.73/7.92 (define @t16 () (@list @t12)) % 7.73/7.92 (define @t17 () (tptp.ssList @t2)) % 7.73/7.92 (define @t18 () (tptp.cons @t1 tptp.nil)) % 7.73/7.92 (define @t19 () (tptp.app @t1 @t12)) % 7.73/7.92 (define @t20 () (tptp.frontsegP @t2 @t1)) % 7.73/7.92 (define @t21 () (tptp.ssList @t1)) % 7.73/7.92 (define @t22 () (tptp.app @t12 @t1)) % 7.73/7.92 (define @t23 () (tptp.rearsegP @t2 @t1)) % 7.73/7.92 (define @t24 () (tptp.app @t22 @t10)) % 7.73/7.92 (define @t25 () (and @t13 (= @t24 @t2))) % 7.73/7.92 (define @t26 () (exists @t14 @t25)) % 7.73/7.92 (define @t27 () (and @t15 @t26)) % 7.73/7.92 (define @t28 () (exists @t16 @t27)) % 7.73/7.92 (define @t29 () (tptp.segmentP @t2 @t1)) % 7.73/7.92 (define @t30 () (= @t29 @t28)) % 7.73/7.92 (define @t31 () (=> @t21 @t30)) % 7.73/7.92 (define @t32 () (forall @t7 @t31)) % 7.73/7.92 (define @t33 () (=> @t17 @t32)) % 7.73/7.92 (define @t34 () (forall @t9 @t33)) % 7.73/7.92 (define @t35 () (tptp.leq @t12 @t1)) % 7.73/7.92 (define @t36 () (tptp.leq @t1 @t12)) % 7.73/7.92 (define @t37 () (@var "Z" $$unsorted)) % 7.73/7.92 (define @t38 () (@var "Y" $$unsorted)) % 7.73/7.92 (define @t39 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t38)) (tptp.cons @t12 @t37)) @t2)) % 7.73/7.92 (define @t40 () (tptp.ssList @t37)) % 7.73/7.92 (define @t41 () (@list @t37)) % 7.73/7.92 (define @t42 () (tptp.ssList @t38)) % 7.73/7.92 (define @t43 () (@list @t38)) % 7.73/7.92 (define @t44 () (tptp.ssItem @t12)) % 7.73/7.92 (define @t45 () (tptp.lt @t1 @t12)) % 7.73/7.92 (define @t46 () (= @t1 @t12)) % 7.73/7.92 (define @t47 () (forall @t7 (=> @t21 @t5))) % 7.73/7.92 (define @t48 () (=> @t17 @t47)) % 7.73/7.92 (define @t49 () (forall @t9 @t48)) % 7.73/7.92 (define @t50 () (tptp.cons @t1 @t2)) % 7.73/7.92 (define @t51 () (tptp.ssList tptp.nil)) % 7.73/7.92 (define @t52 () (not (= @t50 @t2))) % 7.73/7.92 (define @t53 () (=> @t6 @t52)) % 7.73/7.92 (define @t54 () (forall @t7 @t53)) % 7.73/7.92 (define @t55 () (=> @t17 @t54)) % 7.73/7.92 (define @t56 () (forall @t9 @t55)) % 7.73/7.92 (define @t57 () (= @t1 @t2)) % 7.73/7.92 (define @t58 () (tptp.cons @t12 @t1)) % 7.73/7.92 (define @t59 () (= tptp.nil @t2)) % 7.73/7.92 (define @t60 () (tptp.hd @t2)) % 7.73/7.92 (define @t61 () (tptp.ssItem @t60)) % 7.73/7.92 (define @t62 () (not @t59)) % 7.73/7.92 (define @t63 () (=> @t62 @t61)) % 7.73/7.92 (define @t64 () (=> @t17 @t63)) % 7.73/7.92 (define @t65 () (forall @t9 @t64)) % 7.73/7.92 (define @t66 () (tptp.tl @t2)) % 7.73/7.92 (define @t67 () (tptp.ssList @t66)) % 7.73/7.92 (define @t68 () (=> @t62 @t67)) % 7.73/7.92 (define @t69 () (=> @t17 @t68)) % 7.73/7.92 (define @t70 () (forall @t9 @t69)) % 7.73/7.92 (define @t71 () (tptp.app @t2 @t1)) % 7.73/7.92 (define @t72 () (tptp.ssList @t71)) % 7.73/7.92 (define @t73 () (forall @t7 (=> @t21 @t72))) % 7.73/7.92 (define @t74 () (=> @t17 @t73)) % 7.73/7.92 (define @t75 () (forall @t9 @t74)) % 7.73/7.92 (define @t76 () (tptp.app @t1 @t2)) % 7.73/7.92 (define @t77 () (tptp.app tptp.nil @t2)) % 7.73/7.92 (define @t78 () (=> @t17 (= @t77 @t2))) % 7.73/7.92 (define @t79 () (forall @t9 @t78)) % 7.73/7.92 (define @t80 () (tptp.leq @t1 @t2)) % 7.73/7.92 (define @t81 () (tptp.leq @t2 @t1)) % 7.73/7.92 (define @t82 () (tptp.geq @t2 @t1)) % 7.73/7.92 (define @t83 () (tptp.lt @t1 @t2)) % 7.73/7.92 (define @t84 () (tptp.lt @t2 @t1)) % 7.73/7.92 (define @t85 () (tptp.lt @t2 @t12)) % 7.73/7.92 (define @t86 () (tptp.gt @t2 @t1)) % 7.73/7.92 (define @t87 () (tptp.memberP @t12 @t2)) % 7.73/7.92 (define @t88 () (tptp.app @t12 @t2)) % 7.73/7.92 (define @t89 () (tptp.segmentP @t1 @t2)) % 7.73/7.92 (define @t90 () (tptp.cons @t2 tptp.nil)) % 7.73/7.92 (define @t91 () (tptp.hd @t1)) % 7.73/7.92 (define @t92 () (= tptp.nil @t1)) % 7.73/7.92 (define @t93 () (not @t92)) % 7.73/7.92 (define @t94 () (tptp.cons @t2 @t1)) % 7.73/7.92 (define @t95 () (tptp.tl @t1)) % 7.73/7.92 (define @t96 () (tptp.cons @t60 @t66)) % 7.73/7.92 (define @t97 () (=> @t62 (= @t96 @t2))) % 7.73/7.92 (define @t98 () (=> @t17 @t97)) % 7.73/7.92 (define @t99 () (forall @t9 @t98)) % 7.73/7.92 (define @t100 () (= @t12 @t2)) % 7.73/7.92 (define @t101 () (tptp.app @t2 tptp.nil)) % 7.73/7.92 (define @t102 () (=> @t17 (= @t101 @t2))) % 7.73/7.92 (define @t103 () (forall @t9 @t102)) % 7.73/7.92 (define @t104 () (tptp.neq @t1 tptp.nil)) % 7.73/7.92 (define @t105 () (not @t104)) % 7.73/7.92 (define @t106 () (or @t105 (tptp.neq @t10 tptp.nil))) % 7.73/7.92 (define @t107 () (tptp.neq @t2 tptp.nil)) % 7.73/7.92 (define @t108 () (and @t107 @t89)) % 7.73/7.92 (define @t109 () (tptp.neq tptp.nil @t10)) % 7.73/7.92 (define @t110 () (tptp.app @t12 @t37)) % 7.73/7.92 (define @t111 () (tptp.tl @t10)) % 7.73/7.92 (define @t112 () (and @t40 (= @t111 @t37) (= @t110 @t38) @t109)) % 7.73/7.92 (define @t113 () (exists @t41 @t112)) % 7.73/7.92 (define @t114 () (= @t10 @t38)) % 7.73/7.92 (define @t115 () (not @t114)) % 7.73/7.92 (define @t116 () (and @t42 @t115 @t113)) % 7.73/7.92 (define @t117 () (exists @t43 @t116)) % 7.73/7.92 (define @t118 () (or @t105 @t117 @t108)) % 7.73/7.92 (define @t119 () (and @t118 @t106)) % 7.73/7.92 (define @t120 () (not (= @t2 @t12))) % 7.73/7.92 (define @t121 () (not (= @t1 @t10))) % 7.73/7.92 (define @t122 () (or @t121 @t120 @t119)) % 7.73/7.92 (define @t123 () (=> @t13 @t122)) % 7.73/7.92 (define @t124 () (forall @t14 @t123)) % 7.73/7.92 (define @t125 () (=> @t15 @t124)) % 7.73/7.92 (define @t126 () (forall @t16 @t125)) % 7.73/7.92 (define @t127 () (=> @t21 @t126)) % 7.73/7.92 (define @t128 () (forall @t7 @t127)) % 7.73/7.92 (define @t129 () (=> @t17 @t128)) % 7.73/7.92 (define @t130 () (forall @t9 @t129)) % 7.73/7.92 (define @t131 () (not @t130)) % 7.73/7.92 (define @t132 () (= @t2 @t77)) % 7.73/7.92 (define @t133 () (@var "BOUND_VARIABLE_11041" $$unsorted)) % 7.73/7.92 (define @t134 () (tptp.tl @t133)) % 7.73/7.92 (define @t135 () (tptp.app @t2 @t134)) % 7.73/7.92 (define @t136 () (and (tptp.neq tptp.nil @t133) (tptp.ssList @t134) (tptp.ssList @t135) (not (= @t133 @t135)))) % 7.73/7.92 (define @t137 () (and @t107 (tptp.segmentP @t133 @t2))) % 7.73/7.92 (define @t138 () (not (tptp.neq @t133 tptp.nil))) % 7.73/7.92 (define @t139 () (not (tptp.ssList @t133))) % 7.73/7.92 (define @t140 () (not @t17)) % 7.73/7.92 (define @t141 () (or @t140 @t139 @t138 @t137 @t136)) % 7.73/7.92 (define @t142 () (@list @t2 @t133)) % 7.73/7.92 (define @t143 () (forall @t142 @t141)) % 7.73/7.92 (define @t144 () (@quantifiers_skolemize @t143 0)) % 7.73/7.92 (define @t145 () (@list @t144)) % 7.73/7.92 (define @t146 () (or @t139 @t138 @t137 @t136)) % 7.73/7.92 (define @t147 () (or @t140 @t146)) % 7.73/7.92 (define @t148 () (forall @t142 @t147)) % 7.73/7.92 (define @t149 () (@list @t133)) % 7.73/7.92 (define @t150 () (forall @t149 @t147)) % 7.73/7.92 (define @t151 () (forall @t149 @t146)) % 7.73/7.92 (define @t152 () (@list @t1)) % 7.73/7.92 (define @t153 () (or @t140 @t151)) % 7.73/7.92 (define @t154 () (tptp.app @t2 @t95)) % 7.73/7.92 (define @t155 () (tptp.ssList @t95)) % 7.73/7.92 (define @t156 () (tptp.neq tptp.nil @t1)) % 7.73/7.92 (define @t157 () (and @t156 @t155 (tptp.ssList @t154) (not (= @t1 @t154)))) % 7.73/7.92 (define @t158 () (not @t21)) % 7.73/7.92 (define @t159 () (or @t158 @t105 @t108 @t157)) % 7.73/7.92 (define @t160 () (or @t140 (forall @t7 @t159))) % 7.73/7.92 (define @t161 () (or @t140 @t159)) % 7.73/7.92 (define @t162 () (or @t158 @t105 @t108 @t140 @t157)) % 7.73/7.92 (define @t163 () (or @t140 @t157)) % 7.73/7.92 (define @t164 () (not (= @t2 @t2))) % 7.73/7.92 (define @t165 () (or @t140 @t164 @t157)) % 7.73/7.92 (define @t166 () (tptp.app @t12 @t95)) % 7.73/7.92 (define @t167 () (and @t156 @t155 (tptp.ssList @t166) (not (= @t1 @t166)))) % 7.73/7.92 (define @t168 () (not @t15)) % 7.73/7.92 (define @t169 () (or @t120 @t168 @t120 @t167)) % 7.73/7.92 (define @t170 () (or @t168 @t120 @t167)) % 7.73/7.92 (define @t171 () (forall @t16 @t170)) % 7.73/7.92 (define @t172 () (or @t158 @t105 @t108 @t171)) % 7.73/7.92 (define @t173 () (or @t158 @t105 @t108 @t170)) % 7.73/7.92 (define @t174 () (or @t168 @t120 @t158 @t105 @t167 @t108)) % 7.73/7.92 (define @t175 () (or @t105 @t167 @t108)) % 7.73/7.92 (define @t176 () (and @t175 true)) % 7.73/7.92 (define @t177 () (or @t168 @t120 @t158 @t176)) % 7.73/7.92 (define @t178 () (and @t175 (or @t105 @t104))) % 7.73/7.92 (define @t179 () (or @t120 @t158 @t178)) % 7.73/7.92 (define @t180 () (or @t158 @t178)) % 7.73/7.92 (define @t181 () (not (= @t1 @t1))) % 7.73/7.92 (define @t182 () (or @t158 @t181 @t178)) % 7.73/7.92 (define @t183 () (tptp.app @t12 @t111)) % 7.73/7.92 (define @t184 () (= @t10 @t183)) % 7.73/7.92 (define @t185 () (not @t184)) % 7.73/7.92 (define @t186 () (tptp.ssList @t183)) % 7.73/7.92 (define @t187 () (tptp.ssList @t111)) % 7.73/7.92 (define @t188 () (and (or @t105 (and @t109 @t187 @t186 @t185) @t108) @t106)) % 7.73/7.92 (define @t189 () (not @t13)) % 7.73/7.92 (define @t190 () (or @t121 @t189 @t121 @t188)) % 7.73/7.92 (define @t191 () (or @t189 @t121 @t188)) % 7.73/7.92 (define @t192 () (forall @t14 @t191)) % 7.73/7.92 (define @t193 () (or @t120 @t192)) % 7.73/7.92 (define @t194 () (or @t120 @t191)) % 7.73/7.92 (define @t195 () (or @t189 @t121 @t120 @t188)) % 7.73/7.92 (define @t196 () (not @t186)) % 7.73/7.92 (define @t197 () (not @t196)) % 7.73/7.92 (define @t198 () (not @t187)) % 7.73/7.92 (define @t199 () (not @t198)) % 7.73/7.92 (define @t200 () (not @t109)) % 7.73/7.92 (define @t201 () (not @t200)) % 7.73/7.92 (define @t202 () (and @t201 @t199 @t197 @t185)) % 7.73/7.92 (define @t203 () (or @t196 @t184)) % 7.73/7.92 (define @t204 () (or @t200 @t198 @t196 @t184)) % 7.73/7.92 (define @t205 () (or @t105 (not @t204) @t108)) % 7.73/7.92 (define @t206 () (and @t205 @t106)) % 7.73/7.92 (define @t207 () (or @t121 @t120 @t206)) % 7.73/7.92 (define @t208 () (not (= @t183 @t183))) % 7.73/7.92 (define @t209 () (or @t196 @t184 @t208)) % 7.73/7.92 (define @t210 () (not (= @t38 @t183))) % 7.73/7.92 (define @t211 () (not @t42)) % 7.73/7.92 (define @t212 () (or @t210 @t211 @t114 @t210)) % 7.73/7.92 (define @t213 () (or @t211 @t114 @t210)) % 7.73/7.92 (define @t214 () (forall @t43 @t213)) % 7.73/7.92 (define @t215 () (or @t200 @t198 @t214)) % 7.73/7.92 (define @t216 () (or @t200 @t198 @t213)) % 7.73/7.92 (define @t217 () (or @t211 @t114 @t200 @t198 @t210)) % 7.73/7.92 (define @t218 () (or @t200 @t198 @t210)) % 7.73/7.92 (define @t219 () (not @t218)) % 7.73/7.92 (define @t220 () (not @t219)) % 7.73/7.92 (define @t221 () (not @t115)) % 7.73/7.92 (define @t222 () (or @t211 @t221 @t220)) % 7.73/7.92 (define @t223 () (and @t42 @t115 @t219)) % 7.73/7.92 (define @t224 () (forall @t43 (not @t223))) % 7.73/7.92 (define @t225 () (not @t224)) % 7.73/7.92 (define @t226 () (or @t198 @t210)) % 7.73/7.92 (define @t227 () (not (= @t111 @t111))) % 7.73/7.92 (define @t228 () (or @t198 @t227 @t210)) % 7.73/7.92 (define @t229 () (= @t38 @t110)) % 7.73/7.92 (define @t230 () (not @t229)) % 7.73/7.92 (define @t231 () (= @t37 @t111)) % 7.73/7.92 (define @t232 () (not @t231)) % 7.73/7.92 (define @t233 () (not @t40)) % 7.73/7.92 (define @t234 () (or @t232 @t233 @t232 @t230)) % 7.73/7.92 (define @t235 () (or @t233 @t232 @t230)) % 7.73/7.92 (define @t236 () (forall @t41 @t235)) % 7.73/7.92 (define @t237 () (or @t200 @t236)) % 7.73/7.92 (define @t238 () (or @t200 @t235)) % 7.73/7.92 (define @t239 () (or @t233 @t232 @t230 @t200)) % 7.73/7.92 (define @t240 () (and @t40 @t231 @t229 @t109)) % 7.73/7.92 (define @t241 () (forall @t41 (not @t240))) % 7.73/7.92 (define @t242 () (not @t241)) % 7.73/7.92 (define @t243 () (tptp.ssList @t144)) % 7.73/7.92 (define @t244 () (@quantifiers_skolemize @t143 1)) % 7.73/7.92 (define @t245 () (tptp.tl @t244)) % 7.73/7.92 (define @t246 () (tptp.app @t144 @t245)) % 7.73/7.92 (define @t247 () (= @t244 @t246)) % 7.73/7.92 (define @t248 () (not @t247)) % 7.73/7.92 (define @t249 () (tptp.ssList @t246)) % 7.73/7.92 (define @t250 () (tptp.ssList @t245)) % 7.73/7.92 (define @t251 () (tptp.neq tptp.nil @t244)) % 7.73/7.92 (define @t252 () (and @t251 @t250 @t249 @t248)) % 7.73/7.92 (define @t253 () (tptp.segmentP @t244 @t144)) % 7.73/7.92 (define @t254 () (tptp.neq @t144 tptp.nil)) % 7.73/7.92 (define @t255 () (and @t254 @t253)) % 7.73/7.92 (define @t256 () (tptp.neq @t244 tptp.nil)) % 7.73/7.92 (define @t257 () (not @t256)) % 7.73/7.92 (define @t258 () (tptp.ssList @t244)) % 7.73/7.92 (define @t259 () (not @t258)) % 7.73/7.92 (define @t260 () (not @t243)) % 7.73/7.92 (define @t261 () (or @t260 @t259 @t257 @t255 @t252)) % 7.73/7.92 (define @t262 () (@list true)) % 7.73/7.92 (define @t263 () (@list @t261)) % 7.73/7.92 (define @t264 () (tptp.app tptp.nil @t144)) % 7.73/7.92 (define @t265 () (= @t144 @t264)) % 7.73/7.92 (define @t266 () (or @t260 @t265)) % 7.73/7.92 (define @t267 () (@list false false)) % 7.73/7.92 (define @t268 () (= @t2 @t101)) % 7.73/7.92 (define @t269 () (tptp.app @t144 tptp.nil)) % 7.73/7.92 (define @t270 () (= @t144 @t269)) % 7.73/7.92 (define @t271 () (or @t260 @t270)) % 7.73/7.92 (define @t272 () (@var "BOUND_VARIABLE_9371" $$unsorted)) % 7.73/7.92 (define @t273 () (tptp.ssList (tptp.app @t2 @t272))) % 7.73/7.92 (define @t274 () (not (tptp.ssList @t272))) % 7.73/7.92 (define @t275 () (or @t274 @t273)) % 7.73/7.92 (define @t276 () (or @t140 @t275)) % 7.73/7.92 (define @t277 () (forall (@list @t2 @t272) @t276)) % 7.73/7.92 (define @t278 () (@list @t272)) % 7.73/7.92 (define @t279 () (forall @t278 @t276)) % 7.73/7.92 (define @t280 () (forall @t278 @t275)) % 7.73/7.92 (define @t281 () (or @t140 @t280)) % 7.73/7.92 (define @t282 () (forall @t7 (or @t158 @t72))) % 7.73/7.92 (define @t283 () (= @t2 tptp.nil)) % 7.73/7.92 (define @t284 () (or @t140 @t283 @t67)) % 7.73/7.92 (define @t285 () (not @t283)) % 7.73/7.92 (define @t286 () (not @t285)) % 7.73/7.92 (define @t287 () (=> @t285 @t67)) % 7.73/7.92 (define @t288 () (= @t244 tptp.nil)) % 7.73/7.92 (define @t289 () (or @t259 @t288 @t250)) % 7.73/7.92 (define @t290 () (forall @t9 @t284)) % 7.73/7.92 (define @t291 () (@list @t244)) % 7.73/7.92 (define @t292 () (= tptp.nil @t244)) % 7.73/7.92 (define @t293 () (or @t259 @t292 @t250)) % 7.73/7.92 (define @t294 () (@list false)) % 7.73/7.92 (define @t295 () (@var "BOUND_VARIABLE_9106" $$unsorted)) % 7.73/7.92 (define @t296 () (= (tptp.neq @t2 @t295) (not (= @t2 @t295)))) % 7.73/7.92 (define @t297 () (not (tptp.ssList @t295))) % 7.73/7.92 (define @t298 () (or @t140 @t297 @t296)) % 7.73/7.92 (define @t299 () (or @t297 @t296)) % 7.73/7.92 (define @t300 () (or @t140 @t299)) % 7.73/7.92 (define @t301 () (@list @t2 @t295)) % 7.73/7.92 (define @t302 () (forall @t301 @t300)) % 7.73/7.92 (define @t303 () (@list @t295)) % 7.73/7.92 (define @t304 () (forall @t303 @t300)) % 7.73/7.92 (define @t305 () (forall @t303 @t299)) % 7.73/7.92 (define @t306 () (or @t140 @t305)) % 7.73/7.92 (define @t307 () (forall @t7 (or @t158 @t5))) % 7.73/7.92 (define @t308 () (not @t288)) % 7.73/7.92 (define @t309 () (= @t256 @t308)) % 7.73/7.92 (define @t310 () (not @t51)) % 7.73/7.92 (define @t311 () (or @t259 @t310 @t309)) % 7.73/7.92 (define @t312 () (forall @t301 @t298)) % 7.73/7.92 (define @t313 () (not @t292)) % 7.73/7.92 (define @t314 () (= @t256 @t313)) % 7.73/7.92 (define @t315 () (or @t259 @t310 @t314)) % 7.73/7.92 (define @t316 () (@list @t312)) % 7.73/7.92 (define @t317 () (@list false false false)) % 7.73/7.92 (define @t318 () (@list false true false)) % 7.73/7.92 (define @t319 () (not @t250)) % 7.73/7.92 (define @t320 () (or @t260 @t319 @t249)) % 7.73/7.92 (define @t321 () (= @t251 @t313)) % 7.73/7.92 (define @t322 () (or @t310 @t259 @t321)) % 7.73/7.92 (define @t323 () (not @t321)) % 7.73/7.92 (define @t324 () (@list true false)) % 7.73/7.92 (define @t325 () (not @t249)) % 7.73/7.92 (define @t326 () (not @t251)) % 7.73/7.92 (define @t327 () (@list true false false false)) % 7.73/7.92 (define @t328 () (@list @t252 @t251 @t250 @t249)) % 7.73/7.92 (define @t329 () (@var "BOUND_VARIABLE_8388" $$unsorted)) % 7.73/7.92 (define @t330 () (@var "BOUND_VARIABLE_8411" $$unsorted)) % 7.73/7.92 (define @t331 () (not (tptp.ssList @t329))) % 7.73/7.92 (define @t332 () (@list @t12 @t329)) % 7.73/7.92 (define @t333 () (= (tptp.segmentP @t2 @t330) (not (forall @t332 (or @t168 @t331 (not (= @t2 (tptp.app (tptp.app @t12 @t330) @t329)))))))) % 7.73/7.92 (define @t334 () (not (tptp.ssList @t330))) % 7.73/7.92 (define @t335 () (or @t334 @t333)) % 7.73/7.92 (define @t336 () (or @t140 @t335)) % 7.73/7.92 (define @t337 () (forall (@list @t2 @t330) @t336)) % 7.73/7.92 (define @t338 () (@list @t330)) % 7.73/7.92 (define @t339 () (forall @t338 @t336)) % 7.73/7.92 (define @t340 () (forall @t338 @t335)) % 7.73/7.92 (define @t341 () (or @t140 @t340)) % 7.73/7.92 (define @t342 () (not (= @t2 (tptp.app @t22 @t329)))) % 7.73/7.92 (define @t343 () (or @t168 @t331 @t342)) % 7.73/7.92 (define @t344 () (= @t29 (not (forall @t332 @t343)))) % 7.73/7.92 (define @t345 () (forall @t7 (or @t158 @t344))) % 7.73/7.92 (define @t346 () (or @t331 @t342)) % 7.73/7.92 (define @t347 () (or @t168 @t346)) % 7.73/7.92 (define @t348 () (forall @t332 @t347)) % 7.73/7.92 (define @t349 () (@list @t329)) % 7.73/7.92 (define @t350 () (forall @t349 @t347)) % 7.73/7.92 (define @t351 () (forall @t349 @t346)) % 7.73/7.92 (define @t352 () (or @t168 @t351)) % 7.73/7.92 (define @t353 () (= @t2 @t24)) % 7.73/7.92 (define @t354 () (forall @t14 (or @t189 (not @t353)))) % 7.73/7.92 (define @t355 () (not @t354)) % 7.73/7.92 (define @t356 () (and @t15 @t355)) % 7.73/7.92 (define @t357 () (forall @t16 (not @t356))) % 7.73/7.92 (define @t358 () (not @t357)) % 7.73/7.92 (define @t359 () (and @t13 @t353)) % 7.73/7.92 (define @t360 () (forall @t14 (not @t359))) % 7.73/7.92 (define @t361 () (not @t360)) % 7.73/7.92 (define @t362 () (forall @t332 (or @t168 @t331 (not (= @t244 (tptp.app (tptp.app @t12 @t144) @t329)))))) % 7.73/7.92 (define @t363 () (not @t362)) % 7.73/7.92 (define @t364 () (= @t253 @t363)) % 7.73/7.92 (define @t365 () (or @t259 @t260 @t364)) % 7.73/7.92 (define @t366 () (not (= @t144 tptp.nil))) % 7.73/7.92 (define @t367 () (= @t254 @t366)) % 7.73/7.92 (define @t368 () (or @t260 @t310 @t367)) % 7.73/7.92 (define @t369 () (= tptp.nil @t144)) % 7.73/7.92 (define @t370 () (not @t369)) % 7.73/7.92 (define @t371 () (= @t254 @t370)) % 7.73/7.92 (define @t372 () (or @t260 @t310 @t371)) % 7.73/7.92 (define @t373 () (tptp.app tptp.nil @t245)) % 7.73/7.92 (define @t374 () (= @t245 @t373)) % 7.73/7.92 (define @t375 () (or @t319 @t374)) % 7.73/7.92 (define @t376 () (@var "BOUND_VARIABLE_9150" $$unsorted)) % 7.73/7.92 (define @t377 () (not (= @t2 (tptp.cons @t376 @t2)))) % 7.73/7.92 (define @t378 () (not (tptp.ssItem @t376))) % 7.73/7.92 (define @t379 () (or @t378 @t377)) % 7.73/7.92 (define @t380 () (or @t140 @t379)) % 7.73/7.92 (define @t381 () (forall (@list @t2 @t376) @t380)) % 7.73/7.92 (define @t382 () (@list @t376)) % 7.73/7.92 (define @t383 () (forall @t382 @t380)) % 7.73/7.92 (define @t384 () (forall @t382 @t379)) % 7.73/7.92 (define @t385 () (or @t140 @t384)) % 7.73/7.92 (define @t386 () (not (= @t2 @t50))) % 7.73/7.92 (define @t387 () (forall @t7 (or (not @t6) @t386))) % 7.73/7.92 (define @t388 () (tptp.hd @t244)) % 7.73/7.92 (define @t389 () (or @t140 @t283 @t61)) % 7.73/7.92 (define @t390 () (=> @t285 @t61)) % 7.73/7.92 (define @t391 () (tptp.ssItem @t388)) % 7.73/7.92 (define @t392 () (or @t259 @t288 @t391)) % 7.73/7.92 (define @t393 () (forall @t9 @t389)) % 7.73/7.92 (define @t394 () (or @t259 @t292 @t391)) % 7.73/7.92 (define @t395 () (tptp.cons @t388 @t245)) % 7.73/7.92 (define @t396 () (= @t245 @t395)) % 7.73/7.92 (define @t397 () (not @t396)) % 7.73/7.92 (define @t398 () (not @t391)) % 7.73/7.92 (define @t399 () (or @t319 @t398 @t397)) % 7.73/7.92 (define @t400 () (= @t2 @t96)) % 7.73/7.92 (define @t401 () (or @t140 @t283 @t400)) % 7.73/7.92 (define @t402 () (=> @t285 @t400)) % 7.73/7.92 (define @t403 () (= @t244 @t395)) % 7.73/7.92 (define @t404 () (or @t259 @t288 @t403)) % 7.73/7.92 (define @t405 () (forall @t9 @t401)) % 7.73/7.92 (define @t406 () (or @t259 @t292 @t403)) % 7.73/7.92 (define @t407 () (tptp.app @t269 @t245)) % 7.73/7.92 (define @t408 () (and @t247 @t369 @t403 @t270 @t374)) % 7.73/7.92 (define @t409 () (not @t270)) % 7.73/7.92 (define @t410 () (not @t371)) % 7.73/7.92 (define @t411 () (not @t364)) % 7.73/7.92 (define @t412 () (= @t244 (tptp.app @t264 @t245))) % 7.73/7.92 (define @t413 () (not @t412)) % 7.73/7.92 (define @t414 () (or @t310 @t319 @t413)) % 7.73/7.92 (define @t415 () (not @t265)) % 7.73/7.92 (define @t416 () (and @t412 @t413)) % 7.73/7.92 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 7.73/7.92 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 7.73/7.92 (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))))))))))) % 7.73/7.92 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 7.73/7.92 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 7.73/7.92 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 7.73/7.92 (assume @p7 @t34) % 7.73/7.92 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (not (and @t36 @t35))))))))))))))))) % 7.73/7.92 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (or @t36 @t35)))))))))))))))) % 7.73/7.92 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (or @t45 (tptp.lt @t12 @t1))))))))))))))))) % 7.73/7.92 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 @t36))))))))))))))) % 7.73/7.92 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 @t45))))))))))))))) % 7.73/7.92 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (not @t46)))))))))))))))) % 7.73/7.92 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t38))) @t2) @t46))))))))))))) % 7.73/7.92 (assume @p15 @t49) % 7.73/7.92 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t50)))))) % 7.73/7.92 (assume @p17 @t51) % 7.73/7.92 (assume @p18 @t56) % 7.73/7.92 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t44 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t57))))))))))) % 7.73/7.92 (assume @p20 (forall @t9 (=> @t17 (or @t59 (exists @t7 (and @t21 (exists @t16 (and @t44 (= @t58 @t2))))))))) % 7.73/7.92 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t50))))))) % 7.73/7.92 (assume @p22 @t65) % 7.73/7.92 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t50) @t1)))))) % 7.73/7.92 (assume @p24 @t70) % 7.73/7.92 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t50) @t2)))))) % 7.73/7.92 (assume @p26 @t75) % 7.73/7.92 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t44 (= (tptp.cons @t12 @t76) (tptp.app @t58 @t2))))))))) % 7.73/7.92 (assume @p28 @t79) % 7.73/7.92 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t81 @t80) @t3)))))) % 7.73/7.92 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t81 @t36) (tptp.leq @t2 @t12))))))))) % 7.73/7.92 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 7.73/7.92 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t82 @t80)))))) % 7.73/7.92 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t84 (not @t83))))))) % 7.73/7.92 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t84 @t45) @t85)))))))) % 7.73/7.92 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t86 @t83)))))) % 7.73/7.92 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t87))))))))) % 7.73/7.92 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t87))))))))) % 7.73/7.92 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 7.73/7.92 (assume @p39 (not (tptp.singletonP tptp.nil))) % 7.73/7.92 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 7.73/7.92 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 7.73/7.92 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 7.73/7.92 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 7.73/7.92 (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)))))))))))) % 7.73/7.92 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 7.73/7.92 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t59)))) % 7.73/7.92 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 7.73/7.92 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 7.73/7.92 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 7.73/7.92 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t88 @t1))))))))) % 7.73/7.92 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 7.73/7.92 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t59)))) % 7.73/7.92 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t29 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 7.73/7.92 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t29 @t89) @t3)))))) % 7.73/7.92 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 7.73/7.92 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t29 (tptp.segmentP (tptp.app @t88 @t10) @t1))))))))))) % 7.73/7.92 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 7.73/7.92 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t59)))) % 7.73/7.92 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t90)))) % 7.73/7.92 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 7.73/7.92 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t90)))) % 7.73/7.92 (assume @p62 (tptp.totalorderP tptp.nil)) % 7.73/7.92 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t90)))) % 7.73/7.92 (assume @p64 (tptp.strictorderP tptp.nil)) % 7.73/7.92 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t90)))) % 7.73/7.92 (assume @p66 (tptp.totalorderedP tptp.nil)) % 7.73/7.92 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t94) (or @t92 (and @t93 (tptp.totalorderedP @t1) (tptp.leq @t2 @t91))))))))) % 7.73/7.92 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t90)))) % 7.73/7.92 (assume @p69 (tptp.strictorderedP tptp.nil)) % 7.73/7.92 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t94) (or @t92 (and @t93 (tptp.strictorderedP @t1) (tptp.lt @t2 @t91))))))))) % 7.73/7.92 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t90)))) % 7.73/7.92 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 7.73/7.92 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t90)))) % 7.73/7.92 (assume @p74 (tptp.equalelemsP tptp.nil)) % 7.73/7.92 (assume @p75 (forall @t9 (=> @t17 (=> @t62 (exists @t7 (and @t6 (= @t60 @t1))))))) % 7.73/7.92 (assume @p76 (forall @t9 (=> @t17 (=> @t62 (exists @t7 (and @t21 (= @t66 @t1))))))) % 7.73/7.92 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t93 @t62 (= @t91 @t60) (= @t95 @t66)) @t57)))))) % 7.73/7.92 (assume @p78 @t99) % 7.73/7.92 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t71) @t100)))))))) % 7.73/7.92 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t76) @t100)))))))) % 7.73/7.92 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t50 (tptp.app @t18 @t2))))))) % 7.73/7.92 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t71 @t12) (tptp.app @t2 @t19))))))))) % 7.73/7.92 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t71) (and @t92 @t59))))))) % 7.73/7.92 (assume @p84 @t103) % 7.73/7.92 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t62 (= (tptp.hd @t71) @t60))))))) % 7.73/7.92 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t62 (= (tptp.tl @t71) (tptp.app @t66 @t1)))))))) % 7.73/7.92 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t82 (tptp.geq @t1 @t2)) @t3)))))) % 7.73/7.92 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t82 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 7.73/7.92 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 7.73/7.92 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 7.73/7.92 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t81 @t45) @t85)))))))) % 7.73/7.92 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t81 (or @t3 @t84))))))) % 7.73/7.92 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t84 (and @t4 @t81))))))) % 7.73/7.92 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t86 (not (tptp.gt @t1 @t2)))))))) % 7.73/7.92 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t86 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 7.73/7.92 (assume @p96 @t131) % 7.73/7.92 (assume @p97 true) % 7.73/7.92 (step @p98 :rule bool-impl-elim :args (@t17 @t132)) % 7.73/7.92 (step @p99 :rule cong :premises (@p98) :args ((forall @t9 (=> @t17 @t132)))) % 7.73/7.92 (step @p100 :rule eq-symm :args (@t77 @t2)) % 7.73/7.92 (step @p101 :rule refl :args (@t17)) % 7.73/7.92 (step @p102 :rule cong :premises (@p101 @p100) :args (@t78)) % 7.73/7.92 (step @p103 :rule cong :premises (@p102) :args (@t79)) % 7.73/7.92 (step @p104 :rule trans :premises (@p103 @p99)) % 7.73/7.92 (step @p105 :rule eq_resolve :premises (@p28 @p104)) % 7.73/7.92 (step @p106 :rule instantiate :premises (@p105) :args (@t145)) % 7.73/7.92 (step @p107 :rule aci_norm :args ((= @t147 @t141))) % 7.73/7.92 (step @p108 :rule cong :premises (@p107) :args (@t148)) % 7.73/7.92 (step @p109 :rule quant-merge-prenex :args ((= (forall @t9 @t150) @t148))) % 7.73/7.92 (step @p110 :rule alpha_equiv :args (@t151 (@list @t133) @t152)) % 7.73/7.92 (step @p111 :rule refl :args (@t140)) % 7.73/7.92 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t153)) % 7.73/7.92 (step @p113 :rule quant-miniscope-or :args ((= @t150 @t153))) % 7.73/7.92 (step @p114 :rule trans :premises (@p113 @p112)) % 7.73/7.92 (step @p115 :rule symm :premises (@p114)) % 7.73/7.92 (step @p116 :rule cong :premises (@p115) :args ((forall @t9 @t160))) % 7.73/7.92 (step @p117 :rule trans :premises (@p116 @p109)) % 7.73/7.92 (step @p118 :rule trans :premises (@p117 @p108)) % 7.73/7.92 (step @p119 :rule aci_norm :args ((= (or @t140 @t160) @t160))) % 7.73/7.92 (step @p120 :rule bool-impl-elim :args (@t17 @t160)) % 7.73/7.92 (step @p121 :rule trans :premises (@p120 @p119)) % 7.73/7.92 (step @p122 :rule cong :premises (@p121) :args ((forall @t9 (=> @t17 @t160)))) % 7.73/7.92 (step @p123 :rule trans :premises (@p122 @p118)) % 7.73/7.92 (step @p124 :rule quant-miniscope-or :args ((= (forall @t7 @t161) @t160))) % 7.73/7.92 (step @p125 :rule aci_norm :args ((= @t162 @t161))) % 7.73/7.92 (step @p126 :rule cong :premises (@p125) :args ((forall @t7 @t162))) % 7.73/7.92 (step @p127 :rule trans :premises (@p126 @p124)) % 7.73/7.92 (step @p128 :rule aci_norm :args ((= (or @t158 @t162) @t162))) % 7.73/7.92 (step @p129 :rule bool-impl-elim :args (@t21 @t162)) % 7.73/7.92 (step @p130 :rule trans :premises (@p129 @p128)) % 7.73/7.92 (step @p131 :rule cong :premises (@p130) :args ((forall @t7 (=> @t21 @t162)))) % 7.73/7.92 (step @p132 :rule trans :premises (@p131 @p127)) % 7.73/7.92 (step @p133 :rule aci_norm :args ((= (or @t158 @t105 @t108 @t163) @t162))) % 7.73/7.92 (step @p134 :rule aci_norm :args ((= (or @t140 false @t157) @t163))) % 7.73/7.92 (step @p135 :rule refl :args (@t157)) % 7.73/7.92 (step @p136 :rule evaluate :args ((not true))) % 7.73/7.92 (step @p137 :rule eq-refl :args (@t2)) % 7.73/7.92 (step @p138 :rule cong :premises (@p137) :args (@t164)) % 7.73/7.92 (step @p139 :rule trans :premises (@p138 @p136)) % 7.73/7.92 (step @p140 :rule refl :args (@t140)) % 7.73/7.92 (step @p141 :rule nary_cong :premises (@p140 @p139 @p135) :args (@t165)) % 7.73/7.92 (step @p142 :rule trans :premises (@p141 @p134)) % 7.73/7.92 (step @p143 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t100) @t168 @t120 @t167)) @t165))) % 7.73/7.92 (step @p144 :rule refl :args (@t167)) % 7.73/7.92 (step @p145 :rule refl :args (@t120)) % 7.73/7.92 (step @p146 :rule refl :args (@t168)) % 7.73/7.92 (step @p147 :rule eq-symm :args (@t2 @t12)) % 7.73/7.92 (step @p148 :rule cong :premises (@p147) :args (@t120)) % 7.73/7.92 (step @p149 :rule nary_cong :premises (@p148 @p146 @p145 @p144) :args (@t169)) % 7.73/7.92 (step @p150 :rule aci_norm :args ((= @t170 @t169))) % 7.73/7.92 (step @p151 :rule trans :premises (@p150 @p149)) % 7.73/7.92 (step @p152 :rule cong :premises (@p151) :args (@t171)) % 7.73/7.93 (step @p153 :rule trans :premises (@p152 @p143)) % 7.73/7.93 (step @p154 :rule trans :premises (@p153 @p142)) % 7.73/7.93 (step @p155 :rule refl :args (@t108)) % 7.73/7.93 (step @p156 :rule refl :args (@t105)) % 7.73/7.93 (step @p157 :rule refl :args (@t158)) % 7.73/7.93 (step @p158 :rule nary_cong :premises (@p157 @p156 @p155 @p154) :args (@t172)) % 7.73/7.93 (step @p159 :rule trans :premises (@p158 @p133)) % 7.73/7.93 (step @p160 :rule quant-miniscope-or :args ((= (forall @t16 @t173) @t172))) % 7.73/7.93 (step @p161 :rule aci_norm :args ((= @t174 @t173))) % 7.73/7.93 (step @p162 :rule cong :premises (@p161) :args ((forall @t16 @t174))) % 7.73/7.93 (step @p163 :rule trans :premises (@p162 @p160)) % 7.73/7.93 (step @p164 :rule trans :premises (@p163 @p159)) % 7.73/7.93 (step @p165 :rule aci_norm :args ((= (or @t168 @t120 @t158 @t175) @t174))) % 7.73/7.93 (step @p166 :rule aci_norm :args ((= @t176 @t175))) % 7.73/7.93 (step @p167 :rule refl :args (@t120)) % 7.73/7.93 (step @p168 :rule refl :args (@t168)) % 7.73/7.93 (step @p169 :rule nary_cong :premises (@p168 @p167 @p157 @p166) :args (@t177)) % 7.73/7.93 (step @p170 :rule trans :premises (@p169 @p165)) % 7.73/7.93 (step @p171 :rule cong :premises (@p170) :args ((forall @t16 @t177))) % 7.73/7.93 (step @p172 :rule trans :premises (@p171 @p164)) % 7.73/7.93 (step @p173 :rule aci_norm :args ((= (or @t168 (or @t120 @t158 @t176)) @t177))) % 7.73/7.93 (step @p174 :rule bool-or-taut2 :args (false @t104 false false)) % 7.73/7.93 (step @p175 :rule refl :args (@t175)) % 7.73/7.93 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t178)) % 7.73/7.93 (step @p177 :rule refl :args (@t158)) % 7.73/7.93 (step @p178 :rule nary_cong :premises (@p145 @p177 @p176) :args (@t179)) % 7.73/7.93 (step @p179 :rule nary_cong :premises (@p146 @p178) :args ((or @t168 @t179))) % 7.73/7.93 (step @p180 :rule trans :premises (@p179 @p173)) % 7.73/7.93 (step @p181 :rule bool-impl-elim :args (@t15 @t179)) % 7.73/7.93 (step @p182 :rule trans :premises (@p181 @p180)) % 7.73/7.93 (step @p183 :rule cong :premises (@p182) :args ((forall @t16 (=> @t15 @t179)))) % 7.73/7.93 (step @p184 :rule trans :premises (@p183 @p172)) % 7.73/7.93 (step @p185 :rule aci_norm :args ((= (or @t120 @t180) @t179))) % 7.73/7.93 (step @p186 :rule aci_norm :args ((= (or @t158 false @t178) @t180))) % 7.73/7.93 (step @p187 :rule refl :args (@t178)) % 7.73/7.93 (step @p188 :rule eq-refl :args (@t1)) % 7.73/7.93 (step @p189 :rule cong :premises (@p188) :args (@t181)) % 7.73/7.93 (step @p190 :rule trans :premises (@p189 @p136)) % 7.73/7.93 (step @p191 :rule nary_cong :premises (@p157 @p190 @p187) :args (@t182)) % 7.73/7.93 (step @p192 :rule trans :premises (@p191 @p186)) % 7.73/7.93 (step @p193 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t189 @t121 @t188)) @t182))) % 7.73/7.93 (step @p194 :rule refl :args (@t188)) % 7.73/7.93 (step @p195 :rule refl :args (@t121)) % 7.73/7.93 (step @p196 :rule refl :args (@t189)) % 7.73/7.93 (step @p197 :rule eq-symm :args (@t1 @t10)) % 7.73/7.93 (step @p198 :rule cong :premises (@p197) :args (@t121)) % 7.73/7.93 (step @p199 :rule nary_cong :premises (@p198 @p196 @p195 @p194) :args (@t190)) % 7.73/7.93 (step @p200 :rule aci_norm :args ((= @t191 @t190))) % 7.73/7.93 (step @p201 :rule trans :premises (@p200 @p199)) % 7.73/7.93 (step @p202 :rule cong :premises (@p201) :args (@t192)) % 7.73/7.93 (step @p203 :rule trans :premises (@p202 @p193)) % 7.73/7.93 (step @p204 :rule trans :premises (@p203 @p192)) % 7.73/7.93 (step @p205 :rule nary_cong :premises (@p167 @p204) :args (@t193)) % 7.73/7.93 (step @p206 :rule trans :premises (@p205 @p185)) % 7.73/7.93 (step @p207 :rule quant-miniscope-or :args ((= (forall @t14 @t194) @t193))) % 7.73/7.93 (step @p208 :rule aci_norm :args ((= @t195 @t194))) % 7.73/7.93 (step @p209 :rule cong :premises (@p208) :args ((forall @t14 @t195))) % 7.73/7.93 (step @p210 :rule trans :premises (@p209 @p207)) % 7.73/7.93 (step @p211 :rule trans :premises (@p210 @p206)) % 7.73/7.93 (step @p212 :rule aci_norm :args ((= (or @t189 (or @t121 @t120 @t188)) @t195))) % 7.73/7.93 (step @p213 :rule refl :args (@t106)) % 7.73/7.93 (step @p214 :rule refl :args (@t108)) % 7.73/7.93 (step @p215 :rule refl :args (@t185)) % 7.73/7.93 (step @p216 :rule bool-double-not-elim :args (@t186)) % 7.73/7.93 (step @p217 :rule bool-double-not-elim :args (@t187)) % 7.73/7.93 (step @p218 :rule bool-double-not-elim :args (@t109)) % 7.73/7.93 (step @p219 :rule nary_cong :premises (@p218 @p217 @p216 @p215) :args (@t202)) % 7.73/7.93 (step @p220 :rule aci_norm :args ((= (and @t201 (and @t199 (and @t197 @t185))) @t202))) % 7.73/7.93 (step @p221 :rule trans :premises (@p220 @p219)) % 7.73/7.93 (step @p222 :rule bool-or-de-morgan :args (@t196 @t184 false)) % 7.73/7.93 (step @p223 :rule refl :args (@t199)) % 7.73/7.93 (step @p224 :rule nary_cong :premises (@p223 @p222) :args ((and @t199 (not @t203)))) % 7.73/7.93 (step @p225 :rule bool-or-de-morgan :args (@t198 @t196 (or @t184))) % 7.73/7.93 (step @p226 :rule trans :premises (@p225 @p224)) % 7.73/7.93 (step @p227 :rule refl :args (@t201)) % 7.73/7.93 (step @p228 :rule nary_cong :premises (@p227 @p226) :args ((and @t201 (not (or @t198 @t196 @t184))))) % 7.73/7.93 (step @p229 :rule bool-or-de-morgan :args (@t200 @t198 (or @t196 @t184))) % 7.73/7.93 (step @p230 :rule trans :premises (@p229 @p228)) % 7.73/7.93 (step @p231 :rule trans :premises (@p230 @p221)) % 7.73/7.93 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(@p808)) % 7.73/7.93 (step-pop @p810 :rule scope :premises (@p809)) % 7.73/7.93 (step-pop @p811 :rule scope :premises (@p810)) % 7.73/7.93 (step-pop @p812 :rule scope :premises (@p811)) % 7.73/7.93 (step @p707 :rule process_scope :premises (@p812) :args (@t396)) % 7.73/7.93 (step @p713 :rule implies_elim :premises (@p707)) % 7.73/7.93 (step @p714 :rule cnf_and_neg :args (@t408)) % 7.73/7.93 (step @p715 :rule resolution :premises (@p714 @p713) :args (true @t408)) % 7.73/7.93 (step @p716 :rule reordering :premises (@p715) :args ((or @t248 @t370 (not @t403) @t409 @t396 (not @t374)))) % 7.73/7.93 (step @p717 :rule chain_m_resolution :premises (@p716 @p509 @p681 @p374 @p651 @p591) :args (@t370 (@list false false false true false) (@list @t247 @t403 @t270 @t396 @t374))) % 7.73/7.93 (step @p718 :rule bool-double-not-elim :args (@t369)) % 7.73/7.93 (step @p719 :rule refl :args (@t410)) % 7.73/7.93 (step @p720 :rule nary_cong :premises (@p719 @p573 @p718) :args ((or @t410 @t254 (not @t370)))) % 7.73/7.93 (step @p721 :rule cnf_equiv_pos2 :args (@t371)) % 7.73/7.93 (step @p722 :rule eq_resolve :premises (@p721 @p720)) % 7.73/7.93 (step @p723 :rule reordering :premises (@p722) :args ((or @t254 @t369 @t410))) % 7.73/7.93 (step @p724 :rule chain_m_resolution :premises (@p723 @p717 @p587) :args (@t254 @t324 (@list @t369 @t371))) % 7.73/7.93 (step @p725 :rule cnf_or_neg :args (@t261 3)) % 7.73/7.93 (step @p726 :rule chain_m_resolution :premises (@p725 @p353) :args ((not @t255) @t262 @t263)) % 7.73/7.93 (step @p727 :rule cnf_and_neg :args (@t255)) % 7.73/7.93 (step @p728 :rule chain_m_resolution :premises (@p727 @p726 @p724) :args ((not @t253) @t324 (@list @t255 @t254))) % 7.73/7.93 (step @p729 :rule bool-double-not-elim :args (@t362)) % 7.73/7.93 (step @p730 :rule refl :args (@t253)) % 7.73/7.93 (step @p731 :rule refl :args (@t411)) % 7.73/7.93 (step @p732 :rule nary_cong :premises (@p731 @p730 @p729) :args ((or @t411 @t253 (not @t363)))) % 7.73/7.93 (step @p733 :rule cnf_equiv_pos2 :args (@t364)) % 7.73/7.93 (step @p734 :rule eq_resolve :premises (@p733 @p732)) % 7.73/7.93 (step @p735 :rule reordering :premises (@p734) :args ((or @t253 @t362 @t411))) % 7.73/7.93 (step @p736 :rule chain_m_resolution :premises (@p735 @p728 @p570) :args (@t362 @t324 (@list @t253 @t364))) % 7.73/7.93 (assume-push @p813 @t362) % 7.73/7.93 (step @p738 :rule instantiate :premises (@p813) :args ((@list tptp.nil @t245))) % 7.73/7.93 (step-pop @p814 :rule scope :premises (@p738)) % 7.73/7.93 (step @p739 :rule process_scope :premises (@p814) :args (@t414)) % 7.73/7.93 (step @p741 :rule implies_elim :premises (@p739)) % 7.73/7.93 (step @p742 :rule chain_m_resolution :premises (@p741 @p736) :args (@t414 @t294 (@list @t362))) % 7.73/7.93 (step @p743 :rule cnf_or_pos :args (@t414)) % 7.73/7.93 (step @p744 :rule reordering :premises (@p743) :args ((or @t310 @t319 @t413 (not @t414)))) % 7.73/7.93 (step @p745 :rule chain_m_resolution :premises (@p744 @p17 @p482 @p742) :args (@t413 @t317 (@list @t51 @t250 @t414))) % 7.73/7.93 (step @p746 :rule bool-double-not-elim :args (@t412)) % 7.73/7.93 (step @p747 :rule refl :args (@t409)) % 7.73/7.93 (step @p748 :rule refl :args (@t415)) % 7.73/7.93 (step @p749 :rule refl :args (@t248)) % 7.73/7.93 (step @p750 :rule nary_cong :premises (@p749 @p748 @p747 @p746) :args ((or @t248 @t415 @t409 (not @t413)))) % 7.73/7.93 (assume-push @p815 @t412) % 7.73/7.93 (assume-push @p816 @t413) % 7.73/7.93 (step @p753 :rule evaluate :args ((= true false))) % 7.73/7.93 (step @p754 :rule false_intro :premises (@p816)) % 7.73/7.93 (step @p693 :rule refl :args (@t245)) % 7.73/7.93 (step @p694 :rule symm :premises (@p374)) % 7.73/7.93 (step @p755 :rule trans :premises (@p694 @p363)) % 7.73/7.97 (step @p756 :rule cong :premises (@p755 @p693) :args (@t407)) % 7.73/7.97 (step @p757 :rule cong :premises (@p374 @p693) :args (@t246)) % 7.73/7.97 (step @p758 :rule chain_m_resolution :premises (@p508 @p499 @p497 @p482 @p485) :args (@t247 @t327 @t328)) % 7.73/7.97 (step @p759 :rule trans :premises (@p758 @p757 @p756)) % 7.73/7.97 (step @p760 :rule true_intro :premises (@p759)) % 7.73/7.97 (step @p761 :rule symm :premises (@p760)) % 7.73/7.97 (step @p762 :rule trans :premises (@p761 @p754)) % 7.73/7.97 (step @p763 false :rule eq_resolve :premises (@p762 @p753)) % 7.73/7.97 (step-pop @p817 :rule scope :premises (@p763)) % 7.73/7.97 (step-pop @p818 :rule scope :premises (@p817)) % 7.73/7.97 (step @p764 :rule process_scope :premises (@p818) :args (false)) % 7.73/7.97 (assume-push @p819 @t247) % 7.73/7.97 (assume-push @p820 @t265) % 7.73/7.97 (assume-push @p821 @t270) % 7.73/7.97 (assume-push @p822 @t413) % 7.73/7.97 (step @p693 :rule refl :args (@t245)) % 7.73/7.97 (step @p694 :rule symm :premises (@p374)) % 7.73/7.97 (step @p755 :rule trans :premises (@p694 @p363)) % 7.73/7.97 (step @p756 :rule cong :premises (@p755 @p693) :args (@t407)) % 7.73/7.97 (step @p757 :rule cong :premises (@p374 @p693) :args (@t246)) % 7.73/7.97 (step @p771 :rule trans :premises (@p509 @p757 @p756)) % 7.73/7.97 (step @p772 :rule and_intro :premises (@p771 @p822)) % 7.73/7.97 (step-pop @p823 :rule scope :premises (@p772)) % 7.73/7.97 (step-pop @p824 :rule scope :premises (@p823)) % 7.73/7.97 (step-pop @p825 :rule scope :premises (@p824)) % 7.73/7.97 (step-pop @p826 :rule scope :premises (@p825)) % 7.73/7.97 (step @p773 :rule process_scope :premises (@p826) :args (@t416)) % 7.73/7.97 (step @p778 :rule implies_elim :premises (@p773)) % 7.73/7.97 (step @p779 :rule resolution :premises (@p778 @p764) :args (true @t416)) % 7.73/7.97 (step @p780 :rule not_and :premises (@p779)) % 7.73/7.97 (step @p781 :rule eq_resolve :premises (@p780 @p750)) % 7.73/7.97 (step @p782 false :rule chain_m_resolution :premises (@p781 @p745 @p509 @p374 @p363) :args (false @t327 (@list @t412 @t247 @t270 @t265))) % 7.73/7.97 ) % 7.73/7.97 % SZS output end Proof % 7.73/7.97 % cvc5 exiting %------------------------------------------------------------------------------