%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRA009+1 : TPTP v9.2.1. Bugfixed v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:18:31 AM UTC 2026 % Result : Theorem 35.02s 35.27s % Output : Proof 35.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRA009+1 : TPTP v9.2.1. Bugfixed v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n006.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 00:14:19 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.50 %----Proving TF0_NAR, FOF, or CNF % 35.02/35.27 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 35.02/35.27 --- Run --no-e-matching --full-saturate-quant at 6... % 35.02/35.27 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 35.02/35.27 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 35.02/35.27 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 35.02/35.27 % SZS status Theorem % 35.02/35.27 % SZS output start Proof % 35.02/35.27 ( % 35.02/35.27 (declare-sort $$unsorted 0) % 35.02/35.27 (declare-const tptp.graph $$unsorted) % 35.02/35.27 (declare-const tptp.number_of_in (-> $$unsorted $$unsorted $$unsorted)) % 35.02/35.27 (declare-const tptp.edges $$unsorted) % 35.02/35.27 (declare-const tptp.triangle (-> $$unsorted $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.shortest_path (-> $$unsorted $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.less_or_equal (-> $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 35.02/35.27 (declare-const tptp.tail_of (-> $$unsorted $$unsorted)) % 35.02/35.27 (declare-const tptp.triangles $$unsorted) % 35.02/35.27 (declare-const tptp.in_path (-> $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.head_of (-> $$unsorted $$unsorted)) % 35.02/35.27 (declare-const tptp.sequential_pairs $$unsorted) % 35.02/35.27 (declare-const tptp.edge (-> $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.path_cons (-> $$unsorted $$unsorted $$unsorted)) % 35.02/35.27 (declare-const tptp.precedes (-> $$unsorted $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.complete Bool) % 35.02/35.27 (declare-const tptp.path (-> $$unsorted $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.vertex (-> $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.on_path (-> $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.empty $$unsorted) % 35.02/35.27 (declare-const tptp.n1 $$unsorted) % 35.02/35.27 (declare-const tptp.sequential (-> $$unsorted $$unsorted Bool)) % 35.02/35.27 (declare-const tptp.length_of (-> $$unsorted $$unsorted)) % 35.02/35.27 (define @t1 () (@var "E" $$unsorted)) % 35.02/35.27 (define @t2 () (tptp.tail_of @t1)) % 35.02/35.27 (define @t3 () (tptp.head_of @t1)) % 35.02/35.27 (define @t4 () (not (= @t3 @t2))) % 35.02/35.27 (define @t5 () (tptp.edge @t1)) % 35.02/35.27 (define @t6 () (@list @t1)) % 35.02/35.27 (define @t7 () (forall @t6 (=> @t5 @t4))) % 35.02/35.27 (define @t8 () (and (tptp.vertex @t3) (tptp.vertex @t2))) % 35.02/35.27 (define @t9 () (forall @t6 (=> @t5 @t8))) % 35.02/35.27 (define @t10 () (@var "V1" $$unsorted)) % 35.02/35.27 (define @t11 () (= @t10 @t2)) % 35.02/35.27 (define @t12 () (@var "V2" $$unsorted)) % 35.02/35.27 (define @t13 () (= @t12 @t3)) % 35.02/35.27 (define @t14 () (and @t13 @t11)) % 35.02/35.27 (define @t15 () (and (= @t10 @t3) (= @t12 @t2))) % 35.02/35.27 (define @t16 () (xor @t15 @t14)) % 35.02/35.27 (define @t17 () (and @t5 @t16)) % 35.02/35.27 (define @t18 () (exists @t6 @t17)) % 35.02/35.27 (define @t19 () (= @t10 @t12)) % 35.02/35.27 (define @t20 () (not @t19)) % 35.02/35.27 (define @t21 () (tptp.vertex @t12)) % 35.02/35.27 (define @t22 () (tptp.vertex @t10)) % 35.02/35.27 (define @t23 () (and @t22 @t21 @t20)) % 35.02/35.27 (define @t24 () (=> @t23 @t18)) % 35.02/35.27 (define @t25 () (@list @t10 @t12)) % 35.02/35.27 (define @t26 () (forall @t25 @t24)) % 35.02/35.27 (define @t27 () (=> tptp.complete @t26)) % 35.02/35.27 (define @t28 () (@var "P" $$unsorted)) % 35.02/35.27 (define @t29 () (tptp.path @t10 @t12 @t28)) % 35.02/35.27 (define @t30 () (@var "TP" $$unsorted)) % 35.02/35.27 (define @t31 () (exists (@list @t30) (and (tptp.path @t3 @t12 @t30) (= @t28 (tptp.path_cons @t1 @t30))))) % 35.02/35.27 (define @t32 () (and @t13 (= @t28 (tptp.path_cons @t1 tptp.empty)))) % 35.02/35.27 (define @t33 () (@list @t10 @t12 @t28)) % 35.02/35.27 (define @t34 () (tptp.on_path @t1 @t28)) % 35.02/35.27 (define @t35 () (@var "V" $$unsorted)) % 35.02/35.27 (define @t36 () (@var "E2" $$unsorted)) % 35.02/35.27 (define @t37 () (@var "E1" $$unsorted)) % 35.02/35.27 (define @t38 () (tptp.edge @t36)) % 35.02/35.27 (define @t39 () (tptp.edge @t37)) % 35.02/35.27 (define @t40 () (tptp.sequential @t37 @t36)) % 35.02/35.27 (define @t41 () (@list @t37 @t36)) % 35.02/35.27 (define @t42 () (forall @t41 (= @t40 (and @t39 @t38 (not (= @t37 @t36)) (= (tptp.head_of @t37) (tptp.tail_of @t36)))))) % 35.02/35.27 (define @t43 () (tptp.precedes @t37 @t36 @t28)) % 35.02/35.27 (define @t44 () (@var "E3" $$unsorted)) % 35.02/35.27 (define @t45 () (tptp.precedes @t44 @t36 @t28)) % 35.02/35.27 (define @t46 () (tptp.sequential @t37 @t44)) % 35.02/35.27 (define @t47 () (and @t46 @t45)) % 35.02/35.27 (define @t48 () (@list @t44)) % 35.02/35.27 (define @t49 () (exists @t48 @t47)) % 35.02/35.27 (define @t50 () (or @t40 @t49)) % 35.02/35.27 (define @t51 () (tptp.on_path @t36 @t28)) % 35.02/35.27 (define @t52 () (tptp.on_path @t37 @t28)) % 35.02/35.27 (define @t53 () (and @t52 @t51 @t50)) % 35.02/35.27 (define @t54 () (=> @t53 @t43)) % 35.02/35.27 (define @t55 () (forall @t41 @t54)) % 35.02/35.27 (define @t56 () (=> @t29 @t55)) % 35.02/35.27 (define @t57 () (@list @t28 @t10 @t12)) % 35.02/35.27 (define @t58 () (forall @t57 @t56)) % 35.02/35.27 (define @t59 () (tptp.length_of @t28)) % 35.02/35.27 (define @t60 () (@var "SP" $$unsorted)) % 35.02/35.27 (define @t61 () (tptp.less_or_equal (tptp.length_of @t60) @t59)) % 35.02/35.27 (define @t62 () (@list @t28)) % 35.02/35.27 (define @t63 () (forall @t62 (=> @t29 @t61))) % 35.02/35.27 (define @t64 () (tptp.path @t10 @t12 @t60)) % 35.02/35.27 (define @t65 () (and @t64 @t20 @t63)) % 35.02/35.27 (define @t66 () (tptp.shortest_path @t10 @t12 @t60)) % 35.02/35.27 (define @t67 () (= @t66 @t65)) % 35.02/35.27 (define @t68 () (forall (@list @t10 @t12 @t60) @t67)) % 35.02/35.27 (define @t69 () (not (tptp.precedes @t36 @t37 @t28))) % 35.02/35.27 (define @t70 () (tptp.head_of @t36)) % 35.02/35.27 (define @t71 () (= (tptp.head_of @t44) @t70)) % 35.02/35.27 (define @t72 () (tptp.tail_of @t37)) % 35.02/35.27 (define @t73 () (= (tptp.tail_of @t44) @t72)) % 35.02/35.27 (define @t74 () (and @t73 @t71)) % 35.02/35.27 (define @t75 () (exists @t48 @t74)) % 35.02/35.27 (define @t76 () (not @t75)) % 35.02/35.27 (define @t77 () (and @t76 @t69)) % 35.02/35.27 (define @t78 () (tptp.shortest_path @t10 @t12 @t28)) % 35.02/35.27 (define @t79 () (and @t78 @t43)) % 35.02/35.27 (define @t80 () (=> @t79 @t77)) % 35.02/35.27 (define @t81 () (@list @t10 @t12 @t37 @t36 @t28)) % 35.02/35.27 (define @t82 () (forall @t81 @t80)) % 35.02/35.27 (define @t83 () (tptp.triangle @t37 @t36 @t44)) % 35.02/35.27 (define @t84 () (tptp.number_of_in tptp.sequential_pairs @t28)) % 35.02/35.27 (define @t85 () (exists @t48 @t83)) % 35.02/35.27 (define @t86 () (and @t52 @t51 @t40)) % 35.02/35.27 (define @t87 () (@var "Things" $$unsorted)) % 35.02/35.27 (define @t88 () (@var "InThese" $$unsorted)) % 35.02/35.27 (define @t89 () (and @t78 @t52 @t51 @t40)) % 35.02/35.27 (define @t90 () (=> @t89 @t85)) % 35.02/35.27 (define @t91 () (@list @t10 @t12 @t28 @t37 @t36)) % 35.02/35.27 (define @t92 () (forall @t91 @t90)) % 35.02/35.27 (define @t93 () (=> tptp.complete @t92)) % 35.02/35.27 (define @t94 () (not @t93)) % 35.02/35.27 (define @t95 () (not (forall @t48 (not @t83)))) % 35.02/35.27 (define @t96 () (not @t40)) % 35.02/35.27 (define @t97 () (not @t51)) % 35.02/35.27 (define @t98 () (not @t52)) % 35.02/35.27 (define @t99 () (not @t78)) % 35.02/35.27 (define @t100 () (or @t99 @t98 @t97 @t96 @t95)) % 35.02/35.27 (define @t101 () (forall @t91 @t100)) % 35.02/35.27 (define @t102 () (@quantifiers_skolemize @t101 4)) % 35.02/35.27 (define @t103 () (@quantifiers_skolemize @t101 3)) % 35.02/35.27 (define @t104 () (or @t99 @t98 @t97 @t96)) % 35.02/35.27 (define @t105 () (=> tptp.complete @t101)) % 35.02/35.27 (define @t106 () (tptp.sequential @t103 @t102)) % 35.02/35.27 (define @t107 () (forall @t48 (not (tptp.triangle @t103 @t102 @t44)))) % 35.02/35.27 (define @t108 () (not @t107)) % 35.02/35.27 (define @t109 () (not @t106)) % 35.02/35.27 (define @t110 () (@quantifiers_skolemize @t101 2)) % 35.02/35.27 (define @t111 () (tptp.on_path @t102 @t110)) % 35.02/35.27 (define @t112 () (not @t111)) % 35.02/35.27 (define @t113 () (tptp.on_path @t103 @t110)) % 35.02/35.27 (define @t114 () (not @t113)) % 35.02/35.27 (define @t115 () (@quantifiers_skolemize @t101 1)) % 35.02/35.27 (define @t116 () (@quantifiers_skolemize @t101 0)) % 35.02/35.27 (define @t117 () (tptp.shortest_path @t116 @t115 @t110)) % 35.02/35.27 (define @t118 () (not @t117)) % 35.02/35.27 (define @t119 () (or @t118 @t114 @t112 @t109 @t108)) % 35.02/35.27 (define @t120 () (@list true)) % 35.02/35.27 (define @t121 () (@list @t119)) % 35.02/35.27 (define @t122 () (tptp.tail_of @t102)) % 35.02/35.27 (define @t123 () (tptp.head_of @t103)) % 35.02/35.27 (define @t124 () (= @t123 @t122)) % 35.02/35.27 (define @t125 () (= @t103 @t102)) % 35.02/35.27 (define @t126 () (not @t125)) % 35.02/35.27 (define @t127 () (tptp.edge @t102)) % 35.02/35.27 (define @t128 () (tptp.edge @t103)) % 35.02/35.27 (define @t129 () (and @t128 @t127 @t126 @t124)) % 35.02/35.27 (define @t130 () (= @t106 @t129)) % 35.02/35.27 (define @t131 () (@list false false)) % 35.02/35.27 (define @t132 () (not @t129)) % 35.02/35.27 (define @t133 () (@list false)) % 35.02/35.27 (define @t134 () (@list @t129)) % 35.02/35.27 (define @t135 () (tptp.head_of @t102)) % 35.02/35.27 (define @t136 () (not (= @t135 @t122))) % 35.02/35.27 (define @t137 () (not @t127)) % 35.02/35.27 (define @t138 () (or @t137 @t136)) % 35.02/35.27 (define @t139 () (not @t5)) % 35.02/35.27 (define @t140 () (forall @t6 (or @t139 @t4))) % 35.02/35.27 (define @t141 () (@list @t102)) % 35.02/35.27 (define @t142 () (= @t122 @t135)) % 35.02/35.27 (define @t143 () (not @t142)) % 35.02/35.27 (define @t144 () (or @t137 @t143)) % 35.02/35.27 (define @t145 () (and (= @t3 @t12) (= @t2 @t10))) % 35.02/35.27 (define @t146 () (and (= @t3 @t10) (= @t2 @t12))) % 35.02/35.27 (define @t147 () (not (forall @t6 (or @t139 (= @t146 @t145))))) % 35.02/35.27 (define @t148 () (not @t21)) % 35.02/35.27 (define @t149 () (not @t22)) % 35.02/35.27 (define @t150 () (or @t149 @t148 @t19 @t147)) % 35.02/35.27 (define @t151 () (forall @t25 @t150)) % 35.02/35.27 (define @t152 () (not @t20)) % 35.02/35.27 (define @t153 () (or @t149 @t148 @t152)) % 35.02/35.27 (define @t154 () (xor @t146 @t145)) % 35.02/35.27 (define @t155 () (and @t5 @t154)) % 35.02/35.27 (define @t156 () (forall @t6 (not @t155))) % 35.02/35.27 (define @t157 () (not @t156)) % 35.02/35.27 (define @t158 () (tptp.tail_of @t103)) % 35.02/35.27 (define @t159 () (not (= @t102 @t103))) % 35.02/35.27 (define @t160 () (and @t127 @t128 @t159 (= @t135 @t158))) % 35.02/35.27 (define @t161 () (tptp.sequential @t102 @t103)) % 35.02/35.27 (define @t162 () (= @t161 @t160)) % 35.02/35.27 (define @t163 () (= @t158 @t135)) % 35.02/35.27 (define @t164 () (and @t127 @t128 @t126 @t163)) % 35.02/35.27 (define @t165 () (= @t161 @t164)) % 35.02/35.27 (define @t166 () (@list @t42)) % 35.02/35.27 (define @t167 () (@var "BOUND_VARIABLE_7832" $$unsorted)) % 35.02/35.27 (define @t168 () (@var "BOUND_VARIABLE_7830" $$unsorted)) % 35.02/35.27 (define @t169 () (tptp.precedes @t168 @t167 @t28)) % 35.02/35.27 (define @t170 () (@var "BOUND_VARIABLE_7834" $$unsorted)) % 35.02/35.27 (define @t171 () (and (not (tptp.sequential @t168 @t167)) (or (not (tptp.sequential @t168 @t170)) (not (tptp.precedes @t170 @t167 @t28))))) % 35.02/35.27 (define @t172 () (not (tptp.on_path @t167 @t28))) % 35.02/35.27 (define @t173 () (not (tptp.on_path @t168 @t28))) % 35.02/35.27 (define @t174 () (not @t29)) % 35.02/35.27 (define @t175 () (or @t173 @t172 @t171 @t169)) % 35.02/35.27 (define @t176 () (or @t174 @t175)) % 35.02/35.27 (define @t177 () (forall (@list @t28 @t10 @t12 @t168 @t167 @t170) @t176)) % 35.02/35.27 (define @t178 () (@list @t168 @t167 @t170)) % 35.02/35.27 (define @t179 () (forall @t178 @t176)) % 35.02/35.27 (define @t180 () (forall @t178 @t175)) % 35.02/35.27 (define @t181 () (@var "BOUND_VARIABLE_7815" $$unsorted)) % 35.02/35.27 (define @t182 () (or @t174 @t180)) % 35.02/35.27 (define @t183 () (or (not (tptp.sequential @t37 @t181)) (not (tptp.precedes @t181 @t36 @t28)))) % 35.02/35.27 (define @t184 () (and @t96 @t183)) % 35.02/35.27 (define @t185 () (or @t98 @t97 @t184 @t43)) % 35.02/35.27 (define @t186 () (forall (@list @t37 @t36 @t181) @t185)) % 35.02/35.27 (define @t187 () (@list @t181)) % 35.02/35.27 (define @t188 () (forall @t187 @t185)) % 35.02/35.27 (define @t189 () (forall @t187 @t183)) % 35.02/35.27 (define @t190 () (@list @t44)) % 35.02/35.27 (define @t191 () (forall @t187 @t96)) % 35.02/35.27 (define @t192 () (and @t191 @t189)) % 35.02/35.27 (define @t193 () (forall @t187 @t184)) % 35.02/35.27 (define @t194 () (or @t98 @t97 @t193 @t43)) % 35.02/35.27 (define @t195 () (forall @t48 (or (not @t46) (not @t45)))) % 35.02/35.27 (define @t196 () (and @t96 @t195)) % 35.02/35.27 (define @t197 () (or @t98 @t97 @t196 @t43)) % 35.02/35.27 (define @t198 () (not @t195)) % 35.02/35.27 (define @t199 () (or @t40 @t198)) % 35.02/35.27 (define @t200 () (not @t199)) % 35.02/35.27 (define @t201 () (or @t98 @t97 @t200)) % 35.02/35.27 (define @t202 () (and @t52 @t51 @t199)) % 35.02/35.27 (define @t203 () (forall @t48 (not @t47))) % 35.02/35.27 (define @t204 () (not @t203)) % 35.02/35.27 (define @t205 () (@var "BOUND_VARIABLE_7922" $$unsorted)) % 35.02/35.27 (define @t206 () (tptp.head_of @t205)) % 35.02/35.27 (define @t207 () (not (= @t206 @t70))) % 35.02/35.27 (define @t208 () (tptp.tail_of @t205)) % 35.02/35.27 (define @t209 () (not (= @t208 @t72))) % 35.02/35.27 (define @t210 () (or @t209 @t207)) % 35.02/35.27 (define @t211 () (and @t210 @t69)) % 35.02/35.27 (define @t212 () (not @t43)) % 35.02/35.27 (define @t213 () (or @t99 @t212 @t211)) % 35.02/35.27 (define @t214 () (forall (@list @t10 @t12 @t37 @t36 @t28 @t205) @t213)) % 35.02/35.27 (define @t215 () (@list @t205)) % 35.02/35.27 (define @t216 () (forall @t215 @t213)) % 35.02/35.27 (define @t217 () (forall @t215 @t69)) % 35.02/35.27 (define @t218 () (forall @t215 @t210)) % 35.02/35.27 (define @t219 () (and @t218 @t217)) % 35.02/35.27 (define @t220 () (forall @t215 @t211)) % 35.02/35.27 (define @t221 () (or @t99 @t212 @t220)) % 35.02/35.27 (define @t222 () (forall @t48 (or (not @t73) (not @t71)))) % 35.02/35.27 (define @t223 () (and @t222 @t69)) % 35.02/35.27 (define @t224 () (or @t99 @t212 @t223)) % 35.02/35.27 (define @t225 () (forall @t48 (not @t74))) % 35.02/35.27 (define @t226 () (not @t225)) % 35.02/35.27 (define @t227 () (@quantifiers_skolemize (forall @t41 (or (not (tptp.on_path @t37 @t110)) (not (tptp.on_path @t36 @t110)) @t96 @t95)) 0)) % 35.02/35.27 (define @t228 () (and @t109 (or (not (tptp.sequential @t103 @t110)) (not (tptp.precedes @t110 @t102 @t110))))) % 35.02/35.27 (define @t229 () (not @t228)) % 35.02/35.27 (define @t230 () (tptp.path @t116 @t115 @t110)) % 35.02/35.27 (define @t231 () (and @t230 (not (= @t116 @t115)) (forall @t62 (or (not (tptp.path @t116 @t115 @t28)) (tptp.less_or_equal (tptp.length_of @t110) @t59))))) % 35.02/35.27 (define @t232 () (= @t117 @t231)) % 35.02/35.27 (define @t233 () (tptp.precedes @t103 @t102 @t110)) % 35.02/35.27 (define @t234 () (not @t230)) % 35.02/35.27 (define @t235 () (or @t234 @t114 @t112 @t228 @t233)) % 35.02/35.27 (define @t236 () (@list false false false true false)) % 35.02/35.27 (define @t237 () (tptp.precedes @t102 @t103 @t110)) % 35.02/35.27 (define @t238 () (not @t237)) % 35.02/35.27 (define @t239 () (and (or (not (= @t158 (tptp.tail_of @t227))) (not (= @t135 (tptp.head_of @t227)))) @t238)) % 35.02/35.27 (define @t240 () (not @t233)) % 35.02/35.27 (define @t241 () (or @t118 @t240 @t239)) % 35.02/35.27 (define @t242 () (@list false false false)) % 35.02/35.27 (define @t243 () (not @t161)) % 35.02/35.27 (define @t244 () (and @t243 (or (not (tptp.sequential @t102 @t102)) @t238))) % 35.02/35.27 (define @t245 () (or @t234 @t112 @t114 @t244 @t237)) % 35.02/35.27 (define @t246 () (not @t164)) % 35.02/35.27 (define @t247 () (@list true false)) % 35.02/35.27 (define @t248 () (not @t163)) % 35.02/35.27 (define @t249 () (not @t128)) % 35.02/35.27 (define @t250 () (tptp.vertex @t135)) % 35.02/35.27 (define @t251 () (and @t250 (tptp.vertex @t122))) % 35.02/35.27 (define @t252 () (or @t137 @t251)) % 35.02/35.27 (define @t253 () (tptp.vertex @t158)) % 35.02/35.27 (define @t254 () (and (tptp.vertex @t123) @t253)) % 35.02/35.27 (define @t255 () (or @t249 @t254)) % 35.02/35.27 (define @t256 () (forall @t6 (or @t139 (= (and (= @t3 @t158) (= @t2 @t135)) (and (= @t3 @t135) (= @t2 @t158)))))) % 35.02/35.27 (define @t257 () (not @t256)) % 35.02/35.27 (define @t258 () (not @t250)) % 35.02/35.27 (define @t259 () (not @t253)) % 35.02/35.27 (define @t260 () (or @t259 @t258 @t163 @t257)) % 35.02/35.27 (define @t261 () (@list false false true false)) % 35.02/35.27 (define @t262 () (@quantifiers_skolemize @t256 0)) % 35.02/35.27 (define @t263 () (tptp.tail_of @t262)) % 35.02/35.27 (define @t264 () (= @t158 @t263)) % 35.02/35.27 (define @t265 () (tptp.head_of @t262)) % 35.02/35.27 (define @t266 () (= @t135 @t265)) % 35.02/35.27 (define @t267 () (and @t266 @t264)) % 35.02/35.27 (define @t268 () (= @t135 @t263)) % 35.02/35.27 (define @t269 () (= @t158 @t265)) % 35.02/35.27 (define @t270 () (and @t269 @t268)) % 35.02/35.27 (define @t271 () (= @t270 @t267)) % 35.02/35.27 (define @t272 () (tptp.edge @t262)) % 35.02/35.27 (define @t273 () (not @t272)) % 35.02/35.27 (define @t274 () (or @t273 @t271)) % 35.02/35.27 (define @t275 () (not @t274)) % 35.02/35.27 (define @t276 () (and (= @t265 @t135) (= @t263 @t158))) % 35.02/35.27 (define @t277 () (= @t265 @t158)) % 35.02/35.27 (define @t278 () (and @t277 (= @t263 @t135))) % 35.02/35.27 (define @t279 () (= @t278 @t276)) % 35.02/35.27 (define @t280 () (or @t273 @t279)) % 35.02/35.27 (define @t281 () (not @t280)) % 35.02/35.27 (define @t282 () (@list @t274)) % 35.02/35.27 (define @t283 () (not @t267)) % 35.02/35.27 (define @t284 () (not @t266)) % 35.02/35.27 (define @t285 () (not @t264)) % 35.02/35.27 (define @t286 () (or @t285 @t284)) % 35.02/35.27 (define @t287 () (and @t286 @t238)) % 35.02/35.27 (define @t288 () (or @t118 @t240 @t287)) % 35.02/35.27 (define @t289 () (not @t270)) % 35.02/35.27 (define @t290 () (@list @t270)) % 35.02/35.27 (define @t291 () (tptp.sequential @t262 @t103)) % 35.02/35.27 (define @t292 () (tptp.sequential @t102 @t262)) % 35.02/35.27 (define @t293 () (and @t128 @t127 @t272 @t106 @t292 @t291)) % 35.02/35.27 (define @t294 () (tptp.triangle @t103 @t102 @t262)) % 35.02/35.27 (define @t295 () (= @t294 @t293)) % 35.02/35.27 (define @t296 () (not @t293)) % 35.02/35.27 (define @t297 () (not @t292)) % 35.02/35.27 (define @t298 () (not (= @t262 @t103))) % 35.02/35.27 (define @t299 () (and @t272 @t128 @t298 @t277)) % 35.02/35.27 (define @t300 () (= @t291 @t299)) % 35.02/35.27 (define @t301 () (= @t103 @t262)) % 35.02/35.27 (define @t302 () (not @t301)) % 35.02/35.27 (define @t303 () (and @t272 @t128 @t302 @t269)) % 35.02/35.27 (define @t304 () (= @t291 @t303)) % 35.02/35.27 (define @t305 () (not @t269)) % 35.02/35.27 (define @t306 () (= @t102 @t262)) % 35.02/35.27 (define @t307 () (not @t306)) % 35.02/35.27 (define @t308 () (and @t127 @t272 @t307 @t268)) % 35.02/35.27 (define @t309 () (= @t292 @t308)) % 35.02/35.27 (define @t310 () (not @t308)) % 35.02/35.27 (define @t311 () (not @t268)) % 35.02/35.27 (define @t312 () (not @t124)) % 35.02/35.27 (define @t313 () (= @t123 @t263)) % 35.02/35.27 (define @t314 () (and @t124 @t313 @t268 @t143)) % 35.02/35.27 (assume @p1 @t7) % 35.02/35.27 (assume @p2 @t9) % 35.02/35.27 (assume @p3 @t27) % 35.02/35.27 (assume @p4 (forall @t33 (=> (and @t22 @t21 (exists @t6 (and @t5 @t11 (or @t32 @t31)))) @t29))) % 35.02/35.27 (assume @p5 (forall @t33 (=> @t29 (and @t22 @t21 (exists @t6 (and @t5 @t11 (xor @t32 @t31))))))) % 35.02/35.27 (assume @p6 (forall (@list @t10 @t12 @t28 @t1) (=> (and @t29 @t34) (and @t5 (tptp.in_path @t3 @t28) (tptp.in_path @t2 @t28))))) % 35.02/35.27 (assume @p7 (forall (@list @t10 @t12 @t28 @t35) (=> (and @t29 (tptp.in_path @t35 @t28)) (and (tptp.vertex @t35) (exists @t6 (and @t34 (or (= @t35 @t3) (= @t35 @t2)))))))) % 35.02/35.27 (assume @p8 @t42) % 35.02/35.27 (assume @p9 @t58) % 35.02/35.27 (assume @p10 (forall @t57 (=> @t29 (forall @t41 (=> @t43 (and @t52 @t51 (xor @t40 @t49))))))) % 35.02/35.27 (assume @p11 @t68) % 35.02/35.27 (assume @p12 @t82) % 35.02/35.27 (assume @p13 (forall (@list @t37 @t36 @t44) (= @t83 (and @t39 @t38 (tptp.edge @t44) @t40 (tptp.sequential @t36 @t44) (tptp.sequential @t44 @t37))))) % 35.02/35.27 (assume @p14 (forall @t33 (=> @t29 (= @t59 (tptp.number_of_in tptp.edges @t28))))) % 35.02/35.27 (assume @p15 (forall @t33 (=> @t29 (= @t84 (tptp.minus @t59 tptp.n1))))) % 35.02/35.27 (assume @p16 (forall @t57 (=> (and @t29 (forall @t41 (=> @t86 @t85))) (= @t84 (tptp.number_of_in tptp.triangles @t28))))) % 35.02/35.27 (assume @p17 (forall (@list @t87 @t88) (tptp.less_or_equal (tptp.number_of_in @t87 @t88) (tptp.number_of_in @t87 tptp.graph)))) % 35.02/35.27 (assume @p18 @t94) % 35.02/35.27 (assume @p19 true) % 35.02/35.27 (step @p20 :rule instantiate :premises (@p8) :args ((@list @t103 @t102))) % 35.02/35.27 (step @p21 :rule bool-impl-true2 :args (@t101)) % 35.02/35.27 (step @p22 :rule cong :premises (@p21) :args ((not (=> true @t101)))) % 35.02/35.27 (step @p23 :rule refl :args (@t101)) % 35.02/35.27 (step @p24 :rule bool-eq-true :args (tptp.complete)) % 35.02/35.27 (step @p25 :rule symm :premises (@p24)) % 35.02/35.27 (step @p26 :rule aci_norm :args ((= (or @t104 @t95) @t100))) % 35.02/35.27 (step @p27 :rule refl :args (@t95)) % 35.02/35.27 (step @p28 :rule aci_norm :args ((= (or @t99 (or @t98 (or @t97 @t96))) @t104))) % 35.02/35.27 (step @p29 :rule bool-and-de-morgan :args (@t51 @t40 true)) % 35.02/35.27 (step @p30 :rule refl :args (@t98)) % 35.02/35.27 (step @p31 :rule nary_cong :premises (@p30 @p29) :args ((or @t98 (not (and @t51 @t40))))) % 35.02/35.27 (step @p32 :rule bool-and-de-morgan :args (@t52 @t51 (and @t40))) % 35.02/35.27 (step @p33 :rule trans :premises (@p32 @p31)) % 35.02/35.27 (step @p34 :rule refl :args (@t99)) % 35.02/35.27 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t99 (not @t86)))) % 35.02/35.27 (step @p36 :rule bool-and-de-morgan :args (@t78 @t52 (and @t51 @t40))) % 35.02/35.27 (step @p37 :rule trans :premises (@p36 @p35)) % 35.02/35.27 (step @p38 :rule trans :premises (@p37 @p28)) % 35.02/35.27 (step @p39 :rule nary_cong :premises (@p38 @p27) :args ((or (not @t89) @t95))) % 35.02/35.27 (step @p40 :rule trans :premises (@p39 @p26)) % 35.02/35.27 (step @p41 :rule bool-impl-elim :args (@t89 @t95)) % 35.02/35.27 (step @p42 :rule trans :premises (@p41 @p40)) % 35.02/35.27 (step @p43 :rule cong :premises (@p42) :args ((forall @t91 (=> @t89 @t95)))) % 35.02/35.27 (step @p44 :rule exists-elim :args ((= @t85 @t95))) % 35.02/35.27 (step @p45 :rule refl :args (@t89)) % 35.02/35.27 (step @p46 :rule cong :premises (@p45 @p44) :args (@t90)) % 35.02/35.27 (step @p47 :rule cong :premises (@p46) :args (@t92)) % 35.02/35.27 (step @p48 :rule trans :premises (@p47 @p43)) % 35.02/35.27 (step @p49 :rule refl :args (tptp.complete)) % 35.02/35.27 (step @p50 :rule cong :premises (@p49 @p48) :args (@t93)) % 35.02/35.27 (step @p51 :rule cong :premises (@p50) :args (@t94)) % 35.02/35.27 (step @p52 :rule eq_resolve :premises (@p18 @p51)) % 35.02/35.27 (step @p53 :rule not_implies_elim1 :premises (@p52)) % 35.02/35.27 (step @p54 :rule eq_resolve :premises (@p53 @p25)) % 35.02/35.27 (step @p55 :rule cong :premises (@p54 @p23) :args (@t105)) % 35.02/35.27 (step @p56 :rule cong :premises (@p55) :args ((not @t105))) % 35.02/35.27 (step @p57 :rule trans :premises (@p56 @p22)) % 35.02/35.27 (step @p58 :rule trans :premises (@p51 @p57)) % 35.02/35.27 (step @p59 :rule eq_resolve :premises (@p18 @p58)) % 35.02/35.27 (step @p60 :rule skolemize :premises (@p59)) % 35.02/35.27 (step @p61 :rule bool-double-not-elim :args (@t106)) % 35.02/35.27 (step @p62 :rule refl :args (@t119)) % 35.02/35.27 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or @t119 (not @t109)))) % 35.02/35.27 (step @p64 :rule cnf_or_neg :args (@t119 3)) % 35.02/35.27 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 35.02/35.27 (step @p66 :rule reordering :premises (@p65) :args ((or @t106 @t119))) % 35.02/35.27 (step @p67 :rule chain_m_resolution :premises (@p66 @p60) :args (@t106 @t120 @t121)) % 35.02/35.27 (step @p68 :rule cnf_equiv_pos1 :args (@t130)) % 35.02/35.27 (step @p69 :rule reordering :premises (@p68) :args ((or @t109 @t129 (not @t130)))) % 35.02/35.27 (step @p70 :rule chain_m_resolution :premises (@p69 @p67 @p20) :args (@t129 @t131 (@list @t106 @t130))) % 35.02/35.27 (step @p71 :rule cnf_and_pos :args (@t129 3)) % 35.02/35.27 (step @p72 :rule reordering :premises (@p71) :args ((or @t124 @t132))) % 35.02/35.27 (step @p73 :rule chain_m_resolution :premises (@p72 @p70) :args (@t124 @t133 @t134)) % 35.02/35.27 (step @p74 :rule bool-impl-elim :args (@t5 @t4)) % 35.02/35.27 (step @p75 :rule cong :premises (@p74) :args (@t7)) % 35.02/35.27 (step @p76 :rule eq_resolve :premises (@p1 @p75)) % 35.02/35.27 (step @p77 :rule eq-symm :args (@t135 @t122)) % 35.02/35.27 (step @p78 :rule cong :premises (@p77) :args (@t136)) % 35.02/35.27 (step @p79 :rule refl :args (@t137)) % 35.02/35.27 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t138)) % 35.02/35.27 (step @p81 :rule refl :args (@t140)) % 35.02/35.27 (step @p82 :rule cong :premises (@p81 @p80) :args ((=> @t140 @t138))) % 35.02/35.27 (assume-push @p545 @t140) % 35.02/35.27 (step @p84 :rule instantiate :premises (@p76) :args (@t141)) % 35.02/35.27 (step-pop @p546 :rule scope :premises (@p84)) % 35.02/35.27 (step @p85 :rule process_scope :premises (@p546) :args (@t138)) % 35.02/35.27 (step @p87 :rule eq_resolve :premises (@p85 @p82)) % 35.02/35.27 (step @p88 :rule implies_elim :premises (@p87)) % 35.02/35.27 (step @p89 :rule chain_m_resolution :premises (@p88 @p76) :args (@t144 @t133 (@list @t140))) % 35.02/35.27 (step @p90 :rule cnf_and_pos :args (@t129 1)) % 35.02/35.27 (step @p91 :rule reordering :premises (@p90) :args ((or @t127 @t132))) % 35.02/35.27 (step @p92 :rule chain_m_resolution :premises (@p91 @p70) :args (@t127 @t133 @t134)) % 35.02/35.27 (step @p93 :rule cnf_or_pos :args (@t144)) % 35.02/35.27 (step @p94 :rule reordering :premises (@p93) :args ((or @t137 @t143 (not @t144)))) % 35.02/35.27 (step @p95 :rule chain_m_resolution :premises (@p94 @p92 @p89) :args (@t143 @t131 (@list @t127 @t144))) % 35.02/35.27 (step @p96 :rule bool-impl-true2 :args (@t151)) % 35.02/35.27 (step @p97 :rule refl :args (@t151)) % 35.02/35.27 (step @p98 :rule cong :premises (@p54 @p97) :args ((=> tptp.complete @t151))) % 35.02/35.27 (step @p99 :rule trans :premises (@p98 @p96)) % 35.02/35.27 (step @p100 :rule aci_norm :args ((= (or (or @t149 @t148 @t19) @t147) @t150))) % 35.02/35.27 (step @p101 :rule refl :args (@t147)) % 35.02/35.27 (step @p102 :rule bool-double-not-elim :args (@t19)) % 35.02/35.27 (step @p103 :rule refl :args (@t148)) % 35.02/35.27 (step @p104 :rule refl :args (@t149)) % 35.02/35.27 (step @p105 :rule nary_cong :premises (@p104 @p103 @p102) :args (@t153)) % 35.02/35.27 (step @p106 :rule aci_norm :args ((= (or @t149 (or @t148 @t152)) @t153))) % 35.02/35.27 (step @p107 :rule trans :premises (@p106 @p105)) % 35.02/35.27 (step @p108 :rule bool-and-de-morgan :args (@t21 @t20 true)) % 35.02/35.27 (step @p109 :rule nary_cong :premises (@p104 @p108) :args ((or @t149 (not (and @t21 @t20))))) % 35.02/35.27 (step @p110 :rule bool-and-de-morgan :args (@t22 @t21 (and @t20))) % 35.02/35.27 (step @p111 :rule trans :premises (@p110 @p109)) % 35.02/35.27 (step @p112 :rule trans :premises (@p111 @p107)) % 35.02/35.27 (step @p113 :rule nary_cong :premises (@p112 @p101) :args ((or (not @t23) @t147))) % 35.02/35.27 (step @p114 :rule trans :premises (@p113 @p100)) % 35.02/35.27 (step @p115 :rule bool-impl-elim :args (@t23 @t147)) % 35.02/35.27 (step @p116 :rule trans :premises (@p115 @p114)) % 35.02/35.27 (step @p117 :rule cong :premises (@p116) :args ((forall @t25 (=> @t23 @t147)))) % 35.02/35.27 (step @p118 :rule bool-not-xor-elim :args (@t146 @t145)) % 35.02/35.27 (step @p119 :rule refl :args (@t139)) % 35.02/35.27 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or @t139 (not @t154)))) % 35.02/35.27 (step @p121 :rule bool-and-de-morgan :args (@t5 @t154 true)) % 35.02/35.27 (step @p122 :rule trans :premises (@p121 @p120)) % 35.02/35.27 (step @p123 :rule cong :premises (@p122) :args (@t156)) % 35.02/35.27 (step @p124 :rule cong :premises (@p123) :args (@t157)) % 35.02/35.27 (step @p125 :rule exists-elim :args ((= (exists @t6 @t155) @t157))) % 35.02/35.27 (step @p126 :rule trans :premises (@p125 @p124)) % 35.02/35.27 (step @p127 :rule eq-symm :args (@t10 @t2)) % 35.02/35.27 (step @p128 :rule eq-symm :args (@t12 @t3)) % 35.02/35.27 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t14)) % 35.02/35.27 (step @p130 :rule eq-symm :args (@t12 @t2)) % 35.02/35.27 (step @p131 :rule eq-symm :args (@t10 @t3)) % 35.02/35.27 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t15)) % 35.02/35.27 (step @p133 :rule cong :premises (@p132 @p129) :args (@t16)) % 35.02/35.27 (step @p134 :rule refl :args (@t5)) % 35.02/35.27 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t17)) % 35.02/35.27 (step @p136 :rule cong :premises (@p135) :args (@t18)) % 35.02/35.27 (step @p137 :rule trans :premises (@p136 @p126)) % 35.02/35.27 (step @p138 :rule refl :args (@t23)) % 35.02/35.27 (step @p139 :rule cong :premises (@p138 @p137) :args (@t24)) % 35.02/35.27 (step @p140 :rule cong :premises (@p139) :args (@t26)) % 35.02/35.27 (step @p141 :rule trans :premises (@p140 @p117)) % 35.02/35.27 (step @p142 :rule cong :premises (@p49 @p141) :args (@t27)) % 35.02/35.27 (step @p143 :rule trans :premises (@p142 @p99)) % 35.02/35.27 (step @p144 :rule eq_resolve :premises (@p3 @p143)) % 35.02/35.27 (step @p145 :rule instantiate :premises (@p144) :args ((@list @t158 @t135))) % 35.02/35.27 (step @p146 :rule eq-symm :args (@t135 @t158)) % 35.02/35.27 (step @p147 :rule eq-symm :args (@t102 @t103)) % 35.02/35.27 (step @p148 :rule cong :premises (@p147) :args (@t159)) % 35.02/35.27 (step @p149 :rule refl :args (@t128)) % 35.02/35.27 (step @p150 :rule refl :args (@t127)) % 35.02/35.27 (step @p151 :rule nary_cong :premises (@p150 @p149 @p148 @p146) :args (@t160)) % 35.02/35.27 (step @p152 :rule refl :args (@t161)) % 35.02/35.27 (step @p153 :rule cong :premises (@p152 @p151) :args (@t162)) % 35.02/35.27 (step @p154 :rule refl :args (@t42)) % 35.02/35.27 (step @p155 :rule cong :premises (@p154 @p153) :args ((=> @t42 @t162))) % 35.02/35.27 (assume-push @p547 @t42) % 35.02/35.27 (step @p157 :rule instantiate :premises (@p8) :args ((@list @t102 @t103))) % 35.02/35.27 (step-pop @p548 :rule scope :premises (@p157)) % 35.02/35.27 (step @p158 :rule process_scope :premises (@p548) :args (@t162)) % 35.02/35.27 (step @p160 :rule eq_resolve :premises (@p158 @p155)) % 35.02/35.27 (step @p161 :rule implies_elim :premises (@p160)) % 35.02/35.27 (step @p162 :rule chain_m_resolution :premises (@p161 @p8) :args (@t165 @t133 @t166)) % 35.02/35.27 (step @p163 :rule aci_norm :args ((= @t176 (or @t174 @t173 @t172 @t171 @t169)))) % 35.02/35.27 (step @p164 :rule cong :premises (@p163) :args (@t177)) % 35.02/35.27 (step @p165 :rule quant-merge-prenex :args ((= (forall @t57 @t179) @t177))) % 35.02/35.27 (step @p166 :rule alpha_equiv :args (@t180 (@list @t168 @t167 @t170) (@list @t37 @t36 @t181))) % 35.02/35.27 (step @p167 :rule refl :args (@t174)) % 35.02/35.27 (step @p168 :rule nary_cong :premises (@p167 @p166) :args (@t182)) % 35.02/35.27 (step @p169 :rule quant-miniscope-or :args ((= @t179 @t182))) % 35.02/35.27 (step @p170 :rule trans :premises (@p169 @p168)) % 35.02/35.27 (step @p171 :rule symm :premises (@p170)) % 35.02/35.27 (step @p172 :rule cong :premises (@p171) :args ((forall @t57 (or @t174 @t186)))) % 35.02/35.27 (step @p173 :rule trans :premises (@p172 @p165)) % 35.02/35.27 (step @p174 :rule trans :premises (@p173 @p164)) % 35.02/35.27 (step @p175 :rule bool-impl-elim :args (@t29 @t186)) 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35.02/35.27 (step @p312 :rule chain_m_resolution :premises (@p311 @p60) :args (@t111 @t120 @t121)) % 35.02/35.27 (step @p313 :rule bool-double-not-elim :args (@t113)) % 35.02/35.27 (step @p314 :rule nary_cong :premises (@p62 @p313) :args ((or @t119 (not @t114)))) % 35.02/35.27 (step @p315 :rule cnf_or_neg :args (@t119 1)) % 35.02/35.27 (step @p316 :rule eq_resolve :premises (@p315 @p314)) % 35.02/35.27 (step @p317 :rule reordering :premises (@p316) :args ((or @t113 @t119))) % 35.02/35.27 (step @p318 :rule chain_m_resolution :premises (@p317 @p60) :args (@t113 @t120 @t121)) % 35.02/35.27 (step @p319 :rule cnf_or_pos :args (@t235)) % 35.02/35.27 (step @p320 :rule reordering :premises (@p319) :args ((or @t114 @t112 @t234 @t233 @t228 (not @t235)))) % 35.02/35.27 (step @p321 :rule chain_m_resolution :premises (@p320 @p318 @p312 @p306 @p284 @p281) :args (@t233 @t236 (@list @t113 @t111 @t230 @t228 @t235))) % 35.02/35.27 (step @p322 :rule cnf_or_pos :args (@t241)) % 35.02/35.27 (step @p323 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chain_m_resolution :premises (@p367 @p365) :args (@t253 @t133 (@list @t254))) % 35.02/35.27 (step @p369 :rule cnf_or_pos :args (@t260)) % 35.02/35.27 (step @p370 :rule reordering :premises (@p369) :args ((or @t259 @t258 @t163 @t257 (not @t260)))) % 35.02/35.27 (step @p371 :rule chain_m_resolution :premises (@p370 @p368 @p361 @p351 @p145) :args (@t257 @t261 (@list @t253 @t250 @t163 @t260))) % 35.02/35.27 (step @p372 :rule refl :args (@t275)) % 35.02/35.27 (step @p373 :rule bool-double-not-elim :args (@t256)) % 35.02/35.27 (step @p374 :rule nary_cong :premises (@p373 @p372) :args ((or (not @t257) @t275))) % 35.02/35.27 (step @p375 :rule eq-symm :args (@t263 @t158)) % 35.02/35.27 (step @p376 :rule eq-symm :args (@t265 @t135)) % 35.02/35.27 (step @p377 :rule nary_cong :premises (@p376 @p375) :args (@t276)) % 35.02/35.27 (step @p378 :rule eq-symm :args (@t263 @t135)) % 35.02/35.27 (step @p379 :rule eq-symm :args (@t265 @t158)) % 35.02/35.27 (step @p380 :rule nary_cong :premises (@p379 @p378) :args (@t278)) % 35.02/35.27 (step @p381 :rule cong :premises (@p380 @p377) :args (@t279)) % 35.02/35.27 (step @p382 :rule refl :args (@t273)) % 35.02/35.27 (step @p383 :rule nary_cong :premises (@p382 @p381) :args (@t280)) % 35.02/35.27 (step @p384 :rule cong :premises (@p383) :args (@t281)) % 35.02/35.27 (step @p385 :rule refl :args (@t257)) % 35.02/35.27 (step @p386 :rule cong :premises (@p385 @p384) :args ((=> @t257 @t281))) % 35.02/35.27 (assume-push @p549 @t257) % 35.02/35.27 (step @p388 :rule skolemize :premises (@p371)) % 35.02/35.27 (step-pop @p550 :rule scope :premises (@p388)) % 35.02/35.27 (step @p389 :rule process_scope :premises (@p550) :args (@t281)) % 35.02/35.27 (step @p391 :rule eq_resolve :premises (@p389 @p386)) % 35.02/35.27 (step @p392 :rule implies_elim :premises (@p391)) % 35.02/35.27 (step @p393 :rule eq_resolve :premises (@p392 @p374)) % 35.02/35.27 (step @p394 :rule chain_m_resolution :premises (@p393 @p371) :args (@t275 @t120 (@list @t256))) % 35.02/35.27 (step @p395 :rule cnf_or_neg :args (@t274 1)) % 35.02/35.27 (step @p396 :rule chain_m_resolution :premises (@p395 @p394) :args ((not @t271) @t120 @t282)) % 35.02/35.27 (step @p397 :rule cnf_and_pos :args (@t267 0)) % 35.02/35.27 (step @p398 :rule reordering :premises (@p397) :args ((or @t266 @t283))) % 35.02/35.27 (step @p399 :rule cnf_and_pos :args (@t267 1)) % 35.02/35.27 (step @p400 :rule reordering :premises (@p399) :args ((or @t264 @t283))) % 35.02/35.27 (step @p401 :rule instantiate :premises (@p279) :args ((@list @t116 @t115 @t103 @t102 @t110 @t262))) % 35.02/35.27 (step @p402 :rule cnf_or_pos :args (@t288)) % 35.02/35.27 (step @p403 :rule reordering :premises (@p402) :args ((or @t118 @t240 @t287 (not @t288)))) % 35.02/35.27 (step @p404 :rule chain_m_resolution :premises (@p403 @p300 @p321 @p401) :args (@t287 @t242 (@list @t117 @t233 @t288))) % 35.02/35.27 (step @p405 :rule cnf_and_pos :args (@t287 0)) % 35.02/35.27 (step @p406 :rule reordering :premises (@p405) :args ((or @t286 (not @t287)))) % 35.02/35.27 (step @p407 :rule chain_m_resolution :premises (@p406 @p404) :args (@t286 @t133 (@list @t287))) % 35.02/35.27 (step @p408 :rule cnf_or_pos :args (@t286)) % 35.02/35.27 (step @p409 :rule reordering :premises (@p408) :args ((or @t284 @t285 (not @t286)))) % 35.02/35.27 (step @p410 :rule chain_m_resolution :premises (@p409 @p407 @p400 @p398) :args (@t283 @t242 (@list @t286 @t264 @t266))) % 35.02/35.27 (step @p411 :rule cnf_equiv_neg1 :args (@t271)) % 35.02/35.27 (step @p412 :rule reordering :premises (@p411) :args ((or @t270 @t267 @t271))) % 35.02/35.27 (step @p413 :rule chain_m_resolution :premises (@p412 @p410 @p396) :args (@t270 (@list true true) (@list @t267 @t271))) % 35.02/35.27 (step @p414 :rule cnf_and_pos :args (@t270 1)) % 35.02/35.27 (step @p415 :rule reordering :premises (@p414) :args ((or @t268 @t289))) % 35.02/35.27 (step @p416 :rule chain_m_resolution :premises (@p415 @p413) :args (@t268 @t133 @t290)) % 35.02/35.27 (step @p417 :rule instantiate :premises (@p8) :args ((@list @t102 @t262))) % 35.02/35.27 (step @p418 :rule cnf_and_pos :args (@t270 0)) % 35.02/35.27 (step @p419 :rule reordering :premises (@p418) :args ((or @t269 @t289))) % 35.02/35.27 (step @p420 :rule chain_m_resolution :premises (@p419 @p413) :args (@t269 @t133 @t290)) % 35.02/35.27 (step @p421 :rule bool-double-not-elim :args (@t272)) % 35.02/35.27 (step @p422 :rule refl :args (@t274)) % 35.02/35.27 (step @p423 :rule nary_cong :premises (@p422 @p421) :args ((or @t274 (not @t273)))) % 35.02/35.27 (step @p424 :rule cnf_or_neg :args (@t274 0)) % 35.02/35.27 (step @p425 :rule eq_resolve :premises (@p424 @p423)) % 35.02/35.27 (step @p426 :rule reordering :premises (@p425) :args ((or @t272 @t274))) % 35.02/35.27 (step @p427 :rule chain_m_resolution :premises (@p426 @p394) :args (@t272 @t120 @t282)) % 35.02/35.27 (step @p428 :rule instantiate :premises (@p13) :args ((@list @t103 @t102 @t262))) % 35.02/35.27 (step @p429 :rule bool-double-not-elim :args (@t107)) % 35.02/35.27 (step @p430 :rule nary_cong :premises (@p62 @p429) :args ((or @t119 (not @t108)))) % 35.02/35.27 (step @p431 :rule cnf_or_neg :args (@t119 4)) % 35.02/35.27 (step @p432 :rule eq_resolve :premises (@p431 @p430)) % 35.02/35.27 (step @p433 :rule reordering :premises (@p432) :args ((or @t107 @t119))) % 35.02/35.27 (step @p434 :rule chain_m_resolution :premises (@p433 @p60) :args (@t107 @t120 @t121)) % 35.02/35.27 (step @p435 :rule instantiate :premises (@p434) :args ((@list @t262))) % 35.02/35.27 (step @p436 :rule cnf_equiv_pos2 :args (@t295)) % 35.02/35.27 (step @p437 :rule reordering :premises (@p436) :args ((or @t294 @t296 (not @t295)))) % 35.02/35.27 (step @p438 :rule chain_m_resolution :premises (@p437 @p435 @p428) :args (@t296 @t247 (@list @t294 @t295))) % 35.02/35.27 (step @p439 :rule cnf_and_neg :args (@t293)) % 35.02/35.27 (step @p440 :rule reordering :premises (@p439) :args ((or @t109 @t249 @t137 @t273 (not @t291) @t297 @t293))) % 35.02/35.27 (step @p441 :rule eq-symm :args (@t262 @t103)) % 35.02/35.27 (step @p442 :rule cong :premises (@p441) :args (@t298)) % 35.02/35.27 (step @p443 :rule refl :args (@t272)) % 35.02/35.27 (step @p444 :rule nary_cong :premises (@p443 @p149 @p442 @p379) :args (@t299)) % 35.02/35.27 (step @p445 :rule refl :args (@t291)) % 35.02/35.27 (step @p446 :rule cong :premises (@p445 @p444) :args (@t300)) % 35.02/35.27 (step @p447 :rule cong :premises (@p154 @p446) :args ((=> @t42 @t300))) % 35.02/35.27 (assume-push @p551 @t42) % 35.02/35.27 (step @p449 :rule instantiate :premises (@p8) :args ((@list @t262 @t103))) % 35.02/35.27 (step-pop @p552 :rule scope :premises (@p449)) % 35.02/35.27 (step @p450 :rule process_scope :premises (@p552) :args (@t300)) % 35.02/35.27 (step @p452 :rule eq_resolve :premises (@p450 @p447)) % 35.02/35.27 (step @p453 :rule implies_elim :premises (@p452)) % 35.02/35.27 (step @p454 :rule chain_m_resolution :premises (@p453 @p8) :args (@t304 @t133 @t166)) % 35.02/35.27 (step @p455 :rule cnf_equiv_pos2 :args (@t304)) % 35.02/35.27 (step @p456 :rule reordering :premises (@p455) :args ((or @t291 (not @t303) (not @t304)))) % 35.02/35.27 (step @p457 :rule refl :args (@t305)) % 35.02/35.27 (step @p458 :rule bool-double-not-elim :args (@t301)) % 35.02/35.27 (step @p459 :rule refl :args (@t303)) % 35.02/35.27 (step @p460 :rule nary_cong :premises (@p459 @p382 @p345 @p458 @p457) :args ((or @t303 @t273 @t249 (not @t302) @t305))) % 35.02/35.27 (step @p461 :rule cnf_and_neg :args (@t303)) % 35.02/35.27 (step @p462 :rule eq_resolve :premises (@p461 @p460)) % 35.02/35.27 (step @p463 :rule reordering :premises (@p462) :args ((or @t249 @t273 @t305 @t301 @t303))) % 35.02/35.27 (step @p464 :rule refl :args (@t297)) % 35.02/35.27 (step @p465 :rule refl :args (@t302)) % 35.02/35.27 (step @p466 :rule bool-double-not-elim :args (@t161)) % 35.02/35.27 (step @p467 :rule nary_cong :premises (@p466 @p465 @p464) :args ((or (not @t243) @t302 @t297))) % 35.02/35.27 (assume-push @p553 @t243) % 35.02/35.27 (assume-push @p554 @t301) % 35.02/35.27 (assume-push @p555 @t292) % 35.02/35.27 (step @p471 :rule evaluate :args ((= true false))) % 35.02/35.27 (step @p472 :rule false_intro :premises (@p333)) % 35.02/35.27 (step @p473 :rule symm :premises (@p554)) % 35.02/35.27 (step @p474 :rule refl :args (@t102)) % 35.02/35.27 (step @p475 :rule cong :premises (@p474 @p473) :args (@t292)) % 35.02/35.27 (step @p476 :rule true_intro :premises (@p555)) % 35.02/35.27 (step @p477 :rule symm :premises (@p476)) % 35.02/35.27 (step @p478 :rule trans :premises (@p477 @p475 @p472)) % 35.02/35.27 (step @p479 false :rule eq_resolve :premises (@p478 @p471)) % 35.02/35.27 (step-pop @p556 :rule scope :premises (@p479)) % 35.02/35.27 (step-pop @p557 :rule scope :premises (@p556)) % 35.02/35.27 (step-pop @p558 :rule scope :premises (@p557)) % 35.02/35.27 (step @p480 :rule process_scope :premises (@p558) :args (false)) % 35.02/35.27 (step @p484 :rule not_and :premises (@p480)) % 35.02/35.27 (step @p485 :rule eq_resolve :premises (@p484 @p467)) % 35.02/35.27 (step @p486 :rule chain_m_resolution :premises (@p485 @p333 @p463 @p427 @p339 @p456 @p454 @p440 @p438 @p427 @p92 @p339 @p67) :args ((or @t305 @t297) (@list true false false false true false true true false false false false) (@list @t161 @t301 @t272 @t128 @t303 @t304 @t291 @t293 @t272 @t127 @t128 @t106))) % 35.02/35.27 (step @p487 :rule chain_m_resolution :premises (@p486 @p420) :args (@t297 @t133 (@list @t269))) % 35.02/35.28 (step @p488 :rule cnf_equiv_pos2 :args (@t309)) % 35.02/35.28 (step @p489 :rule reordering :premises (@p488) :args ((or @t292 @t310 (not @t309)))) % 35.02/35.28 (step @p490 :rule chain_m_resolution :premises (@p489 @p487 @p417) :args (@t310 @t247 (@list @t292 @t309))) % 35.02/35.28 (step @p491 :rule refl :args (@t311)) % 35.02/35.28 (step @p492 :rule bool-double-not-elim :args (@t306)) % 35.02/35.28 (step @p493 :rule refl :args (@t308)) % 35.02/35.28 (step @p494 :rule nary_cong :premises (@p493 @p79 @p382 @p492 @p491) :args ((or @t308 @t137 @t273 (not @t307) @t311))) % 35.02/35.28 (step @p495 :rule cnf_and_neg :args (@t308)) % 35.02/35.28 (step @p496 :rule eq_resolve :premises (@p495 @p494)) % 35.02/35.28 (step @p497 :rule reordering :premises (@p496) :args ((or @t137 @t273 @t311 @t306 @t308))) % 35.02/35.28 (step @p498 :rule chain_m_resolution :premises (@p497 @p92 @p427 @p416 @p490) :args (@t306 (@list false false false true) (@list @t127 @t272 @t268 @t308))) % 35.02/35.28 (step @p499 :rule refl :args (@t307)) % 35.02/35.28 (step @p500 :rule bool-double-not-elim :args (@t142)) % 35.02/35.28 (step @p501 :rule refl :args (@t312)) % 35.02/35.28 (step @p502 :rule nary_cong :premises (@p501 @p500 @p491 @p499) :args ((or @t312 (not @t143) @t311 @t307))) % 35.02/35.28 (assume-push @p559 @t124) % 35.02/35.28 (assume-push @p560 @t313) % 35.02/35.28 (assume-push @p561 @t268) % 35.02/35.28 (assume-push @p562 @t143) % 35.02/35.28 (step @p507 :rule evaluate :args ((= false true))) % 35.02/35.28 (step @p508 :rule symm :premises (@p560)) % 35.02/35.28 (step @p509 :rule trans :premises (@p416 @p508 @p73)) % 35.02/35.28 (step @p510 :rule symm :premises (@p509)) % 35.02/35.28 (step @p511 :rule true_intro :premises (@p510)) % 35.02/35.28 (step @p512 :rule false_intro :premises (@p95)) % 35.02/35.28 (step @p513 :rule symm :premises (@p512)) % 35.02/35.28 (step @p514 :rule trans :premises (@p513 @p511)) % 35.02/35.28 (step @p515 false :rule eq_resolve :premises (@p514 @p507)) % 35.02/35.28 (step-pop @p563 :rule scope :premises (@p515)) % 35.02/35.28 (step-pop @p564 :rule scope :premises (@p563)) % 35.02/35.28 (step-pop @p565 :rule scope :premises (@p564)) % 35.02/35.28 (step-pop @p566 :rule scope :premises (@p565)) % 35.02/35.28 (step @p516 :rule process_scope :premises (@p566) :args (false)) % 35.02/35.28 (assume-push @p567 @t124) % 35.02/35.28 (assume-push @p568 @t143) % 35.02/35.28 (assume-push @p569 @t268) % 35.02/35.28 (assume-push @p570 @t306) % 35.02/35.28 (assume-push @p571 @t306) % 35.02/35.28 (assume-push @p572 @t124) % 35.02/35.28 (step @p527 :rule cong :premises (@p570) :args (@t122)) % 35.02/35.28 (step @p528 :rule trans :premises (@p73 @p527)) % 35.02/35.28 (step-pop @p573 :rule scope :premises (@p528)) % 35.02/35.28 (step-pop @p574 :rule scope :premises (@p573)) % 35.02/35.28 (step @p529 :rule process_scope :premises (@p574) :args (@t313)) % 35.02/35.28 (step @p532 :rule and_intro :premises (@p570 @p73)) % 35.02/35.28 (step @p533 :rule modus_ponens :premises (@p532 @p529)) % 35.02/35.28 (step @p534 :rule and_intro :premises (@p73 @p533 @p416 @p95)) % 35.02/35.28 (step-pop @p575 :rule scope :premises (@p534)) % 35.02/35.28 (step-pop @p576 :rule scope :premises (@p575)) % 35.02/35.28 (step-pop @p577 :rule scope :premises (@p576)) % 35.02/35.28 (step-pop @p578 :rule scope :premises (@p577)) % 35.02/35.28 (step @p535 :rule process_scope :premises (@p578) :args (@t314)) % 35.02/35.28 (step @p540 :rule implies_elim :premises (@p535)) % 35.02/35.28 (step @p541 :rule resolution :premises (@p540 @p516) :args (true @t314)) % 35.02/35.28 (step @p542 :rule not_and :premises (@p541)) % 35.02/35.28 (step @p543 :rule eq_resolve :premises (@p542 @p502)) % 35.02/35.28 (step @p544 false :rule chain_m_resolution :premises (@p543 @p498 @p416 @p95 @p73) :args (false @t261 (@list @t306 @t268 @t142 @t124))) % 35.02/35.28 ) % 35.02/35.28 % SZS output end Proof % 35.02/35.28 % cvc5 exiting %------------------------------------------------------------------------------