%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM473+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n024.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 08:39:32 AM UTC 2026 % Result : Theorem 33.49s 33.79s % Output : Proof 33.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM473+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.06/0.24 % Computer : n024.cluster.edu % 0.06/0.24 % Model : x86_64 x86_64 % 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.24 % Memory : 8042.1875MB % 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.24 % CPULimit : 300 % 0.06/0.24 % WCLimit : 300 % 0.06/0.24 % DateTime : Tue Jun 2 06:22:15 EDT 2026 % 0.06/0.24 % CPUTime : % 0.13/0.34 %----Proving TF0_NAR, FOF, or CNF % 33.49/33.79 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.49/33.79 --- Run --no-e-matching --full-saturate-quant at 6... % 33.49/33.79 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.49/33.79 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.49/33.79 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.49/33.79 % SZS status Theorem % 33.49/33.79 % SZS output start Proof % 33.49/33.79 ( % 33.49/33.79 (declare-sort $$unsorted 0) % 33.49/33.79 (declare-const tptp.xq $$unsorted) % 33.49/33.79 (declare-const tptp.xp $$unsorted) % 33.49/33.79 (declare-const tptp.sz10 $$unsorted) % 33.49/33.79 (declare-const tptp.xl $$unsorted) % 33.49/33.79 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 33.49/33.79 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 33.49/33.79 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 33.49/33.79 (declare-const tptp.sz00 $$unsorted) % 33.49/33.79 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 33.49/33.79 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 33.49/33.79 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 33.49/33.79 (declare-const tptp.xn $$unsorted) % 33.49/33.79 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 33.49/33.79 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 33.49/33.79 (declare-const tptp.xm $$unsorted) % 33.49/33.79 (define @t1 () (@var "W0" $$unsorted)) % 33.49/33.79 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 33.49/33.79 (define @t3 () (@list @t1)) % 33.49/33.79 (define @t4 () (@var "W1" $$unsorted)) % 33.49/33.79 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 33.49/33.79 (define @t6 () (tptp.aNaturalNumber0 @t5)) % 33.49/33.79 (define @t7 () (tptp.aNaturalNumber0 @t4)) % 33.49/33.79 (define @t8 () (and @t2 @t7)) % 33.49/33.79 (define @t9 () (@list @t1 @t4)) % 33.49/33.79 (define @t10 () (forall @t9 (=> @t8 @t6))) % 33.49/33.79 (define @t11 () (tptp.sdtasdt0 @t1 @t4)) % 33.49/33.79 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 33.49/33.79 (define @t13 () (@var "W2" $$unsorted)) % 33.49/33.79 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 33.49/33.79 (define @t15 () (tptp.aNaturalNumber0 @t13)) % 33.49/33.79 (define @t16 () (and @t2 @t7 @t15)) % 33.49/33.79 (define @t17 () (@list @t1 @t4 @t13)) % 33.49/33.79 (define @t18 () (tptp.sdtasdt0 @t4 @t1)) % 33.49/33.79 (define @t19 () (tptp.sdtasdt0 @t13 @t1)) % 33.49/33.79 (define @t20 () (tptp.sdtasdt0 @t1 @t13)) % 33.49/33.79 (define @t21 () (= @t4 @t13)) % 33.49/33.79 (define @t22 () (tptp.sdtpldt0 @t13 @t1)) % 33.49/33.79 (define @t23 () (tptp.sdtpldt0 @t1 @t13)) % 33.49/33.79 (define @t24 () (= @t18 @t19)) % 33.49/33.79 (define @t25 () (= @t11 @t20)) % 33.49/33.79 (define @t26 () (and @t7 @t15)) % 33.49/33.79 (define @t27 () (= @t1 tptp.sz00)) % 33.49/33.79 (define @t28 () (not @t27)) % 33.49/33.79 (define @t29 () (= @t4 tptp.sz00)) % 33.49/33.79 (define @t30 () (and @t15 (= @t23 @t4))) % 33.49/33.79 (define @t31 () (@list @t13)) % 33.49/33.79 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 33.49/33.79 (define @t33 () (= @t1 @t4)) % 33.49/33.79 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 33.49/33.79 (define @t35 () (and @t32 @t34)) % 33.49/33.79 (define @t36 () (=> @t35 @t33)) % 33.49/33.79 (define @t37 () (forall @t9 (=> @t8 @t36))) % 33.49/33.79 (define @t38 () (tptp.sdtlseqdt0 @t4 @t13)) % 33.49/33.79 (define @t39 () (not (= @t4 @t1))) % 33.49/33.79 (define @t40 () (and @t39 @t34)) % 33.49/33.79 (define @t41 () (or @t32 @t40)) % 33.49/33.79 (define @t42 () (=> @t8 @t41)) % 33.49/33.79 (define @t43 () (forall @t9 @t42)) % 33.49/33.79 (define @t44 () (tptp.sdtpldt0 @t13 @t4)) % 33.49/33.79 (define @t45 () (not @t33)) % 33.49/33.79 (define @t46 () (and @t45 @t32)) % 33.49/33.79 (define @t47 () (and (not @t25) (tptp.sdtlseqdt0 @t11 @t20) (not @t24) (tptp.sdtlseqdt0 @t18 @t19))) % 33.49/33.79 (define @t48 () (not @t21)) % 33.49/33.79 (define @t49 () (and @t28 @t48 @t38)) % 33.49/33.79 (define @t50 () (=> @t49 @t47)) % 33.49/33.79 (define @t51 () (forall @t17 (=> @t16 @t50))) % 33.49/33.79 (define @t52 () (tptp.iLess0 @t1 @t4)) % 33.49/33.79 (define @t53 () (and @t15 (= @t4 @t20))) % 33.49/33.79 (define @t54 () (tptp.doDivides0 @t1 @t4)) % 33.49/33.79 (define @t55 () (tptp.sdtsldt0 @t4 @t1)) % 33.49/33.79 (define @t56 () (= @t13 @t55)) % 33.49/33.79 (define @t57 () (forall @t31 (= @t56 @t53))) % 33.49/33.79 (define @t58 () (and @t28 @t54)) % 33.49/33.79 (define @t59 () (=> @t58 @t57)) % 33.49/33.79 (define @t60 () (=> @t8 @t59)) % 33.49/33.79 (define @t61 () (forall @t9 @t60)) % 33.49/33.79 (define @t62 () (tptp.doDivides0 @t1 @t13)) % 33.49/33.79 (define @t63 () (tptp.aNaturalNumber0 tptp.xn)) % 33.49/33.79 (define @t64 () (tptp.aNaturalNumber0 tptp.xm)) % 33.49/33.79 (define @t65 () (tptp.aNaturalNumber0 tptp.xl)) % 33.49/33.79 (define @t66 () (tptp.sdtpldt0 tptp.xm tptp.xn)) % 33.49/33.79 (define @t67 () (tptp.doDivides0 tptp.xl @t66)) % 33.49/33.79 (define @t68 () (tptp.doDivides0 tptp.xl tptp.xm)) % 33.49/33.79 (define @t69 () (= tptp.xl tptp.sz00)) % 33.49/33.79 (define @t70 () (tptp.sdtsldt0 tptp.xm tptp.xl)) % 33.49/33.79 (define @t71 () (tptp.sdtsldt0 @t66 tptp.xl)) % 33.49/33.79 (define @t72 () (tptp.sdtlseqdt0 tptp.xm @t66)) % 33.49/33.79 (define @t73 () (tptp.sdtlseqdt0 tptp.xp tptp.xq)) % 33.49/33.79 (define @t74 () (not @t73)) % 33.49/33.79 (define @t75 () (not @t34)) % 33.49/33.79 (define @t76 () (not @t32)) % 33.49/33.79 (define @t77 () (not @t7)) % 33.49/33.79 (define @t78 () (not @t2)) % 33.49/33.79 (define @t79 () (or @t76 @t75 @t33)) % 33.49/33.79 (define @t80 () (or @t78 @t77)) % 33.49/33.79 (define @t81 () (not @t8)) % 33.49/33.79 (define @t82 () (tptp.aNaturalNumber0 @t66)) % 33.49/33.79 (define @t83 () (not @t63)) % 33.49/33.79 (define @t84 () (not @t64)) % 33.49/33.79 (define @t85 () (or @t84 @t83 @t82)) % 33.49/33.79 (define @t86 () (not @t38)) % 33.49/33.79 (define @t87 () (not @t15)) % 33.49/33.79 (define @t88 () (or @t78 @t77 @t87 @t27 @t21 @t86 @t47)) % 33.49/33.79 (define @t89 () (or @t27 @t21 @t86 @t47)) % 33.49/33.79 (define @t90 () (or @t78 @t77 @t87)) % 33.49/33.79 (define @t91 () (not @t48)) % 33.49/33.79 (define @t92 () (not @t28)) % 33.49/33.79 (define @t93 () (or @t92 @t91 @t86)) % 33.49/33.79 (define @t94 () (tptp.sdtasdt0 @t70 tptp.xl)) % 33.49/33.79 (define @t95 () (tptp.sdtasdt0 @t71 tptp.xl)) % 33.49/33.79 (define @t96 () (tptp.sdtlseqdt0 @t95 @t94)) % 33.49/33.79 (define @t97 () (not (= @t95 @t94))) % 33.49/33.79 (define @t98 () (tptp.sdtasdt0 tptp.xl @t70)) % 33.49/33.79 (define @t99 () (tptp.sdtasdt0 tptp.xl @t71)) % 33.49/33.79 (define @t100 () (tptp.sdtlseqdt0 @t99 @t98)) % 33.49/33.79 (define @t101 () (not (= @t99 @t98))) % 33.49/33.79 (define @t102 () (and @t101 @t100 @t97 @t96)) % 33.49/33.79 (define @t103 () (tptp.sdtlseqdt0 @t71 @t70)) % 33.49/33.79 (define @t104 () (not @t103)) % 33.49/33.79 (define @t105 () (tptp.aNaturalNumber0 @t70)) % 33.49/33.79 (define @t106 () (not @t105)) % 33.49/33.79 (define @t107 () (tptp.aNaturalNumber0 @t71)) % 33.49/33.79 (define @t108 () (not @t107)) % 33.49/33.79 (define @t109 () (not @t65)) % 33.49/33.79 (define @t110 () (= @t71 @t70)) % 33.49/33.79 (define @t111 () (or @t109 @t108 @t106 @t69 @t110 @t104 @t102)) % 33.49/33.79 (define @t112 () (forall @t17 @t88)) % 33.49/33.79 (define @t113 () (not (= @t98 @t99))) % 33.49/33.79 (define @t114 () (and @t113 @t100 @t97 @t96)) % 33.49/33.79 (define @t115 () (= @t70 @t71)) % 33.49/33.79 (define @t116 () (= tptp.sz00 tptp.xl)) % 33.49/33.79 (define @t117 () (or @t109 @t108 @t106 @t116 @t115 @t104 @t114)) % 33.49/33.79 (define @t118 () (@list false)) % 33.49/33.79 (define @t119 () (and @t45 @t34)) % 33.49/33.79 (define @t120 () (or @t78 @t77 @t32 @t119)) % 33.49/33.79 (define @t121 () (or @t32 @t119)) % 33.49/33.79 (define @t122 () (tptp.sdtlseqdt0 @t70 @t71)) % 33.49/33.79 (define @t123 () (not @t110)) % 33.49/33.79 (define @t124 () (and @t123 @t122)) % 33.49/33.79 (define @t125 () (or @t108 @t106 @t103 @t124)) % 33.49/33.79 (define @t126 () (forall @t9 @t120)) % 33.49/33.79 (define @t127 () (not @t115)) % 33.49/33.79 (define @t128 () (and @t127 @t122)) % 33.49/33.79 (define @t129 () (or @t108 @t106 @t103 @t128)) % 33.49/33.79 (define @t130 () (not @t128)) % 33.49/33.79 (define @t131 () (@var "BOUND_VARIABLE_7934" $$unsorted)) % 33.49/33.79 (define @t132 () (and (tptp.aNaturalNumber0 @t131) (= @t4 (tptp.sdtasdt0 @t1 @t131)))) % 33.49/33.79 (define @t133 () (= @t132 (= @t131 @t55))) % 33.49/33.79 (define @t134 () (not @t54)) % 33.49/33.79 (define @t135 () (or @t78 @t77 @t27 @t134 @t133)) % 33.49/33.79 (define @t136 () (@list @t1 @t4 @t131)) % 33.49/33.79 (define @t137 () (forall @t136 @t135)) % 33.49/33.79 (define @t138 () (@list @t131)) % 33.49/33.79 (define @t139 () (forall @t138 @t135)) % 33.49/33.79 (define @t140 () (forall @t138 @t133)) % 33.49/33.79 (define @t141 () (or @t78 @t77 @t27 @t134 @t140)) % 33.49/33.79 (define @t142 () (forall @t31 (= @t53 @t56))) % 33.49/33.79 (define @t143 () (or @t78 @t77 @t27 @t134 @t142)) % 33.49/33.79 (define @t144 () (or @t27 @t134 @t142)) % 33.49/33.79 (define @t145 () (=> @t58 @t142)) % 33.49/33.79 (define @t146 () (= @t66 @t99)) % 33.49/33.79 (define @t147 () (and @t107 @t146)) % 33.49/33.79 (define @t148 () (= @t71 @t71)) % 33.49/33.79 (define @t149 () (not @t67)) % 33.49/33.79 (define @t150 () (not @t82)) % 33.49/33.79 (define @t151 () (or @t109 @t150 @t69 @t149 (= @t147 @t148))) % 33.49/33.79 (define @t152 () (forall @t136 (or @t78 @t77 @t27 @t134 (= @t132 (= @t55 @t131))))) % 33.49/33.79 (define @t153 () (or @t109 @t150 @t116 @t149 @t147)) % 33.49/33.79 (define @t154 () (@list @t152)) % 33.49/33.79 (define @t155 () (@list true false false false false)) % 33.49/33.79 (define @t156 () (not @t147)) % 33.49/33.79 (define @t157 () (@list @t147)) % 33.49/33.79 (define @t158 () (= tptp.xm @t98)) % 33.49/33.79 (define @t159 () (and @t105 @t158)) % 33.49/33.79 (define @t160 () (= @t70 @t70)) % 33.49/33.79 (define @t161 () (not @t68)) % 33.49/33.79 (define @t162 () (or @t109 @t84 @t69 @t161 (= @t159 @t160))) % 33.49/33.79 (define @t163 () (or @t109 @t84 @t116 @t161 @t159)) % 33.49/33.79 (define @t164 () (not @t159)) % 33.49/33.79 (define @t165 () (@list @t159)) % 33.49/33.79 (define @t166 () (and @t127 @t103)) % 33.49/33.79 (define @t167 () (or @t106 @t108 @t122 @t166)) % 33.49/33.79 (define @t168 () (not @t114)) % 33.49/33.79 (define @t169 () (@list @t114)) % 33.49/33.79 (define @t170 () (= tptp.xm @t66)) % 33.49/33.79 (define @t171 () (tptp.sdtlseqdt0 @t66 tptp.xm)) % 33.49/33.79 (define @t172 () (not @t171)) % 33.49/33.79 (define @t173 () (not @t72)) % 33.49/33.79 (define @t174 () (or @t84 @t150 @t173 @t172 @t170)) % 33.49/33.79 (assume @p1 (forall @t3 (=> @t2 true))) % 33.49/33.79 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 33.49/33.79 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 33.49/33.79 (assume @p4 @t10) % 33.49/33.79 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t11)))) % 33.49/33.79 (assume @p6 (forall @t9 (=> @t8 (= @t5 @t12)))) % 33.49/33.79 (assume @p7 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t5 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 33.49/33.79 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 33.49/33.79 (assume @p9 (forall @t9 (=> @t8 (= @t11 @t18)))) % 33.49/33.79 (assume @p10 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t11 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 33.49/33.79 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 33.49/33.79 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 33.49/33.79 (assume @p13 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t11 @t20)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t18 @t19)))))) % 33.49/33.79 (assume @p14 (forall @t17 (=> @t16 (=> (or (= @t5 @t23) (= @t12 @t22)) @t21)))) % 33.49/33.79 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> @t26 (=> (or @t25 @t24) @t21))))))) % 33.49/33.79 (assume @p16 (forall @t9 (=> @t8 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 33.49/33.79 (assume @p17 (forall @t9 (=> @t8 (=> (= @t11 tptp.sz00) (or @t27 @t29))))) % 33.49/33.79 (assume @p18 (forall @t9 (=> @t8 (= @t32 (exists @t31 @t30))))) % 33.49/33.79 (assume @p19 (forall @t9 (=> @t8 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 33.49/33.79 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 33.49/33.79 (assume @p21 @t37) % 33.49/33.79 (assume @p22 (forall @t17 (=> @t16 (=> (and @t32 @t38) (tptp.sdtlseqdt0 @t1 @t13))))) % 33.49/33.79 (assume @p23 @t43) % 33.49/33.79 (assume @p24 (forall @t9 (=> @t8 (=> @t46 (forall @t31 (=> @t15 (and (not (= @t22 @t44)) (tptp.sdtlseqdt0 @t22 @t44) (not (= @t23 @t14)) (tptp.sdtlseqdt0 @t23 @t14)))))))) % 33.49/33.79 (assume @p25 @t51) % 33.49/33.79 (assume @p26 (forall @t3 (=> @t2 (or @t27 (= @t1 tptp.sz10) (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 33.49/33.79 (assume @p27 (forall @t9 (=> @t8 (=> @t28 (tptp.sdtlseqdt0 @t4 @t18))))) % 33.49/33.79 (assume @p28 (forall @t9 (=> @t8 (=> @t52 true)))) % 33.49/33.79 (assume @p29 (forall @t9 (=> @t8 (=> @t46 @t52)))) % 33.49/33.79 (assume @p30 (forall @t9 (=> @t8 (= @t54 (exists @t31 @t53))))) % 33.49/33.79 (assume @p31 @t61) % 33.49/33.79 (assume @p32 (forall @t17 (=> @t16 (=> (and @t54 (tptp.doDivides0 @t4 @t13)) @t62)))) % 33.49/33.79 (assume @p33 (forall @t17 (=> @t16 (=> (and @t54 @t62) (tptp.doDivides0 @t1 @t14))))) % 33.49/33.79 (assume @p34 (and @t65 @t64 @t63)) % 33.49/33.79 (assume @p35 (and @t68 @t67)) % 33.49/33.79 (assume @p36 (not @t69)) % 33.49/33.79 (assume @p37 (= tptp.xp @t70)) % 33.49/33.79 (assume @p38 (= tptp.xq @t71)) % 33.49/33.79 (assume @p39 @t72) % 33.49/33.79 (assume @p40 @t74) % 33.49/33.79 (assume @p41 true) % 33.49/33.79 (step @p42 :rule and_elim :premises (@p34) :args (1)) % 33.49/33.79 (step @p43 :rule aci_norm :args ((= (or @t80 @t79) (or @t78 @t77 @t76 @t75 @t33)))) % 33.49/33.79 (step @p44 :rule aci_norm :args ((= (or (or @t76 @t75) @t33) @t79))) % 33.49/33.79 (step @p45 :rule refl :args (@t33)) % 33.49/33.79 (step @p46 :rule bool-and-de-morgan :args (@t32 @t34 true)) % 33.49/33.79 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or (not @t35) @t33))) % 33.49/33.79 (step @p48 :rule trans :premises (@p47 @p44)) % 33.49/33.79 (step @p49 :rule bool-impl-elim :args (@t35 @t33)) % 33.49/33.79 (step @p50 :rule trans :premises (@p49 @p48)) % 33.49/33.79 (step @p51 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 33.49/33.79 (step @p52 :rule nary_cong :premises (@p51 @p50) :args ((or @t81 @t36))) % 33.49/33.79 (step @p53 :rule trans :premises (@p52 @p43)) % 33.49/33.79 (step @p54 :rule bool-impl-elim :args (@t8 @t36)) % 33.49/33.79 (step @p55 :rule trans :premises (@p54 @p53)) % 33.49/33.79 (step @p56 :rule cong :premises (@p55) :args (@t37)) % 33.49/33.79 (step @p57 :rule eq_resolve :premises (@p21 @p56)) % 33.49/33.79 (step @p58 :rule instantiate :premises (@p57) :args ((@list tptp.xm @t66))) % 33.49/33.79 (step @p59 :rule aci_norm :args ((= (or @t80 @t6) (or @t78 @t77 @t6)))) % 33.49/33.79 (step @p60 :rule refl :args (@t6)) % 33.49/33.79 (step @p61 :rule nary_cong :premises (@p51 @p60) :args ((or @t81 @t6))) % 33.49/33.79 (step @p62 :rule trans :premises (@p61 @p59)) % 33.49/33.79 (step @p63 :rule bool-impl-elim :args (@t8 @t6)) % 33.49/33.79 (step @p64 :rule trans :premises (@p63 @p62)) % 33.49/33.79 (step @p65 :rule cong :premises (@p64) :args (@t10)) % 33.49/33.79 (step @p66 :rule eq_resolve :premises (@p4 @p65)) % 33.49/33.79 (step @p67 :rule instantiate :premises (@p66) :args ((@list tptp.xm tptp.xn))) % 33.49/33.79 (step @p68 :rule and_elim :premises (@p34) :args (2)) % 33.49/33.79 (step @p69 :rule cnf_or_pos :args (@t85)) % 33.49/33.79 (step @p70 :rule reordering :premises (@p69) :args ((or @t84 @t83 @t82 (not @t85)))) % 33.49/33.79 (step @p71 :rule chain_m_resolution :premises (@p70 @p42 @p68 @p67) :args (@t82 (@list false false false) (@list @t64 @t63 @t85))) % 33.49/33.79 (step @p72 :rule aci_norm :args ((= (or @t90 @t89) @t88))) % 33.49/33.79 (step @p73 :rule aci_norm :args ((= (or (or @t27 @t21 @t86) @t47) @t89))) % 33.49/33.79 (step @p74 :rule refl :args (@t47)) % 33.49/33.79 (step @p75 :rule refl :args (@t86)) % 33.49/33.79 (step @p76 :rule bool-double-not-elim :args (@t21)) % 33.49/33.79 (step @p77 :rule bool-double-not-elim :args (@t27)) % 33.49/33.79 (step @p78 :rule nary_cong :premises (@p77 @p76 @p75) :args (@t93)) % 33.49/33.79 (step @p79 :rule aci_norm :args ((= (or @t92 (or @t91 @t86)) @t93))) % 33.49/33.79 (step @p80 :rule trans :premises (@p79 @p78)) % 33.49/33.79 (step @p81 :rule bool-and-de-morgan :args (@t48 @t38 true)) % 33.49/33.79 (step @p82 :rule refl :args (@t92)) % 33.49/33.79 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t92 (not (and @t48 @t38))))) % 33.49/33.79 (step @p84 :rule bool-and-de-morgan :args (@t28 @t48 (and @t38))) % 33.49/33.79 (step @p85 :rule trans :premises (@p84 @p83)) % 33.49/33.79 (step @p86 :rule trans :premises (@p85 @p80)) % 33.49/33.79 (step @p87 :rule nary_cong :premises (@p86 @p74) :args ((or (not @t49) @t47))) % 33.49/33.79 (step @p88 :rule trans :premises (@p87 @p73)) % 33.49/33.79 (step @p89 :rule bool-impl-elim :args (@t49 @t47)) % 33.49/33.79 (step @p90 :rule trans :premises (@p89 @p88)) % 33.49/33.79 (step @p91 :rule aci_norm :args ((= (or @t78 (or @t77 @t87)) @t90))) % 33.49/33.79 (step @p92 :rule bool-and-de-morgan :args (@t7 @t15 true)) % 33.49/33.79 (step @p93 :rule refl :args (@t78)) % 33.49/33.79 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or @t78 (not @t26)))) % 33.49/33.79 (step @p95 :rule bool-and-de-morgan :args (@t2 @t7 (and @t15))) % 33.49/33.79 (step @p96 :rule trans :premises (@p95 @p94)) % 33.49/33.79 (step @p97 :rule trans :premises (@p96 @p91)) % 33.49/33.79 (step @p98 :rule nary_cong :premises (@p97 @p90) :args ((or (not @t16) @t50))) % 33.49/33.79 (step @p99 :rule trans :premises (@p98 @p72)) % 33.49/33.79 (step @p100 :rule bool-impl-elim :args (@t16 @t50)) % 33.49/33.79 (step @p101 :rule trans :premises (@p100 @p99)) % 33.49/33.79 (step @p102 :rule cong :premises (@p101) :args (@t51)) % 33.49/33.79 (step @p103 :rule eq_resolve :premises (@p25 @p102)) % 33.49/33.79 (step @p104 :rule refl :args (@t96)) % 33.49/33.79 (step @p105 :rule refl :args (@t97)) % 33.49/33.79 (step @p106 :rule refl :args (@t100)) % 33.49/33.79 (step @p107 :rule eq-symm :args (@t99 @t98)) % 33.49/33.79 (step @p108 :rule cong :premises (@p107) :args (@t101)) % 33.49/33.79 (step @p109 :rule nary_cong :premises (@p108 @p106 @p105 @p104) :args (@t102)) % 33.49/33.79 (step @p110 :rule refl :args (@t104)) % 33.49/33.79 (step @p111 :rule eq-symm :args (@t71 @t70)) % 33.49/33.79 (step @p112 :rule eq-symm :args (tptp.xl tptp.sz00)) % 33.49/33.79 (step @p113 :rule refl :args (@t106)) % 33.49/33.79 (step @p114 :rule refl :args (@t108)) % 33.49/33.79 (step @p115 :rule refl :args (@t109)) % 33.49/33.79 (step @p116 :rule nary_cong :premises (@p115 @p114 @p113 @p112 @p111 @p110 @p109) :args (@t111)) % 33.49/33.79 (step @p117 :rule refl :args (@t112)) % 33.49/33.79 (step @p118 :rule cong :premises (@p117 @p116) :args ((=> @t112 @t111))) % 33.49/33.79 (assume-push @p302 @t112) % 33.49/33.79 (step @p120 :rule instantiate :premises (@p103) :args ((@list tptp.xl @t71 @t70))) % 33.49/33.79 (step-pop @p303 :rule scope :premises (@p120)) % 33.49/33.79 (step @p121 :rule process_scope :premises (@p303) :args (@t111)) % 33.49/33.79 (step @p123 :rule eq_resolve :premises (@p121 @p118)) % 33.49/33.79 (step @p124 :rule implies_elim :premises (@p123)) % 33.49/33.79 (step @p125 :rule chain_m_resolution :premises (@p124 @p103) :args (@t117 @t118 (@list @t112))) % 33.49/33.79 (step @p126 :rule aci_norm :args ((= (or @t80 @t121) @t120))) % 33.49/33.79 (step @p127 :rule refl :args (@t121)) % 33.49/33.79 (step @p128 :rule nary_cong :premises (@p51 @p127) :args ((or @t81 @t121))) % 33.49/33.79 (step @p129 :rule trans :premises (@p128 @p126)) % 33.49/33.79 (step @p130 :rule bool-impl-elim :args (@t8 @t121)) % 33.49/33.79 (step @p131 :rule trans :premises (@p130 @p129)) % 33.49/33.79 (step @p132 :rule cong :premises (@p131) :args ((forall @t9 (=> @t8 @t121)))) % 33.49/33.79 (step @p133 :rule refl :args (@t34)) % 33.49/33.79 (step @p134 :rule eq-symm :args (@t4 @t1)) % 33.49/33.79 (step @p135 :rule cong :premises (@p134) :args (@t39)) % 33.49/33.79 (step @p136 :rule nary_cong :premises (@p135 @p133) :args (@t40)) % 33.49/33.79 (step @p137 :rule refl :args (@t32)) % 33.49/33.79 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t41)) % 33.49/33.79 (step @p139 :rule refl :args (@t8)) % 33.49/33.79 (step @p140 :rule cong :premises (@p139 @p138) :args (@t42)) % 33.49/33.79 (step @p141 :rule cong :premises (@p140) :args (@t43)) % 33.49/33.79 (step @p142 :rule trans :premises (@p141 @p132)) % 33.49/33.79 (step @p143 :rule eq_resolve :premises (@p23 @p142)) % 33.49/33.79 (step @p144 :rule refl :args (@t122)) % 33.49/33.79 (step @p145 :rule cong :premises (@p111) :args (@t123)) % 33.49/33.79 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t124)) % 33.49/33.79 (step @p147 :rule refl :args (@t103)) % 33.49/33.79 (step @p148 :rule nary_cong :premises (@p114 @p113 @p147 @p146) :args (@t125)) % 33.49/33.79 (step @p149 :rule refl :args (@t126)) % 33.49/33.79 (step @p150 :rule cong :premises (@p149 @p148) :args ((=> @t126 @t125))) % 33.49/33.79 (assume-push @p304 @t126) % 33.49/33.79 (step @p152 :rule instantiate :premises (@p143) :args ((@list @t71 @t70))) % 33.49/33.79 (step-pop @p305 :rule scope :premises (@p152)) % 33.49/33.79 (step @p153 :rule process_scope :premises (@p305) :args (@t125)) % 33.49/33.79 (step @p155 :rule eq_resolve :premises (@p153 @p150)) % 33.49/33.79 (step @p156 :rule implies_elim :premises (@p155)) % 33.49/33.79 (step @p157 :rule chain_m_resolution :premises (@p156 @p143) :args (@t129 @t118 (@list @t126))) % 33.49/33.79 (step @p158 :rule cong :premises (@p37 @p38) :args (@t73)) % 33.49/33.79 (step @p159 :rule cong :premises (@p158) :args (@t74)) % 33.49/33.79 (step @p160 :rule eq_resolve :premises (@p40 @p159)) % 33.49/33.79 (step @p161 :rule cnf_and_pos :args (@t128 1)) % 33.49/33.79 (step @p162 :rule reordering :premises (@p161) :args ((or @t122 @t130))) % 33.49/33.79 (step @p163 :rule chain_m_resolution :premises (@p162 @p160) :args (@t130 (@list true) (@list @t122))) % 33.49/33.79 (step @p164 :rule eq-symm :args (@t131 @t55)) % 33.49/33.79 (step @p165 :rule refl :args (@t132)) % 33.49/33.79 (step @p166 :rule cong :premises (@p165 @p164) :args (@t133)) % 33.49/33.79 (step @p167 :rule refl :args (@t134)) % 33.49/33.79 (step @p168 :rule refl :args (@t27)) % 33.49/33.79 (step @p169 :rule refl :args (@t77)) % 33.49/33.79 (step @p170 :rule refl :args (@t78)) % 33.49/33.79 (step @p171 :rule nary_cong :premises (@p170 @p169 @p168 @p167 @p166) :args (@t135)) % 33.49/33.79 (step @p172 :rule cong :premises (@p171) :args (@t137)) % 33.49/33.79 (step @p173 :rule quant-merge-prenex :args ((= (forall @t9 @t139) @t137))) % 33.49/33.79 (step @p174 :rule alpha_equiv :args (@t140 (@list @t131) (@list @t13))) % 33.49/33.79 (step @p175 :rule refl :args (@t134)) % 33.49/33.79 (step @p176 :rule refl :args (@t27)) % 33.49/33.79 (step @p177 :rule refl :args (@t77)) % 33.49/33.79 (step @p178 :rule nary_cong :premises (@p93 @p177 @p176 @p175 @p174) :args (@t141)) % 33.49/33.79 (step @p179 :rule quant-miniscope-or :args ((= @t139 @t141))) % 33.49/33.79 (step @p180 :rule trans :premises (@p179 @p178)) % 33.49/33.79 (step @p181 :rule symm :premises (@p180)) % 33.49/33.79 (step @p182 :rule cong :premises (@p181) :args ((forall @t9 @t143))) % 33.49/33.79 (step @p183 :rule trans :premises (@p182 @p173)) % 33.49/33.79 (step @p184 :rule trans :premises (@p183 @p172)) % 33.49/33.79 (step @p185 :rule aci_norm :args ((= (or @t80 @t144) @t143))) % 33.49/33.79 (step @p186 :rule aci_norm :args ((= (or (or @t27 @t134) @t142) @t144))) % 33.49/33.79 (step @p187 :rule refl :args (@t142)) % 33.49/33.79 (step @p188 :rule nary_cong :premises (@p77 @p175) :args ((or @t92 @t134))) % 33.49/33.79 (step @p189 :rule bool-and-de-morgan :args (@t28 @t54 true)) % 33.49/33.79 (step @p190 :rule trans :premises (@p189 @p188)) % 33.49/33.79 (step @p191 :rule nary_cong :premises (@p190 @p187) :args ((or (not @t58) @t142))) % 33.49/33.79 (step @p192 :rule trans :premises (@p191 @p186)) % 33.49/33.79 (step @p193 :rule bool-impl-elim :args (@t58 @t142)) % 33.49/33.79 (step @p194 :rule trans :premises (@p193 @p192)) % 33.49/33.79 (step @p195 :rule nary_cong :premises (@p51 @p194) :args ((or @t81 @t145))) % 33.49/33.79 (step @p196 :rule trans :premises (@p195 @p185)) % 33.49/33.79 (step @p197 :rule bool-impl-elim :args (@t8 @t145)) % 33.49/33.79 (step @p198 :rule trans :premises (@p197 @p196)) % 33.49/33.79 (step @p199 :rule cong :premises (@p198) :args ((forall @t9 (=> @t8 @t145)))) % 33.49/33.79 (step @p200 :rule trans :premises (@p199 @p184)) % 33.49/33.79 (step @p201 :rule eq-symm :args (@t56 @t53)) % 33.49/33.79 (step @p202 :rule cong :premises (@p201) :args (@t57)) % 33.49/33.79 (step @p203 :rule refl :args (@t58)) % 33.49/33.79 (step @p204 :rule cong :premises (@p203 @p202) :args (@t59)) % 33.49/33.79 (step @p205 :rule cong :premises (@p139 @p204) :args (@t60)) % 33.49/33.79 (step @p206 :rule cong :premises (@p205) :args (@t61)) % 33.49/33.79 (step @p207 :rule trans :premises (@p206 @p200)) % 33.49/33.79 (step @p208 :rule eq_resolve :premises (@p31 @p207)) % 33.49/33.79 (step @p209 :rule bool-eq-true :args (@t147)) % 33.49/33.79 (step @p210 :rule eq-symm :args (true @t147)) % 33.49/33.79 (step @p211 :rule trans :premises (@p210 @p209)) % 33.49/33.79 (step @p212 :rule refl :args (@t147)) % 33.49/33.79 (step @p213 :rule eq-refl :args (@t71)) % 33.49/33.79 (step @p214 :rule cong :premises (@p213 @p212) :args ((= @t148 @t147))) % 33.49/33.79 (step @p215 :rule trans :premises (@p214 @p211)) % 33.49/33.79 (step @p216 :rule eq-symm :args (@t147 @t148)) % 33.49/33.79 (step @p217 :rule trans :premises (@p216 @p215)) % 33.49/33.79 (step @p218 :rule refl :args (@t149)) % 33.49/33.79 (step @p219 :rule refl :args (@t150)) % 33.49/33.79 (step @p220 :rule nary_cong :premises (@p115 @p219 @p112 @p218 @p217) :args (@t151)) % 33.49/33.79 (step @p221 :rule refl :args (@t152)) % 33.49/33.79 (step @p222 :rule cong :premises (@p221 @p220) :args ((=> @t152 @t151))) % 33.49/33.79 (assume-push @p306 @t152) % 33.49/33.79 (step @p224 :rule instantiate :premises (@p208) :args ((@list tptp.xl @t66 @t71))) % 33.49/33.79 (step-pop @p307 :rule scope :premises (@p224)) % 33.49/33.79 (step @p225 :rule process_scope :premises (@p307) :args (@t151)) % 33.49/33.79 (step @p227 :rule eq_resolve :premises (@p225 @p222)) % 33.49/33.79 (step @p228 :rule implies_elim :premises (@p227)) % 33.49/33.79 (step @p229 :rule chain_m_resolution :premises (@p228 @p208) :args (@t153 @t118 @t154)) % 33.49/33.79 (step @p230 :rule and_elim :premises (@p35) :args (1)) % 33.49/33.79 (step @p231 :rule and_elim :premises (@p34) :args (0)) % 33.49/33.79 (step @p232 :rule symm :premises (@p36)) % 33.49/33.79 (step @p233 :rule cnf_or_pos :args (@t153)) % 33.49/33.79 (step @p234 :rule reordering :premises (@p233) :args ((or @t116 @t109 @t149 @t150 @t147 (not @t153)))) % 33.49/33.79 (step @p235 :rule chain_m_resolution :premises (@p234 @p232 @p231 @p230 @p71 @p229) :args (@t147 @t155 (@list @t116 @t65 @t67 @t82 @t153))) % 33.49/33.79 (step @p236 :rule cnf_and_pos :args (@t147 0)) % 33.49/33.79 (step @p237 :rule reordering :premises (@p236) :args ((or @t107 @t156))) % 33.49/33.79 (step @p238 :rule chain_m_resolution :premises (@p237 @p235) :args (@t107 @t118 @t157)) % 33.49/33.79 (step @p239 :rule bool-eq-true :args (@t159)) % 33.49/33.79 (step @p240 :rule eq-symm :args (true @t159)) % 33.49/33.79 (step @p241 :rule trans :premises (@p240 @p239)) % 33.49/33.79 (step @p242 :rule refl :args (@t159)) % 33.49/33.79 (step @p243 :rule eq-refl :args (@t70)) % 33.49/33.79 (step @p244 :rule cong :premises (@p243 @p242) :args ((= @t160 @t159))) % 33.49/33.79 (step @p245 :rule trans :premises (@p244 @p241)) % 33.49/33.79 (step @p246 :rule eq-symm :args (@t159 @t160)) % 33.49/33.79 (step @p247 :rule trans :premises (@p246 @p245)) % 33.49/33.79 (step @p248 :rule refl :args (@t161)) % 33.49/33.79 (step @p249 :rule refl :args (@t84)) % 33.49/33.79 (step @p250 :rule nary_cong :premises (@p115 @p249 @p112 @p248 @p247) :args (@t162)) % 33.49/33.79 (step @p251 :rule cong :premises (@p221 @p250) :args ((=> @t152 @t162))) % 33.49/33.79 (assume-push @p308 @t152) % 33.49/33.79 (step @p253 :rule instantiate :premises (@p208) :args ((@list tptp.xl tptp.xm @t70))) % 33.49/33.79 (step-pop @p309 :rule scope :premises (@p253)) % 33.49/33.79 (step @p254 :rule process_scope :premises (@p309) :args (@t162)) % 33.49/33.79 (step @p256 :rule eq_resolve :premises (@p254 @p251)) % 33.49/33.79 (step @p257 :rule implies_elim :premises (@p256)) % 33.49/33.79 (step @p258 :rule chain_m_resolution :premises (@p257 @p208) :args (@t163 @t118 @t154)) % 33.49/33.79 (step @p259 :rule and_elim :premises (@p35) :args (0)) % 33.49/33.79 (step @p260 :rule cnf_or_pos :args (@t163)) % 33.49/33.79 (step @p261 :rule reordering :premises (@p260) :args ((or @t116 @t109 @t84 @t161 @t159 (not @t163)))) % 33.49/33.79 (step @p262 :rule chain_m_resolution :premises (@p261 @p232 @p231 @p42 @p259 @p258) :args (@t159 @t155 (@list @t116 @t65 @t64 @t68 @t163))) % 33.49/33.79 (step @p263 :rule cnf_and_pos :args (@t159 0)) % 33.49/33.79 (step @p264 :rule reordering :premises (@p263) :args ((or @t105 @t164))) % 33.49/33.79 (step @p265 :rule chain_m_resolution :premises (@p264 @p262) :args (@t105 @t118 @t165)) % 33.49/33.79 (step @p266 :rule cnf_or_pos :args (@t129)) % 33.49/33.79 (step @p267 :rule reordering :premises (@p266) :args ((or @t106 @t108 @t103 @t128 (not @t129)))) % 33.49/33.79 (step @p268 :rule chain_m_resolution :premises (@p267 @p265 @p238 @p163 @p157) :args (@t103 (@list false false true false) (@list @t105 @t107 @t128 @t129))) % 33.49/33.79 (step @p269 :rule instantiate :premises (@p143) :args ((@list @t70 @t71))) % 33.49/33.79 (step @p270 :rule cnf_or_pos :args (@t167)) % 33.49/33.79 (step @p271 :rule reordering :premises (@p270) :args ((or @t122 @t106 @t108 @t166 (not @t167)))) % 33.49/33.79 (step @p272 :rule chain_m_resolution :premises (@p271 @p160 @p265 @p238 @p269) :args (@t166 (@list true false false false) (@list @t122 @t105 @t107 @t167))) % 33.49/33.79 (step @p273 :rule cnf_and_pos :args (@t166 0)) % 33.49/33.79 (step @p274 :rule reordering :premises (@p273) :args ((or @t127 (not @t166)))) % 33.49/33.79 (step @p275 :rule chain_m_resolution :premises (@p274 @p272) :args (@t127 @t118 (@list @t166))) % 33.49/33.79 (step @p276 :rule cnf_or_pos :args (@t117)) % 33.49/33.79 (step @p277 :rule reordering :premises (@p276) :args ((or @t116 @t109 @t106 @t108 @t115 @t104 @t114 (not @t117)))) % 33.49/33.80 (step @p278 :rule chain_m_resolution :premises (@p277 @p232 @p231 @p265 @p238 @p275 @p268 @p125) :args (@t114 (@list true false false false true false false) (@list @t116 @t65 @t105 @t107 @t115 @t103 @t117))) % 33.49/33.80 (step @p279 :rule cnf_and_pos :args (@t114 0)) % 33.49/33.80 (step @p280 :rule reordering :premises (@p279) :args ((or @t113 @t168))) % 33.49/33.80 (step @p281 :rule chain_m_resolution :premises (@p280 @p278) :args (@t113 @t118 @t169)) % 33.49/33.80 (step @p282 :rule false_intro :premises (@p281)) % 33.49/33.80 (step @p283 :rule cnf_and_pos :args (@t147 1)) % 33.49/33.80 (step @p284 :rule reordering :premises (@p283) :args ((or @t146 @t156))) % 33.49/33.80 (step @p285 :rule chain_m_resolution :premises (@p284 @p235) :args (@t146 @t118 @t157)) % 33.49/33.80 (step @p286 :rule cnf_and_pos :args (@t159 1)) % 33.49/33.80 (step @p287 :rule reordering :premises (@p286) :args ((or @t158 @t164))) % 33.49/33.80 (step @p288 :rule chain_m_resolution :premises (@p287 @p262) :args (@t158 @t118 @t165)) % 33.49/33.80 (step @p289 :rule cong :premises (@p288 @p285) :args (@t170)) % 33.49/33.80 (step @p290 :rule trans :premises (@p289 @p282)) % 33.49/33.80 (step @p291 :rule false_elim :premises (@p290)) % 33.49/33.80 (step @p292 :rule cnf_and_pos :args (@t114 1)) % 33.49/33.80 (step @p293 :rule reordering :premises (@p292) :args ((or @t100 @t168))) % 33.49/33.80 (step @p294 :rule chain_m_resolution :premises (@p293 @p278) :args (@t100 @t118 @t169)) % 33.49/33.80 (step @p295 :rule true_intro :premises (@p294)) % 33.49/33.80 (step @p296 :rule cong :premises (@p285 @p288) :args (@t171)) % 33.49/33.80 (step @p297 :rule trans :premises (@p296 @p295)) % 33.49/33.80 (step @p298 :rule true_elim :premises (@p297)) % 33.49/33.80 (step @p299 :rule cnf_or_pos :args (@t174)) % 33.49/33.80 (step @p300 :rule reordering :premises (@p299) :args ((or @t84 @t173 @t150 @t172 @t170 (not @t174)))) % 33.49/33.80 (step @p301 false :rule chain_m_resolution :premises (@p300 @p298 @p291 @p71 @p58 @p39 @p42) :args (false (@list false true false false false false) (@list @t171 @t170 @t82 @t174 @t72 @t64))) % 33.49/33.80 ) % 33.49/33.80 % SZS output end Proof % 33.49/33.80 % cvc5 exiting %------------------------------------------------------------------------------