%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM500+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 : n026.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 08:39:37 AM UTC 2026 % Result : Theorem 16.85s 17.09s % Output : Proof 16.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM500+1 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n026.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 11:24:40 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 16.85/17.09 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.85/17.09 --- Run --no-e-matching --full-saturate-quant at 6... % 16.85/17.09 % SZS status Theorem % 16.85/17.09 % SZS output start Proof % 16.85/17.09 ( % 16.85/17.09 (declare-sort $$unsorted 0) % 16.85/17.09 (declare-const tptp.xk $$unsorted) % 16.85/17.09 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 16.85/17.09 (declare-const tptp.xm $$unsorted) % 16.85/17.09 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.85/17.09 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 16.85/17.09 (declare-const tptp.xn $$unsorted) % 16.85/17.09 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 16.85/17.09 (declare-const tptp.sz00 $$unsorted) % 16.85/17.09 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.85/17.09 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.85/17.09 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.85/17.09 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 16.85/17.09 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 16.85/17.09 (declare-const tptp.sz10 $$unsorted) % 16.85/17.09 (declare-const tptp.xp $$unsorted) % 16.85/17.09 (define @t1 () (@var "W0" $$unsorted)) % 16.85/17.09 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 16.85/17.09 (define @t3 () (@list @t1)) % 16.85/17.09 (define @t4 () (@var "W1" $$unsorted)) % 16.85/17.09 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 16.85/17.09 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 16.85/17.09 (define @t7 () (and @t2 @t6)) % 16.85/17.09 (define @t8 () (@list @t1 @t4)) % 16.85/17.09 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 16.85/17.09 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 16.85/17.09 (define @t11 () (forall @t8 (=> @t7 @t10))) % 16.85/17.09 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 16.85/17.09 (define @t13 () (@var "W2" $$unsorted)) % 16.85/17.09 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 16.85/17.09 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 16.85/17.09 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 16.85/17.09 (define @t17 () (and @t2 @t6 @t16)) % 16.85/17.09 (define @t18 () (@list @t1 @t4 @t13)) % 16.85/17.09 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 16.85/17.09 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 16.85/17.09 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 16.85/17.09 (define @t22 () (= @t4 @t13)) % 16.85/17.09 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 16.85/17.09 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 16.85/17.09 (define @t25 () (= @t19 @t20)) % 16.85/17.09 (define @t26 () (= @t9 @t21)) % 16.85/17.09 (define @t27 () (= @t1 tptp.sz00)) % 16.85/17.09 (define @t28 () (not @t27)) % 16.85/17.09 (define @t29 () (= @t4 tptp.sz00)) % 16.85/17.09 (define @t30 () (and @t16 (= @t24 @t4))) % 16.85/17.09 (define @t31 () (@list @t13)) % 16.85/17.09 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 16.85/17.09 (define @t33 () (= @t1 @t4)) % 16.85/17.09 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 16.85/17.09 (define @t35 () (tptp.sdtlseqdt0 @t4 @t13)) % 16.85/17.09 (define @t36 () (= @t4 @t1)) % 16.85/17.09 (define @t37 () (tptp.sdtpldt0 @t13 @t4)) % 16.85/17.09 (define @t38 () (and (not @t33) @t32)) % 16.85/17.09 (define @t39 () (= @t1 tptp.sz10)) % 16.85/17.09 (define @t40 () (tptp.iLess0 @t1 @t4)) % 16.85/17.09 (define @t41 () (and @t16 (= @t4 @t21))) % 16.85/17.09 (define @t42 () (tptp.doDivides0 @t1 @t4)) % 16.85/17.09 (define @t43 () (tptp.sdtsldt0 @t4 @t1)) % 16.85/17.09 (define @t44 () (= @t13 @t43)) % 16.85/17.09 (define @t45 () (forall @t31 (= @t44 @t41))) % 16.85/17.09 (define @t46 () (and @t28 @t42)) % 16.85/17.09 (define @t47 () (=> @t46 @t45)) % 16.85/17.09 (define @t48 () (=> @t7 @t47)) % 16.85/17.09 (define @t49 () (forall @t8 @t48)) % 16.85/17.09 (define @t50 () (tptp.doDivides0 @t1 @t13)) % 16.85/17.09 (define @t51 () (tptp.doDivides0 @t1 @t14)) % 16.85/17.09 (define @t52 () (or (= @t4 tptp.sz10) @t36)) % 16.85/17.09 (define @t53 () (tptp.doDivides0 @t4 @t1)) % 16.85/17.09 (define @t54 () (and @t6 @t53)) % 16.85/17.09 (define @t55 () (=> @t54 @t52)) % 16.85/17.09 (define @t56 () (@list @t4)) % 16.85/17.09 (define @t57 () (forall @t56 @t55)) % 16.85/17.09 (define @t58 () (not @t39)) % 16.85/17.09 (define @t59 () (and @t28 @t58 @t57)) % 16.85/17.09 (define @t60 () (tptp.isPrime0 @t1)) % 16.85/17.09 (define @t61 () (= @t60 @t59)) % 16.85/17.09 (define @t62 () (=> @t2 @t61)) % 16.85/17.09 (define @t63 () (forall @t3 @t62)) % 16.85/17.09 (define @t64 () (tptp.isPrime0 @t4)) % 16.85/17.09 (define @t65 () (and @t6 @t53 @t64)) % 16.85/17.09 (define @t66 () (exists @t56 @t65)) % 16.85/17.09 (define @t67 () (and @t2 @t28 @t58)) % 16.85/17.09 (define @t68 () (=> @t67 @t66)) % 16.85/17.09 (define @t69 () (forall @t3 @t68)) % 16.85/17.09 (define @t70 () (tptp.aNaturalNumber0 tptp.xp)) % 16.85/17.09 (define @t71 () (tptp.aNaturalNumber0 tptp.xm)) % 16.85/17.09 (define @t72 () (tptp.aNaturalNumber0 tptp.xn)) % 16.85/17.09 (define @t73 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 16.85/17.09 (define @t74 () (tptp.doDivides0 tptp.xp @t73)) % 16.85/17.09 (define @t75 () (tptp.isPrime0 tptp.xp)) % 16.85/17.09 (define @t76 () (tptp.sdtsldt0 @t73 tptp.xp)) % 16.85/17.09 (define @t77 () (= tptp.xk tptp.sz10)) % 16.85/17.09 (define @t78 () (= tptp.xk tptp.sz00)) % 16.85/17.09 (define @t79 () (or @t78 @t77)) % 16.85/17.09 (define @t80 () (not @t79)) % 16.85/17.09 (define @t81 () (tptp.doDivides0 @t1 tptp.xk)) % 16.85/17.09 (define @t82 () (and @t2 @t81 @t60)) % 16.85/17.09 (define @t83 () (exists @t3 @t82)) % 16.85/17.09 (define @t84 () (not @t83)) % 16.85/17.09 (define @t85 () (= tptp.sz10 tptp.xk)) % 16.85/17.09 (define @t86 () (= tptp.sz00 tptp.xk)) % 16.85/17.09 (define @t87 () (or @t86 @t85)) % 16.85/17.09 (define @t88 () (@var "BOUND_VARIABLE_8007" $$unsorted)) % 16.85/17.09 (define @t89 () (and (tptp.aNaturalNumber0 @t88) (= @t4 (tptp.sdtasdt0 @t1 @t88)))) % 16.85/17.09 (define @t90 () (= @t89 (= @t88 @t43))) % 16.85/17.09 (define @t91 () (not @t42)) % 16.85/17.09 (define @t92 () (not @t6)) % 16.85/17.09 (define @t93 () (not @t2)) % 16.85/17.09 (define @t94 () (or @t93 @t92 @t27 @t91 @t90)) % 16.85/17.09 (define @t95 () (@list @t1 @t4 @t88)) % 16.85/17.09 (define @t96 () (forall @t95 @t94)) % 16.85/17.09 (define @t97 () (@list @t88)) % 16.85/17.09 (define @t98 () (forall @t97 @t94)) % 16.85/17.09 (define @t99 () (forall @t97 @t90)) % 16.85/17.09 (define @t100 () (or @t93 @t92 @t27 @t91 @t99)) % 16.85/17.09 (define @t101 () (forall @t31 (= @t41 @t44))) % 16.85/17.09 (define @t102 () (or @t93 @t92 @t27 @t91 @t101)) % 16.85/17.09 (define @t103 () (or @t27 @t91 @t101)) % 16.85/17.09 (define @t104 () (or @t93 @t92)) % 16.85/17.09 (define @t105 () (not @t28)) % 16.85/17.09 (define @t106 () (=> @t46 @t101)) % 16.85/17.09 (define @t107 () (not @t7)) % 16.85/17.09 (define @t108 () (tptp.aNaturalNumber0 @t76)) % 16.85/17.09 (define @t109 () (and @t108 (= @t73 (tptp.sdtasdt0 tptp.xp @t76)))) % 16.85/17.09 (define @t110 () (= @t76 @t76)) % 16.85/17.09 (define @t111 () (not @t74)) % 16.85/17.09 (define @t112 () (tptp.aNaturalNumber0 @t73)) % 16.85/17.09 (define @t113 () (not @t112)) % 16.85/17.09 (define @t114 () (not @t70)) % 16.85/17.09 (define @t115 () (= tptp.xp tptp.sz00)) % 16.85/17.09 (define @t116 () (or @t114 @t113 @t115 @t111 (= @t109 @t110))) % 16.85/17.09 (define @t117 () (forall @t95 (or @t93 @t92 @t27 @t91 (= @t89 (= @t43 @t88))))) % 16.85/17.09 (define @t118 () (= tptp.sz00 tptp.xp)) % 16.85/17.09 (define @t119 () (or @t114 @t113 @t118 @t111 @t109)) % 16.85/17.09 (define @t120 () (@list false)) % 16.85/17.09 (define @t121 () (not @t71)) % 16.85/17.09 (define @t122 () (not @t72)) % 16.85/17.09 (define @t123 () (or @t122 @t121 @t112)) % 16.85/17.09 (define @t124 () (= tptp.sz10 @t4)) % 16.85/17.09 (define @t125 () (not @t53)) % 16.85/17.09 (define @t126 () (or @t92 @t125 @t124 @t33)) % 16.85/17.09 (define @t127 () (= @t60 (and @t28 @t58 (forall @t56 @t126)))) % 16.85/17.09 (define @t128 () (or @t124 @t33)) % 16.85/17.09 (define @t129 () (not (tptp.doDivides0 @t4 tptp.xp))) % 16.85/17.09 (define @t130 () (or @t92 @t129 @t124 (= tptp.xp @t4))) % 16.85/17.09 (define @t131 () (forall @t56 @t130)) % 16.85/17.09 (define @t132 () (not (= tptp.xp tptp.sz10))) % 16.85/17.09 (define @t133 () (not @t115)) % 16.85/17.09 (define @t134 () (and @t133 @t132 @t131)) % 16.85/17.09 (define @t135 () (= @t75 @t134)) % 16.85/17.09 (define @t136 () (or @t114 @t135)) % 16.85/17.09 (define @t137 () (forall @t3 (or @t93 @t127))) % 16.85/17.09 (define @t138 () (not @t118)) % 16.85/17.09 (define @t139 () (and @t138 (not (= tptp.sz10 tptp.xp)) (forall @t56 (or @t92 @t129 @t124 (= @t4 tptp.xp))))) % 16.85/17.09 (define @t140 () (= @t75 @t139)) % 16.85/17.09 (define @t141 () (or @t114 @t140)) % 16.85/17.09 (define @t142 () (@list false false)) % 16.85/17.09 (define @t143 () (not @t60)) % 16.85/17.09 (define @t144 () (not @t81)) % 16.85/17.09 (define @t145 () (or @t93 @t144 @t143)) % 16.85/17.09 (define @t146 () (forall @t3 @t145)) % 16.85/17.09 (define @t147 () (forall @t3 (not @t82))) % 16.85/17.09 (define @t148 () (not @t147)) % 16.85/17.09 (define @t149 () (forall @t3 (or @t93 (not (tptp.doDivides0 @t1 @t76)) @t143))) % 16.85/17.09 (define @t150 () (not @t64)) % 16.85/17.09 (define @t151 () (forall @t56 (or @t92 (not (tptp.doDivides0 @t4 @t76)) @t150))) % 16.85/17.09 (define @t152 () (or @t92 @t125 @t150)) % 16.85/17.09 (define @t153 () (not (forall @t56 @t152))) % 16.85/17.09 (define @t154 () (or @t93 @t27 @t39 @t153)) % 16.85/17.09 (define @t155 () (not @t58)) % 16.85/17.09 (define @t156 () (or @t93 @t105 @t155)) % 16.85/17.09 (define @t157 () (forall @t56 (not @t65))) % 16.85/17.09 (define @t158 () (not @t157)) % 16.85/17.09 (define @t159 () (not @t151)) % 16.85/17.09 (define @t160 () (not @t108)) % 16.85/17.09 (define @t161 () (or @t160 (= @t76 tptp.sz00) (= @t76 tptp.sz10) @t159)) % 16.85/17.09 (define @t162 () (forall @t3 @t154)) % 16.85/17.09 (define @t163 () (= tptp.sz10 @t76)) % 16.85/17.09 (define @t164 () (= tptp.sz00 @t76)) % 16.85/17.09 (define @t165 () (or @t160 @t164 @t163 @t159)) % 16.85/17.09 (assume @p1 (forall @t3 (=> @t2 true))) % 16.85/17.09 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 16.85/17.09 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 16.85/17.09 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 16.85/17.09 (assume @p5 @t11) % 16.85/17.09 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 16.85/17.09 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 16.85/17.09 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 16.85/17.09 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t19)))) % 16.85/17.09 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 16.85/17.09 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 16.85/17.09 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 16.85/17.09 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 16.85/17.09 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 16.85/17.09 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> (and @t6 @t16) (=> (or @t26 @t25) @t22))))))) % 16.85/17.09 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 16.85/17.09 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t27 @t29))))) % 16.85/17.09 (assume @p18 (forall @t8 (=> @t7 (= @t32 (exists @t31 @t30))))) % 16.85/17.09 (assume @p19 (forall @t8 (=> @t7 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 16.85/17.09 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 16.85/17.09 (assume @p21 (forall @t8 (=> @t7 (=> (and @t32 @t34) @t33)))) % 16.85/17.09 (assume @p22 (forall @t18 (=> @t17 (=> (and @t32 @t35) (tptp.sdtlseqdt0 @t1 @t13))))) % 16.85/17.09 (assume @p23 (forall @t8 (=> @t7 (or @t32 (and (not @t36) @t34))))) % 16.85/17.09 (assume @p24 (forall @t8 (=> @t7 (=> @t38 (forall @t31 (=> @t16 (and (not (= @t23 @t37)) (tptp.sdtlseqdt0 @t23 @t37) (not (= @t24 @t14)) (tptp.sdtlseqdt0 @t24 @t14)))))))) % 16.85/17.09 (assume @p25 (forall @t18 (=> @t17 (=> (and @t28 (not @t22) @t35) (and (not @t26) (tptp.sdtlseqdt0 @t9 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 16.85/17.09 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t39 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 16.85/17.09 (assume @p27 (forall @t8 (=> @t7 (=> @t28 (tptp.sdtlseqdt0 @t4 @t19))))) % 16.85/17.09 (assume @p28 (forall @t8 (=> @t7 (=> @t40 true)))) % 16.85/17.09 (assume @p29 (forall @t8 (=> @t7 (=> @t38 @t40)))) % 16.85/17.09 (assume @p30 (forall @t8 (=> @t7 (= @t42 (exists @t31 @t41))))) % 16.85/17.09 (assume @p31 @t49) % 16.85/17.09 (assume @p32 (forall @t18 (=> @t17 (=> (and @t42 (tptp.doDivides0 @t4 @t13)) @t50)))) % 16.85/17.09 (assume @p33 (forall @t18 (=> @t17 (=> (and @t42 @t50) @t51)))) % 16.85/17.09 (assume @p34 (forall @t18 (=> @t17 (=> (and @t42 @t51) @t50)))) % 16.85/17.09 (assume @p35 (forall @t8 (=> @t7 (=> (and @t42 (not @t29)) @t32)))) % 16.85/17.09 (assume @p36 (forall @t8 (=> @t7 (=> @t46 (forall @t31 (=> @t16 (= (tptp.sdtasdt0 @t13 @t43) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 16.85/17.09 (assume @p37 @t63) % 16.85/17.09 (assume @p38 @t69) % 16.85/17.09 (assume @p39 (and @t72 @t71 @t70)) % 16.85/17.09 (assume @p40 (forall @t18 (=> @t17 (=> (and (tptp.isPrime0 @t13) (tptp.doDivides0 @t13 @t9)) (=> (tptp.iLess0 @t15 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 @t13 @t1) (tptp.doDivides0 @t13 @t4))))))) % 16.85/17.09 (assume @p41 (and @t75 @t74)) % 16.85/17.09 (assume @p42 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 16.85/17.09 (assume @p43 (not (tptp.sdtlseqdt0 tptp.xp tptp.xm))) % 16.85/17.09 (assume @p44 (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 16.85/17.09 (assume @p45 (= tptp.xk @t76)) % 16.85/17.09 (assume @p46 @t80) % 16.85/17.09 (assume @p47 (and (not @t78) (not @t77))) % 16.85/17.09 (assume @p48 @t84) % 16.85/17.09 (assume @p49 true) % 16.85/17.09 (step @p50 :rule refl :args (tptp.sz10)) % 16.85/17.09 (step @p51 :rule cong :premises (@p50 @p45) :args (@t85)) % 16.85/17.09 (step @p52 :rule refl :args (tptp.sz00)) % 16.85/17.09 (step @p53 :rule cong :premises (@p52 @p45) :args (@t86)) % 16.85/17.09 (step @p54 :rule nary_cong :premises (@p53 @p51) :args (@t87)) % 16.85/17.09 (step @p55 :rule cong :premises (@p54) :args ((not @t87))) % 16.85/17.09 (step @p56 :rule eq-symm :args (tptp.xk tptp.sz10)) % 16.85/17.09 (step @p57 :rule eq-symm :args (tptp.xk tptp.sz00)) % 16.85/17.09 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t79)) % 16.85/17.09 (step @p59 :rule cong :premises (@p58) :args (@t80)) % 16.85/17.09 (step @p60 :rule trans :premises (@p59 @p55)) % 16.85/17.09 (step @p61 :rule eq_resolve :premises (@p46 @p60)) % 16.85/17.09 (step @p62 :rule not_or_elim :premises (@p61) :args (0)) % 16.85/17.09 (step @p63 :rule not_or_elim :premises (@p61) :args (1)) % 16.85/17.09 (step @p64 :rule eq-symm :args (@t88 @t43)) % 16.85/17.09 (step @p65 :rule refl :args (@t89)) % 16.85/17.09 (step @p66 :rule cong :premises (@p65 @p64) :args (@t90)) % 16.85/17.09 (step @p67 :rule refl :args (@t91)) % 16.85/17.09 (step @p68 :rule refl :args (@t27)) % 16.85/17.09 (step @p69 :rule refl :args (@t92)) % 16.85/17.09 (step @p70 :rule refl :args (@t93)) % 16.85/17.09 (step @p71 :rule nary_cong :premises (@p70 @p69 @p68 @p67 @p66) :args (@t94)) % 16.85/17.09 (step @p72 :rule cong :premises (@p71) :args (@t96)) % 16.85/17.09 (step @p73 :rule quant-merge-prenex :args ((= (forall @t8 @t98) @t96))) % 16.85/17.09 (step @p74 :rule alpha_equiv :args (@t99 (@list @t88) (@list @t13))) % 16.85/17.09 (step @p75 :rule refl :args (@t91)) % 16.85/17.09 (step @p76 :rule refl :args (@t27)) % 16.85/17.09 (step @p77 :rule refl :args (@t92)) % 16.85/17.09 (step @p78 :rule refl :args (@t93)) % 16.85/17.09 (step @p79 :rule nary_cong :premises (@p78 @p77 @p76 @p75 @p74) :args (@t100)) % 16.85/17.09 (step @p80 :rule quant-miniscope-or :args ((= @t98 @t100))) % 16.85/17.09 (step @p81 :rule trans :premises (@p80 @p79)) % 16.85/17.09 (step @p82 :rule symm :premises (@p81)) % 16.85/17.09 (step @p83 :rule cong :premises (@p82) :args ((forall @t8 @t102))) % 16.85/17.09 (step @p84 :rule trans :premises (@p83 @p73)) % 16.85/17.09 (step @p85 :rule trans :premises (@p84 @p72)) % 16.85/17.09 (step @p86 :rule aci_norm :args ((= (or @t104 @t103) @t102))) % 16.85/17.09 (step @p87 :rule aci_norm :args ((= (or (or @t27 @t91) @t101) @t103))) % 16.85/17.09 (step @p88 :rule refl :args (@t101)) % 16.85/17.09 (step @p89 :rule bool-double-not-elim :args (@t27)) % 16.85/17.09 (step @p90 :rule nary_cong :premises (@p89 @p75) :args ((or @t105 @t91))) % 16.85/17.09 (step @p91 :rule bool-and-de-morgan :args (@t28 @t42 true)) % 16.85/17.09 (step @p92 :rule trans :premises (@p91 @p90)) % 16.85/17.09 (step @p93 :rule nary_cong :premises (@p92 @p88) :args ((or (not @t46) @t101))) % 16.85/17.09 (step @p94 :rule trans :premises (@p93 @p87)) % 16.85/17.09 (step @p95 :rule bool-impl-elim :args (@t46 @t101)) % 16.85/17.09 (step @p96 :rule trans :premises (@p95 @p94)) % 16.85/17.09 (step @p97 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 16.85/17.09 (step @p98 :rule nary_cong :premises (@p97 @p96) :args ((or @t107 @t106))) % 16.85/17.09 (step @p99 :rule trans :premises (@p98 @p86)) % 16.85/17.09 (step @p100 :rule bool-impl-elim :args (@t7 @t106)) % 16.85/17.09 (step @p101 :rule trans :premises (@p100 @p99)) % 16.85/17.09 (step @p102 :rule cong :premises (@p101) :args ((forall @t8 (=> @t7 @t106)))) % 16.85/17.09 (step @p103 :rule trans :premises (@p102 @p85)) % 16.85/17.09 (step @p104 :rule eq-symm :args (@t44 @t41)) % 16.85/17.09 (step @p105 :rule cong :premises (@p104) :args (@t45)) % 16.85/17.09 (step @p106 :rule refl :args (@t46)) % 16.85/17.09 (step @p107 :rule cong :premises (@p106 @p105) :args (@t47)) % 16.85/17.09 (step @p108 :rule refl :args (@t7)) % 16.85/17.09 (step @p109 :rule cong :premises (@p108 @p107) :args (@t48)) % 16.85/17.09 (step @p110 :rule cong :premises (@p109) :args (@t49)) % 16.85/17.09 (step @p111 :rule trans :premises (@p110 @p103)) % 16.85/17.09 (step @p112 :rule eq_resolve :premises (@p31 @p111)) % 16.85/17.09 (step @p113 :rule bool-eq-true :args (@t109)) % 16.85/17.09 (step @p114 :rule eq-symm :args (true @t109)) % 16.85/17.09 (step @p115 :rule trans :premises (@p114 @p113)) % 16.85/17.09 (step @p116 :rule refl :args (@t109)) % 16.85/17.09 (step @p117 :rule eq-refl :args (@t76)) % 16.85/17.09 (step @p118 :rule cong :premises (@p117 @p116) :args ((= @t110 @t109))) % 16.85/17.09 (step @p119 :rule trans :premises (@p118 @p115)) % 16.85/17.09 (step @p120 :rule eq-symm :args (@t109 @t110)) % 16.85/17.09 (step @p121 :rule trans :premises (@p120 @p119)) % 16.85/17.09 (step @p122 :rule refl :args (@t111)) % 16.85/17.09 (step @p123 :rule eq-symm :args (tptp.xp tptp.sz00)) % 16.85/17.09 (step @p124 :rule refl :args (@t113)) % 16.85/17.09 (step @p125 :rule refl :args (@t114)) % 16.85/17.09 (step @p126 :rule nary_cong :premises (@p125 @p124 @p123 @p122 @p121) :args (@t116)) % 16.85/17.09 (step @p127 :rule refl :args (@t117)) % 16.85/17.09 (step @p128 :rule cong :premises (@p127 @p126) :args ((=> @t117 @t116))) % 16.85/17.09 (assume-push @p288 @t117) % 16.85/17.09 (step @p130 :rule instantiate :premises (@p112) :args ((@list tptp.xp @t73 @t76))) % 16.85/17.09 (step-pop @p289 :rule scope :premises (@p130)) % 16.85/17.09 (step @p131 :rule process_scope :premises (@p289) :args (@t116)) % 16.85/17.09 (step @p133 :rule eq_resolve :premises (@p131 @p128)) % 16.85/17.09 (step @p134 :rule implies_elim :premises (@p133)) % 16.85/17.09 (step @p135 :rule chain_m_resolution :premises (@p134 @p112) :args (@t119 @t120 (@list @t117))) % 16.85/17.09 (step @p136 :rule aci_norm :args ((= (or @t104 @t10) (or @t93 @t92 @t10)))) % 16.85/17.09 (step @p137 :rule refl :args (@t10)) % 16.85/17.09 (step @p138 :rule nary_cong :premises (@p97 @p137) :args ((or @t107 @t10))) % 16.85/17.09 (step @p139 :rule trans :premises (@p138 @p136)) % 16.85/17.09 (step @p140 :rule bool-impl-elim :args (@t7 @t10)) % 16.85/17.09 (step @p141 :rule trans :premises (@p140 @p139)) % 16.85/17.09 (step @p142 :rule cong :premises (@p141) :args (@t11)) % 16.85/17.09 (step @p143 :rule eq_resolve :premises (@p5 @p142)) % 16.85/17.09 (step @p144 :rule instantiate :premises (@p143) :args ((@list tptp.xn tptp.xm))) % 16.85/17.09 (step @p145 :rule and_elim :premises (@p39) :args (1)) % 16.85/17.09 (step @p146 :rule and_elim :premises (@p39) :args (0)) % 16.85/17.09 (step @p147 :rule cnf_or_pos :args (@t123)) % 16.85/17.09 (step @p148 :rule reordering :premises (@p147) :args ((or @t122 @t121 @t112 (not @t123)))) % 16.85/17.09 (step @p149 :rule chain_m_resolution :premises (@p148 @p146 @p145 @p144) :args (@t112 (@list false false false) (@list @t72 @t71 @t123))) % 16.85/17.09 (step @p150 :rule bool-impl-elim :args (@t2 @t127)) % 16.85/17.09 (step @p151 :rule cong :premises (@p150) :args ((forall @t3 (=> @t2 @t127)))) % 16.85/17.09 (step @p152 :rule aci_norm :args ((= (or (or @t92 @t125) @t128) @t126))) % 16.85/17.09 (step @p153 :rule refl :args (@t128)) % 16.85/17.09 (step @p154 :rule bool-and-de-morgan :args (@t6 @t53 true)) % 16.85/17.09 (step @p155 :rule nary_cong :premises (@p154 @p153) :args ((or (not @t54) @t128))) % 16.85/17.09 (step @p156 :rule trans :premises (@p155 @p152)) % 16.85/17.09 (step @p157 :rule bool-impl-elim :args (@t54 @t128)) % 16.85/17.09 (step @p158 :rule trans :premises (@p157 @p156)) % 16.85/17.09 (step @p159 :rule cong :premises (@p158) :args ((forall @t56 (=> @t54 @t128)))) % 16.85/17.09 (step @p160 :rule eq-symm :args (@t4 @t1)) % 16.85/17.09 (step @p161 :rule eq-symm :args (@t4 tptp.sz10)) % 16.85/17.09 (step @p162 :rule nary_cong :premises (@p161 @p160) :args (@t52)) % 16.85/17.09 (step @p163 :rule refl :args (@t54)) % 16.85/17.09 (step @p164 :rule cong :premises (@p163 @p162) :args (@t55)) % 16.85/17.09 (step @p165 :rule cong :premises (@p164) :args (@t57)) % 16.85/17.09 (step @p166 :rule trans :premises (@p165 @p159)) % 16.85/17.09 (step @p167 :rule refl :args (@t58)) % 16.85/17.09 (step @p168 :rule refl :args (@t28)) % 16.85/17.09 (step @p169 :rule nary_cong :premises (@p168 @p167 @p166) :args (@t59)) % 16.85/17.09 (step @p170 :rule refl :args (@t60)) % 16.85/17.09 (step @p171 :rule cong :premises (@p170 @p169) :args (@t61)) % 16.85/17.09 (step @p172 :rule refl :args (@t2)) % 16.85/17.09 (step @p173 :rule cong :premises (@p172 @p171) :args (@t62)) % 16.85/17.09 (step @p174 :rule cong :premises (@p173) :args (@t63)) % 16.85/17.09 (step @p175 :rule trans :premises (@p174 @p151)) % 16.85/17.09 (step @p176 :rule eq_resolve :premises (@p37 @p175)) % 16.85/17.09 (step @p177 :rule eq-symm :args (tptp.xp @t4)) % 16.85/17.09 (step @p178 :rule refl :args (@t124)) % 16.85/17.09 (step @p179 :rule refl :args (@t129)) % 16.85/17.09 (step @p180 :rule nary_cong :premises (@p69 @p179 @p178 @p177) :args (@t130)) % 16.85/17.09 (step @p181 :rule cong :premises (@p180) :args (@t131)) % 16.85/17.09 (step @p182 :rule eq-symm :args (tptp.xp tptp.sz10)) % 16.85/17.09 (step @p183 :rule cong :premises (@p182) :args (@t132)) % 16.85/17.09 (step @p184 :rule cong :premises (@p123) :args (@t133)) % 16.85/17.09 (step @p185 :rule nary_cong :premises (@p184 @p183 @p181) :args (@t134)) % 16.85/17.09 (step @p186 :rule refl :args (@t75)) % 16.85/17.09 (step @p187 :rule cong :premises (@p186 @p185) :args (@t135)) % 16.85/17.09 (step @p188 :rule nary_cong :premises (@p125 @p187) :args (@t136)) % 16.85/17.09 (step @p189 :rule refl :args (@t137)) % 16.85/17.09 (step @p190 :rule cong :premises (@p189 @p188) :args ((=> @t137 @t136))) % 16.85/17.09 (assume-push @p290 @t137) % 16.85/17.09 (step @p192 :rule instantiate :premises (@p176) :args ((@list tptp.xp))) % 16.85/17.09 (step-pop @p291 :rule scope :premises (@p192)) % 16.85/17.09 (step @p193 :rule process_scope :premises (@p291) :args (@t136)) % 16.85/17.09 (step @p195 :rule eq_resolve :premises (@p193 @p190)) % 16.85/17.09 (step @p196 :rule implies_elim :premises (@p195)) % 16.85/17.09 (step @p197 :rule chain_m_resolution :premises (@p196 @p176) :args (@t141 @t120 (@list @t137))) % 16.85/17.09 (step @p198 :rule and_elim :premises (@p39) :args (2)) % 16.85/17.09 (step @p199 :rule cnf_or_pos :args (@t141)) % 16.85/17.09 (step @p200 :rule reordering :premises (@p199) :args ((or @t114 @t140 (not @t141)))) % 16.85/17.09 (step @p201 :rule chain_m_resolution :premises (@p200 @p198 @p197) :args (@t140 @t142 (@list @t70 @t141))) % 16.85/17.09 (step @p202 :rule and_elim :premises (@p41) :args (0)) % 16.85/17.09 (step @p203 :rule cnf_equiv_pos1 :args (@t140)) % 16.85/17.09 (step @p204 :rule reordering :premises (@p203) :args ((or (not @t75) @t139 (not @t140)))) % 16.85/17.09 (step @p205 :rule chain_m_resolution :premises (@p204 @p202 @p201) :args (@t139 @t142 (@list @t75 @t140))) % 16.85/17.09 (step @p206 :rule cnf_and_pos :args (@t139 0)) % 16.85/17.09 (step @p207 :rule reordering :premises (@p206) :args ((or @t138 (not @t139)))) % 16.85/17.09 (step @p208 :rule chain_m_resolution :premises (@p207 @p205) :args (@t138 @t120 (@list @t139))) % 16.85/17.09 (step @p209 :rule and_elim :premises (@p41) :args (1)) % 16.85/17.09 (step @p210 :rule cnf_or_pos :args (@t119)) % 16.85/17.09 (step @p211 :rule reordering :premises (@p210) :args ((or @t114 @t111 @t118 @t113 @t109 (not @t119)))) % 16.85/17.09 (step @p212 :rule chain_m_resolution :premises (@p211 @p198 @p209 @p208 @p149 @p135) :args (@t109 (@list false false true false false) (@list @t70 @t74 @t118 @t112 @t119))) % 16.85/17.09 (step @p213 :rule cnf_and_pos :args (@t109 0)) % 16.85/17.09 (step @p214 :rule reordering :premises (@p213) :args ((or @t108 (not @t109)))) % 16.85/17.09 (step @p215 :rule chain_m_resolution :premises (@p214 @p212) :args (@t108 @t120 (@list @t109))) % 16.85/17.09 (step @p216 :rule refl :args (@t143)) % 16.85/17.09 (step @p217 :rule refl :args (@t1)) % 16.85/17.09 (step @p218 :rule cong :premises (@p217 @p45) :args (@t81)) % 16.85/17.09 (step @p219 :rule cong :premises (@p218) :args (@t144)) % 16.85/17.09 (step @p220 :rule nary_cong :premises (@p70 @p219 @p216) :args (@t145)) % 16.85/17.09 (step @p221 :rule cong :premises (@p220) :args (@t146)) % 16.85/17.09 (step @p222 :rule bool-double-not-elim :args (@t146)) % 16.85/17.09 (step @p223 :rule aci_norm :args ((= (or @t93 (or @t144 @t143)) @t145))) % 16.85/17.09 (step @p224 :rule bool-and-de-morgan :args (@t81 @t60 true)) % 16.85/17.09 (step @p225 :rule nary_cong :premises (@p78 @p224) :args ((or @t93 (not (and @t81 @t60))))) % 16.85/17.09 (step @p226 :rule bool-and-de-morgan :args (@t2 @t81 (and @t60))) % 16.85/17.09 (step @p227 :rule trans :premises (@p226 @p225)) % 16.85/17.09 (step @p228 :rule trans :premises (@p227 @p223)) % 16.85/17.09 (step @p229 :rule cong :premises (@p228) :args (@t147)) % 16.85/17.09 (step @p230 :rule cong :premises (@p229) :args (@t148)) % 16.85/17.09 (step @p231 :rule exists-elim :args ((= @t83 @t148))) % 16.85/17.09 (step @p232 :rule trans :premises (@p231 @p230)) % 16.85/17.09 (step @p233 :rule cong :premises (@p232) :args (@t84)) % 16.85/17.09 (step @p234 :rule trans :premises (@p233 @p222)) % 16.85/17.09 (step @p235 :rule trans :premises (@p234 @p221)) % 16.85/17.09 (step @p236 :rule eq_resolve :premises (@p48 @p235)) % 16.85/17.09 (step @p237 :rule alpha_equiv :args (@t149 (@list @t1) (@list @t4))) % 16.85/17.09 (step @p238 :rule equiv_elim1 :premises (@p237)) % 16.85/17.09 (step @p239 :rule chain_m_resolution :premises (@p238 @p236) :args (@t151 @t120 (@list @t149))) % 16.85/17.09 (step @p240 :rule aci_norm :args ((= (or (or @t93 @t27 @t39) @t153) @t154))) % 16.85/17.09 (step @p241 :rule refl :args (@t153)) % 16.85/17.09 (step @p242 :rule bool-double-not-elim :args (@t39)) % 16.85/17.09 (step @p243 :rule nary_cong :premises (@p78 @p89 @p242) :args (@t156)) % 16.85/17.09 (step @p244 :rule aci_norm :args ((= (or @t93 (or @t105 @t155)) @t156))) % 16.85/17.09 (step @p245 :rule trans :premises (@p244 @p243)) % 16.85/17.09 (step @p246 :rule bool-and-de-morgan :args (@t28 @t58 true)) % 16.85/17.09 (step @p247 :rule nary_cong :premises (@p78 @p246) :args ((or @t93 (not (and @t28 @t58))))) % 16.85/17.09 (step @p248 :rule bool-and-de-morgan :args (@t2 @t28 (and @t58))) % 16.85/17.09 (step @p249 :rule trans :premises (@p248 @p247)) % 16.85/17.09 (step @p250 :rule trans :premises (@p249 @p245)) % 16.85/17.09 (step @p251 :rule nary_cong :premises (@p250 @p241) :args ((or (not @t67) @t153))) % 16.85/17.09 (step @p252 :rule trans :premises (@p251 @p240)) % 16.85/17.09 (step @p253 :rule bool-impl-elim :args (@t67 @t153)) % 16.85/17.09 (step @p254 :rule trans :premises (@p253 @p252)) % 16.85/17.09 (step @p255 :rule cong :premises (@p254) :args ((forall @t3 (=> @t67 @t153)))) % 16.85/17.09 (step @p256 :rule aci_norm :args ((= (or @t92 (or @t125 @t150)) @t152))) % 16.85/17.09 (step @p257 :rule bool-and-de-morgan :args (@t53 @t64 true)) % 16.85/17.09 (step @p258 :rule nary_cong :premises (@p77 @p257) :args ((or @t92 (not (and @t53 @t64))))) % 16.85/17.09 (step @p259 :rule bool-and-de-morgan :args (@t6 @t53 (and @t64))) % 16.85/17.09 (step @p260 :rule trans :premises (@p259 @p258)) % 16.85/17.09 (step @p261 :rule trans :premises (@p260 @p256)) % 16.85/17.09 (step @p262 :rule cong :premises (@p261) :args (@t157)) % 16.85/17.09 (step @p263 :rule cong :premises (@p262) :args (@t158)) % 16.85/17.09 (step @p264 :rule exists-elim :args ((= @t66 @t158))) % 16.85/17.09 (step @p265 :rule trans :premises (@p264 @p263)) % 16.85/17.09 (step @p266 :rule refl :args (@t67)) % 16.85/17.09 (step @p267 :rule cong :premises (@p266 @p265) :args (@t68)) % 16.85/17.09 (step @p268 :rule cong :premises (@p267) :args (@t69)) % 16.85/17.09 (step @p269 :rule trans :premises (@p268 @p255)) % 16.85/17.09 (step @p270 :rule eq_resolve :premises (@p38 @p269)) % 16.85/17.09 (step @p271 :rule refl :args (@t159)) % 16.85/17.09 (step @p272 :rule eq-symm :args (@t76 tptp.sz10)) % 16.85/17.09 (step @p273 :rule eq-symm :args (@t76 tptp.sz00)) % 16.85/17.09 (step @p274 :rule refl :args (@t160)) % 16.85/17.09 (step @p275 :rule nary_cong :premises (@p274 @p273 @p272 @p271) :args (@t161)) % 16.85/17.09 (step @p276 :rule refl :args (@t162)) % 16.85/17.09 (step @p277 :rule cong :premises (@p276 @p275) :args ((=> @t162 @t161))) % 16.85/17.09 (assume-push @p292 @t162) % 16.85/17.09 (step @p279 :rule instantiate :premises (@p270) :args ((@list @t76))) % 16.85/17.09 (step-pop @p293 :rule scope :premises (@p279)) % 16.85/17.09 (step @p280 :rule process_scope :premises (@p293) :args (@t161)) % 16.85/17.10 (step @p282 :rule eq_resolve :premises (@p280 @p277)) % 16.85/17.10 (step @p283 :rule implies_elim :premises (@p282)) % 16.85/17.10 (step @p284 :rule chain_m_resolution :premises (@p283 @p270) :args (@t165 @t120 (@list @t162))) % 16.85/17.10 (step @p285 :rule cnf_or_pos :args (@t165)) % 16.85/17.10 (step @p286 :rule reordering :premises (@p285) :args ((or @t164 @t163 @t160 @t159 (not @t165)))) % 16.85/17.10 (step @p287 false :rule chain_m_resolution :premises (@p286 @p284 @p239 @p215 @p63 @p62) :args (false (@list false false false true true) (@list @t165 @t151 @t108 @t163 @t164))) % 16.85/17.10 ) % 16.85/17.10 % SZS output end Proof % 16.85/17.10 % cvc5 exiting %------------------------------------------------------------------------------