%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM845+1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:40:48 AM UTC 2026 % Result : Theorem 0.37s 0.63s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : NUM845+1 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n013.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 12:29:30 EDT 2026 % 0.18/0.35 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.63 % SZS status Theorem % 0.37/0.63 % SZS output start Proof % 0.37/0.63 ( % 0.37/0.63 (declare-sort $$unsorted 0) % 0.37/0.63 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.less (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.v1 $$unsorted) % 0.37/0.63 (declare-const tptp.vskolem2 (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.vplus (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.vmul (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.vd411 $$unsorted) % 0.37/0.63 (declare-const tptp.vsucc (-> $$unsorted $$unsorted)) % 0.37/0.63 (define @t1 () (@var "Vd416" $$unsorted)) % 0.37/0.63 (define @t2 () (tptp.vsucc @t1)) % 0.37/0.63 (define @t3 () (tptp.vsucc tptp.vd411)) % 0.37/0.63 (define @t4 () (= (tptp.vmul @t3 @t2) (tptp.vplus (tptp.vmul tptp.vd411 @t2) @t2))) % 0.37/0.63 (define @t5 () (= (tptp.vmul @t3 @t1) (tptp.vplus (tptp.vmul tptp.vd411 @t1) @t1))) % 0.37/0.63 (define @t6 () (@list @t1)) % 0.37/0.63 (define @t7 () (forall @t6 (=> @t5 @t4))) % 0.37/0.63 (define @t8 () (not @t7)) % 0.37/0.63 (define @t9 () (@var "Vd413" $$unsorted)) % 0.37/0.63 (define @t10 () (tptp.vsucc @t9)) % 0.37/0.63 (define @t11 () (tptp.vmul tptp.vd411 @t9)) % 0.37/0.63 (define @t12 () (tptp.vplus (tptp.vplus @t11 tptp.vd411) @t10)) % 0.37/0.63 (define @t13 () (= @t12 (tptp.vplus (tptp.vmul tptp.vd411 @t10) @t10))) % 0.37/0.63 (define @t14 () (tptp.vplus @t11 @t9)) % 0.37/0.63 (define @t15 () (tptp.vmul @t3 @t9)) % 0.37/0.63 (define @t16 () (= @t15 @t14)) % 0.37/0.63 (define @t17 () (@list @t9)) % 0.37/0.63 (define @t18 () (forall @t17 (=> @t16 @t13))) % 0.37/0.63 (define @t19 () (tptp.vplus @t11 (tptp.vplus tptp.vd411 @t10))) % 0.37/0.63 (define @t20 () (=> @t16 (= @t19 @t12))) % 0.37/0.63 (define @t21 () (forall @t17 @t20)) % 0.37/0.63 (define @t22 () (tptp.vplus @t11 (tptp.vsucc (tptp.vplus tptp.vd411 @t9)))) % 0.37/0.63 (define @t23 () (=> @t16 (= @t22 @t19))) % 0.37/0.63 (define @t24 () (forall @t17 @t23)) % 0.37/0.63 (define @t25 () (tptp.vplus @t11 (tptp.vplus @t3 @t9))) % 0.37/0.63 (define @t26 () (=> @t16 (= @t25 @t22))) % 0.37/0.63 (define @t27 () (forall @t17 @t26)) % 0.37/0.63 (define @t28 () (tptp.vplus @t11 (tptp.vplus @t9 @t3))) % 0.37/0.63 (define @t29 () (=> @t16 (= @t28 @t25))) % 0.37/0.63 (define @t30 () (forall @t17 @t29)) % 0.37/0.63 (define @t31 () (tptp.vplus @t14 @t3)) % 0.37/0.63 (define @t32 () (=> @t16 (= @t31 @t28))) % 0.37/0.63 (define @t33 () (forall @t17 @t32)) % 0.37/0.63 (define @t34 () (tptp.vplus @t15 @t3)) % 0.37/0.63 (define @t35 () (tptp.vmul tptp.vd411 tptp.v1)) % 0.37/0.63 (define @t36 () (tptp.vsucc @t35)) % 0.37/0.63 (define @t37 () (@var "Vd400" $$unsorted)) % 0.37/0.63 (define @t38 () (@var "Vd396" $$unsorted)) % 0.37/0.63 (define @t39 () (tptp.vmul @t38 tptp.v1)) % 0.37/0.63 (define @t40 () (@var "Vd397" $$unsorted)) % 0.37/0.63 (define @t41 () (= (tptp.vmul @t38 (tptp.vsucc @t40)) (tptp.vplus (tptp.vmul @t38 @t40) @t38))) % 0.37/0.63 (define @t42 () (and @t41 (= @t39 @t38))) % 0.37/0.63 (define @t43 () (@list @t38 @t40)) % 0.37/0.63 (define @t44 () (forall @t43 @t42)) % 0.37/0.63 (define @t45 () (@var "Vd387" $$unsorted)) % 0.37/0.63 (define @t46 () (@var "Vd386" $$unsorted)) % 0.37/0.63 (define @t47 () (@var "Vd376" $$unsorted)) % 0.37/0.63 (define @t48 () (@var "Vd375" $$unsorted)) % 0.37/0.63 (define @t49 () (@var "Vd369" $$unsorted)) % 0.37/0.63 (define @t50 () (@var "Vd366" $$unsorted)) % 0.37/0.63 (define @t51 () (@var "Vd363" $$unsorted)) % 0.37/0.63 (define @t52 () (@var "Vd365" $$unsorted)) % 0.37/0.63 (define @t53 () (@var "Vd362" $$unsorted)) % 0.37/0.63 (define @t54 () (@var "Vd356" $$unsorted)) % 0.37/0.63 (define @t55 () (@var "Vd354" $$unsorted)) % 0.37/0.63 (define @t56 () (@var "Vd355" $$unsorted)) % 0.37/0.63 (define @t57 () (@var "Vd353" $$unsorted)) % 0.37/0.63 (define @t58 () (@var "Vd341" $$unsorted)) % 0.37/0.63 (define @t59 () (@var "Vd338" $$unsorted)) % 0.37/0.63 (define @t60 () (@var "Vd340" $$unsorted)) % 0.37/0.63 (define @t61 () (@var "Vd337" $$unsorted)) % 0.37/0.63 (define @t62 () (@var "Vd329" $$unsorted)) % 0.37/0.63 (define @t63 () (@var "Vd328" $$unsorted)) % 0.37/0.63 (define @t64 () (@var "Vd330" $$unsorted)) % 0.37/0.63 (define @t65 () (tptp.vplus @t62 @t64)) % 0.37/0.63 (define @t66 () (tptp.vplus @t63 @t64)) % 0.37/0.63 (define @t67 () (@list @t63 @t62 @t64)) % 0.37/0.63 (define @t68 () (@var "Vd303" $$unsorted)) % 0.37/0.63 (define @t69 () (@var "Vd302" $$unsorted)) % 0.37/0.63 (define @t70 () (tptp.vplus @t69 @t68)) % 0.37/0.63 (define @t71 () (@var "Vd301" $$unsorted)) % 0.37/0.63 (define @t72 () (tptp.vplus @t71 @t68)) % 0.37/0.63 (define @t73 () (@list @t71 @t69 @t68)) % 0.37/0.63 (define @t74 () (@var "Vd295" $$unsorted)) % 0.37/0.63 (define @t75 () (@var "Vd296" $$unsorted)) % 0.37/0.63 (define @t76 () (@var "Vd292" $$unsorted)) % 0.37/0.63 (define @t77 () (@var "Vd289" $$unsorted)) % 0.37/0.63 (define @t78 () (@var "Vd290" $$unsorted)) % 0.37/0.63 (define @t79 () (@var "Vd283" $$unsorted)) % 0.37/0.63 (define @t80 () (@var "Vd281" $$unsorted)) % 0.37/0.63 (define @t81 () (@var "Vd282" $$unsorted)) % 0.37/0.63 (define @t82 () (@var "Vd265" $$unsorted)) % 0.37/0.63 (define @t83 () (@var "Vd262" $$unsorted)) % 0.37/0.63 (define @t84 () (@var "Vd263" $$unsorted)) % 0.37/0.63 (define @t85 () (@var "Vd258" $$unsorted)) % 0.37/0.63 (define @t86 () (@var "Vd259" $$unsorted)) % 0.37/0.63 (define @t87 () (@var "Vd254" $$unsorted)) % 0.37/0.63 (define @t88 () (@var "Vd255" $$unsorted)) % 0.37/0.63 (define @t89 () (@var "Vd249" $$unsorted)) % 0.37/0.63 (define @t90 () (@var "Vd250" $$unsorted)) % 0.37/0.63 (define @t91 () (@var "Vd244" $$unsorted)) % 0.37/0.63 (define @t92 () (@var "Vd245" $$unsorted)) % 0.37/0.63 (define @t93 () (@var "Vd226" $$unsorted)) % 0.37/0.63 (define @t94 () (@var "Vd227" $$unsorted)) % 0.37/0.63 (define @t95 () (@var "Vd208" $$unsorted)) % 0.37/0.63 (define @t96 () (@var "Vd209" $$unsorted)) % 0.37/0.63 (define @t97 () (@var "Vd204" $$unsorted)) % 0.37/0.63 (define @t98 () (@var "Vd203" $$unsorted)) % 0.37/0.63 (define @t99 () (tptp.less @t98 @t97)) % 0.37/0.63 (define @t100 () (tptp.greater @t98 @t97)) % 0.37/0.63 (define @t101 () (= @t98 @t97)) % 0.37/0.63 (define @t102 () (@list @t98 @t97)) % 0.37/0.63 (define @t103 () (not @t99)) % 0.37/0.63 (define @t104 () (not @t101)) % 0.37/0.63 (define @t105 () (not @t100)) % 0.37/0.63 (define @t106 () (@var "Vd201" $$unsorted)) % 0.37/0.63 (define @t107 () (@var "Vd199" $$unsorted)) % 0.37/0.63 (define @t108 () (@var "Vd198" $$unsorted)) % 0.37/0.63 (define @t109 () (@var "Vd196" $$unsorted)) % 0.37/0.63 (define @t110 () (@var "Vd193" $$unsorted)) % 0.37/0.63 (define @t111 () (@var "Vd194" $$unsorted)) % 0.37/0.63 (define @t112 () (@var "Vd125" $$unsorted)) % 0.37/0.63 (define @t113 () (@var "Vd120" $$unsorted)) % 0.37/0.63 (define @t114 () (@var "Vd121" $$unsorted)) % 0.37/0.63 (define @t115 () (exists (@list @t112) (= @t114 (tptp.vplus @t113 @t112)))) % 0.37/0.63 (define @t116 () (@var "Vd123" $$unsorted)) % 0.37/0.63 (define @t117 () (exists (@list @t116) (= @t113 (tptp.vplus @t114 @t116)))) % 0.37/0.63 (define @t118 () (= @t113 @t114)) % 0.37/0.63 (define @t119 () (@list @t113 @t114)) % 0.37/0.63 (define @t120 () (not @t115)) % 0.37/0.63 (define @t121 () (not @t118)) % 0.37/0.63 (define @t122 () (not @t117)) % 0.37/0.63 (define @t123 () (@var "Vd105" $$unsorted)) % 0.37/0.63 (define @t124 () (@var "Vd107" $$unsorted)) % 0.37/0.63 (define @t125 () (@var "Vd104" $$unsorted)) % 0.37/0.63 (define @t126 () (@var "Vd93" $$unsorted)) % 0.37/0.63 (define @t127 () (@var "Vd92" $$unsorted)) % 0.37/0.63 (define @t128 () (@var "Vd79" $$unsorted)) % 0.37/0.63 (define @t129 () (@var "Vd78" $$unsorted)) % 0.37/0.63 (define @t130 () (@var "Vd69" $$unsorted)) % 0.37/0.63 (define @t131 () (@var "Vd68" $$unsorted)) % 0.37/0.63 (define @t132 () (@var "Vd59" $$unsorted)) % 0.37/0.63 (define @t133 () (@var "Vd48" $$unsorted)) % 0.37/0.63 (define @t134 () (@var "Vd47" $$unsorted)) % 0.37/0.63 (define @t135 () (@var "Vd46" $$unsorted)) % 0.37/0.63 (define @t136 () (@var "Vd42" $$unsorted)) % 0.37/0.63 (define @t137 () (@var "Vd43" $$unsorted)) % 0.37/0.63 (define @t138 () (@var "Vd24" $$unsorted)) % 0.37/0.63 (define @t139 () (@var "Vd16" $$unsorted)) % 0.37/0.63 (define @t140 () (@var "Vd8" $$unsorted)) % 0.37/0.63 (define @t141 () (@var "Vd7" $$unsorted)) % 0.37/0.63 (define @t142 () (@var "Vd4" $$unsorted)) % 0.37/0.63 (define @t143 () (@var "Vd3" $$unsorted)) % 0.37/0.63 (define @t144 () (@var "Vd1" $$unsorted)) % 0.37/0.63 (define @t145 () (@quantifiers_skolemize (forall @t6 (or (not @t5) @t4)) 0)) % 0.37/0.63 (define @t146 () (tptp.vmul tptp.vd411 @t145)) % 0.37/0.63 (define @t147 () (tptp.vplus @t146 @t145)) % 0.37/0.63 (define @t148 () (tptp.vmul @t3 @t145)) % 0.37/0.63 (define @t149 () (= @t148 @t147)) % 0.37/0.63 (define @t150 () (tptp.vsucc @t145)) % 0.37/0.63 (define @t151 () (tptp.vplus (tptp.vmul tptp.vd411 @t150) @t150)) % 0.37/0.63 (define @t152 () (tptp.vmul @t3 @t150)) % 0.37/0.63 (define @t153 () (= @t152 @t151)) % 0.37/0.63 (define @t154 () (not @t149)) % 0.37/0.63 (define @t155 () (or @t154 @t153)) % 0.37/0.63 (define @t156 () (@list true)) % 0.37/0.63 (define @t157 () (@list @t155)) % 0.37/0.63 (define @t158 () (not @t153)) % 0.37/0.63 (define @t159 () (@var "BOUND_VARIABLE_7932" $$unsorted)) % 0.37/0.63 (define @t160 () (= @t159 (tptp.vmul @t159 tptp.v1))) % 0.37/0.63 (define @t161 () (@var "BOUND_VARIABLE_7934" $$unsorted)) % 0.37/0.63 (define @t162 () (forall (@list @t159 @t161) @t160)) % 0.37/0.63 (define @t163 () (@var "BOUND_VARIABLE_7921" $$unsorted)) % 0.37/0.63 (define @t164 () (@var "BOUND_VARIABLE_7923" $$unsorted)) % 0.37/0.63 (define @t165 () (forall (@list @t163 @t164) (= (tptp.vmul @t163 (tptp.vsucc @t164)) (tptp.vplus (tptp.vmul @t163 @t164) @t163)))) % 0.37/0.63 (define @t166 () (= @t38 @t39)) % 0.37/0.63 (define @t167 () (forall @t43 @t166)) % 0.37/0.63 (define @t168 () (@list @t38 @t40)) % 0.37/0.63 (define @t169 () (forall @t43 @t41)) % 0.37/0.63 (define @t170 () (and @t169 @t167)) % 0.37/0.63 (define @t171 () (tptp.vplus (tptp.vplus @t146 tptp.vd411) @t150)) % 0.37/0.63 (define @t172 () (or @t154 (= @t171 @t151))) % 0.37/0.63 (define @t173 () (forall @t17 (or (not @t16) @t13))) % 0.37/0.63 (define @t174 () (@list @t145)) % 0.37/0.63 (define @t175 () (= @t151 @t171)) % 0.37/0.63 (define @t176 () (or @t154 @t175)) % 0.37/0.63 (define @t177 () (@list false false)) % 0.37/0.63 (define @t178 () (= @t12 @t19)) % 0.37/0.63 (define @t179 () (tptp.vplus @t146 (tptp.vplus tptp.vd411 @t150))) % 0.37/0.63 (define @t180 () (= @t171 @t179)) % 0.37/0.63 (define @t181 () (or @t154 @t180)) % 0.37/0.63 (define @t182 () (= @t19 @t22)) % 0.37/0.63 (define @t183 () (tptp.vplus @t146 (tptp.vsucc (tptp.vplus tptp.vd411 @t145)))) % 0.37/0.63 (define @t184 () (= @t179 @t183)) % 0.37/0.63 (define @t185 () (or @t154 @t184)) % 0.37/0.63 (define @t186 () (= @t22 @t25)) % 0.37/0.63 (define @t187 () (tptp.vplus @t146 (tptp.vplus @t3 @t145))) % 0.37/0.63 (define @t188 () (= @t183 @t187)) % 0.37/0.63 (define @t189 () (or @t154 @t188)) % 0.37/0.63 (define @t190 () (= @t25 @t28)) % 0.37/0.63 (define @t191 () (tptp.vplus @t146 (tptp.vplus @t145 @t3))) % 0.37/0.63 (define @t192 () (= @t187 @t191)) % 0.37/0.63 (define @t193 () (or @t154 @t192)) % 0.37/0.63 (define @t194 () (= @t28 @t31)) % 0.37/0.63 (define @t195 () (tptp.vplus @t147 @t3)) % 0.37/0.63 (define @t196 () (= @t191 @t195)) % 0.37/0.63 (define @t197 () (or @t154 @t196)) % 0.37/0.63 (define @t198 () (tptp.vplus @t148 @t3)) % 0.37/0.63 (define @t199 () (= @t152 @t198)) % 0.37/0.63 (define @t200 () (not @t199)) % 0.37/0.63 (define @t201 () (not @t196)) % 0.37/0.63 (define @t202 () (not @t192)) % 0.37/0.63 (define @t203 () (not @t188)) % 0.37/0.63 (define @t204 () (not @t184)) % 0.37/0.63 (define @t205 () (not @t180)) % 0.37/0.63 (define @t206 () (not @t175)) % 0.37/0.63 (define @t207 () (= @t195 @t198)) % 0.37/0.63 (define @t208 () (and @t199 @t207 @t196 @t184 @t180 @t192 @t188 @t175 @t158)) % 0.37/0.63 (assume @p1 @t8) % 0.37/0.63 (assume @p2 @t18) % 0.37/0.63 (assume @p3 @t21) % 0.37/0.63 (assume @p4 @t24) % 0.37/0.63 (assume @p5 @t27) % 0.37/0.63 (assume @p6 @t30) % 0.37/0.63 (assume @p7 @t33) % 0.37/0.63 (assume @p8 (forall @t17 (=> @t16 (= @t34 @t31)))) % 0.37/0.63 (assume @p9 (forall @t17 (=> @t16 (= (tptp.vmul @t3 @t10) @t34)))) % 0.37/0.63 (assume @p10 (= @t36 (tptp.vplus @t35 tptp.v1))) % 0.37/0.63 (assume @p11 (= @t3 @t36)) % 0.37/0.63 (assume @p12 (= (tptp.vmul @t3 tptp.v1) @t3)) % 0.37/0.63 (assume @p13 (forall (@list @t37) (= (tptp.vmul tptp.v1 @t37) @t37))) % 0.37/0.63 (assume @p14 @t44) % 0.37/0.63 (assume @p15 (forall (@list @t46 @t45) (=> (tptp.less @t46 (tptp.vplus @t45 tptp.v1)) (tptp.leq @t46 @t45)))) % 0.37/0.63 (assume @p16 (forall (@list @t48 @t47) (=> (tptp.greater @t48 @t47) (tptp.geq @t48 (tptp.vplus @t47 tptp.v1))))) % 0.37/0.63 (assume @p17 (forall (@list @t49) (tptp.geq @t49 tptp.v1))) % 0.37/0.63 (assume @p18 (forall (@list @t53 @t51 @t52 @t50) (=> (and (tptp.geq @t52 @t50) (tptp.geq @t53 @t51)) (tptp.geq (tptp.vplus @t53 @t52) (tptp.vplus @t51 @t50))))) % 0.37/0.63 (assume @p19 (forall (@list @t57 @t55 @t56 @t54) (=> (or (and (tptp.greater @t56 @t54) (tptp.geq @t57 @t55)) (and (tptp.geq @t56 @t54) (tptp.greater @t57 @t55))) (tptp.greater (tptp.vplus @t57 @t56) (tptp.vplus @t55 @t54))))) % 0.37/0.63 (assume @p20 (forall (@list @t61 @t59 @t60 @t58) (=> (and (tptp.greater @t60 @t58) (tptp.greater @t61 @t59)) (tptp.greater (tptp.vplus @t61 @t60) (tptp.vplus @t59 @t58))))) % 0.37/0.63 (assume @p21 (forall @t67 (=> (tptp.less @t66 @t65) (tptp.less @t63 @t62)))) % 0.37/0.63 (assume @p22 (forall @t67 (=> (= @t66 @t65) (= @t63 @t62)))) % 0.37/0.63 (assume @p23 (forall @t67 (=> (tptp.greater @t66 @t65) (tptp.greater @t63 @t62)))) % 0.37/0.63 (assume @p24 (forall @t73 (=> (tptp.less @t71 @t69) (tptp.less @t72 @t70)))) % 0.37/0.63 (assume @p25 (forall @t73 (=> (= @t71 @t69) (= @t72 @t70)))) % 0.37/0.63 (assume @p26 (forall @t73 (=> (tptp.greater @t71 @t69) (tptp.greater @t72 @t70)))) % 0.37/0.63 (assume @p27 (forall (@list @t74 @t75) (tptp.greater (tptp.vplus @t74 @t75) @t74))) % 0.37/0.63 (assume @p28 (forall (@list @t77 @t78 @t76) (=> (and (tptp.leq @t78 @t76) (tptp.leq @t77 @t78)) (tptp.leq @t77 @t76)))) % 0.37/0.63 (assume @p29 (forall (@list @t80 @t81 @t79) (=> (or (and (tptp.less @t81 @t79) (tptp.leq @t80 @t81)) (and (tptp.leq @t81 @t79) (tptp.less @t80 @t81))) (tptp.less @t80 @t79)))) % 0.37/0.63 (assume @p30 (forall (@list @t83 @t84 @t82) (=> (and (tptp.less @t84 @t82) (tptp.less @t83 @t84)) (tptp.less @t83 @t82)))) % 0.37/0.63 (assume @p31 (forall (@list @t85 @t86) (=> (tptp.leq @t85 @t86) (tptp.geq @t86 @t85)))) % 0.37/0.63 (assume @p32 (forall (@list @t87 @t88) (=> (tptp.geq @t87 @t88) (tptp.leq @t88 @t87)))) % 0.37/0.63 (assume @p33 (forall (@list @t89 @t90) (= (tptp.leq @t90 @t89) (or (tptp.less @t90 @t89) (= @t90 @t89))))) % 0.37/0.63 (assume @p34 (forall (@list @t91 @t92) (= (tptp.geq @t92 @t91) (or (tptp.greater @t92 @t91) (= @t92 @t91))))) % 0.37/0.63 (assume @p35 (forall (@list @t93 @t94) (=> (tptp.less @t93 @t94) (tptp.greater @t94 @t93)))) % 0.37/0.63 (assume @p36 (forall (@list @t95 @t96) (=> (tptp.greater @t95 @t96) (tptp.less @t96 @t95)))) % 0.37/0.63 (assume @p37 (forall @t102 (or @t101 @t100 @t99))) % 0.37/0.63 (assume @p38 (forall @t102 (or @t104 @t103))) % 0.37/0.63 (assume @p39 (forall @t102 (or @t105 @t103))) % 0.37/0.63 (assume @p40 (forall @t102 (or @t104 @t105))) % 0.37/0.63 (assume @p41 (forall (@list @t108 @t107) (= (tptp.less @t107 @t108) (exists (@list @t106) (= @t108 (tptp.vplus @t107 @t106)))))) % 0.37/0.63 (assume @p42 (forall (@list @t110 @t111) (= (tptp.greater @t111 @t110) (exists (@list @t109) (= @t111 (tptp.vplus @t110 @t109)))))) % 0.37/0.63 (assume @p43 (forall @t119 (or @t118 @t117 @t115))) % 0.37/0.63 (assume @p44 (forall @t119 (or @t121 @t120))) % 0.37/0.63 (assume @p45 (forall @t119 (or @t122 @t120))) % 0.37/0.63 (assume @p46 (forall @t119 (or @t121 @t122))) % 0.37/0.63 (assume @p47 (forall (@list @t125 @t123) (=> (not (= @t125 @t123)) (forall (@list @t124) (not (= (tptp.vplus @t124 @t125) (tptp.vplus @t124 @t123))))))) % 0.37/0.63 (assume @p48 (forall (@list @t127 @t126) (not (= @t126 (tptp.vplus @t127 @t126))))) % 0.37/0.63 (assume @p49 (forall (@list @t129 @t128) (= (tptp.vplus @t128 @t129) (tptp.vplus @t129 @t128)))) % 0.37/0.63 (assume @p50 (forall (@list @t131 @t130) (= (tptp.vplus (tptp.vsucc @t131) @t130) (tptp.vsucc (tptp.vplus @t131 @t130))))) % 0.37/0.63 (assume @p51 (forall (@list @t132) (= (tptp.vplus tptp.v1 @t132) (tptp.vsucc @t132)))) % 0.37/0.63 (assume @p52 (forall (@list @t135 @t134 @t133) (= (tptp.vplus (tptp.vplus @t135 @t134) @t133) (tptp.vplus @t135 (tptp.vplus @t134 @t133))))) % 0.37/0.63 (assume @p53 (forall (@list @t136 @t137) (and (= (tptp.vplus @t136 (tptp.vsucc @t137)) (tptp.vsucc (tptp.vplus @t136 @t137))) (= (tptp.vplus @t136 tptp.v1) (tptp.vsucc @t136))))) % 0.37/0.63 (assume @p54 (forall (@list @t138) (=> (not (= @t138 tptp.v1)) (= @t138 (tptp.vsucc (tptp.vskolem2 @t138)))))) % 0.37/0.63 (assume @p55 (forall (@list @t139) (not (= (tptp.vsucc @t139) @t139)))) % 0.37/0.63 (assume @p56 (forall (@list @t141 @t140) (=> (not (= @t141 @t140)) (not (= (tptp.vsucc @t141) (tptp.vsucc @t140)))))) % 0.37/0.63 (assume @p57 (forall (@list @t143 @t142) (=> (= (tptp.vsucc @t143) (tptp.vsucc @t142)) (= @t143 @t142)))) % 0.37/0.63 (assume @p58 (forall (@list @t144) (not (= (tptp.vsucc @t144) tptp.v1)))) % 0.37/0.63 (assume @p59 true) % 0.37/0.63 (step @p60 :rule bool-impl-elim :args (@t5 @t4)) % 0.37/0.63 (step @p61 :rule cong :premises (@p60) :args (@t7)) % 0.37/0.63 (step @p62 :rule cong :premises (@p61) :args (@t8)) % 0.37/0.63 (step @p63 :rule eq_resolve :premises (@p1 @p62)) % 0.37/0.63 (step @p64 :rule skolemize :premises (@p63)) % 0.37/0.63 (step @p65 :rule bool-double-not-elim :args (@t149)) % 0.37/0.63 (step @p66 :rule refl :args (@t155)) % 0.37/0.63 (step @p67 :rule nary_cong :premises (@p66 @p65) :args ((or @t155 (not @t154)))) % 0.37/0.63 (step @p68 :rule cnf_or_neg :args (@t155 0)) % 0.37/0.63 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.37/0.63 (step @p70 :rule reordering :premises (@p69) :args ((or @t149 @t155))) % 0.37/0.63 (step @p71 :rule chain_m_resolution :premises (@p70 @p64) :args (@t149 @t156 @t157)) % 0.37/0.63 (step @p72 :rule cnf_or_neg :args (@t155 1)) % 0.37/0.63 (step @p73 :rule chain_m_resolution :premises (@p72 @p64) :args (@t158 @t156 @t157)) % 0.37/0.63 (step @p74 :rule quant-unused-vars :args ((= @t162 (forall (@list @t159) @t160)))) % 0.37/0.63 (step @p75 :rule refl :args (@t165)) % 0.37/0.63 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((and @t165 @t162))) % 0.37/0.63 (step @p77 :rule alpha_equiv :args (@t167 @t168 (@list @t159 @t161))) % 0.37/0.63 (step @p78 :rule alpha_equiv :args (@t169 @t168 (@list @t163 @t164))) % 0.37/0.63 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t170)) % 0.37/0.63 (step @p80 :rule quant-miniscope-and :args ((= (forall @t43 (and @t41 @t166)) @t170))) % 0.37/0.63 (step @p81 :rule trans :premises (@p80 @p79)) % 0.37/0.63 (step @p82 :rule trans :premises (@p81 @p76)) % 0.37/0.63 (step @p83 :rule eq-symm :args (@t39 @t38)) % 0.37/0.63 (step @p84 :rule refl :args (@t41)) % 0.37/0.63 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t42)) % 0.37/0.63 (step @p86 :rule cong :premises (@p85) :args (@t44)) % 0.37/0.63 (step @p87 :rule trans :premises (@p86 @p82)) % 0.37/0.63 (step @p88 :rule eq_resolve :premises (@p14 @p87)) % 0.37/0.63 (step @p89 :rule and_elim :premises (@p88) :args (0)) % 0.37/0.63 (step @p90 :rule instantiate :premises (@p89) :args ((@list @t3 @t145))) % 0.37/0.63 (step @p91 :rule bool-impl-elim :args (@t16 @t13)) % 0.37/0.63 (step @p92 :rule cong :premises (@p91) :args (@t18)) % 0.37/0.63 (step @p93 :rule eq_resolve :premises (@p2 @p92)) % 0.37/0.63 (step @p94 :rule eq-symm :args (@t171 @t151)) % 0.37/0.63 (step @p95 :rule refl :args (@t154)) % 0.37/0.63 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t172)) % 0.37/0.63 (step @p97 :rule refl :args (@t173)) % 0.37/0.63 (step @p98 :rule cong :premises (@p97 @p96) :args ((=> @t173 @t172))) % 0.37/0.63 (assume-push @p236 @t173) % 0.37/0.63 (step @p100 :rule instantiate :premises (@p93) :args (@t174)) % 0.37/0.63 (step-pop @p237 :rule scope :premises (@p100)) % 0.37/0.63 (step @p101 :rule process_scope :premises (@p237) :args (@t172)) % 0.37/0.63 (step @p103 :rule eq_resolve :premises (@p101 @p98)) % 0.37/0.63 (step @p104 :rule implies_elim :premises (@p103)) % 0.37/0.63 (step @p105 :rule chain_m_resolution :premises (@p104 @p93) :args (@t176 (@list false) (@list @t173))) % 0.37/0.63 (step @p106 :rule cnf_or_pos :args (@t176)) % 0.37/0.63 (step @p107 :rule reordering :premises (@p106) :args ((or @t154 @t175 (not @t176)))) % 0.37/0.63 (step @p108 :rule chain_m_resolution :premises (@p107 @p71 @p105) :args (@t175 @t177 (@list @t149 @t176))) % 0.37/0.63 (step @p109 :rule bool-impl-elim :args (@t16 @t178)) % 0.37/0.63 (step @p110 :rule cong :premises (@p109) :args ((forall @t17 (=> @t16 @t178)))) % 0.37/0.63 (step @p111 :rule eq-symm :args (@t19 @t12)) % 0.37/0.63 (step @p112 :rule refl :args (@t16)) % 0.37/0.63 (step @p113 :rule cong :premises (@p112 @p111) :args (@t20)) % 0.37/0.63 (step @p114 :rule cong :premises (@p113) :args (@t21)) % 0.37/0.63 (step @p115 :rule trans :premises (@p114 @p110)) % 0.37/0.63 (step @p116 :rule eq_resolve :premises (@p3 @p115)) % 0.37/0.63 (step @p117 :rule instantiate :premises (@p116) :args (@t174)) % 0.37/0.63 (step @p118 :rule cnf_or_pos :args (@t181)) % 0.37/0.63 (step @p119 :rule reordering :premises (@p118) :args ((or @t154 @t180 (not @t181)))) % 0.37/0.63 (step @p120 :rule chain_m_resolution :premises (@p119 @p71 @p117) :args (@t180 @t177 (@list @t149 @t181))) % 0.37/0.63 (step @p121 :rule bool-impl-elim :args (@t16 @t182)) % 0.37/0.63 (step @p122 :rule cong :premises (@p121) :args ((forall @t17 (=> @t16 @t182)))) % 0.37/0.63 (step @p123 :rule eq-symm :args (@t22 @t19)) % 0.37/0.63 (step @p124 :rule cong :premises (@p112 @p123) :args (@t23)) % 0.37/0.63 (step @p125 :rule cong :premises (@p124) :args (@t24)) % 0.37/0.63 (step @p126 :rule trans :premises (@p125 @p122)) % 0.37/0.63 (step @p127 :rule eq_resolve :premises (@p4 @p126)) % 0.37/0.63 (step @p128 :rule instantiate :premises (@p127) :args (@t174)) % 0.37/0.63 (step @p129 :rule cnf_or_pos :args (@t185)) % 0.37/0.63 (step @p130 :rule reordering :premises (@p129) :args ((or @t154 @t184 (not @t185)))) % 0.37/0.63 (step @p131 :rule chain_m_resolution :premises (@p130 @p71 @p128) :args (@t184 @t177 (@list @t149 @t185))) % 0.37/0.63 (step @p132 :rule bool-impl-elim :args (@t16 @t186)) % 0.37/0.63 (step @p133 :rule cong :premises (@p132) :args ((forall @t17 (=> @t16 @t186)))) % 0.37/0.63 (step @p134 :rule eq-symm :args (@t25 @t22)) % 0.37/0.63 (step @p135 :rule cong :premises (@p112 @p134) :args (@t26)) % 0.37/0.63 (step @p136 :rule cong :premises (@p135) :args (@t27)) % 0.37/0.63 (step @p137 :rule trans :premises (@p136 @p133)) % 0.37/0.63 (step @p138 :rule eq_resolve :premises (@p5 @p137)) % 0.37/0.63 (step @p139 :rule instantiate :premises (@p138) :args (@t174)) % 0.37/0.63 (step @p140 :rule cnf_or_pos :args (@t189)) % 0.37/0.63 (step @p141 :rule reordering :premises (@p140) :args ((or @t154 @t188 (not @t189)))) % 0.37/0.63 (step @p142 :rule chain_m_resolution :premises (@p141 @p71 @p139) :args (@t188 @t177 (@list @t149 @t189))) % 0.37/0.63 (step @p143 :rule bool-impl-elim :args (@t16 @t190)) % 0.37/0.63 (step @p144 :rule cong :premises (@p143) :args ((forall @t17 (=> @t16 @t190)))) % 0.37/0.63 (step @p145 :rule eq-symm :args (@t28 @t25)) % 0.37/0.63 (step @p146 :rule cong :premises (@p112 @p145) :args (@t29)) % 0.37/0.63 (step @p147 :rule cong :premises (@p146) :args (@t30)) % 0.37/0.63 (step @p148 :rule trans :premises (@p147 @p144)) % 0.37/0.63 (step @p149 :rule eq_resolve :premises (@p6 @p148)) % 0.37/0.63 (step @p150 :rule instantiate :premises (@p149) :args (@t174)) % 0.37/0.63 (step @p151 :rule cnf_or_pos :args (@t193)) % 0.37/0.63 (step @p152 :rule reordering :premises (@p151) :args ((or @t154 @t192 (not @t193)))) % 0.37/0.63 (step @p153 :rule chain_m_resolution :premises (@p152 @p71 @p150) :args (@t192 @t177 (@list @t149 @t193))) % 0.37/0.63 (step @p154 :rule bool-impl-elim :args (@t16 @t194)) % 0.37/0.63 (step @p155 :rule cong :premises (@p154) :args ((forall @t17 (=> @t16 @t194)))) % 0.37/0.63 (step @p156 :rule eq-symm :args (@t31 @t28)) % 0.37/0.63 (step @p157 :rule cong :premises (@p112 @p156) :args (@t32)) % 0.37/0.63 (step @p158 :rule cong :premises (@p157) :args (@t33)) % 0.37/0.63 (step @p159 :rule trans :premises (@p158 @p155)) % 0.37/0.63 (step @p160 :rule eq_resolve :premises (@p7 @p159)) % 0.37/0.63 (step @p161 :rule instantiate :premises (@p160) :args (@t174)) % 0.37/0.63 (step @p162 :rule cnf_or_pos :args (@t197)) % 0.37/0.63 (step @p163 :rule reordering :premises (@p162) :args ((or @t154 @t196 (not @t197)))) % 0.37/0.63 (step @p164 :rule chain_m_resolution :premises (@p163 @p71 @p161) :args (@t196 @t177 (@list @t149 @t197))) % 0.37/0.63 (step @p165 :rule refl :args (@t200)) % 0.37/0.63 (step @p166 :rule refl :args (@t201)) % 0.37/0.63 (step @p167 :rule refl :args (@t202)) % 0.37/0.63 (step @p168 :rule refl :args (@t203)) % 0.37/0.63 (step @p169 :rule refl :args (@t204)) % 0.37/0.63 (step @p170 :rule refl :args (@t205)) % 0.37/0.63 (step @p171 :rule refl :args (@t206)) % 0.37/0.63 (step @p172 :rule bool-double-not-elim :args (@t153)) % 0.37/0.63 (step @p173 :rule nary_cong :premises (@p95 @p172 @p171 @p170 @p169 @p168 @p167 @p166 @p165) :args ((or @t154 (not @t158) @t206 @t205 @t204 @t203 @t202 @t201 @t200))) % 0.37/0.63 (assume-push @p238 @t199) % 0.37/0.63 (assume-push @p239 @t207) % 0.37/0.63 (assume-push @p240 @t196) % 0.37/0.63 (assume-push @p241 @t184) % 0.37/0.63 (assume-push @p242 @t180) % 0.37/0.63 (assume-push @p243 @t192) % 0.37/0.63 (assume-push @p244 @t188) % 0.37/0.63 (assume-push @p245 @t175) % 0.37/0.63 (assume-push @p246 @t158) % 0.37/0.63 (step @p183 :rule evaluate :args ((= false true))) % 0.37/0.63 (step @p184 :rule symm :premises (@p108)) % 0.37/0.63 (step @p185 :rule symm :premises (@p120)) % 0.37/0.63 (step @p186 :rule symm :premises (@p131)) % 0.37/0.63 (step @p187 :rule symm :premises (@p142)) % 0.37/0.63 (step @p188 :rule symm :premises (@p153)) % 0.37/0.63 (step @p189 :rule symm :premises (@p164)) % 0.37/0.63 (step @p190 :rule refl :args (@t3)) % 0.37/0.63 (step @p191 :rule symm :premises (@p71)) % 0.37/0.63 (step @p192 :rule cong :premises (@p191 @p190) :args (@t195)) % 0.37/0.63 (step @p193 :rule symm :premises (@p192)) % 0.37/0.63 (step @p194 :rule trans :premises (@p90 @p193 @p189 @p188 @p187 @p186 @p185 @p184)) % 0.37/0.63 (step @p195 :rule true_intro :premises (@p194)) % 0.37/0.63 (step @p196 :rule false_intro :premises (@p73)) % 0.37/0.63 (step @p197 :rule symm :premises (@p196)) % 0.37/0.63 (step @p198 :rule trans :premises (@p197 @p195)) % 0.37/0.63 (step @p199 false :rule eq_resolve :premises (@p198 @p183)) % 0.37/0.63 (step-pop @p247 :rule scope :premises (@p199)) % 0.37/0.63 (step-pop @p248 :rule scope :premises (@p247)) % 0.37/0.63 (step-pop @p249 :rule scope :premises (@p248)) % 0.37/0.63 (step-pop @p250 :rule scope :premises (@p249)) % 0.37/0.63 (step-pop @p251 :rule scope :premises (@p250)) % 0.37/0.63 (step-pop @p252 :rule scope :premises (@p251)) % 0.37/0.63 (step-pop @p253 :rule scope :premises (@p252)) % 0.37/0.63 (step-pop @p254 :rule scope :premises (@p253)) % 0.37/0.63 (step-pop @p255 :rule scope :premises (@p254)) % 0.37/0.63 (step @p200 :rule process_scope :premises (@p255) :args (false)) % 0.37/0.63 (assume-push @p256 @t149) % 0.37/0.63 (assume-push @p257 @t158) % 0.37/0.63 (assume-push @p258 @t175) % 0.37/0.63 (assume-push @p259 @t180) % 0.37/0.63 (assume-push @p260 @t184) % 0.37/0.63 (assume-push @p261 @t188) % 0.37/0.63 (assume-push @p262 @t192) % 0.37/0.63 (assume-push @p263 @t196) % 0.37/0.63 (assume-push @p264 @t199) % 0.37/0.63 (step @p190 :rule refl :args (@t3)) % 0.37/0.63 (step @p191 :rule symm :premises (@p71)) % 0.37/0.63 (step @p219 :rule cong :premises (@p191 @p190) :args (@t195)) % 0.37/0.63 (step @p220 :rule and_intro :premises (@p90 @p219 @p164 @p131 @p120 @p153 @p142 @p108 @p73)) % 0.37/0.63 (step-pop @p265 :rule scope :premises (@p220)) % 0.37/0.63 (step-pop @p266 :rule scope :premises (@p265)) % 0.37/0.63 (step-pop @p267 :rule scope :premises (@p266)) % 0.37/0.63 (step-pop @p268 :rule scope :premises (@p267)) % 0.37/0.63 (step-pop @p269 :rule scope :premises (@p268)) % 0.37/0.63 (step-pop @p270 :rule scope :premises (@p269)) % 0.37/0.63 (step-pop @p271 :rule scope :premises (@p270)) % 0.37/0.63 (step-pop @p272 :rule scope :premises (@p271)) % 0.37/0.63 (step-pop @p273 :rule scope :premises (@p272)) % 0.37/0.63 (step @p221 :rule process_scope :premises (@p273) :args (@t208)) % 0.37/0.63 (step @p231 :rule implies_elim :premises (@p221)) % 0.37/0.63 (step @p232 :rule resolution :premises (@p231 @p200) :args (true @t208)) % 0.37/0.63 (step @p233 :rule not_and :premises (@p232)) % 0.37/0.63 (step @p234 :rule eq_resolve :premises (@p233 @p173)) % 0.37/0.63 (step @p235 false :rule chain_m_resolution :premises (@p234 @p164 @p153 @p142 @p131 @p120 @p108 @p90 @p73 @p71) :args (false (@list false false false false false false false true false) (@list @t196 @t192 @t188 @t184 @t180 @t175 @t199 @t153 @t149))) % 0.37/0.63 ) % 0.37/0.63 % SZS output end Proof % 0.37/0.63 % cvc5 exiting %------------------------------------------------------------------------------