%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC373+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:59:04 AM UTC 2026 % Result : Theorem 0.88s 1.06s % Output : Proof 0.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC373+1 : TPTP v9.2.1. Released v2.4.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n019.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 19:44:49 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.88/1.06 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.88/1.06 % SZS status Theorem % 0.88/1.06 % SZS output start Proof % 0.88/1.06 ( % 0.88/1.06 (declare-sort $$unsorted 0) % 0.88/1.06 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.88/1.06 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.88/1.06 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.88/1.06 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.88/1.06 (declare-const tptp.nil $$unsorted) % 0.88/1.06 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.88/1.06 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.88/1.06 (define @t1 () (@var "V" $$unsorted)) % 0.88/1.06 (define @t2 () (@var "U" $$unsorted)) % 0.88/1.06 (define @t3 () (= @t2 @t1)) % 0.88/1.06 (define @t4 () (not @t3)) % 0.88/1.06 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.88/1.06 (define @t6 () (tptp.ssItem @t1)) % 0.88/1.06 (define @t7 () (@list @t1)) % 0.88/1.06 (define @t8 () (tptp.ssItem @t2)) % 0.88/1.06 (define @t9 () (@list @t2)) % 0.88/1.06 (define @t10 () (@var "X" $$unsorted)) % 0.88/1.06 (define @t11 () (tptp.cons @t1 @t10)) % 0.88/1.06 (define @t12 () (@var "W" $$unsorted)) % 0.88/1.06 (define @t13 () (tptp.ssList @t10)) % 0.88/1.06 (define @t14 () (@list @t10)) % 0.88/1.06 (define @t15 () (tptp.ssList @t12)) % 0.88/1.06 (define @t16 () (@list @t12)) % 0.88/1.06 (define @t17 () (tptp.ssList @t2)) % 0.88/1.06 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.88/1.06 (define @t19 () (tptp.app @t1 @t12)) % 0.88/1.06 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.88/1.06 (define @t21 () (tptp.ssList @t1)) % 0.88/1.06 (define @t22 () (tptp.app @t12 @t1)) % 0.88/1.06 (define @t23 () (and @t15 (= @t22 @t2))) % 0.88/1.06 (define @t24 () (exists @t16 @t23)) % 0.88/1.06 (define @t25 () (tptp.rearsegP @t2 @t1)) % 0.88/1.06 (define @t26 () (= @t25 @t24)) % 0.88/1.06 (define @t27 () (=> @t21 @t26)) % 0.88/1.06 (define @t28 () (forall @t7 @t27)) % 0.88/1.06 (define @t29 () (=> @t17 @t28)) % 0.88/1.06 (define @t30 () (forall @t9 @t29)) % 0.88/1.06 (define @t31 () (tptp.app @t22 @t10)) % 0.88/1.06 (define @t32 () (and @t13 (= @t31 @t2))) % 0.88/1.06 (define @t33 () (exists @t14 @t32)) % 0.88/1.06 (define @t34 () (and @t15 @t33)) % 0.88/1.06 (define @t35 () (exists @t16 @t34)) % 0.88/1.06 (define @t36 () (tptp.segmentP @t2 @t1)) % 0.88/1.06 (define @t37 () (= @t36 @t35)) % 0.88/1.06 (define @t38 () (=> @t21 @t37)) % 0.88/1.06 (define @t39 () (forall @t7 @t38)) % 0.88/1.06 (define @t40 () (=> @t17 @t39)) % 0.88/1.06 (define @t41 () (forall @t9 @t40)) % 0.88/1.06 (define @t42 () (tptp.leq @t12 @t1)) % 0.88/1.06 (define @t43 () (tptp.leq @t1 @t12)) % 0.88/1.06 (define @t44 () (@var "Z" $$unsorted)) % 0.88/1.06 (define @t45 () (@var "Y" $$unsorted)) % 0.88/1.06 (define @t46 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t45)) (tptp.cons @t12 @t44)) @t2)) % 0.88/1.06 (define @t47 () (tptp.ssList @t44)) % 0.88/1.06 (define @t48 () (@list @t44)) % 0.88/1.06 (define @t49 () (tptp.ssList @t45)) % 0.88/1.06 (define @t50 () (@list @t45)) % 0.88/1.06 (define @t51 () (tptp.ssItem @t12)) % 0.88/1.06 (define @t52 () (tptp.lt @t1 @t12)) % 0.88/1.06 (define @t53 () (= @t1 @t12)) % 0.88/1.06 (define @t54 () (tptp.cons @t1 @t2)) % 0.88/1.06 (define @t55 () (tptp.ssList tptp.nil)) % 0.88/1.06 (define @t56 () (= @t1 @t2)) % 0.88/1.06 (define @t57 () (tptp.cons @t12 @t1)) % 0.88/1.06 (define @t58 () (= tptp.nil @t2)) % 0.88/1.06 (define @t59 () (tptp.hd @t2)) % 0.88/1.06 (define @t60 () (not @t58)) % 0.88/1.06 (define @t61 () (tptp.tl @t2)) % 0.88/1.06 (define @t62 () (tptp.app @t2 @t1)) % 0.88/1.06 (define @t63 () (tptp.app @t1 @t2)) % 0.88/1.06 (define @t64 () (tptp.leq @t1 @t2)) % 0.88/1.06 (define @t65 () (tptp.leq @t2 @t1)) % 0.88/1.06 (define @t66 () (tptp.geq @t2 @t1)) % 0.88/1.06 (define @t67 () (tptp.lt @t1 @t2)) % 0.88/1.06 (define @t68 () (tptp.lt @t2 @t1)) % 0.88/1.06 (define @t69 () (tptp.lt @t2 @t12)) % 0.88/1.06 (define @t70 () (tptp.gt @t2 @t1)) % 0.88/1.06 (define @t71 () (tptp.memberP @t12 @t2)) % 0.88/1.06 (define @t72 () (tptp.rearsegP @t1 @t12)) % 0.88/1.06 (define @t73 () (tptp.rearsegP @t1 @t2)) % 0.88/1.06 (define @t74 () (tptp.app @t12 @t2)) % 0.88/1.06 (define @t75 () (tptp.segmentP @t1 @t2)) % 0.88/1.06 (define @t76 () (tptp.cons @t2 tptp.nil)) % 0.88/1.06 (define @t77 () (tptp.hd @t1)) % 0.88/1.06 (define @t78 () (= tptp.nil @t1)) % 0.88/1.06 (define @t79 () (not @t78)) % 0.88/1.06 (define @t80 () (tptp.cons @t2 @t1)) % 0.88/1.06 (define @t81 () (= @t12 @t2)) % 0.88/1.06 (define @t82 () (tptp.app @t2 tptp.nil)) % 0.88/1.06 (define @t83 () (=> @t17 (= @t82 @t2))) % 0.88/1.06 (define @t84 () (forall @t9 @t83)) % 0.88/1.06 (define @t85 () (not (tptp.rearsegP @t10 @t12))) % 0.88/1.06 (define @t86 () (not (= @t2 @t12))) % 0.88/1.06 (define @t87 () (not (= @t1 @t10))) % 0.88/1.06 (define @t88 () (or @t87 @t86 @t85 @t75)) % 0.88/1.06 (define @t89 () (forall @t14 (=> @t13 @t88))) % 0.88/1.06 (define @t90 () (=> @t15 @t89)) % 0.88/1.06 (define @t91 () (forall @t16 @t90)) % 0.88/1.06 (define @t92 () (=> @t21 @t91)) % 0.88/1.06 (define @t93 () (forall @t7 @t92)) % 0.88/1.06 (define @t94 () (=> @t17 @t93)) % 0.88/1.06 (define @t95 () (forall @t9 @t94)) % 0.88/1.06 (define @t96 () (not @t95)) % 0.88/1.06 (define @t97 () (= @t2 @t82)) % 0.88/1.06 (define @t98 () (@var "BOUND_VARIABLE_10946" $$unsorted)) % 0.88/1.06 (define @t99 () (not (tptp.rearsegP @t98 @t2))) % 0.88/1.06 (define @t100 () (tptp.segmentP @t98 @t2)) % 0.88/1.06 (define @t101 () (not (tptp.ssList @t98))) % 0.88/1.06 (define @t102 () (not @t17)) % 0.88/1.06 (define @t103 () (or @t102 @t101 @t100 @t99)) % 0.88/1.06 (define @t104 () (@list @t2 @t98)) % 0.88/1.06 (define @t105 () (forall @t104 @t103)) % 0.88/1.06 (define @t106 () (@quantifiers_skolemize @t105 1)) % 0.88/1.06 (define @t107 () (or @t101 @t100 @t99)) % 0.88/1.06 (define @t108 () (or @t102 @t107)) % 0.88/1.06 (define @t109 () (forall @t104 @t108)) % 0.88/1.06 (define @t110 () (@list @t98)) % 0.88/1.06 (define @t111 () (forall @t110 @t108)) % 0.88/1.06 (define @t112 () (forall @t110 @t107)) % 0.88/1.06 (define @t113 () (@list @t1)) % 0.88/1.06 (define @t114 () (or @t102 @t112)) % 0.88/1.06 (define @t115 () (not @t73)) % 0.88/1.06 (define @t116 () (not @t21)) % 0.88/1.06 (define @t117 () (or @t116 @t75 @t115)) % 0.88/1.06 (define @t118 () (or @t102 (forall @t7 @t117))) % 0.88/1.06 (define @t119 () (or @t102 @t117)) % 0.88/1.06 (define @t120 () (or @t116 @t75 @t102 @t115)) % 0.88/1.06 (define @t121 () (or @t75 @t116 @t102 @t115)) % 0.88/1.06 (define @t122 () (or @t102 @t115)) % 0.88/1.06 (define @t123 () (not (= @t2 @t2))) % 0.88/1.06 (define @t124 () (or @t102 @t123 @t115)) % 0.88/1.06 (define @t125 () (not @t72)) % 0.88/1.06 (define @t126 () (not @t15)) % 0.88/1.06 (define @t127 () (or @t86 @t126 @t86 @t125)) % 0.88/1.06 (define @t128 () (or @t126 @t86 @t125)) % 0.88/1.06 (define @t129 () (forall @t16 @t128)) % 0.88/1.06 (define @t130 () (or @t75 @t116 @t129)) % 0.88/1.06 (define @t131 () (or @t75 @t116 @t128)) % 0.88/1.06 (define @t132 () (or @t126 @t86 @t75 @t116 @t125)) % 0.88/1.06 (define @t133 () (or @t86 @t75 @t116 @t125)) % 0.88/1.06 (define @t134 () (or @t116 @t125)) % 0.88/1.06 (define @t135 () (not (= @t1 @t1))) % 0.88/1.06 (define @t136 () (or @t116 @t135 @t125)) % 0.88/1.06 (define @t137 () (not @t13)) % 0.88/1.06 (define @t138 () (or @t87 @t137 @t87 @t85)) % 0.88/1.06 (define @t139 () (or @t137 @t87 @t85)) % 0.88/1.06 (define @t140 () (forall @t14 @t139)) % 0.88/1.06 (define @t141 () (or @t86 @t75 @t140)) % 0.88/1.06 (define @t142 () (or @t86 @t75 @t139)) % 0.88/1.06 (define @t143 () (or @t137 @t87 @t86 @t85 @t75)) % 0.88/1.06 (define @t144 () (tptp.ssList @t106)) % 0.88/1.06 (define @t145 () (@quantifiers_skolemize @t105 0)) % 0.88/1.06 (define @t146 () (tptp.rearsegP @t106 @t145)) % 0.88/1.06 (define @t147 () (not @t146)) % 0.88/1.06 (define @t148 () (tptp.segmentP @t106 @t145)) % 0.88/1.06 (define @t149 () (not @t144)) % 0.88/1.06 (define @t150 () (tptp.ssList @t145)) % 0.88/1.06 (define @t151 () (not @t150)) % 0.88/1.06 (define @t152 () (or @t151 @t149 @t148 @t147)) % 0.88/1.06 (define @t153 () (@list true)) % 0.88/1.06 (define @t154 () (@list @t152)) % 0.88/1.06 (define @t155 () (tptp.app @t106 tptp.nil)) % 0.88/1.06 (define @t156 () (= @t106 @t155)) % 0.88/1.06 (define @t157 () (or @t149 @t156)) % 0.88/1.06 (define @t158 () (@list false false)) % 0.88/1.06 (define @t159 () (@list @t144 @t157)) % 0.88/1.06 (define @t160 () (@var "BOUND_VARIABLE_8335" $$unsorted)) % 0.88/1.06 (define @t161 () (= (tptp.rearsegP @t2 @t160) (not (forall @t16 (or @t126 (not (= @t2 (tptp.app @t12 @t160)))))))) % 0.88/1.06 (define @t162 () (not (tptp.ssList @t160))) % 0.88/1.06 (define @t163 () (or @t162 @t161)) % 0.88/1.06 (define @t164 () (or @t102 @t163)) % 0.88/1.06 (define @t165 () (forall (@list @t2 @t160) @t164)) % 0.88/1.06 (define @t166 () (@list @t160)) % 0.88/1.06 (define @t167 () (forall @t166 @t164)) % 0.88/1.06 (define @t168 () (forall @t166 @t163)) % 0.88/1.06 (define @t169 () (or @t102 @t168)) % 0.88/1.06 (define @t170 () (= @t2 @t22)) % 0.88/1.06 (define @t171 () (= @t25 (not (forall @t16 (or @t126 (not @t170)))))) % 0.88/1.06 (define @t172 () (forall @t7 (or @t116 @t171))) % 0.88/1.06 (define @t173 () (and @t15 @t170)) % 0.88/1.06 (define @t174 () (forall @t16 (not @t173))) % 0.88/1.06 (define @t175 () (not @t174)) % 0.88/1.06 (define @t176 () (@list @t106 @t145)) % 0.88/1.06 (define @t177 () (tptp.app @t12 @t145)) % 0.88/1.06 (define @t178 () (forall @t16 (or @t126 (not (= @t106 @t177))))) % 0.88/1.06 (define @t179 () (not @t178)) % 0.88/1.06 (define @t180 () (= @t146 @t179)) % 0.88/1.06 (define @t181 () (or @t149 @t151 @t180)) % 0.88/1.06 (define @t182 () (@list false false false)) % 0.88/1.06 (define @t183 () (@quantifiers_skolemize @t178 0)) % 0.88/1.06 (define @t184 () (tptp.app @t183 @t145)) % 0.88/1.06 (define @t185 () (= @t106 @t184)) % 0.88/1.06 (define @t186 () (not @t185)) % 0.88/1.06 (define @t187 () (tptp.ssList @t183)) % 0.88/1.06 (define @t188 () (not @t187)) % 0.88/1.06 (define @t189 () (or @t188 @t186)) % 0.88/1.06 (define @t190 () (@list @t189)) % 0.88/1.06 (define @t191 () (@var "BOUND_VARIABLE_8371" $$unsorted)) % 0.88/1.06 (define @t192 () (@var "BOUND_VARIABLE_8394" $$unsorted)) % 0.88/1.06 (define @t193 () (not (tptp.ssList @t191))) % 0.88/1.06 (define @t194 () (@list @t12 @t191)) % 0.88/1.06 (define @t195 () (= (tptp.segmentP @t2 @t192) (not (forall @t194 (or @t126 @t193 (not (= @t2 (tptp.app (tptp.app @t12 @t192) @t191)))))))) % 0.88/1.06 (define @t196 () (not (tptp.ssList @t192))) % 0.88/1.06 (define @t197 () (or @t196 @t195)) % 0.88/1.06 (define @t198 () (or @t102 @t197)) % 0.88/1.06 (define @t199 () (forall (@list @t2 @t192) @t198)) % 0.88/1.06 (define @t200 () (@list @t192)) % 0.88/1.06 (define @t201 () (forall @t200 @t198)) % 0.88/1.06 (define @t202 () (forall @t200 @t197)) % 0.88/1.06 (define @t203 () (or @t102 @t202)) % 0.88/1.06 (define @t204 () (not (= @t2 (tptp.app @t22 @t191)))) % 0.88/1.06 (define @t205 () (or @t126 @t193 @t204)) % 0.88/1.06 (define @t206 () (= @t36 (not (forall @t194 @t205)))) % 0.88/1.06 (define @t207 () (forall @t7 (or @t116 @t206))) % 0.88/1.06 (define @t208 () (or @t193 @t204)) % 0.88/1.06 (define @t209 () (or @t126 @t208)) % 0.88/1.06 (define @t210 () (forall @t194 @t209)) % 0.88/1.06 (define @t211 () (@list @t191)) % 0.88/1.06 (define @t212 () (forall @t211 @t209)) % 0.88/1.06 (define @t213 () (forall @t211 @t208)) % 0.88/1.06 (define @t214 () (or @t126 @t213)) % 0.88/1.06 (define @t215 () (= @t2 @t31)) % 0.88/1.06 (define @t216 () (forall @t14 (or @t137 (not @t215)))) % 0.88/1.06 (define @t217 () (not @t216)) % 0.88/1.06 (define @t218 () (and @t15 @t217)) % 0.88/1.06 (define @t219 () (forall @t16 (not @t218))) % 0.88/1.06 (define @t220 () (not @t219)) % 0.88/1.06 (define @t221 () (and @t13 @t215)) % 0.88/1.06 (define @t222 () (forall @t14 (not @t221))) % 0.88/1.06 (define @t223 () (not @t222)) % 0.88/1.06 (define @t224 () (forall @t194 (or @t126 @t193 (not (= @t106 (tptp.app @t177 @t191)))))) % 0.88/1.06 (define @t225 () (not @t224)) % 0.88/1.06 (define @t226 () (= @t148 @t225)) % 0.88/1.06 (define @t227 () (or @t149 @t151 @t226)) % 0.88/1.06 (define @t228 () (not @t226)) % 0.88/1.06 (define @t229 () (= @t106 (tptp.app @t184 tptp.nil))) % 0.88/1.06 (define @t230 () (not @t229)) % 0.88/1.06 (define @t231 () (not @t55)) % 0.88/1.06 (define @t232 () (or @t188 @t231 @t230)) % 0.88/1.06 (define @t233 () (not @t156)) % 0.88/1.06 (define @t234 () (and @t229 @t230)) % 0.88/1.06 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.88/1.06 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.88/1.06 (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))))))))))) % 0.88/1.06 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.88/1.06 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.88/1.06 (assume @p6 @t30) % 0.88/1.06 (assume @p7 @t41) % 0.88/1.06 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t51 (forall @t14 (=> @t13 (forall @t50 (=> @t49 (forall @t48 (=> @t47 (=> @t46 (not (and @t43 @t42))))))))))))))))) % 0.88/1.06 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t51 (forall @t14 (=> @t13 (forall @t50 (=> @t49 (forall @t48 (=> @t47 (=> @t46 (or @t43 @t42)))))))))))))))) % 0.88/1.06 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t51 (forall @t14 (=> @t13 (forall @t50 (=> @t49 (forall @t48 (=> @t47 (=> @t46 (or @t52 (tptp.lt @t12 @t1))))))))))))))))) % 0.88/1.06 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t51 (forall @t14 (=> @t13 (forall @t50 (=> @t49 (forall @t48 (=> @t47 (=> @t46 @t43))))))))))))))) % 0.88/1.06 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t51 (forall @t14 (=> @t13 (forall @t50 (=> @t49 (forall @t48 (=> @t47 (=> @t46 @t52))))))))))))))) % 0.88/1.06 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t51 (forall @t14 (=> @t13 (forall @t50 (=> @t49 (forall @t48 (=> @t47 (=> @t46 (not @t53)))))))))))))))) % 0.88/1.06 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t51 (forall @t14 (=> @t13 (forall @t50 (=> @t49 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t45))) @t2) @t53))))))))))))) % 0.88/1.06 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.88/1.06 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t54)))))) % 0.88/1.06 (assume @p17 @t55) % 0.88/1.06 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t54 @t2))))))) % 0.88/1.06 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t51 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t56))))))))))) % 0.88/1.06 (assume @p20 (forall @t9 (=> @t17 (or @t58 (exists @t7 (and @t21 (exists @t16 (and @t51 (= @t57 @t2))))))))) % 0.88/1.06 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t54))))))) % 0.88/1.06 (assume @p22 (forall @t9 (=> @t17 (=> @t60 (tptp.ssItem @t59))))) % 0.88/1.06 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t54) @t1)))))) % 0.88/1.06 (assume @p24 (forall @t9 (=> @t17 (=> @t60 (tptp.ssList @t61))))) % 0.88/1.06 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t54) @t2)))))) % 0.88/1.06 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t62)))))) % 0.88/1.06 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t51 (= (tptp.cons @t12 @t63) (tptp.app @t57 @t2))))))))) % 0.88/1.06 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.88/1.06 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t65 @t64) @t3)))))) % 0.88/1.06 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t51 (=> (and @t65 @t43) (tptp.leq @t2 @t12))))))))) % 0.88/1.06 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.88/1.06 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t66 @t64)))))) % 0.88/1.06 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t68 (not @t67))))))) % 0.88/1.06 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t51 (=> (and @t68 @t52) @t69)))))))) % 0.88/1.06 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t70 @t67)))))) % 0.88/1.06 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t71))))))))) % 0.88/1.06 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t71))))))))) % 0.88/1.06 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.88/1.06 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.88/1.06 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.88/1.06 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.88/1.06 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.88/1.06 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.88/1.06 (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)))))))))))) % 0.88/1.06 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.88/1.06 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t58)))) % 0.88/1.06 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t25 @t72) (tptp.rearsegP @t2 @t12))))))))) % 0.88/1.06 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t25 @t73) @t3)))))) % 0.88/1.06 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.88/1.06 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t25 (tptp.rearsegP @t74 @t1))))))))) % 0.88/1.06 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.88/1.06 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t58)))) % 0.88/1.06 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t36 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.88/1.06 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t36 @t75) @t3)))))) % 0.88/1.06 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.88/1.06 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t36 (tptp.segmentP (tptp.app @t74 @t10) @t1))))))))))) % 0.88/1.06 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.88/1.06 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t58)))) % 0.88/1.06 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t76)))) % 0.88/1.06 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.88/1.06 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t76)))) % 0.88/1.06 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.88/1.06 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t76)))) % 0.88/1.06 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.88/1.06 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t76)))) % 0.88/1.06 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.88/1.06 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t80) (or @t78 (and @t79 (tptp.totalorderedP @t1) (tptp.leq @t2 @t77))))))))) % 0.88/1.06 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t76)))) % 0.88/1.06 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.88/1.06 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t80) (or @t78 (and @t79 (tptp.strictorderedP @t1) (tptp.lt @t2 @t77))))))))) % 0.88/1.06 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t76)))) % 0.88/1.06 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.88/1.06 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t76)))) % 0.88/1.06 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.88/1.06 (assume @p75 (forall @t9 (=> @t17 (=> @t60 (exists @t7 (and @t6 (= @t59 @t1))))))) % 0.88/1.06 (assume @p76 (forall @t9 (=> @t17 (=> @t60 (exists @t7 (and @t21 (= @t61 @t1))))))) % 0.88/1.06 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t79 @t60 (= @t77 @t59) (= (tptp.tl @t1) @t61)) @t56)))))) % 0.88/1.06 (assume @p78 (forall @t9 (=> @t17 (=> @t60 (= (tptp.cons @t59 @t61) @t2))))) % 0.88/1.06 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t62) @t81)))))))) % 0.88/1.06 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t63) @t81)))))))) % 0.88/1.06 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t54 (tptp.app @t18 @t2))))))) % 0.88/1.06 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t62 @t12) (tptp.app @t2 @t19))))))))) % 0.88/1.06 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t62) (and @t78 @t58))))))) % 0.88/1.06 (assume @p84 @t84) % 0.88/1.06 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t60 (= (tptp.hd @t62) @t59))))))) % 0.88/1.06 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t60 (= (tptp.tl @t62) (tptp.app @t61 @t1)))))))) % 0.88/1.06 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t66 (tptp.geq @t1 @t2)) @t3)))))) % 0.88/1.06 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t51 (=> (and @t66 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.88/1.06 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.88/1.06 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.88/1.06 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t51 (=> (and @t65 @t52) @t69)))))))) % 0.88/1.06 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t65 (or @t3 @t68))))))) % 0.88/1.06 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t68 (and @t4 @t65))))))) % 0.88/1.06 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t70 (not (tptp.gt @t1 @t2)))))))) % 0.88/1.06 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t51 (=> (and @t70 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.88/1.06 (assume @p96 @t96) % 0.88/1.06 (assume @p97 true) % 0.88/1.06 (step @p98 :rule bool-impl-elim :args (@t17 @t97)) % 0.88/1.06 (step @p99 :rule cong :premises (@p98) :args ((forall @t9 (=> @t17 @t97)))) % 0.88/1.06 (step @p100 :rule eq-symm :args (@t82 @t2)) % 0.88/1.06 (step @p101 :rule refl :args (@t17)) % 0.88/1.06 (step @p102 :rule cong :premises (@p101 @p100) :args (@t83)) % 0.88/1.06 (step @p103 :rule cong :premises (@p102) :args (@t84)) % 0.88/1.06 (step @p104 :rule trans :premises (@p103 @p99)) % 0.88/1.06 (step @p105 :rule eq_resolve :premises (@p84 @p104)) % 0.88/1.06 (step @p106 :rule instantiate :premises (@p105) :args ((@list @t106))) % 0.88/1.06 (step @p107 :rule aci_norm :args ((= @t108 @t103))) % 0.88/1.06 (step @p108 :rule cong :premises (@p107) :args (@t109)) % 0.88/1.06 (step @p109 :rule quant-merge-prenex :args ((= (forall @t9 @t111) @t109))) % 0.88/1.06 (step @p110 :rule alpha_equiv :args (@t112 (@list @t98) @t113)) % 0.88/1.06 (step @p111 :rule refl :args (@t102)) % 0.88/1.06 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t114)) % 0.88/1.06 (step @p113 :rule quant-miniscope-or :args ((= @t111 @t114))) % 0.88/1.06 (step @p114 :rule trans :premises (@p113 @p112)) % 0.88/1.06 (step @p115 :rule symm :premises (@p114)) % 0.88/1.06 (step @p116 :rule cong :premises (@p115) :args ((forall @t9 @t118))) % 0.88/1.06 (step @p117 :rule trans :premises (@p116 @p109)) % 0.88/1.06 (step @p118 :rule trans :premises (@p117 @p108)) % 0.88/1.06 (step @p119 :rule aci_norm :args ((= (or @t102 @t118) @t118))) % 0.88/1.06 (step @p120 :rule bool-impl-elim :args (@t17 @t118)) % 0.88/1.06 (step @p121 :rule trans :premises (@p120 @p119)) % 0.88/1.06 (step @p122 :rule cong :premises (@p121) :args ((forall @t9 (=> @t17 @t118)))) % 0.88/1.06 (step @p123 :rule trans :premises (@p122 @p118)) % 0.88/1.06 (step @p124 :rule quant-miniscope-or :args ((= (forall @t7 @t119) @t118))) % 0.88/1.06 (step @p125 :rule aci_norm :args ((= @t120 @t119))) % 0.88/1.06 (step @p126 :rule cong :premises (@p125) :args ((forall @t7 @t120))) % 0.88/1.06 (step @p127 :rule trans :premises (@p126 @p124)) % 0.88/1.06 (step @p128 :rule aci_norm :args ((= (or @t116 @t121) @t120))) % 0.88/1.06 (step @p129 :rule bool-impl-elim :args (@t21 @t121)) % 0.88/1.06 (step @p130 :rule trans :premises (@p129 @p128)) % 0.88/1.06 (step @p131 :rule cong :premises (@p130) :args ((forall @t7 (=> @t21 @t121)))) % 0.88/1.06 (step @p132 :rule trans :premises (@p131 @p127)) % 0.88/1.06 (step @p133 :rule aci_norm :args ((= (or @t75 @t116 @t122) @t121))) % 0.88/1.06 (step @p134 :rule aci_norm :args ((= (or @t102 false @t115) @t122))) % 0.88/1.06 (step @p135 :rule refl :args (@t115)) % 0.88/1.06 (step @p136 :rule evaluate :args ((not true))) % 0.88/1.06 (step @p137 :rule eq-refl :args (@t2)) % 0.88/1.06 (step @p138 :rule cong :premises (@p137) :args (@t123)) % 0.88/1.06 (step @p139 :rule trans :premises (@p138 @p136)) % 0.88/1.06 (step @p140 :rule refl :args (@t102)) % 0.88/1.06 (step @p141 :rule nary_cong :premises (@p140 @p139 @p135) :args (@t124)) % 0.88/1.06 (step @p142 :rule trans :premises (@p141 @p134)) % 0.88/1.06 (step @p143 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t81) @t126 @t86 @t125)) @t124))) % 0.88/1.06 (step @p144 :rule refl :args (@t125)) % 0.88/1.06 (step @p145 :rule refl :args (@t86)) % 0.88/1.06 (step @p146 :rule refl :args (@t126)) % 0.88/1.06 (step @p147 :rule eq-symm :args (@t2 @t12)) % 0.88/1.06 (step @p148 :rule cong :premises (@p147) :args (@t86)) % 0.88/1.06 (step @p149 :rule nary_cong :premises (@p148 @p146 @p145 @p144) :args (@t127)) % 0.88/1.06 (step @p150 :rule aci_norm :args ((= @t128 @t127))) % 0.88/1.06 (step @p151 :rule trans :premises (@p150 @p149)) % 0.88/1.06 (step @p152 :rule cong :premises (@p151) :args (@t129)) % 0.88/1.06 (step @p153 :rule trans :premises (@p152 @p143)) % 0.88/1.06 (step @p154 :rule trans :premises (@p153 @p142)) % 0.88/1.06 (step @p155 :rule refl :args (@t116)) % 0.88/1.06 (step @p156 :rule refl :args (@t75)) % 0.88/1.06 (step @p157 :rule nary_cong :premises (@p156 @p155 @p154) :args (@t130)) % 0.88/1.06 (step @p158 :rule trans :premises (@p157 @p133)) % 0.88/1.06 (step @p159 :rule quant-miniscope-or :args ((= (forall @t16 @t131) @t130))) % 0.88/1.06 (step @p160 :rule aci_norm :args ((= @t132 @t131))) % 0.88/1.06 (step @p161 :rule cong :premises (@p160) :args ((forall @t16 @t132))) % 0.88/1.06 (step @p162 :rule trans :premises (@p161 @p159)) % 0.88/1.06 (step @p163 :rule trans :premises (@p162 @p158)) % 0.88/1.06 (step @p164 :rule aci_norm :args ((= (or @t126 @t133) @t132))) % 0.88/1.06 (step @p165 :rule bool-impl-elim :args (@t15 @t133)) % 0.88/1.06 (step @p166 :rule trans :premises (@p165 @p164)) % 0.88/1.06 (step @p167 :rule cong :premises (@p166) :args ((forall @t16 (=> @t15 @t133)))) % 0.88/1.06 (step @p168 :rule trans :premises (@p167 @p163)) % 0.88/1.06 (step @p169 :rule aci_norm :args ((= (or @t86 @t75 @t134) @t133))) % 0.88/1.06 (step @p170 :rule aci_norm :args ((= (or @t116 false @t125) @t134))) % 0.88/1.06 (step @p171 :rule refl :args (@t125)) % 0.88/1.06 (step @p172 :rule eq-refl :args (@t1)) % 0.88/1.06 (step @p173 :rule cong :premises (@p172) :args (@t135)) % 0.88/1.06 (step @p174 :rule trans :premises (@p173 @p136)) % 0.88/1.06 (step @p175 :rule nary_cong :premises (@p155 @p174 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(step @p221 :rule reordering :premises (@p220) :args ((or @t144 @t152))) % 0.88/1.06 (step @p222 :rule chain_m_resolution :premises (@p221 @p215) :args (@t144 @t153 @t154)) % 0.88/1.06 (step @p223 :rule cnf_or_pos :args (@t157)) % 0.88/1.06 (step @p224 :rule reordering :premises (@p223) :args ((or @t149 @t156 (not @t157)))) % 0.88/1.06 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p106) :args (@t156 @t158 @t159)) % 0.88/1.06 (step @p226 :rule aci_norm :args ((= @t164 (or @t102 @t162 @t161)))) % 0.88/1.06 (step @p227 :rule cong :premises (@p226) :args (@t165)) % 0.88/1.06 (step @p228 :rule quant-merge-prenex :args ((= (forall @t9 @t167) @t165))) % 0.88/1.06 (step @p229 :rule alpha_equiv :args (@t168 (@list @t160) @t113)) % 0.88/1.06 (step @p230 :rule nary_cong :premises (@p111 @p229) :args (@t169)) % 0.88/1.06 (step @p231 :rule quant-miniscope-or :args ((= @t167 @t169))) % 0.88/1.06 (step @p232 :rule trans :premises (@p231 @p230)) % 0.88/1.06 (step @p233 :rule symm :premises (@p232)) % 0.88/1.06 (step @p234 :rule cong :premises (@p233) :args ((forall @t9 (or @t102 @t172)))) % 0.88/1.06 (step @p235 :rule trans :premises (@p234 @p228)) % 0.88/1.06 (step @p236 :rule trans :premises (@p235 @p227)) % 0.88/1.06 (step @p237 :rule bool-impl-elim :args (@t17 @t172)) % 0.88/1.06 (step @p238 :rule cong :premises (@p237) :args ((forall @t9 (=> @t17 @t172)))) % 0.88/1.06 (step @p239 :rule trans :premises (@p238 @p236)) % 0.88/1.06 (step @p240 :rule bool-impl-elim :args (@t21 @t171)) % 0.88/1.06 (step @p241 :rule cong :premises (@p240) :args ((forall @t7 (=> @t21 @t171)))) % 0.88/1.06 (step @p242 :rule bool-and-de-morgan :args (@t15 @t170 true)) % 0.88/1.06 (step @p243 :rule cong :premises (@p242) :args (@t174)) % 0.88/1.06 (step @p244 :rule cong :premises (@p243) :args (@t175)) % 0.88/1.06 (step @p245 :rule exists-elim :args ((= (exists @t16 @t173) @t175))) % 0.88/1.06 (step @p246 :rule trans :premises (@p245 @p244)) % 0.88/1.06 (step @p247 :rule eq-symm :args (@t22 @t2)) % 0.88/1.06 (step @p248 :rule nary_cong :premises (@p202 @p247) :args (@t23)) % 0.88/1.06 (step @p249 :rule cong :premises (@p248) :args (@t24)) % 0.88/1.06 (step @p250 :rule trans :premises (@p249 @p246)) % 0.88/1.06 (step @p251 :rule refl :args (@t25)) % 0.88/1.06 (step @p252 :rule cong :premises (@p251 @p250) :args (@t26)) % 0.88/1.06 (step @p253 :rule cong :premises (@p206 @p252) :args (@t27)) % 0.88/1.06 (step @p254 :rule cong :premises (@p253) :args (@t28)) % 0.88/1.06 (step @p255 :rule trans :premises (@p254 @p241)) % 0.88/1.06 (step @p256 :rule cong :premises (@p101 @p255) :args (@t29)) % 0.88/1.06 (step @p257 :rule cong :premises (@p256) :args (@t30)) % 0.88/1.06 (step @p258 :rule trans :premises (@p257 @p239)) % 0.88/1.06 (step @p259 :rule eq_resolve :premises (@p6 @p258)) % 0.88/1.06 (step @p260 :rule instantiate :premises (@p259) :args (@t176)) % 0.88/1.06 (step @p261 :rule bool-double-not-elim :args (@t150)) % 0.88/1.06 (step @p262 :rule nary_cong :premises (@p217 @p261) :args ((or @t152 (not @t151)))) % 0.88/1.06 (step @p263 :rule cnf_or_neg :args (@t152 0)) % 0.88/1.06 (step @p264 :rule eq_resolve :premises (@p263 @p262)) % 0.88/1.06 (step @p265 :rule reordering :premises (@p264) :args ((or @t150 @t152))) % 0.88/1.06 (step @p266 :rule chain_m_resolution :premises (@p265 @p215) :args (@t150 @t153 @t154)) % 0.88/1.06 (step @p267 :rule cnf_or_pos :args (@t181)) % 0.88/1.06 (step @p268 :rule reordering :premises (@p267) :args ((or @t151 @t149 @t180 (not @t181)))) % 0.88/1.06 (step @p269 :rule chain_m_resolution :premises (@p268 @p266 @p222 @p260) :args (@t180 @t182 (@list @t150 @t144 @t181))) % 0.88/1.06 (step @p270 :rule bool-double-not-elim :args (@t146)) % 0.88/1.06 (step @p271 :rule nary_cong :premises (@p217 @p270) :args ((or @t152 (not @t147)))) % 0.88/1.06 (step @p272 :rule cnf_or_neg :args (@t152 3)) % 0.88/1.06 (step @p273 :rule eq_resolve :premises (@p272 @p271)) % 0.88/1.06 (step @p274 :rule reordering :premises (@p273) :args ((or @t146 @t152))) % 0.88/1.06 (step @p275 :rule chain_m_resolution :premises (@p274 @p215) :args (@t146 @t153 @t154)) % 0.88/1.06 (step @p276 :rule cnf_equiv_pos1 :args (@t180)) % 0.88/1.06 (step @p277 :rule reordering :premises (@p276) :args ((or @t147 @t179 (not @t180)))) % 0.88/1.06 (step @p278 :rule chain_m_resolution :premises (@p277 @p275 @p269) :args (@t179 @t158 (@list @t146 @t180))) % 0.88/1.06 (step @p279 :rule skolemize :premises (@p278)) % 0.88/1.06 (step @p280 :rule bool-double-not-elim :args (@t185)) % 0.88/1.06 (step @p281 :rule refl :args (@t189)) % 0.88/1.06 (step @p282 :rule nary_cong :premises (@p281 @p280) :args ((or @t189 (not @t186)))) % 0.88/1.06 (step @p283 :rule cnf_or_neg :args (@t189 1)) % 0.88/1.06 (step @p284 :rule eq_resolve :premises (@p283 @p282)) % 0.88/1.06 (step @p285 :rule reordering :premises (@p284) :args ((or @t185 @t189))) % 0.88/1.06 (step @p286 :rule chain_m_resolution :premises (@p285 @p279) :args (@t185 @t153 @t190)) % 0.88/1.06 (step @p287 :rule aci_norm :args ((= @t198 (or @t102 @t196 @t195)))) % 0.88/1.06 (step @p288 :rule cong :premises (@p287) :args (@t199)) % 0.88/1.06 (step @p289 :rule quant-merge-prenex :args ((= (forall @t9 @t201) @t199))) % 0.88/1.06 (step @p290 :rule alpha_equiv :args (@t202 (@list @t192) @t113)) % 0.88/1.06 (step @p291 :rule nary_cong :premises (@p111 @p290) :args (@t203)) % 0.88/1.06 (step @p292 :rule quant-miniscope-or :args ((= @t201 @t203))) % 0.88/1.06 (step @p293 :rule trans :premises (@p292 @p291)) % 0.88/1.06 (step @p294 :rule symm :premises (@p293)) % 0.88/1.06 (step @p295 :rule cong :premises (@p294) :args ((forall @t9 (or @t102 @t207)))) % 0.88/1.06 (step @p296 :rule trans :premises (@p295 @p289)) % 0.88/1.06 (step @p297 :rule trans :premises (@p296 @p288)) % 0.88/1.06 (step @p298 :rule bool-impl-elim :args (@t17 @t207)) % 0.88/1.06 (step @p299 :rule cong :premises (@p298) :args ((forall @t9 (=> @t17 @t207)))) % 0.88/1.06 (step @p300 :rule trans :premises (@p299 @p297)) % 0.88/1.06 (step @p301 :rule bool-impl-elim :args (@t21 @t206)) % 0.88/1.06 (step @p302 :rule cong :premises (@p301) :args ((forall @t7 (=> @t21 @t206)))) % 0.88/1.06 (step @p303 :rule aci_norm :args ((= @t209 @t205))) % 0.88/1.06 (step @p304 :rule cong :premises (@p303) :args (@t210)) % 0.88/1.06 (step @p305 :rule quant-merge-prenex :args ((= (forall @t16 @t212) @t210))) % 0.88/1.06 (step @p306 :rule alpha_equiv :args (@t213 (@list @t191) (@list @t10))) % 0.88/1.06 (step @p307 :rule nary_cong :premises (@p146 @p306) :args (@t214)) % 0.88/1.06 (step @p308 :rule quant-miniscope-or :args ((= @t212 @t214))) % 0.88/1.06 (step @p309 :rule trans :premises (@p308 @p307)) % 0.88/1.06 (step @p310 :rule symm :premises (@p309)) % 0.88/1.06 (step @p311 :rule cong :premises (@p310) :args ((forall @t16 (or @t126 @t216)))) % 0.88/1.06 (step @p312 :rule trans :premises (@p311 @p305)) % 0.88/1.06 (step @p313 :rule trans :premises (@p312 @p304)) % 0.88/1.06 (step @p314 :rule bool-double-not-elim :args (@t216)) % 0.88/1.06 (step @p315 :rule nary_cong :premises (@p146 @p314) :args ((or @t126 (not @t217)))) % 0.88/1.06 (step @p316 :rule bool-and-de-morgan :args (@t15 @t217 true)) % 0.88/1.06 (step @p317 :rule trans :premises (@p316 @p315)) % 0.88/1.06 (step @p318 :rule cong :premises (@p317) :args (@t219)) % 0.88/1.06 (step @p319 :rule trans :premises (@p318 @p313)) % 0.88/1.06 (step @p320 :rule cong :premises (@p319) :args (@t220)) % 0.88/1.06 (step @p321 :rule exists-elim :args ((= (exists @t16 @t218) @t220))) % 0.88/1.06 (step @p322 :rule trans :premises (@p321 @p320)) % 0.88/1.06 (step @p323 :rule bool-and-de-morgan :args (@t13 @t215 true)) % 0.88/1.06 (step @p324 :rule cong :premises (@p323) :args (@t222)) % 0.88/1.06 (step @p325 :rule cong :premises (@p324) :args (@t223)) % 0.88/1.06 (step @p326 :rule exists-elim :args ((= (exists @t14 @t221) @t223))) % 0.88/1.06 (step @p327 :rule trans :premises (@p326 @p325)) % 0.88/1.06 (step @p328 :rule eq-symm :args (@t31 @t2)) % 0.88/1.06 (step @p329 :rule refl :args (@t13)) % 0.88/1.06 (step @p330 :rule nary_cong :premises (@p329 @p328) :args (@t32)) % 0.88/1.06 (step @p331 :rule cong :premises (@p330) :args (@t33)) % 0.88/1.06 (step @p332 :rule trans :premises (@p331 @p327)) % 0.88/1.06 (step @p333 :rule nary_cong :premises (@p202 @p332) :args (@t34)) % 0.88/1.06 (step @p334 :rule cong :premises (@p333) :args (@t35)) % 0.88/1.06 (step @p335 :rule trans :premises (@p334 @p322)) % 0.88/1.06 (step @p336 :rule refl :args (@t36)) % 0.88/1.06 (step @p337 :rule cong :premises (@p336 @p335) :args (@t37)) % 0.88/1.06 (step @p338 :rule cong :premises (@p206 @p337) :args (@t38)) % 0.88/1.06 (step @p339 :rule cong :premises (@p338) :args (@t39)) % 0.88/1.06 (step @p340 :rule trans :premises (@p339 @p302)) % 0.88/1.06 (step @p341 :rule cong :premises (@p101 @p340) :args (@t40)) % 0.88/1.06 (step @p342 :rule cong :premises (@p341) :args (@t41)) % 0.88/1.06 (step @p343 :rule trans :premises (@p342 @p300)) % 0.88/1.06 (step @p344 :rule eq_resolve :premises (@p7 @p343)) % 0.88/1.06 (step @p345 :rule instantiate :premises (@p344) :args (@t176)) % 0.88/1.06 (step @p346 :rule cnf_or_pos :args (@t227)) % 0.88/1.06 (step @p347 :rule reordering :premises (@p346) :args ((or @t151 @t149 @t226 (not @t227)))) % 0.88/1.06 (step @p348 :rule chain_m_resolution :premises (@p347 @p266 @p222 @p345) :args (@t226 @t182 (@list @t150 @t144 @t227))) % 0.88/1.06 (step @p349 :rule cnf_or_neg :args (@t152 2)) % 0.88/1.06 (step @p350 :rule chain_m_resolution :premises (@p349 @p215) :args ((not @t148) @t153 @t154)) % 0.88/1.06 (step @p351 :rule bool-double-not-elim :args (@t224)) % 0.88/1.06 (step @p352 :rule refl :args (@t148)) % 0.88/1.06 (step @p353 :rule refl :args (@t228)) % 0.88/1.06 (step @p354 :rule nary_cong :premises (@p353 @p352 @p351) :args ((or @t228 @t148 (not @t225)))) % 0.88/1.06 (step @p355 :rule cnf_equiv_pos2 :args (@t226)) % 0.88/1.06 (step @p356 :rule eq_resolve :premises (@p355 @p354)) % 0.88/1.06 (step @p357 :rule reordering :premises (@p356) :args ((or @t148 @t224 @t228))) % 0.88/1.06 (step @p358 :rule chain_m_resolution :premises (@p357 @p350 @p348) :args (@t224 (@list true false) (@list @t148 @t226))) % 0.88/1.06 (step @p359 :rule instantiate :premises (@p358) :args ((@list @t183 tptp.nil))) % 0.88/1.06 (step @p360 :rule bool-double-not-elim :args (@t187)) % 0.88/1.06 (step @p361 :rule nary_cong :premises (@p281 @p360) :args ((or @t189 (not @t188)))) % 0.88/1.06 (step @p362 :rule cnf_or_neg :args (@t189 0)) % 0.88/1.06 (step @p363 :rule eq_resolve :premises (@p362 @p361)) % 0.88/1.06 (step @p364 :rule reordering :premises (@p363) :args ((or @t187 @t189))) % 0.88/1.06 (step @p365 :rule chain_m_resolution :premises (@p364 @p279) :args (@t187 @t153 @t190)) % 0.88/1.06 (step @p366 :rule cnf_or_pos :args (@t232)) % 0.88/1.06 (step @p367 :rule reordering :premises (@p366) :args ((or @t231 @t188 @t230 (not @t232)))) % 0.88/1.06 (step @p368 :rule chain_m_resolution :premises (@p367 @p17 @p365 @p359) :args (@t230 @t182 (@list @t55 @t187 @t232))) % 0.88/1.06 (step @p369 :rule bool-double-not-elim :args (@t229)) % 0.88/1.06 (step @p370 :rule refl :args (@t186)) % 0.88/1.06 (step @p371 :rule refl :args (@t233)) % 0.88/1.06 (step @p372 :rule nary_cong :premises (@p371 @p370 @p369) :args ((or @t233 @t186 (not @t230)))) % 0.88/1.06 (assume-push @p402 @t229) % 0.88/1.06 (assume-push @p403 @t230) % 0.88/1.06 (step @p375 :rule evaluate :args ((= true false))) % 0.88/1.06 (step @p376 :rule false_intro :premises (@p368)) % 0.88/1.06 (step @p377 :rule refl :args (tptp.nil)) % 0.88/1.06 (step @p378 :rule cong :premises (@p286 @p377) :args (@t155)) % 0.88/1.06 (step @p379 :rule chain_m_resolution :premises (@p224 @p222 @p106) :args (@t156 @t158 @t159)) % 0.88/1.06 (step @p380 :rule trans :premises (@p379 @p378)) % 0.88/1.06 (step @p381 :rule true_intro :premises (@p380)) % 0.88/1.06 (step @p382 :rule symm :premises (@p381)) % 0.88/1.06 (step @p383 :rule trans :premises (@p382 @p376)) % 0.88/1.06 (step @p384 false :rule eq_resolve :premises (@p383 @p375)) % 0.88/1.06 (step-pop @p404 :rule scope :premises (@p384)) % 0.88/1.06 (step-pop @p405 :rule scope :premises (@p404)) % 0.88/1.06 (step @p385 :rule process_scope :premises (@p405) :args (false)) % 0.88/1.06 (assume-push @p406 @t156) % 0.88/1.06 (assume-push @p407 @t185) % 0.88/1.06 (assume-push @p408 @t230) % 0.88/1.06 (step @p377 :rule refl :args (tptp.nil)) % 0.88/1.06 (step @p378 :rule cong :premises (@p286 @p377) :args (@t155)) % 0.88/1.06 (step @p391 :rule trans :premises (@p225 @p378)) % 0.88/1.06 (step @p392 :rule and_intro :premises (@p391 @p368)) % 0.88/1.06 (step-pop @p409 :rule scope :premises (@p392)) % 0.88/1.06 (step-pop @p410 :rule scope :premises (@p409)) % 0.88/1.06 (step-pop @p411 :rule scope :premises (@p410)) % 0.88/1.06 (step @p393 :rule process_scope :premises (@p411) :args (@t234)) % 0.88/1.06 (step @p397 :rule implies_elim :premises (@p393)) % 0.88/1.06 (step @p398 :rule resolution :premises (@p397 @p385) :args (true @t234)) % 0.88/1.06 (step @p399 :rule not_and :premises (@p398)) % 0.88/1.06 (step @p400 :rule eq_resolve :premises (@p399 @p372)) % 0.88/1.06 (step @p401 false :rule chain_m_resolution :premises (@p400 @p368 @p286 @p225) :args (false (@list true false false) (@list @t229 @t185 @t156))) % 0.88/1.06 ) % 0.88/1.06 % SZS output end Proof % 0.88/1.06 % cvc5 exiting %------------------------------------------------------------------------------