%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRA004+1 : TPTP v9.2.1. Bugfixed v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n007.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 08:18:30 AM UTC 2026 % Result : Theorem 0.96s 1.17s % Output : Proof 0.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRA004+1 : TPTP v9.2.1. Bugfixed v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n007.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 00:13:26 EDT 2026 % 0.17/0.34 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.96/1.17 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.96/1.17 % SZS status Theorem % 0.96/1.17 % SZS output start Proof % 0.96/1.17 ( % 0.96/1.17 (declare-sort $$unsorted 0) % 0.96/1.17 (declare-const tptp.graph $$unsorted) % 0.96/1.17 (declare-const tptp.number_of_in (-> $$unsorted $$unsorted $$unsorted)) % 0.96/1.17 (declare-const tptp.edges $$unsorted) % 0.96/1.17 (declare-const tptp.triangle (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.shortest_path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.less_or_equal (-> $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.96/1.17 (declare-const tptp.tail_of (-> $$unsorted $$unsorted)) % 0.96/1.17 (declare-const tptp.triangles $$unsorted) % 0.96/1.17 (declare-const tptp.in_path (-> $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.head_of (-> $$unsorted $$unsorted)) % 0.96/1.17 (declare-const tptp.sequential_pairs $$unsorted) % 0.96/1.17 (declare-const tptp.edge (-> $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.path_cons (-> $$unsorted $$unsorted $$unsorted)) % 0.96/1.17 (declare-const tptp.precedes (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.complete Bool) % 0.96/1.17 (declare-const tptp.path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.vertex (-> $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.on_path (-> $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.empty $$unsorted) % 0.96/1.17 (declare-const tptp.n1 $$unsorted) % 0.96/1.17 (declare-const tptp.sequential (-> $$unsorted $$unsorted Bool)) % 0.96/1.17 (declare-const tptp.length_of (-> $$unsorted $$unsorted)) % 0.96/1.17 (define @t1 () (@var "E" $$unsorted)) % 0.96/1.17 (define @t2 () (tptp.tail_of @t1)) % 0.96/1.17 (define @t3 () (tptp.head_of @t1)) % 0.96/1.17 (define @t4 () (not (= @t3 @t2))) % 0.96/1.17 (define @t5 () (tptp.edge @t1)) % 0.96/1.17 (define @t6 () (@list @t1)) % 0.96/1.17 (define @t7 () (forall @t6 (=> @t5 @t4))) % 0.96/1.17 (define @t8 () (@var "V1" $$unsorted)) % 0.96/1.17 (define @t9 () (= @t8 @t2)) % 0.96/1.17 (define @t10 () (@var "V2" $$unsorted)) % 0.96/1.17 (define @t11 () (= @t10 @t3)) % 0.96/1.17 (define @t12 () (not (= @t8 @t10))) % 0.96/1.17 (define @t13 () (tptp.vertex @t10)) % 0.96/1.17 (define @t14 () (tptp.vertex @t8)) % 0.96/1.17 (define @t15 () (@var "P" $$unsorted)) % 0.96/1.17 (define @t16 () (tptp.path @t8 @t10 @t15)) % 0.96/1.17 (define @t17 () (@var "TP" $$unsorted)) % 0.96/1.17 (define @t18 () (exists (@list @t17) (and (tptp.path @t3 @t10 @t17) (= @t15 (tptp.path_cons @t1 @t17))))) % 0.96/1.17 (define @t19 () (and @t11 (= @t15 (tptp.path_cons @t1 tptp.empty)))) % 0.96/1.17 (define @t20 () (@list @t8 @t10 @t15)) % 0.96/1.17 (define @t21 () (and @t5 (tptp.in_path @t3 @t15) (tptp.in_path @t2 @t15))) % 0.96/1.17 (define @t22 () (tptp.on_path @t1 @t15)) % 0.96/1.17 (define @t23 () (and @t16 @t22)) % 0.96/1.17 (define @t24 () (forall (@list @t8 @t10 @t15 @t1) (=> @t23 @t21))) % 0.96/1.17 (define @t25 () (@var "V" $$unsorted)) % 0.96/1.17 (define @t26 () (@var "E2" $$unsorted)) % 0.96/1.17 (define @t27 () (@var "E1" $$unsorted)) % 0.96/1.17 (define @t28 () (tptp.head_of @t27)) % 0.96/1.17 (define @t29 () (tptp.edge @t26)) % 0.96/1.17 (define @t30 () (tptp.edge @t27)) % 0.96/1.17 (define @t31 () (tptp.sequential @t27 @t26)) % 0.96/1.17 (define @t32 () (@list @t27 @t26)) % 0.96/1.17 (define @t33 () (forall @t32 (= @t31 (and @t30 @t29 (not (= @t27 @t26)) (= @t28 (tptp.tail_of @t26)))))) % 0.96/1.17 (define @t34 () (tptp.precedes @t27 @t26 @t15)) % 0.96/1.17 (define @t35 () (@var "E3" $$unsorted)) % 0.96/1.17 (define @t36 () (tptp.precedes @t35 @t26 @t15)) % 0.96/1.17 (define @t37 () (tptp.sequential @t27 @t35)) % 0.96/1.17 (define @t38 () (and @t37 @t36)) % 0.96/1.17 (define @t39 () (@list @t35)) % 0.96/1.17 (define @t40 () (exists @t39 @t38)) % 0.96/1.17 (define @t41 () (or @t31 @t40)) % 0.96/1.17 (define @t42 () (tptp.on_path @t26 @t15)) % 0.96/1.17 (define @t43 () (tptp.on_path @t27 @t15)) % 0.96/1.17 (define @t44 () (and @t43 @t42 @t41)) % 0.96/1.17 (define @t45 () (=> @t44 @t34)) % 0.96/1.17 (define @t46 () (forall @t32 @t45)) % 0.96/1.17 (define @t47 () (=> @t16 @t46)) % 0.96/1.17 (define @t48 () (@list @t15 @t8 @t10)) % 0.96/1.17 (define @t49 () (forall @t48 @t47)) % 0.96/1.17 (define @t50 () (xor @t31 @t40)) % 0.96/1.17 (define @t51 () (and @t43 @t42 @t50)) % 0.96/1.17 (define @t52 () (=> @t34 @t51)) % 0.96/1.17 (define @t53 () (forall @t32 @t52)) % 0.96/1.17 (define @t54 () (=> @t16 @t53)) % 0.96/1.17 (define @t55 () (forall @t48 @t54)) % 0.96/1.17 (define @t56 () (tptp.length_of @t15)) % 0.96/1.17 (define @t57 () (@var "SP" $$unsorted)) % 0.96/1.17 (define @t58 () (tptp.less_or_equal (tptp.length_of @t57) @t56)) % 0.96/1.17 (define @t59 () (@list @t15)) % 0.96/1.17 (define @t60 () (forall @t59 (=> @t16 @t58))) % 0.96/1.17 (define @t61 () (tptp.path @t8 @t10 @t57)) % 0.96/1.17 (define @t62 () (and @t61 @t12 @t60)) % 0.96/1.17 (define @t63 () (tptp.shortest_path @t8 @t10 @t57)) % 0.96/1.17 (define @t64 () (= @t63 @t62)) % 0.96/1.17 (define @t65 () (forall (@list @t8 @t10 @t57) @t64)) % 0.96/1.17 (define @t66 () (not (tptp.precedes @t26 @t27 @t15))) % 0.96/1.17 (define @t67 () (tptp.head_of @t26)) % 0.96/1.17 (define @t68 () (= (tptp.head_of @t35) @t67)) % 0.96/1.17 (define @t69 () (tptp.tail_of @t27)) % 0.96/1.17 (define @t70 () (= (tptp.tail_of @t35) @t69)) % 0.96/1.17 (define @t71 () (and @t70 @t68)) % 0.96/1.17 (define @t72 () (exists @t39 @t71)) % 0.96/1.17 (define @t73 () (not @t72)) % 0.96/1.17 (define @t74 () (and @t73 @t66)) % 0.96/1.17 (define @t75 () (tptp.shortest_path @t8 @t10 @t15)) % 0.96/1.17 (define @t76 () (and @t75 @t34)) % 0.96/1.17 (define @t77 () (=> @t76 @t74)) % 0.96/1.17 (define @t78 () (@list @t8 @t10 @t27 @t26 @t15)) % 0.96/1.17 (define @t79 () (forall @t78 @t77)) % 0.96/1.17 (define @t80 () (tptp.triangle @t27 @t26 @t35)) % 0.96/1.17 (define @t81 () (tptp.number_of_in tptp.sequential_pairs @t15)) % 0.96/1.17 (define @t82 () (@var "Things" $$unsorted)) % 0.96/1.17 (define @t83 () (@var "InThese" $$unsorted)) % 0.96/1.17 (define @t84 () (not (= @t67 @t28))) % 0.96/1.17 (define @t85 () (not (= @t67 @t69))) % 0.96/1.17 (define @t86 () (and @t73 @t85 @t84)) % 0.96/1.17 (define @t87 () (=> @t76 @t86)) % 0.96/1.17 (define @t88 () (forall @t78 @t87)) % 0.96/1.17 (define @t89 () (not @t88)) % 0.96/1.17 (define @t90 () (not (= @t28 @t67))) % 0.96/1.17 (define @t91 () (not (= @t69 @t67))) % 0.96/1.17 (define @t92 () (@var "BOUND_VARIABLE_7979" $$unsorted)) % 0.96/1.17 (define @t93 () (tptp.head_of @t92)) % 0.96/1.17 (define @t94 () (tptp.tail_of @t92)) % 0.96/1.17 (define @t95 () (not @t34)) % 0.96/1.17 (define @t96 () (not @t75)) % 0.96/1.17 (define @t97 () (@list @t8 @t10 @t27 @t26 @t15 @t92)) % 0.96/1.17 (define @t98 () (forall @t97 (or @t96 @t95 (and (or (not (= @t69 @t94)) (not (= @t67 @t93))) @t91 @t90)))) % 0.96/1.17 (define @t99 () (@quantifiers_skolemize @t98 3)) % 0.96/1.17 (define @t100 () (not @t22)) % 0.96/1.17 (define @t101 () (not @t16)) % 0.96/1.17 (define @t102 () (@quantifiers_skolemize @t98 4)) % 0.96/1.17 (define @t103 () (@quantifiers_skolemize @t98 1)) % 0.96/1.17 (define @t104 () (@quantifiers_skolemize @t98 0)) % 0.96/1.17 (define @t105 () (@var "BOUND_VARIABLE_7877" $$unsorted)) % 0.96/1.17 (define @t106 () (@var "BOUND_VARIABLE_7875" $$unsorted)) % 0.96/1.17 (define @t107 () (and (tptp.on_path @t106 @t15) (tptp.on_path @t105 @t15) (= (not (forall @t39 (or (not (tptp.sequential @t106 @t35)) (not (tptp.precedes @t35 @t105 @t15))))) (not (tptp.sequential @t106 @t105))))) % 0.96/1.17 (define @t108 () (not (tptp.precedes @t106 @t105 @t15))) % 0.96/1.17 (define @t109 () (or @t108 @t107)) % 0.96/1.17 (define @t110 () (or @t101 @t109)) % 0.96/1.17 (define @t111 () (forall (@list @t15 @t8 @t10 @t106 @t105) @t110)) % 0.96/1.17 (define @t112 () (@list @t106 @t105)) % 0.96/1.17 (define @t113 () (forall @t112 @t110)) % 0.96/1.17 (define @t114 () (forall @t112 @t109)) % 0.96/1.17 (define @t115 () (or @t101 @t114)) % 0.96/1.17 (define @t116 () (not @t31)) % 0.96/1.17 (define @t117 () (forall @t39 (or (not @t37) (not @t36)))) % 0.96/1.17 (define @t118 () (not @t117)) % 0.96/1.17 (define @t119 () (forall @t32 (or @t95 (and @t43 @t42 (= @t118 @t116))))) % 0.96/1.17 (define @t120 () (and @t43 @t42 (= @t116 @t118))) % 0.96/1.17 (define @t121 () (or @t95 @t120)) % 0.96/1.17 (define @t122 () (and @t43 @t42 (xor @t31 @t118))) % 0.96/1.17 (define @t123 () (forall @t39 (not @t38))) % 0.96/1.17 (define @t124 () (not @t123)) % 0.96/1.17 (define @t125 () (@quantifiers_skolemize @t98 2)) % 0.96/1.17 (define @t126 () (not (= @t93 @t67))) % 0.96/1.17 (define @t127 () (not (= @t94 @t69))) % 0.96/1.17 (define @t128 () (or @t127 @t126)) % 0.96/1.17 (define @t129 () (and @t128 @t91 @t90)) % 0.96/1.17 (define @t130 () (or @t96 @t95 @t129)) % 0.96/1.17 (define @t131 () (forall @t97 @t130)) % 0.96/1.17 (define @t132 () (@list @t92)) % 0.96/1.17 (define @t133 () (forall @t132 @t130)) % 0.96/1.17 (define @t134 () (forall @t132 @t90)) % 0.96/1.17 (define @t135 () (forall @t132 @t91)) % 0.96/1.17 (define @t136 () (forall @t132 @t128)) % 0.96/1.17 (define @t137 () (@list @t35)) % 0.96/1.17 (define @t138 () (and @t136 @t135 @t134)) % 0.96/1.17 (define @t139 () (forall @t132 @t129)) % 0.96/1.17 (define @t140 () (or @t96 @t95 @t139)) % 0.96/1.17 (define @t141 () (forall @t39 (or (not @t70) (not @t68)))) % 0.96/1.17 (define @t142 () (and @t141 @t91 @t90)) % 0.96/1.17 (define @t143 () (or @t96 @t95 @t142)) % 0.96/1.17 (define @t144 () (or @t96 @t95)) % 0.96/1.17 (define @t145 () (not @t76)) % 0.96/1.17 (define @t146 () (forall @t39 (not @t71))) % 0.96/1.17 (define @t147 () (not @t146)) % 0.96/1.17 (define @t148 () (tptp.head_of @t125)) % 0.96/1.17 (define @t149 () (tptp.head_of @t99)) % 0.96/1.17 (define @t150 () (= @t149 @t148)) % 0.96/1.17 (define @t151 () (not @t150)) % 0.96/1.17 (define @t152 () (tptp.tail_of @t125)) % 0.96/1.17 (define @t153 () (= @t152 @t149)) % 0.96/1.17 (define @t154 () (not @t153)) % 0.96/1.17 (define @t155 () (@quantifiers_skolemize @t98 5)) % 0.96/1.17 (define @t156 () (or (not (= @t152 (tptp.tail_of @t155))) (not (= @t149 (tptp.head_of @t155))))) % 0.96/1.17 (define @t157 () (and @t156 @t154 @t151)) % 0.96/1.17 (define @t158 () (tptp.precedes @t125 @t99 @t102)) % 0.96/1.17 (define @t159 () (not @t158)) % 0.96/1.17 (define @t160 () (tptp.shortest_path @t104 @t103 @t102)) % 0.96/1.17 (define @t161 () (not @t160)) % 0.96/1.17 (define @t162 () (or @t161 @t159 @t157)) % 0.96/1.17 (define @t163 () (not @t162)) % 0.96/1.17 (define @t164 () (not @t98)) % 0.96/1.17 (define @t165 () (not (= @t148 @t149))) % 0.96/1.17 (define @t166 () (and @t156 @t154 @t165)) % 0.96/1.17 (define @t167 () (or @t161 @t159 @t166)) % 0.96/1.17 (define @t168 () (not @t167)) % 0.96/1.17 (define @t169 () (@list true)) % 0.96/1.17 (define @t170 () (@list @t162)) % 0.96/1.17 (define @t171 () (tptp.path @t104 @t103 @t102)) % 0.96/1.17 (define @t172 () (and @t171 (not (= @t104 @t103)) (forall @t59 (or (not (tptp.path @t104 @t103 @t15)) (tptp.less_or_equal (tptp.length_of @t102) @t56))))) % 0.96/1.17 (define @t173 () (= @t160 @t172)) % 0.96/1.17 (define @t174 () (@list false false)) % 0.96/1.17 (define @t175 () (@list false)) % 0.96/1.17 (define @t176 () (tptp.sequential @t125 @t99)) % 0.96/1.17 (define @t177 () (not @t176)) % 0.96/1.17 (define @t178 () (forall @t39 (or (not (tptp.sequential @t125 @t35)) (not (tptp.precedes @t35 @t99 @t102))))) % 0.96/1.17 (define @t179 () (not @t178)) % 0.96/1.17 (define @t180 () (= @t179 @t177)) % 0.96/1.17 (define @t181 () (tptp.on_path @t99 @t102)) % 0.96/1.17 (define @t182 () (tptp.on_path @t125 @t102)) % 0.96/1.17 (define @t183 () (and @t182 @t181 @t180)) % 0.96/1.17 (define @t184 () (not @t171)) % 0.96/1.17 (define @t185 () (or @t184 @t159 @t183)) % 0.96/1.17 (define @t186 () (@list false false false)) % 0.96/1.17 (define @t187 () (not @t183)) % 0.96/1.17 (define @t188 () (@list @t183)) % 0.96/1.17 (define @t189 () (tptp.tail_of @t99)) % 0.96/1.17 (define @t190 () (tptp.edge @t99)) % 0.96/1.17 (define @t191 () (and @t190 (tptp.in_path @t149 @t102) (tptp.in_path @t189 @t102))) % 0.96/1.17 (define @t192 () (not @t181)) % 0.96/1.17 (define @t193 () (or @t184 @t192 @t191)) % 0.96/1.17 (define @t194 () (= @t149 @t189)) % 0.96/1.17 (define @t195 () (not @t194)) % 0.96/1.17 (define @t196 () (not @t190)) % 0.96/1.17 (define @t197 () (or @t196 @t195)) % 0.96/1.17 (define @t198 () (@var "BOUND_VARIABLE_7924" $$unsorted)) % 0.96/1.17 (define @t199 () (tptp.head_of @t198)) % 0.96/1.17 (define @t200 () (not (= @t199 @t67))) % 0.96/1.17 (define @t201 () (tptp.tail_of @t198)) % 0.96/1.17 (define @t202 () (not (= @t201 @t69))) % 0.96/1.17 (define @t203 () (or @t202 @t200)) % 0.96/1.17 (define @t204 () (and @t203 @t66)) % 0.96/1.17 (define @t205 () (or @t96 @t95 @t204)) % 0.96/1.17 (define @t206 () (@list @t8 @t10 @t27 @t26 @t15 @t198)) % 0.96/1.17 (define @t207 () (forall @t206 @t205)) % 0.96/1.17 (define @t208 () (@list @t198)) % 0.96/1.17 (define @t209 () (forall @t208 @t205)) % 0.96/1.17 (define @t210 () (forall @t208 @t66)) % 0.96/1.17 (define @t211 () (forall @t208 @t203)) % 0.96/1.17 (define @t212 () (and @t211 @t210)) % 0.96/1.17 (define @t213 () (forall @t208 @t204)) % 0.96/1.17 (define @t214 () (or @t96 @t95 @t213)) % 0.96/1.17 (define @t215 () (and @t141 @t66)) % 0.96/1.17 (define @t216 () (or @t96 @t95 @t215)) % 0.96/1.17 (define @t217 () (tptp.precedes @t99 @t125 @t102)) % 0.96/1.17 (define @t218 () (not @t217)) % 0.96/1.17 (define @t219 () (and @t156 @t218)) % 0.96/1.17 (define @t220 () (or @t161 @t159 @t219)) % 0.96/1.17 (define @t221 () (not @t219)) % 0.96/1.17 (define @t222 () (@list @t219)) % 0.96/1.17 (define @t223 () (not (= @t152 @t152))) % 0.96/1.17 (define @t224 () (or @t223 @t151)) % 0.96/1.17 (define @t225 () (and @t224 @t218)) % 0.96/1.17 (define @t226 () (or @t161 @t159 @t225)) % 0.96/1.17 (define @t227 () (forall @t206 (or @t96 @t95 (and (or (not (= @t69 @t201)) (not (= @t67 @t199))) @t66)))) % 0.96/1.17 (define @t228 () (and @t151 @t218)) % 0.96/1.17 (define @t229 () (or @t161 @t159 @t228)) % 0.96/1.17 (define @t230 () (not @t156)) % 0.96/1.17 (define @t231 () (not (= @t99 @t125))) % 0.96/1.17 (define @t232 () (tptp.edge @t125)) % 0.96/1.17 (define @t233 () (and @t190 @t232 @t231 (= @t149 @t152))) % 0.96/1.17 (define @t234 () (tptp.sequential @t99 @t125)) % 0.96/1.17 (define @t235 () (= @t234 @t233)) % 0.96/1.17 (define @t236 () (= @t125 @t99)) % 0.96/1.17 (define @t237 () (not @t236)) % 0.96/1.17 (define @t238 () (and @t190 @t232 @t237 @t153)) % 0.96/1.17 (define @t239 () (= @t234 @t238)) % 0.96/1.17 (define @t240 () (@var "BOUND_VARIABLE_7834" $$unsorted)) % 0.96/1.17 (define @t241 () (@var "BOUND_VARIABLE_7832" $$unsorted)) % 0.96/1.17 (define @t242 () (tptp.precedes @t241 @t240 @t15)) % 0.96/1.17 (define @t243 () (@var "BOUND_VARIABLE_7836" $$unsorted)) % 0.96/1.17 (define @t244 () (and (not (tptp.sequential @t241 @t240)) (or (not (tptp.sequential @t241 @t243)) (not (tptp.precedes @t243 @t240 @t15))))) % 0.96/1.17 (define @t245 () (not (tptp.on_path @t240 @t15))) % 0.96/1.17 (define @t246 () (not (tptp.on_path @t241 @t15))) % 0.96/1.17 (define @t247 () (or @t246 @t245 @t244 @t242)) % 0.96/1.17 (define @t248 () (or @t101 @t247)) % 0.96/1.17 (define @t249 () (forall (@list @t15 @t8 @t10 @t241 @t240 @t243) @t248)) % 0.96/1.17 (define @t250 () (@list @t241 @t240 @t243)) % 0.96/1.17 (define @t251 () (forall @t250 @t248)) % 0.96/1.17 (define @t252 () (forall @t250 @t247)) % 0.96/1.17 (define @t253 () (@var "BOUND_VARIABLE_7817" $$unsorted)) % 0.96/1.17 (define @t254 () (or @t101 @t252)) % 0.96/1.17 (define @t255 () (or (not (tptp.sequential @t27 @t253)) (not (tptp.precedes @t253 @t26 @t15)))) % 0.96/1.17 (define @t256 () (and @t116 @t255)) % 0.96/1.17 (define @t257 () (not @t42)) % 0.96/1.17 (define @t258 () (not @t43)) % 0.96/1.17 (define @t259 () (or @t258 @t257 @t256 @t34)) % 0.96/1.17 (define @t260 () (forall (@list @t27 @t26 @t253) @t259)) % 0.96/1.17 (define @t261 () (@list @t253)) % 0.96/1.17 (define @t262 () (forall @t261 @t259)) % 0.96/1.17 (define @t263 () (forall @t261 @t255)) % 0.96/1.17 (define @t264 () (forall @t261 @t116)) % 0.96/1.17 (define @t265 () (and @t264 @t263)) % 0.96/1.17 (define @t266 () (forall @t261 @t256)) % 0.96/1.17 (define @t267 () (or @t258 @t257 @t266 @t34)) % 0.96/1.17 (define @t268 () (and @t116 @t117)) % 0.96/1.17 (define @t269 () (or @t258 @t257 @t268 @t34)) % 0.96/1.17 (define @t270 () (or @t31 @t118)) % 0.96/1.17 (define @t271 () (not @t270)) % 0.96/1.17 (define @t272 () (or @t258 @t257 @t271)) % 0.96/1.17 (define @t273 () (and @t43 @t42 @t270)) % 0.96/1.17 (define @t274 () (not @t234)) % 0.96/1.17 (define @t275 () (and @t274 (or (not (tptp.sequential @t99 @t99)) @t218))) % 0.96/1.17 (define @t276 () (not @t182)) % 0.96/1.17 (define @t277 () (or @t184 @t192 @t276 @t275 @t217)) % 0.96/1.17 (define @t278 () (not @t238)) % 0.96/1.17 (define @t279 () (@quantifiers_skolemize @t178 0)) % 0.96/1.17 (define @t280 () (and @t232 (tptp.edge @t279) (not (= @t125 @t279)) (= @t148 (tptp.tail_of @t279)))) % 0.96/1.17 (define @t281 () (and @t232 @t190 @t237 (= @t148 @t189))) % 0.96/1.17 (define @t282 () (tptp.sequential @t125 @t279)) % 0.96/1.17 (define @t283 () (= @t282 @t280)) % 0.96/1.17 (define @t284 () (not @t282)) % 0.96/1.17 (define @t285 () (= @t176 @t281)) % 0.96/1.17 (define @t286 () (or @t284 (not (tptp.precedes @t279 @t99 @t102)))) % 0.96/1.17 (define @t287 () (not @t180)) % 0.96/1.17 (define @t288 () (not @t286)) % 0.96/1.17 (define @t289 () (not @t232)) % 0.96/1.17 (define @t290 () (and @t153 @t236)) % 0.96/1.17 (assume @p1 @t7) % 0.96/1.17 (assume @p2 (forall @t6 (=> @t5 (and (tptp.vertex @t3) (tptp.vertex @t2))))) % 0.96/1.17 (assume @p3 (=> tptp.complete (forall (@list @t8 @t10) (=> (and @t14 @t13 @t12) (exists @t6 (and @t5 (xor (and (= @t8 @t3) (= @t10 @t2)) (and @t11 @t9)))))))) % 0.96/1.17 (assume @p4 (forall @t20 (=> (and @t14 @t13 (exists @t6 (and @t5 @t9 (or @t19 @t18)))) @t16))) % 0.96/1.17 (assume @p5 (forall @t20 (=> @t16 (and @t14 @t13 (exists @t6 (and @t5 @t9 (xor @t19 @t18))))))) % 0.96/1.17 (assume @p6 @t24) % 0.96/1.17 (assume @p7 (forall (@list @t8 @t10 @t15 @t25) (=> (and @t16 (tptp.in_path @t25 @t15)) (and (tptp.vertex @t25) (exists @t6 (and @t22 (or (= @t25 @t3) (= @t25 @t2)))))))) % 0.96/1.17 (assume @p8 @t33) % 0.96/1.17 (assume @p9 @t49) % 0.96/1.17 (assume @p10 @t55) % 0.96/1.17 (assume @p11 @t65) % 0.96/1.17 (assume @p12 @t79) % 0.96/1.17 (assume @p13 (forall (@list @t27 @t26 @t35) (= @t80 (and @t30 @t29 (tptp.edge @t35) @t31 (tptp.sequential @t26 @t35) (tptp.sequential @t35 @t27))))) % 0.96/1.17 (assume @p14 (forall @t20 (=> @t16 (= @t56 (tptp.number_of_in tptp.edges @t15))))) % 0.96/1.17 (assume @p15 (forall @t20 (=> @t16 (= @t81 (tptp.minus @t56 tptp.n1))))) % 0.96/1.17 (assume @p16 (forall @t48 (=> (and @t16 (forall @t32 (=> (and @t43 @t42 @t31) (exists @t39 @t80)))) (= @t81 (tptp.number_of_in tptp.triangles @t15))))) % 0.96/1.17 (assume @p17 (forall (@list @t82 @t83) (tptp.less_or_equal (tptp.number_of_in @t82 @t83) (tptp.number_of_in @t82 tptp.graph)))) % 0.96/1.17 (assume @p18 @t89) % 0.96/1.17 (assume @p19 true) % 0.96/1.17 (step @p20 :rule bool-impl-elim :args (@t5 @t4)) % 0.96/1.17 (step @p21 :rule cong :premises (@p20) :args (@t7)) % 0.96/1.17 (step @p22 :rule eq_resolve :premises (@p1 @p21)) % 0.96/1.17 (step @p23 :rule instantiate :premises (@p22) :args ((@list @t99))) % 0.96/1.17 (step @p24 :rule aci_norm :args ((= (or (or @t101 @t100) @t21) (or @t101 @t100 @t21)))) % 0.96/1.17 (step @p25 :rule refl :args (@t21)) % 0.96/1.17 (step @p26 :rule bool-and-de-morgan :args (@t16 @t22 true)) % 0.96/1.17 (step @p27 :rule nary_cong :premises (@p26 @p25) :args ((or (not @t23) @t21))) % 0.96/1.17 (step @p28 :rule trans :premises (@p27 @p24)) % 0.96/1.17 (step @p29 :rule bool-impl-elim :args (@t23 @t21)) % 0.96/1.17 (step @p30 :rule trans :premises (@p29 @p28)) % 0.96/1.17 (step @p31 :rule cong :premises (@p30) :args (@t24)) % 0.96/1.17 (step @p32 :rule eq_resolve :premises (@p6 @p31)) % 0.96/1.17 (step @p33 :rule instantiate :premises (@p32) :args ((@list @t104 @t103 @t102 @t99))) % 0.96/1.17 (step @p34 :rule aci_norm :args ((= @t110 (or @t101 @t108 @t107)))) % 0.96/1.17 (step @p35 :rule cong :premises (@p34) :args (@t111)) % 0.96/1.17 (step @p36 :rule quant-merge-prenex :args ((= (forall @t48 @t113) @t111))) % 0.96/1.17 (step @p37 :rule alpha_equiv :args (@t114 (@list @t106 @t105) (@list @t27 @t26))) % 0.96/1.17 (step @p38 :rule refl :args (@t101)) % 0.96/1.17 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t115)) % 0.96/1.17 (step @p40 :rule quant-miniscope-or :args ((= @t113 @t115))) % 0.96/1.17 (step @p41 :rule trans :premises (@p40 @p39)) % 0.96/1.17 (step @p42 :rule symm :premises (@p41)) % 0.96/1.17 (step @p43 :rule cong :premises (@p42) :args ((forall @t48 (or @t101 @t119)))) % 0.96/1.17 (step @p44 :rule trans :premises (@p43 @p36)) % 0.96/1.17 (step @p45 :rule trans :premises (@p44 @p35)) % 0.96/1.17 (step @p46 :rule bool-impl-elim :args (@t16 @t119)) % 0.96/1.17 (step @p47 :rule cong :premises (@p46) :args ((forall @t48 (=> @t16 @t119)))) % 0.96/1.17 (step @p48 :rule trans :premises (@p47 @p45)) % 0.96/1.17 (step @p49 :rule eq-symm :args (@t116 @t118)) % 0.96/1.17 (step @p50 :rule refl :args (@t42)) % 0.96/1.17 (step @p51 :rule refl :args (@t43)) % 0.96/1.17 (step @p52 :rule nary_cong :premises (@p51 @p50 @p49) :args (@t120)) % 0.96/1.17 (step @p53 :rule refl :args (@t95)) % 0.96/1.17 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t121)) % 0.96/1.17 (step @p55 :rule cong :premises (@p54) :args ((forall @t32 @t121))) % 0.96/1.17 (step @p56 :rule bool-xor-elim :args (@t31 @t118)) % 0.96/1.17 (step @p57 :rule refl :args (@t42)) % 0.96/1.17 (step @p58 :rule refl :args (@t43)) % 0.96/1.17 (step @p59 :rule nary_cong :premises (@p58 @p57 @p56) :args (@t122)) % 0.96/1.17 (step @p60 :rule refl :args (@t95)) % 0.96/1.17 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or @t95 @t122))) % 0.96/1.17 (step @p62 :rule bool-impl-elim :args (@t34 @t122)) % 0.96/1.17 (step @p63 :rule trans :premises (@p62 @p61)) % 0.96/1.17 (step @p64 :rule cong :premises (@p63) :args ((forall @t32 (=> @t34 @t122)))) % 0.96/1.17 (step @p65 :rule trans :premises (@p64 @p55)) % 0.96/1.17 (step @p66 :rule bool-and-de-morgan :args (@t37 @t36 true)) % 0.96/1.17 (step @p67 :rule cong :premises (@p66) :args (@t123)) % 0.96/1.17 (step @p68 :rule cong :premises (@p67) :args (@t124)) % 0.96/1.17 (step @p69 :rule exists-elim :args ((= @t40 @t124))) % 0.96/1.17 (step @p70 :rule trans :premises (@p69 @p68)) % 0.96/1.17 (step @p71 :rule refl :args (@t31)) % 0.96/1.17 (step @p72 :rule cong :premises (@p71 @p70) :args (@t50)) % 0.96/1.17 (step @p73 :rule nary_cong :premises (@p51 @p50 @p72) :args (@t51)) % 0.96/1.17 (step @p74 :rule refl :args (@t34)) % 0.96/1.17 (step @p75 :rule cong :premises (@p74 @p73) :args (@t52)) % 0.96/1.17 (step @p76 :rule cong :premises (@p75) :args (@t53)) % 0.96/1.17 (step @p77 :rule trans :premises (@p76 @p65)) % 0.96/1.17 (step @p78 :rule refl :args (@t16)) % 0.96/1.17 (step @p79 :rule cong :premises (@p78 @p77) :args (@t54)) % 0.96/1.17 (step @p80 :rule cong :premises (@p79) :args (@t55)) % 0.96/1.17 (step @p81 :rule trans :premises (@p80 @p48)) % 0.96/1.17 (step @p82 :rule eq_resolve :premises (@p10 @p81)) % 0.96/1.17 (step @p83 :rule instantiate :premises (@p82) :args ((@list @t102 @t104 @t103 @t125 @t99))) % 0.96/1.17 (step @p84 :rule bool-impl-elim :args (@t16 @t58)) % 0.96/1.17 (step @p85 :rule cong :premises (@p84) :args (@t60)) % 0.96/1.17 (step @p86 :rule refl :args (@t12)) % 0.96/1.17 (step @p87 :rule refl :args (@t61)) % 0.96/1.17 (step @p88 :rule nary_cong :premises (@p87 @p86 @p85) :args (@t62)) % 0.96/1.17 (step @p89 :rule refl :args (@t63)) % 0.96/1.17 (step @p90 :rule cong :premises (@p89 @p88) :args (@t64)) % 0.96/1.17 (step @p91 :rule cong :premises (@p90) :args (@t65)) % 0.96/1.17 (step @p92 :rule eq_resolve :premises (@p11 @p91)) % 0.96/1.17 (step @p93 :rule instantiate :premises (@p92) :args ((@list @t104 @t103 @t102))) % 0.96/1.17 (step @p94 :rule refl :args (@t90)) % 0.96/1.17 (step @p95 :rule refl :args (@t91)) % 0.96/1.17 (step @p96 :rule eq-symm :args (@t93 @t67)) % 0.96/1.17 (step @p97 :rule cong :premises (@p96) :args (@t126)) % 0.96/1.17 (step @p98 :rule eq-symm :args (@t94 @t69)) % 0.96/1.17 (step @p99 :rule cong :premises (@p98) :args (@t127)) % 0.96/1.17 (step @p100 :rule nary_cong :premises (@p99 @p97) :args (@t128)) % 0.96/1.17 (step @p101 :rule nary_cong :premises (@p100 @p95 @p94) :args (@t129)) % 0.96/1.17 (step @p102 :rule refl :args (@t96)) % 0.96/1.17 (step @p103 :rule nary_cong :premises (@p102 @p53 @p101) :args (@t130)) % 0.96/1.17 (step @p104 :rule cong :premises (@p103) :args (@t131)) % 0.96/1.17 (step @p105 :rule quant-merge-prenex :args ((= (forall @t78 @t133) @t131))) % 0.96/1.17 (step @p106 :rule quant-unused-vars :args ((= @t134 @t90))) % 0.96/1.17 (step @p107 :rule quant-unused-vars :args ((= @t135 @t91))) % 0.96/1.17 (step @p108 :rule alpha_equiv :args (@t136 (@list @t92) @t137)) % 0.96/1.17 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106) :args (@t138)) % 0.96/1.17 (step @p110 :rule quant-miniscope-and :args ((= @t139 @t138))) % 0.96/1.17 (step @p111 :rule trans :premises (@p110 @p109)) % 0.96/1.17 (step @p112 :rule refl :args (@t96)) % 0.96/1.17 (step @p113 :rule nary_cong :premises (@p112 @p60 @p111) :args (@t140)) % 0.96/1.17 (step @p114 :rule quant-miniscope-or :args ((= @t133 @t140))) % 0.96/1.17 (step @p115 :rule trans :premises (@p114 @p113)) % 0.96/1.17 (step @p116 :rule symm :premises (@p115)) % 0.96/1.17 (step @p117 :rule cong :premises (@p116) :args ((forall @t78 @t143))) % 0.96/1.17 (step @p118 :rule trans :premises (@p117 @p105)) % 0.96/1.17 (step @p119 :rule trans :premises (@p118 @p104)) % 0.96/1.17 (step @p120 :rule aci_norm :args ((= (or @t144 @t142) @t143))) % 0.96/1.17 (step @p121 :rule refl :args (@t142)) % 0.96/1.17 (step @p122 :rule bool-and-de-morgan :args (@t75 @t34 true)) % 0.96/1.17 (step @p123 :rule nary_cong :premises (@p122 @p121) :args ((or @t145 @t142))) % 0.96/1.17 (step @p124 :rule trans :premises (@p123 @p120)) % 0.96/1.17 (step @p125 :rule bool-impl-elim :args (@t76 @t142)) % 0.96/1.17 (step @p126 :rule trans :premises (@p125 @p124)) % 0.96/1.17 (step @p127 :rule cong :premises (@p126) :args ((forall @t78 (=> @t76 @t142)))) % 0.96/1.17 (step @p128 :rule trans :premises (@p127 @p119)) % 0.96/1.17 (step @p129 :rule eq-symm :args (@t67 @t28)) % 0.96/1.17 (step @p130 :rule cong :premises (@p129) :args (@t84)) % 0.96/1.17 (step @p131 :rule eq-symm :args (@t67 @t69)) % 0.96/1.17 (step @p132 :rule cong :premises (@p131) :args (@t85)) % 0.96/1.17 (step @p133 :rule bool-double-not-elim :args (@t141)) % 0.96/1.17 (step @p134 :rule bool-and-de-morgan :args (@t70 @t68 true)) % 0.96/1.17 (step @p135 :rule cong :premises (@p134) :args (@t146)) % 0.96/1.17 (step @p136 :rule cong :premises (@p135) :args (@t147)) % 0.96/1.17 (step @p137 :rule exists-elim :args ((= @t72 @t147))) % 0.96/1.17 (step @p138 :rule trans :premises (@p137 @p136)) % 0.96/1.17 (step @p139 :rule cong :premises (@p138) :args (@t73)) % 0.96/1.17 (step @p140 :rule trans :premises (@p139 @p133)) % 0.96/1.17 (step @p141 :rule nary_cong :premises (@p140 @p132 @p130) :args (@t86)) % 0.96/1.17 (step @p142 :rule refl :args (@t76)) % 0.96/1.17 (step @p143 :rule cong :premises (@p142 @p141) :args (@t87)) % 0.96/1.17 (step @p144 :rule cong :premises (@p143) :args (@t88)) % 0.96/1.17 (step @p145 :rule trans :premises (@p144 @p128)) % 0.96/1.17 (step @p146 :rule cong :premises (@p145) :args (@t89)) % 0.96/1.17 (step @p147 :rule eq_resolve :premises (@p18 @p146)) % 0.96/1.17 (step @p148 :rule refl :args (@t163)) % 0.96/1.17 (step @p149 :rule bool-double-not-elim :args (@t98)) % 0.96/1.17 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or (not @t164) @t163))) % 0.96/1.17 (step @p151 :rule eq-symm :args (@t148 @t149)) % 0.96/1.17 (step @p152 :rule cong :premises (@p151) :args (@t165)) % 0.96/1.17 (step @p153 :rule refl :args (@t154)) % 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:rule reordering :premises (@p390) :args ((or @t180 @t187))) % 0.96/1.18 (step @p392 :rule chain_m_resolution :premises (@p391 @p191) :args (@t180 @t175 @t188)) % 0.96/1.18 (step @p393 :rule bool-double-not-elim :args (@t176)) % 0.96/1.18 (step @p394 :rule refl :args (@t179)) % 0.96/1.18 (step @p395 :rule refl :args (@t287)) % 0.96/1.18 (step @p396 :rule nary_cong :premises (@p395 @p394 @p393) :args ((or @t287 @t179 (not @t177)))) % 0.96/1.18 (step @p397 :rule cnf_equiv_pos2 :args (@t180)) % 0.96/1.18 (step @p398 :rule eq_resolve :premises (@p397 @p396)) % 0.96/1.18 (step @p399 :rule reordering :premises (@p398) :args ((or @t179 @t176 @t287))) % 0.96/1.18 (step @p400 :rule refl :args (@t288)) % 0.96/1.18 (step @p401 :rule bool-double-not-elim :args (@t178)) % 0.96/1.18 (step @p402 :rule nary_cong :premises (@p401 @p400) :args ((or (not @t179) @t288))) % 0.96/1.18 (assume-push @p445 @t179) % 0.96/1.18 (step @p404 :rule skolemize :premises (@p445)) % 0.96/1.18 (step-pop @p446 :rule scope :premises (@p404)) % 0.96/1.18 (step @p405 :rule process_scope :premises (@p446) :args (@t288)) % 0.96/1.18 (step @p407 :rule implies_elim :premises (@p405)) % 0.96/1.18 (step @p408 :rule eq_resolve :premises (@p407 @p402)) % 0.96/1.18 (step @p409 :rule chain_m_resolution :premises (@p408 @p399 @p392 @p389 @p383 @p381 @p380 @p378 @p377 @p375) :args (@t232 (@list true false false true false true false true true) (@list @t178 @t180 @t286 @t176 @t285 @t282 @t283 @t281 @t280))) % 0.96/1.18 (step @p410 :rule bool-double-not-elim :args (@t236)) % 0.96/1.18 (step @p411 :rule refl :args (@t289)) % 0.96/1.18 (step @p412 :rule refl :args (@t196)) % 0.96/1.18 (step @p413 :rule refl :args (@t238)) % 0.96/1.18 (step @p414 :rule nary_cong :premises (@p413 @p412 @p411 @p410 @p153) :args ((or @t238 @t196 @t289 (not @t237) @t154))) % 0.96/1.18 (step @p415 :rule cnf_and_neg :args (@t238)) % 0.96/1.18 (step @p416 :rule eq_resolve :premises (@p415 @p414)) % 0.96/1.18 (step @p417 :rule reordering :premises (@p416) :args ((or @t154 @t289 @t196 @t236 @t238))) % 0.96/1.18 (step @p418 :rule chain_m_resolution :premises (@p417 @p282 @p409 @p200 @p373) :args (@t236 (@list false false false true) (@list @t153 @t232 @t190 @t238))) % 0.96/1.18 (assume-push @p447 @t153) % 0.96/1.18 (assume-push @p448 @t236) % 0.96/1.18 (assume-push @p449 @t236) % 0.96/1.18 (assume-push @p450 @t153) % 0.96/1.18 (step @p423 :rule cong :premises (@p448) :args (@t152)) % 0.96/1.18 (step @p424 :rule symm :premises (@p282)) % 0.96/1.18 (step @p425 :rule trans :premises (@p424 @p423)) % 0.96/1.18 (step-pop @p451 :rule scope :premises (@p425)) % 0.96/1.18 (step-pop @p452 :rule scope :premises (@p451)) % 0.96/1.18 (step @p426 :rule process_scope :premises (@p452) :args (@t194)) % 0.96/1.18 (step @p429 :rule and_intro :premises (@p448 @p282)) % 0.96/1.18 (step @p430 :rule modus_ponens :premises (@p429 @p426)) % 0.96/1.18 (step-pop @p453 :rule scope :premises (@p430)) % 0.96/1.18 (step-pop @p454 :rule scope :premises (@p453)) % 0.96/1.18 (step @p431 :rule process_scope :premises (@p454) :args (@t194)) % 0.96/1.18 (step @p434 :rule implies_elim :premises (@p431)) % 0.96/1.18 (step @p435 :rule cnf_and_neg :args (@t290)) % 0.96/1.18 (step @p436 :rule resolution :premises (@p435 @p434) :args (true @t290)) % 0.96/1.18 (step @p437 :rule reordering :premises (@p436) :args ((or @t154 @t194 @t237))) % 0.96/1.18 (step @p438 false :rule chain_m_resolution :premises (@p437 @p418 @p282 @p203) :args (false (@list false false true) (@list @t236 @t153 @t194))) % 0.96/1.18 ) % 0.96/1.18 % SZS output end Proof % 0.96/1.18 % cvc5 exiting %------------------------------------------------------------------------------