%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM495+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 : n003.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 08:39:36 AM UTC 2026 % Result : Theorem 34.07s 34.34s % Output : Proof 34.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM495+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 11:23:59 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 34.07/34.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 34.07/34.34 --- Run --no-e-matching --full-saturate-quant at 6... % 34.07/34.34 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 34.07/34.34 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 34.07/34.34 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 34.07/34.34 % SZS status Theorem % 34.07/34.34 % SZS output start Proof % 34.07/34.34 ( % 34.07/34.34 (declare-sort $$unsorted 0) % 34.07/34.34 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 34.07/34.34 (declare-const tptp.xm $$unsorted) % 34.07/34.34 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.07/34.34 (declare-const tptp.xr $$unsorted) % 34.07/34.34 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 34.07/34.34 (declare-const tptp.xn $$unsorted) % 34.07/34.34 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 34.07/34.34 (declare-const tptp.sz00 $$unsorted) % 34.07/34.34 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.07/34.34 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.07/34.34 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.07/34.34 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 34.07/34.34 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 34.07/34.34 (declare-const tptp.sz10 $$unsorted) % 34.07/34.34 (declare-const tptp.xp $$unsorted) % 34.07/34.34 (define @t1 () (@var "W0" $$unsorted)) % 34.07/34.34 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 34.07/34.34 (define @t3 () (@list @t1)) % 34.07/34.34 (define @t4 () (@var "W1" $$unsorted)) % 34.07/34.34 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 34.07/34.34 (define @t6 () (tptp.aNaturalNumber0 @t5)) % 34.07/34.34 (define @t7 () (tptp.aNaturalNumber0 @t4)) % 34.07/34.34 (define @t8 () (and @t2 @t7)) % 34.07/34.34 (define @t9 () (@list @t1 @t4)) % 34.07/34.34 (define @t10 () (forall @t9 (=> @t8 @t6))) % 34.07/34.34 (define @t11 () (tptp.sdtasdt0 @t1 @t4)) % 34.07/34.34 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 34.07/34.34 (define @t13 () (@var "W2" $$unsorted)) % 34.07/34.34 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 34.07/34.34 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 34.07/34.34 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 34.07/34.34 (define @t17 () (and @t2 @t7 @t16)) % 34.07/34.34 (define @t18 () (@list @t1 @t4 @t13)) % 34.07/34.34 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 34.07/34.34 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 34.07/34.34 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 34.07/34.34 (define @t22 () (= @t4 @t13)) % 34.07/34.34 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 34.07/34.34 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 34.07/34.34 (define @t25 () (= @t19 @t20)) % 34.07/34.34 (define @t26 () (= @t11 @t21)) % 34.07/34.34 (define @t27 () (and @t7 @t16)) % 34.07/34.34 (define @t28 () (= @t1 tptp.sz00)) % 34.07/34.34 (define @t29 () (not @t28)) % 34.07/34.34 (define @t30 () (= @t4 tptp.sz00)) % 34.07/34.34 (define @t31 () (and @t16 (= @t24 @t4))) % 34.07/34.34 (define @t32 () (@list @t13)) % 34.07/34.34 (define @t33 () (tptp.sdtlseqdt0 @t1 @t4)) % 34.07/34.34 (define @t34 () (tptp.sdtmndt0 @t4 @t1)) % 34.07/34.34 (define @t35 () (= @t13 @t34)) % 34.07/34.34 (define @t36 () (forall @t32 (= @t35 @t31))) % 34.07/34.34 (define @t37 () (=> @t33 @t36)) % 34.07/34.34 (define @t38 () (=> @t8 @t37)) % 34.07/34.34 (define @t39 () (forall @t9 @t38)) % 34.07/34.34 (define @t40 () (= @t1 @t4)) % 34.07/34.34 (define @t41 () (tptp.sdtlseqdt0 @t4 @t1)) % 34.07/34.34 (define @t42 () (tptp.sdtlseqdt0 @t4 @t13)) % 34.07/34.34 (define @t43 () (= @t4 @t1)) % 34.07/34.34 (define @t44 () (tptp.sdtpldt0 @t13 @t4)) % 34.07/34.34 (define @t45 () (not @t40)) % 34.07/34.34 (define @t46 () (and @t45 @t33)) % 34.07/34.34 (define @t47 () (= @t1 tptp.sz10)) % 34.07/34.34 (define @t48 () (tptp.iLess0 @t1 @t4)) % 34.07/34.34 (define @t49 () (=> @t46 @t48)) % 34.07/34.34 (define @t50 () (forall @t9 (=> @t8 @t49))) % 34.07/34.34 (define @t51 () (and @t16 (= @t4 @t21))) % 34.07/34.34 (define @t52 () (tptp.doDivides0 @t1 @t4)) % 34.07/34.34 (define @t53 () (tptp.sdtsldt0 @t4 @t1)) % 34.07/34.34 (define @t54 () (and @t29 @t52)) % 34.07/34.34 (define @t55 () (tptp.doDivides0 @t1 @t13)) % 34.07/34.34 (define @t56 () (tptp.doDivides0 @t1 @t14)) % 34.07/34.34 (define @t57 () (tptp.doDivides0 @t4 @t1)) % 34.07/34.34 (define @t58 () (@list @t4)) % 34.07/34.34 (define @t59 () (not @t47)) % 34.07/34.34 (define @t60 () (tptp.aNaturalNumber0 tptp.xp)) % 34.07/34.34 (define @t61 () (tptp.aNaturalNumber0 tptp.xm)) % 34.07/34.34 (define @t62 () (tptp.aNaturalNumber0 tptp.xn)) % 34.07/34.34 (define @t63 () (tptp.doDivides0 @t13 @t4)) % 34.07/34.34 (define @t64 () (tptp.doDivides0 @t13 @t1)) % 34.07/34.34 (define @t65 () (or @t64 @t63)) % 34.07/34.34 (define @t66 () (tptp.sdtpldt0 tptp.xn tptp.xm)) % 34.07/34.34 (define @t67 () (tptp.sdtpldt0 @t66 tptp.xp)) % 34.07/34.34 (define @t68 () (tptp.iLess0 @t15 @t67)) % 34.07/34.34 (define @t69 () (=> @t68 @t65)) % 34.07/34.34 (define @t70 () (tptp.doDivides0 @t13 @t11)) % 34.07/34.34 (define @t71 () (tptp.isPrime0 @t13)) % 34.07/34.34 (define @t72 () (and @t71 @t70)) % 34.07/34.34 (define @t73 () (=> @t72 @t69)) % 34.07/34.34 (define @t74 () (forall @t18 (=> @t17 @t73))) % 34.07/34.34 (define @t75 () (tptp.isPrime0 tptp.xp)) % 34.07/34.34 (define @t76 () (tptp.sdtlseqdt0 tptp.xp tptp.xn)) % 34.07/34.34 (define @t77 () (tptp.sdtmndt0 tptp.xn tptp.xp)) % 34.07/34.34 (define @t78 () (tptp.sdtasdt0 tptp.xr tptp.xm)) % 34.07/34.34 (define @t79 () (tptp.doDivides0 tptp.xp @t78)) % 34.07/34.34 (define @t80 () (tptp.sdtpldt0 tptp.xr tptp.xm)) % 34.07/34.34 (define @t81 () (tptp.sdtpldt0 @t80 tptp.xp)) % 34.07/34.34 (define @t82 () (tptp.sdtlseqdt0 @t81 @t67)) % 34.07/34.34 (define @t83 () (not (= @t81 @t67))) % 34.07/34.34 (define @t84 () (tptp.doDivides0 tptp.xp tptp.xm)) % 34.07/34.34 (define @t85 () (tptp.doDivides0 tptp.xp tptp.xr)) % 34.07/34.34 (define @t86 () (or @t85 @t84)) % 34.07/34.34 (define @t87 () (not @t86)) % 34.07/34.34 (define @t88 () (= @t67 @t81)) % 34.07/34.34 (define @t89 () (not @t33)) % 34.07/34.34 (define @t90 () (not @t7)) % 34.07/34.34 (define @t91 () (not @t2)) % 34.07/34.34 (define @t92 () (or @t91 @t90 @t40 @t89 @t48)) % 34.07/34.34 (define @t93 () (or @t40 @t89 @t48)) % 34.07/34.34 (define @t94 () (or @t91 @t90)) % 34.07/34.34 (define @t95 () (not @t8)) % 34.07/34.34 (define @t96 () (tptp.sdtpldt0 @t77 tptp.xm)) % 34.07/34.34 (define @t97 () (tptp.sdtpldt0 @t96 tptp.xp)) % 34.07/34.34 (define @t98 () (tptp.iLess0 @t97 @t67)) % 34.07/34.34 (define @t99 () (tptp.sdtlseqdt0 @t97 @t67)) % 34.07/34.34 (define @t100 () (not @t99)) % 34.07/34.34 (define @t101 () (tptp.aNaturalNumber0 @t67)) % 34.07/34.34 (define @t102 () (not @t101)) % 34.07/34.34 (define @t103 () (tptp.aNaturalNumber0 @t97)) % 34.07/34.34 (define @t104 () (not @t103)) % 34.07/34.34 (define @t105 () (or @t104 @t102 (= @t97 @t67) @t100 @t98)) % 34.07/34.34 (define @t106 () (forall @t9 @t92)) % 34.07/34.34 (define @t107 () (= @t67 @t97)) % 34.07/34.34 (define @t108 () (or @t104 @t102 @t107 @t100 @t98)) % 34.07/34.34 (define @t109 () (@list false)) % 34.07/34.34 (define @t110 () (tptp.aNaturalNumber0 @t66)) % 34.07/34.34 (define @t111 () (not @t61)) % 34.07/34.34 (define @t112 () (not @t62)) % 34.07/34.34 (define @t113 () (or @t112 @t111 @t110)) % 34.07/34.34 (define @t114 () (@list false false false)) % 34.07/34.34 (define @t115 () (not @t60)) % 34.07/34.34 (define @t116 () (not @t110)) % 34.07/34.34 (define @t117 () (or @t116 @t115 @t101)) % 34.07/34.34 (define @t118 () (not @t68)) % 34.07/34.34 (define @t119 () (not @t70)) % 34.07/34.34 (define @t120 () (not @t71)) % 34.07/34.34 (define @t121 () (not @t16)) % 34.07/34.34 (define @t122 () (or @t120 @t119 @t118 @t64 @t63)) % 34.07/34.34 (define @t123 () (or @t91 @t90 @t121)) % 34.07/34.34 (define @t124 () (or @t118 @t64 @t63)) % 34.07/34.34 (define @t125 () (@var "BOUND_VARIABLE_7871" $$unsorted)) % 34.07/34.34 (define @t126 () (= @t34 @t125)) % 34.07/34.34 (define @t127 () (and (tptp.aNaturalNumber0 @t125) (= @t4 (tptp.sdtpldt0 @t1 @t125)))) % 34.07/34.34 (define @t128 () (= (= @t125 @t34) @t127)) % 34.07/34.34 (define @t129 () (or @t91 @t90 @t89 @t128)) % 34.07/34.34 (define @t130 () (@list @t1 @t4 @t125)) % 34.07/34.34 (define @t131 () (forall @t130 @t129)) % 34.07/34.34 (define @t132 () (@list @t125)) % 34.07/34.34 (define @t133 () (forall @t132 @t129)) % 34.07/34.34 (define @t134 () (forall @t132 @t128)) % 34.07/34.34 (define @t135 () (or @t91 @t90 @t89 @t134)) % 34.07/34.34 (define @t136 () (and @t16 (= @t4 @t24))) % 34.07/34.34 (define @t137 () (forall @t32 (= @t35 @t136))) % 34.07/34.34 (define @t138 () (or @t91 @t90 @t89 @t137)) % 34.07/34.34 (define @t139 () (=> @t33 @t137)) % 34.07/34.34 (define @t140 () (tptp.aNaturalNumber0 @t77)) % 34.07/34.34 (define @t141 () (and @t140 (= tptp.xn (tptp.sdtpldt0 tptp.xp @t77)))) % 34.07/34.34 (define @t142 () (= @t77 @t77)) % 34.07/34.34 (define @t143 () (not @t76)) % 34.07/34.34 (define @t144 () (or @t115 @t112 @t143 (= @t141 @t142))) % 34.07/34.34 (define @t145 () (forall @t130 (or @t91 @t90 @t89 (= @t127 @t126)))) % 34.07/34.34 (define @t146 () (or @t115 @t112 @t143 @t141)) % 34.07/34.34 (define @t147 () (tptp.doDivides0 tptp.xp @t77)) % 34.07/34.34 (define @t148 () (not @t98)) % 34.07/34.34 (define @t149 () (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 @t77 tptp.xm))) % 34.07/34.34 (define @t150 () (not @t149)) % 34.07/34.34 (define @t151 () (not @t75)) % 34.07/34.34 (define @t152 () (not @t140)) % 34.07/34.34 (define @t153 () (or @t152 @t111 @t115 @t151 @t150 @t148 @t147 @t84)) % 34.07/34.34 (define @t154 () (tptp.aNaturalNumber0 @t96)) % 34.07/34.34 (define @t155 () (or @t152 @t111 @t154)) % 34.07/34.34 (define @t156 () (not @t154)) % 34.07/34.34 (define @t157 () (or @t156 @t115 @t103)) % 34.07/34.34 (assume @p1 (forall @t3 (=> @t2 true))) % 34.07/34.34 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 34.07/34.34 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 34.07/34.34 (assume @p4 @t10) % 34.07/34.34 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t11)))) % 34.07/34.34 (assume @p6 (forall @t9 (=> @t8 (= @t5 @t12)))) % 34.07/34.34 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 34.07/34.34 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 34.07/34.34 (assume @p9 (forall @t9 (=> @t8 (= @t11 @t19)))) % 34.07/34.34 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t11 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 34.07/34.34 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 34.07/34.34 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 34.07/34.34 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t11 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 34.07/34.34 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 34.07/34.34 (assume @p15 (forall @t3 (=> @t2 (=> @t29 (forall (@list @t4 @t13) (=> @t27 (=> (or @t26 @t25) @t22))))))) % 34.07/34.34 (assume @p16 (forall @t9 (=> @t8 (=> (= @t5 tptp.sz00) (and @t28 @t30))))) % 34.07/34.34 (assume @p17 (forall @t9 (=> @t8 (=> (= @t11 tptp.sz00) (or @t28 @t30))))) % 34.07/34.34 (assume @p18 (forall @t9 (=> @t8 (= @t33 (exists @t32 @t31))))) % 34.07/34.34 (assume @p19 @t39) % 34.07/34.34 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 34.07/34.34 (assume @p21 (forall @t9 (=> @t8 (=> (and @t33 @t41) @t40)))) % 34.07/34.34 (assume @p22 (forall @t18 (=> @t17 (=> (and @t33 @t42) (tptp.sdtlseqdt0 @t1 @t13))))) % 34.07/34.34 (assume @p23 (forall @t9 (=> @t8 (or @t33 (and (not @t43) @t41))))) % 34.07/34.34 (assume @p24 (forall @t9 (=> @t8 (=> @t46 (forall @t32 (=> @t16 (and (not (= @t23 @t44)) (tptp.sdtlseqdt0 @t23 @t44) (not (= @t24 @t14)) (tptp.sdtlseqdt0 @t24 @t14)))))))) % 34.07/34.34 (assume @p25 (forall @t18 (=> @t17 (=> (and @t29 (not @t22) @t42) (and (not @t26) (tptp.sdtlseqdt0 @t11 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 34.07/34.34 (assume @p26 (forall @t3 (=> @t2 (or @t28 @t47 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 34.07/34.34 (assume @p27 (forall @t9 (=> @t8 (=> @t29 (tptp.sdtlseqdt0 @t4 @t19))))) % 34.07/34.34 (assume @p28 (forall @t9 (=> @t8 (=> @t48 true)))) % 34.07/34.34 (assume @p29 @t50) % 34.07/34.34 (assume @p30 (forall @t9 (=> @t8 (= @t52 (exists @t32 @t51))))) % 34.07/34.34 (assume @p31 (forall @t9 (=> @t8 (=> @t54 (forall @t32 (= (= @t13 @t53) @t51)))))) % 34.07/34.34 (assume @p32 (forall @t18 (=> @t17 (=> (and @t52 (tptp.doDivides0 @t4 @t13)) @t55)))) % 34.07/34.34 (assume @p33 (forall @t18 (=> @t17 (=> (and @t52 @t55) @t56)))) % 34.07/34.34 (assume @p34 (forall @t18 (=> @t17 (=> (and @t52 @t56) @t55)))) % 34.07/34.34 (assume @p35 (forall @t9 (=> @t8 (=> (and @t52 (not @t30)) @t33)))) % 34.07/34.34 (assume @p36 (forall @t9 (=> @t8 (=> @t54 (forall @t32 (=> @t16 (= (tptp.sdtasdt0 @t13 @t53) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 34.07/34.34 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t29 @t59 (forall @t58 (=> (and @t7 @t57) (or (= @t4 tptp.sz10) @t43)))))))) % 34.07/34.34 (assume @p38 (forall @t3 (=> (and @t2 @t29 @t59) (exists @t58 (and @t7 @t57 (tptp.isPrime0 @t4)))))) % 34.07/34.34 (assume @p39 (and @t62 @t61 @t60)) % 34.07/34.34 (assume @p40 @t74) % 34.07/34.34 (assume @p41 (and @t75 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xm)))) % 34.07/34.34 (assume @p42 @t76) % 34.07/34.34 (assume @p43 (= tptp.xr @t77)) % 34.07/34.34 (assume @p44 (and (not (= tptp.xr tptp.xn)) (tptp.sdtlseqdt0 tptp.xr tptp.xn))) % 34.07/34.34 (assume @p45 @t79) % 34.07/34.34 (assume @p46 (and @t83 @t82)) % 34.07/34.34 (assume @p47 @t87) % 34.07/34.34 (assume @p48 true) % 34.07/34.34 (step @p49 :rule refl :args (tptp.xp)) % 34.07/34.34 (step @p50 :rule refl :args (tptp.xm)) % 34.07/34.34 (step @p51 :rule cong :premises (@p43 @p50) :args (@t80)) % 34.07/34.34 (step @p52 :rule cong :premises (@p51 @p49) :args (@t81)) % 34.07/34.34 (step @p53 :rule refl :args (@t67)) % 34.07/34.34 (step @p54 :rule cong :premises (@p53 @p52) :args (@t88)) % 34.07/34.34 (step @p55 :rule cong :premises (@p54) :args ((not @t88))) % 34.07/34.34 (step @p56 :rule eq-symm :args (@t81 @t67)) % 34.07/34.34 (step @p57 :rule cong :premises (@p56) :args (@t83)) % 34.07/34.34 (step @p58 :rule trans :premises (@p57 @p55)) % 34.07/34.34 (step @p59 :rule and_elim :premises (@p46) :args (0)) % 34.07/34.34 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 34.07/34.34 (step @p61 :rule cong :premises (@p52 @p53) :args (@t82)) % 34.07/34.34 (step @p62 :rule and_elim :premises (@p46) :args (1)) % 34.07/34.34 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 34.07/34.34 (step @p64 :rule aci_norm :args ((= (or @t94 @t93) @t92))) % 34.07/34.34 (step @p65 :rule aci_norm :args ((= (or (or @t40 @t89) @t48) @t93))) % 34.07/34.34 (step @p66 :rule refl :args (@t48)) % 34.07/34.34 (step @p67 :rule refl :args (@t89)) % 34.07/34.34 (step @p68 :rule bool-double-not-elim :args (@t40)) % 34.07/34.34 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or (not @t45) @t89))) % 34.07/34.34 (step @p70 :rule bool-and-de-morgan :args (@t45 @t33 true)) % 34.07/34.34 (step @p71 :rule trans :premises (@p70 @p69)) % 34.07/34.34 (step @p72 :rule nary_cong :premises (@p71 @p66) :args ((or (not @t46) @t48))) % 34.07/34.34 (step @p73 :rule trans :premises (@p72 @p65)) % 34.07/34.34 (step @p74 :rule bool-impl-elim :args (@t46 @t48)) % 34.07/34.34 (step @p75 :rule trans :premises (@p74 @p73)) % 34.07/34.34 (step @p76 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 34.07/34.34 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or @t95 @t49))) % 34.07/34.34 (step @p78 :rule trans :premises (@p77 @p64)) % 34.07/34.34 (step @p79 :rule bool-impl-elim :args (@t8 @t49)) % 34.07/34.34 (step @p80 :rule trans :premises (@p79 @p78)) % 34.07/34.34 (step @p81 :rule cong :premises (@p80) :args (@t50)) % 34.07/34.34 (step @p82 :rule eq_resolve :premises (@p29 @p81)) % 34.07/34.34 (step @p83 :rule refl :args (@t98)) % 34.07/34.34 (step @p84 :rule refl :args (@t100)) % 34.07/34.34 (step @p85 :rule eq-symm :args (@t97 @t67)) % 34.07/34.34 (step @p86 :rule refl :args (@t102)) % 34.07/34.34 (step @p87 :rule refl :args (@t104)) % 34.07/34.34 (step @p88 :rule nary_cong :premises (@p87 @p86 @p85 @p84 @p83) :args (@t105)) % 34.07/34.34 (step @p89 :rule refl :args (@t106)) % 34.07/34.34 (step @p90 :rule cong :premises (@p89 @p88) :args ((=> @t106 @t105))) % 34.07/34.34 (assume-push @p239 @t106) % 34.07/34.34 (step @p92 :rule instantiate :premises (@p82) :args ((@list @t97 @t67))) % 34.07/34.34 (step-pop @p240 :rule scope :premises (@p92)) % 34.07/34.34 (step @p93 :rule process_scope :premises (@p240) :args (@t105)) % 34.07/34.34 (step @p95 :rule eq_resolve :premises (@p93 @p90)) % 34.07/34.34 (step @p96 :rule implies_elim :premises (@p95)) % 34.07/34.34 (step @p97 :rule chain_m_resolution :premises (@p96 @p82) :args (@t108 @t109 (@list @t106))) % 34.07/34.34 (step @p98 :rule aci_norm :args ((= (or @t94 @t6) (or @t91 @t90 @t6)))) % 34.07/34.34 (step @p99 :rule refl :args (@t6)) % 34.07/34.34 (step @p100 :rule nary_cong :premises (@p76 @p99) :args ((or @t95 @t6))) % 34.07/34.34 (step @p101 :rule trans :premises (@p100 @p98)) % 34.07/34.34 (step @p102 :rule bool-impl-elim :args (@t8 @t6)) % 34.07/34.34 (step @p103 :rule trans :premises (@p102 @p101)) % 34.07/34.34 (step @p104 :rule cong :premises (@p103) :args (@t10)) % 34.07/34.34 (step @p105 :rule eq_resolve :premises (@p4 @p104)) % 34.07/34.34 (step @p106 :rule instantiate :premises (@p105) :args ((@list @t66 tptp.xp))) % 34.07/34.34 (step @p107 :rule instantiate :premises (@p105) :args ((@list tptp.xn tptp.xm))) % 34.07/34.34 (step @p108 :rule and_elim :premises (@p39) :args (1)) % 34.07/34.34 (step @p109 :rule and_elim :premises (@p39) :args (0)) % 34.07/34.34 (step @p110 :rule cnf_or_pos :args (@t113)) % 34.07/34.34 (step @p111 :rule reordering :premises (@p110) :args ((or @t112 @t111 @t110 (not @t113)))) % 34.07/34.34 (step @p112 :rule chain_m_resolution :premises (@p111 @p109 @p108 @p107) :args (@t110 @t114 (@list @t62 @t61 @t113))) % 34.07/34.34 (step @p113 :rule and_elim :premises (@p39) :args (2)) % 34.07/34.34 (step @p114 :rule cnf_or_pos :args (@t117)) % 34.07/34.34 (step @p115 :rule reordering :premises (@p114) :args ((or @t115 @t116 @t101 (not @t117)))) % 34.07/34.34 (step @p116 :rule chain_m_resolution :premises (@p115 @p113 @p112 @p106) :args (@t101 @t114 (@list @t60 @t110 @t117))) % 34.07/34.34 (step @p117 :rule aci_norm :args ((= (or @t123 @t122) (or @t91 @t90 @t121 @t120 @t119 @t118 @t64 @t63)))) % 34.07/34.34 (step @p118 :rule aci_norm :args ((= (or (or @t120 @t119) @t124) @t122))) % 34.07/34.34 (step @p119 :rule aci_norm :args ((= (or @t118 @t65) @t124))) % 34.07/34.34 (step @p120 :rule bool-impl-elim :args (@t68 @t65)) % 34.07/34.34 (step @p121 :rule trans :premises (@p120 @p119)) % 34.07/34.34 (step @p122 :rule bool-and-de-morgan :args (@t71 @t70 true)) % 34.07/34.34 (step @p123 :rule nary_cong :premises (@p122 @p121) :args ((or (not @t72) @t69))) % 34.07/34.34 (step @p124 :rule trans :premises (@p123 @p118)) % 34.07/34.34 (step @p125 :rule bool-impl-elim :args (@t72 @t69)) % 34.07/34.34 (step @p126 :rule trans :premises (@p125 @p124)) % 34.07/34.34 (step @p127 :rule aci_norm :args ((= (or @t91 (or @t90 @t121)) @t123))) % 34.07/34.34 (step @p128 :rule bool-and-de-morgan :args (@t7 @t16 true)) % 34.07/34.34 (step @p129 :rule refl :args (@t91)) % 34.07/34.34 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or @t91 (not @t27)))) % 34.07/34.34 (step @p131 :rule bool-and-de-morgan :args (@t2 @t7 (and @t16))) % 34.07/34.34 (step @p132 :rule trans :premises (@p131 @p130)) % 34.07/34.34 (step @p133 :rule trans :premises (@p132 @p127)) % 34.07/34.34 (step @p134 :rule nary_cong :premises (@p133 @p126) :args ((or (not @t17) @t73))) % 34.07/34.34 (step @p135 :rule trans :premises (@p134 @p117)) % 34.07/34.34 (step @p136 :rule bool-impl-elim :args (@t17 @t73)) % 34.07/34.34 (step @p137 :rule trans :premises (@p136 @p135)) % 34.07/34.34 (step @p138 :rule cong :premises (@p137) :args (@t74)) % 34.07/34.34 (step @p139 :rule eq_resolve :premises (@p40 @p138)) % 34.07/34.34 (step @p140 :rule instantiate :premises (@p139) :args ((@list @t77 tptp.xm tptp.xp))) % 34.07/34.34 (step @p141 :rule eq-symm :args (@t126 @t127)) % 34.07/34.34 (step @p142 :rule refl :args (@t127)) % 34.07/34.34 (step @p143 :rule eq-symm :args (@t125 @t34)) % 34.07/34.34 (step @p144 :rule cong :premises (@p143 @p142) :args (@t128)) % 34.07/34.34 (step @p145 :rule trans :premises (@p144 @p141)) % 34.07/34.34 (step @p146 :rule refl :args (@t89)) % 34.07/34.34 (step @p147 :rule refl :args (@t90)) % 34.07/34.34 (step @p148 :rule refl :args (@t91)) % 34.07/34.34 (step @p149 :rule nary_cong :premises (@p148 @p147 @p146 @p145) :args (@t129)) % 34.07/34.34 (step @p150 :rule cong :premises (@p149) :args (@t131)) % 34.07/34.34 (step @p151 :rule quant-merge-prenex :args ((= (forall @t9 @t133) @t131))) % 34.07/34.34 (step @p152 :rule alpha_equiv :args (@t134 (@list @t125) (@list @t13))) % 34.07/34.34 (step @p153 :rule refl :args (@t90)) % 34.07/34.34 (step @p154 :rule nary_cong :premises (@p129 @p153 @p67 @p152) :args (@t135)) % 34.07/34.34 (step @p155 :rule quant-miniscope-or :args ((= @t133 @t135))) % 34.07/34.34 (step @p156 :rule trans :premises (@p155 @p154)) % 34.07/34.34 (step @p157 :rule symm :premises (@p156)) % 34.07/34.34 (step @p158 :rule cong :premises (@p157) :args ((forall @t9 @t138))) % 34.07/34.34 (step @p159 :rule trans :premises (@p158 @p151)) % 34.07/34.34 (step @p160 :rule trans :premises (@p159 @p150)) % 34.07/34.34 (step @p161 :rule aci_norm :args ((= (or @t94 (or @t89 @t137)) @t138))) % 34.07/34.34 (step @p162 :rule bool-impl-elim :args (@t33 @t137)) % 34.07/34.34 (step @p163 :rule nary_cong :premises (@p76 @p162) :args ((or @t95 @t139))) % 34.07/34.34 (step @p164 :rule trans :premises (@p163 @p161)) % 34.07/34.34 (step @p165 :rule bool-impl-elim :args (@t8 @t139)) % 34.07/34.34 (step @p166 :rule trans :premises (@p165 @p164)) % 34.07/34.34 (step @p167 :rule cong :premises (@p166) :args ((forall @t9 (=> @t8 @t139)))) % 34.07/34.34 (step @p168 :rule trans :premises (@p167 @p160)) % 34.07/34.34 (step @p169 :rule eq-symm :args (@t136 @t35)) % 34.07/34.34 (step @p170 :rule refl :args (@t35)) % 34.07/34.34 (step @p171 :rule eq-symm :args (@t24 @t4)) % 34.07/34.34 (step @p172 :rule refl :args (@t16)) % 34.07/34.34 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t31)) % 34.07/34.34 (step @p174 :rule cong :premises (@p173 @p170) :args ((= @t31 @t35))) % 34.07/34.34 (step @p175 :rule trans :premises (@p174 @p169)) % 34.07/34.34 (step @p176 :rule eq-symm :args (@t35 @t31)) % 34.07/34.34 (step @p177 :rule trans :premises (@p176 @p175)) % 34.07/34.34 (step @p178 :rule cong :premises (@p177) :args (@t36)) % 34.07/34.34 (step @p179 :rule refl :args (@t33)) % 34.07/34.34 (step @p180 :rule cong :premises (@p179 @p178) :args (@t37)) % 34.07/34.34 (step @p181 :rule refl :args (@t8)) % 34.07/34.34 (step @p182 :rule cong :premises (@p181 @p180) :args (@t38)) % 34.07/34.34 (step @p183 :rule cong :premises (@p182) :args (@t39)) % 34.07/34.34 (step @p184 :rule trans :premises (@p183 @p168)) % 34.07/34.34 (step @p185 :rule eq_resolve :premises (@p19 @p184)) % 34.07/34.34 (step @p186 :rule bool-eq-true :args (@t141)) % 34.07/34.34 (step @p187 :rule eq-symm :args (true @t141)) % 34.07/34.34 (step @p188 :rule trans :premises (@p187 @p186)) % 34.07/34.34 (step @p189 :rule refl :args (@t141)) % 34.07/34.34 (step @p190 :rule eq-refl :args (@t77)) % 34.07/34.34 (step @p191 :rule cong :premises (@p190 @p189) :args ((= @t142 @t141))) % 34.07/34.34 (step @p192 :rule trans :premises (@p191 @p188)) % 34.07/34.34 (step @p193 :rule eq-symm :args (@t141 @t142)) % 34.07/34.34 (step @p194 :rule trans :premises (@p193 @p192)) % 34.07/34.34 (step @p195 :rule refl :args (@t143)) % 34.07/34.34 (step @p196 :rule refl :args (@t112)) % 34.07/34.34 (step @p197 :rule refl :args (@t115)) % 34.07/34.34 (step @p198 :rule nary_cong :premises (@p197 @p196 @p195 @p194) :args (@t144)) % 34.07/34.34 (step @p199 :rule refl :args (@t145)) % 34.07/34.34 (step @p200 :rule cong :premises (@p199 @p198) :args ((=> @t145 @t144))) % 34.07/34.34 (assume-push @p241 @t145) % 34.07/34.34 (step @p202 :rule instantiate :premises (@p185) :args ((@list tptp.xp tptp.xn @t77))) % 34.07/34.34 (step-pop @p242 :rule scope :premises (@p202)) % 34.07/34.34 (step @p203 :rule process_scope :premises (@p242) :args (@t144)) % 34.07/34.34 (step @p205 :rule eq_resolve :premises (@p203 @p200)) % 34.07/34.34 (step @p206 :rule implies_elim :premises (@p205)) % 34.07/34.34 (step @p207 :rule chain_m_resolution :premises (@p206 @p185) :args (@t146 @t109 (@list @t145))) % 34.07/34.34 (step @p208 :rule cnf_or_pos :args (@t146)) % 34.07/34.34 (step @p209 :rule reordering :premises (@p208) :args ((or @t112 @t115 @t143 @t141 (not @t146)))) % 34.07/34.34 (step @p210 :rule chain_m_resolution :premises (@p209 @p109 @p113 @p42 @p207) :args (@t141 (@list false false false false) (@list @t62 @t60 @t76 @t146))) % 34.07/34.34 (step @p211 :rule cnf_and_pos :args (@t141 0)) % 34.07/34.34 (step @p212 :rule reordering :premises (@p211) :args ((or @t140 (not @t141)))) % 34.07/34.34 (step @p213 :rule chain_m_resolution :premises (@p212 @p210) :args (@t140 @t109 (@list @t141))) % 34.07/34.34 (step @p214 :rule cong :premises (@p43 @p50) :args (@t78)) % 34.07/34.34 (step @p215 :rule cong :premises (@p49 @p214) :args (@t79)) % 34.07/34.34 (step @p216 :rule eq_resolve :premises (@p45 @p215)) % 34.07/34.34 (step @p217 :rule and_elim :premises (@p41) :args (0)) % 34.07/34.34 (step @p218 :rule refl :args (@t84)) % 34.07/34.34 (step @p219 :rule cong :premises (@p49 @p43) :args (@t85)) % 34.07/34.34 (step @p220 :rule nary_cong :premises (@p219 @p218) :args (@t86)) % 34.07/34.34 (step @p221 :rule cong :premises (@p220) :args (@t87)) % 34.07/34.34 (step @p222 :rule eq_resolve :premises (@p47 @p221)) % 34.07/34.34 (step @p223 :rule not_or_elim :premises (@p222) :args (0)) % 34.07/34.34 (step @p224 :rule not_or_elim :premises (@p222) :args (1)) % 34.07/34.34 (step @p225 :rule cnf_or_pos :args (@t153)) % 34.07/34.34 (step @p226 :rule reordering :premises (@p225) :args ((or @t84 @t147 @t111 @t115 @t151 @t150 @t152 @t148 (not @t153)))) % 34.07/34.34 (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p223 @p108 @p113 @p217 @p216 @p213 @p140) :args (@t148 (@list true true false false false false false false) (@list @t84 @t147 @t61 @t60 @t75 @t149 @t140 @t153))) % 34.07/34.34 (step @p228 :rule instantiate :premises (@p105) :args ((@list @t96 tptp.xp))) % 34.07/34.34 (step @p229 :rule instantiate :premises (@p105) :args ((@list @t77 tptp.xm))) % 34.07/34.34 (step @p230 :rule cnf_or_pos :args (@t155)) % 34.07/34.34 (step @p231 :rule reordering :premises (@p230) :args ((or @t111 @t152 @t154 (not @t155)))) % 34.07/34.34 (step @p232 :rule chain_m_resolution :premises (@p231 @p108 @p213 @p229) :args (@t154 @t114 (@list @t61 @t140 @t155))) % 34.07/34.34 (step @p233 :rule cnf_or_pos :args (@t157)) % 34.07/34.34 (step @p234 :rule reordering :premises (@p233) :args ((or @t115 @t156 @t103 (not @t157)))) % 34.07/34.34 (step @p235 :rule chain_m_resolution :premises (@p234 @p113 @p232 @p228) :args (@t103 @t114 (@list @t60 @t154 @t157))) % 34.07/34.34 (step @p236 :rule cnf_or_pos :args (@t108)) % 34.07/34.34 (step @p237 :rule reordering :premises (@p236) :args ((or @t107 @t100 @t104 @t102 @t98 (not @t108)))) % 34.07/34.34 (step @p238 false :rule chain_m_resolution :premises (@p237 @p235 @p227 @p116 @p97 @p63 @p60) :args (false (@list false true false false false true) (@list @t103 @t98 @t101 @t108 @t99 @t107))) % 34.07/34.34 ) % 34.07/34.34 % SZS output end Proof % 34.07/34.34 % cvc5 exiting %------------------------------------------------------------------------------