%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM521+3 : 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 : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:39:42 AM UTC 2026 % Result : Theorem 0.45s 0.63s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM521+3 : 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 : n007.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 11:26:26 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.63 % SZS status Theorem % 0.45/0.63 % SZS output start Proof % 0.45/0.63 ( % 0.45/0.63 (declare-sort $$unsorted 0) % 0.45/0.63 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.xm $$unsorted) % 0.45/0.63 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.xn $$unsorted) % 0.45/0.63 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.sz00 $$unsorted) % 0.45/0.63 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.sz10 $$unsorted) % 0.45/0.63 (declare-const tptp.xp $$unsorted) % 0.45/0.63 (define @t1 () (@var "W0" $$unsorted)) % 0.45/0.63 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.45/0.63 (define @t3 () (@list @t1)) % 0.45/0.64 (define @t4 () (@var "W1" $$unsorted)) % 0.45/0.64 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.45/0.64 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 0.45/0.64 (define @t7 () (and @t2 @t6)) % 0.45/0.64 (define @t8 () (@list @t1 @t4)) % 0.45/0.64 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 0.45/0.64 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 0.45/0.64 (define @t11 () (@var "W2" $$unsorted)) % 0.45/0.64 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 0.45/0.64 (define @t13 () (tptp.sdtpldt0 @t5 @t11)) % 0.45/0.64 (define @t14 () (tptp.aNaturalNumber0 @t11)) % 0.45/0.64 (define @t15 () (and @t2 @t6 @t14)) % 0.45/0.64 (define @t16 () (@list @t1 @t4 @t11)) % 0.45/0.64 (define @t17 () (tptp.sdtasdt0 @t4 @t1)) % 0.45/0.64 (define @t18 () (tptp.sdtasdt0 @t11 @t1)) % 0.45/0.64 (define @t19 () (tptp.sdtasdt0 @t1 @t11)) % 0.45/0.64 (define @t20 () (= @t4 @t11)) % 0.45/0.64 (define @t21 () (tptp.sdtpldt0 @t11 @t1)) % 0.45/0.64 (define @t22 () (tptp.sdtpldt0 @t1 @t11)) % 0.45/0.64 (define @t23 () (= @t17 @t18)) % 0.45/0.64 (define @t24 () (= @t9 @t19)) % 0.45/0.64 (define @t25 () (= @t1 tptp.sz00)) % 0.45/0.64 (define @t26 () (not @t25)) % 0.45/0.64 (define @t27 () (= @t4 tptp.sz00)) % 0.45/0.64 (define @t28 () (and @t14 (= @t22 @t4))) % 0.45/0.64 (define @t29 () (@list @t11)) % 0.45/0.64 (define @t30 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.45/0.64 (define @t31 () (= @t1 @t4)) % 0.45/0.64 (define @t32 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.45/0.64 (define @t33 () (tptp.sdtlseqdt0 @t4 @t11)) % 0.45/0.64 (define @t34 () (= @t4 @t1)) % 0.45/0.64 (define @t35 () (not @t34)) % 0.45/0.64 (define @t36 () (and @t35 @t32)) % 0.45/0.64 (define @t37 () (or @t30 @t36)) % 0.45/0.64 (define @t38 () (=> @t7 @t37)) % 0.45/0.64 (define @t39 () (forall @t8 @t38)) % 0.45/0.64 (define @t40 () (tptp.sdtpldt0 @t11 @t4)) % 0.45/0.64 (define @t41 () (not @t31)) % 0.45/0.64 (define @t42 () (and @t41 @t30)) % 0.45/0.64 (define @t43 () (= @t1 tptp.sz10)) % 0.45/0.64 (define @t44 () (tptp.iLess0 @t1 @t4)) % 0.45/0.64 (define @t45 () (and @t14 (= @t4 @t19))) % 0.45/0.64 (define @t46 () (tptp.doDivides0 @t1 @t4)) % 0.45/0.64 (define @t47 () (tptp.sdtsldt0 @t4 @t1)) % 0.45/0.64 (define @t48 () (and @t26 @t46)) % 0.45/0.64 (define @t49 () (tptp.doDivides0 @t1 @t11)) % 0.45/0.64 (define @t50 () (tptp.doDivides0 @t1 @t12)) % 0.45/0.64 (define @t51 () (tptp.doDivides0 @t4 @t1)) % 0.45/0.64 (define @t52 () (@list @t4)) % 0.45/0.64 (define @t53 () (not @t43)) % 0.45/0.64 (define @t54 () (tptp.aNaturalNumber0 tptp.xp)) % 0.45/0.64 (define @t55 () (tptp.aNaturalNumber0 tptp.xm)) % 0.45/0.64 (define @t56 () (tptp.aNaturalNumber0 tptp.xn)) % 0.45/0.64 (define @t57 () (@var "W3" $$unsorted)) % 0.45/0.64 (define @t58 () (tptp.sdtasdt0 @t11 @t57)) % 0.45/0.64 (define @t59 () (tptp.aNaturalNumber0 @t57)) % 0.45/0.64 (define @t60 () (@list @t57)) % 0.45/0.64 (define @t61 () (@var "W4" $$unsorted)) % 0.45/0.64 (define @t62 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 0.45/0.64 (define @t63 () (tptp.sdtasdt0 tptp.xp @t1)) % 0.45/0.64 (define @t64 () (tptp.sdtlseqdt0 tptp.xp tptp.xn)) % 0.45/0.64 (define @t65 () (tptp.sdtpldt0 tptp.xp @t1)) % 0.45/0.64 (define @t66 () (and @t2 (= @t65 tptp.xn))) % 0.45/0.64 (define @t67 () (exists @t3 @t66)) % 0.45/0.64 (define @t68 () (or @t67 @t64)) % 0.45/0.64 (define @t69 () (not @t68)) % 0.45/0.64 (define @t70 () (tptp.sdtlseqdt0 tptp.xp tptp.xm)) % 0.45/0.64 (define @t71 () (and @t2 (= @t65 tptp.xm))) % 0.45/0.64 (define @t72 () (exists @t3 @t71)) % 0.45/0.64 (define @t73 () (or @t72 @t70)) % 0.45/0.64 (define @t74 () (not @t73)) % 0.45/0.64 (define @t75 () (tptp.sdtlseqdt0 tptp.xm tptp.xp)) % 0.45/0.64 (define @t76 () (tptp.sdtpldt0 tptp.xm @t1)) % 0.45/0.64 (define @t77 () (and @t2 (= @t76 tptp.xp))) % 0.45/0.64 (define @t78 () (exists @t3 @t77)) % 0.45/0.64 (define @t79 () (or @t78 @t75)) % 0.45/0.64 (define @t80 () (= tptp.xm tptp.xp)) % 0.45/0.64 (define @t81 () (not @t80)) % 0.45/0.64 (define @t82 () (tptp.sdtlseqdt0 tptp.xn tptp.xp)) % 0.45/0.64 (define @t83 () (tptp.sdtpldt0 tptp.xn @t1)) % 0.45/0.64 (define @t84 () (and @t2 (= @t83 tptp.xp))) % 0.45/0.64 (define @t85 () (exists @t3 @t84)) % 0.45/0.64 (define @t86 () (or @t85 @t82)) % 0.45/0.64 (define @t87 () (= tptp.xn tptp.xp)) % 0.45/0.64 (define @t88 () (not @t87)) % 0.45/0.64 (define @t89 () (and @t88 @t86 @t81 @t79)) % 0.45/0.64 (define @t90 () (not @t89)) % 0.45/0.64 (define @t91 () (and @t41 @t32)) % 0.45/0.64 (define @t92 () (not @t6)) % 0.45/0.64 (define @t93 () (not @t2)) % 0.45/0.64 (define @t94 () (or @t93 @t92 @t30 @t91)) % 0.45/0.64 (define @t95 () (or @t30 @t91)) % 0.45/0.64 (define @t96 () (not (= tptp.xp tptp.xm))) % 0.45/0.64 (define @t97 () (and @t96 @t75)) % 0.45/0.64 (define @t98 () (not @t55)) % 0.45/0.64 (define @t99 () (not @t54)) % 0.45/0.64 (define @t100 () (or @t99 @t98 @t70 @t97)) % 0.45/0.64 (define @t101 () (forall @t8 @t94)) % 0.45/0.64 (define @t102 () (and @t81 @t75)) % 0.45/0.64 (define @t103 () (or @t99 @t98 @t70 @t102)) % 0.45/0.64 (define @t104 () (@list false)) % 0.45/0.64 (define @t105 () (@list @t101)) % 0.45/0.64 (define @t106 () (= tptp.xm @t65)) % 0.45/0.64 (define @t107 () (and @t2 @t106)) % 0.45/0.64 (define @t108 () (forall @t3 (not @t107))) % 0.45/0.64 (define @t109 () (not @t108)) % 0.45/0.64 (define @t110 () (@list true false false false)) % 0.45/0.64 (define @t111 () (not (= tptp.xp tptp.xn))) % 0.45/0.64 (define @t112 () (and @t111 @t82)) % 0.45/0.64 (define @t113 () (not @t56)) % 0.45/0.64 (define @t114 () (or @t99 @t113 @t64 @t112)) % 0.45/0.64 (define @t115 () (and @t88 @t82)) % 0.45/0.64 (define @t116 () (or @t99 @t113 @t64 @t115)) % 0.45/0.64 (define @t117 () (= tptp.xn @t65)) % 0.45/0.64 (define @t118 () (and @t2 @t117)) % 0.45/0.64 (define @t119 () (forall @t3 (not @t118))) % 0.45/0.64 (define @t120 () (not @t119)) % 0.45/0.64 (define @t121 () (and @t88 @t64)) % 0.45/0.64 (define @t122 () (not @t121)) % 0.45/0.64 (define @t123 () (@list true)) % 0.45/0.64 (define @t124 () (or @t113 @t99 @t82 @t121)) % 0.45/0.64 (define @t125 () (@list false false true false)) % 0.45/0.64 (define @t126 () (= tptp.xp @t83)) % 0.45/0.64 (define @t127 () (or (not (forall @t3 (or @t93 (not @t126)))) @t82)) % 0.45/0.64 (define @t128 () (and @t81 @t70)) % 0.45/0.64 (define @t129 () (not @t128)) % 0.45/0.64 (define @t130 () (or @t98 @t99 @t75 @t128)) % 0.45/0.64 (define @t131 () (= tptp.xp @t76)) % 0.45/0.64 (define @t132 () (or (not (forall @t3 (or @t93 (not @t131)))) @t75)) % 0.45/0.64 (define @t133 () (not @t132)) % 0.45/0.64 (define @t134 () (not @t127)) % 0.45/0.64 (define @t135 () (and @t2 @t131)) % 0.45/0.64 (define @t136 () (forall @t3 (not @t135))) % 0.45/0.64 (define @t137 () (not @t136)) % 0.45/0.64 (define @t138 () (and @t2 @t126)) % 0.45/0.64 (define @t139 () (forall @t3 (not @t138))) % 0.45/0.64 (define @t140 () (not @t139)) % 0.45/0.64 (assume @p1 (forall @t3 (=> @t2 true))) % 0.45/0.64 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.45/0.64 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.45/0.64 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 0.45/0.64 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 0.45/0.64 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 0.45/0.64 (assume @p7 (forall @t16 (=> @t15 (= @t13 (tptp.sdtpldt0 @t1 @t12))))) % 0.45/0.64 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.45/0.64 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t17)))) % 0.45/0.64 (assume @p10 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))))) % 0.45/0.64 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.45/0.64 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.45/0.64 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t19)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t17 @t18)))))) % 0.45/0.64 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t5 @t22) (= @t10 @t21)) @t20)))) % 0.45/0.64 (assume @p15 (forall @t3 (=> @t2 (=> @t26 (forall (@list @t4 @t11) (=> (and @t6 @t14) (=> (or @t24 @t23) @t20))))))) % 0.45/0.64 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t25 @t27))))) % 0.45/0.64 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t25 @t27))))) % 0.45/0.64 (assume @p18 (forall @t8 (=> @t7 (= @t30 (exists @t29 @t28))))) % 0.45/0.64 (assume @p19 (forall @t8 (=> @t7 (=> @t30 (forall @t29 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t28)))))) % 0.45/0.64 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.45/0.64 (assume @p21 (forall @t8 (=> @t7 (=> (and @t30 @t32) @t31)))) % 0.45/0.64 (assume @p22 (forall @t16 (=> @t15 (=> (and @t30 @t33) (tptp.sdtlseqdt0 @t1 @t11))))) % 0.45/0.64 (assume @p23 @t39) % 0.45/0.64 (assume @p24 (forall @t8 (=> @t7 (=> @t42 (forall @t29 (=> @t14 (and (not (= @t21 @t40)) (tptp.sdtlseqdt0 @t21 @t40) (not (= @t22 @t12)) (tptp.sdtlseqdt0 @t22 @t12)))))))) % 0.45/0.64 (assume @p25 (forall @t16 (=> @t15 (=> (and @t26 (not @t20) @t33) (and (not @t24) (tptp.sdtlseqdt0 @t9 @t19) (not @t23) (tptp.sdtlseqdt0 @t17 @t18)))))) % 0.45/0.64 (assume @p26 (forall @t3 (=> @t2 (or @t25 @t43 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.45/0.64 (assume @p27 (forall @t8 (=> @t7 (=> @t26 (tptp.sdtlseqdt0 @t4 @t17))))) % 0.45/0.64 (assume @p28 (forall @t8 (=> @t7 (=> @t44 true)))) % 0.45/0.64 (assume @p29 (forall @t8 (=> @t7 (=> @t42 @t44)))) % 0.45/0.64 (assume @p30 (forall @t8 (=> @t7 (= @t46 (exists @t29 @t45))))) % 0.45/0.64 (assume @p31 (forall @t8 (=> @t7 (=> @t48 (forall @t29 (= (= @t11 @t47) @t45)))))) % 0.45/0.64 (assume @p32 (forall @t16 (=> @t15 (=> (and @t46 (tptp.doDivides0 @t4 @t11)) @t49)))) % 0.45/0.64 (assume @p33 (forall @t16 (=> @t15 (=> (and @t46 @t49) @t50)))) % 0.45/0.64 (assume @p34 (forall @t16 (=> @t15 (=> (and @t46 @t50) @t49)))) % 0.45/0.64 (assume @p35 (forall @t8 (=> @t7 (=> (and @t46 (not @t27)) @t30)))) % 0.45/0.64 (assume @p36 (forall @t8 (=> @t7 (=> @t48 (forall @t29 (=> @t14 (= (tptp.sdtasdt0 @t11 @t47) (tptp.sdtsldt0 (tptp.sdtasdt0 @t11 @t4) @t1)))))))) % 0.45/0.64 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t26 @t53 (forall @t52 (=> (and @t6 @t51) (or (= @t4 tptp.sz10) @t34)))))))) % 0.45/0.64 (assume @p38 (forall @t3 (=> (and @t2 @t26 @t53) (exists @t52 (and @t6 @t51 (tptp.isPrime0 @t4)))))) % 0.45/0.64 (assume @p39 (and @t56 @t55 @t54)) % 0.45/0.64 (assume @p40 (forall @t16 (=> @t15 (=> (and (or (and (not (= @t11 tptp.sz00)) (not (= @t11 tptp.sz10)) (forall @t60 (=> (and @t59 (exists (@list @t61) (and (tptp.aNaturalNumber0 @t61) (= @t11 (tptp.sdtasdt0 @t57 @t61)))) (tptp.doDivides0 @t57 @t11)) (or (= @t57 tptp.sz10) (= @t57 @t11))))) (tptp.isPrime0 @t11)) (or (exists @t60 (and @t59 (= @t9 @t58))) (tptp.doDivides0 @t11 @t9))) (=> (tptp.iLess0 @t13 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t60 (and @t59 (= @t1 @t58))) (tptp.doDivides0 @t11 @t1)) (and (exists @t60 (and @t59 (= @t4 @t58))) (tptp.doDivides0 @t11 @t4)))))))) % 0.45/0.64 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t52 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t43 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t62 @t63))) (tptp.doDivides0 tptp.xp @t62))) % 0.45/0.64 (assume @p42 @t69) % 0.45/0.64 (assume @p43 @t74) % 0.45/0.64 (assume @p44 @t90) % 0.45/0.64 (assume @p45 (not (or (exists @t3 (and @t2 (= tptp.xn @t63))) (tptp.doDivides0 tptp.xp tptp.xn) (exists @t3 (and @t2 (= tptp.xm @t63))) (tptp.doDivides0 tptp.xp tptp.xm)))) % 0.45/0.64 (assume @p46 true) % 0.45/0.64 (step @p47 :rule aci_norm :args ((= (or (or @t93 @t92) @t95) @t94))) % 0.45/0.64 (step @p48 :rule refl :args (@t95)) % 0.45/0.64 (step @p49 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 0.45/0.64 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t7) @t95))) % 0.45/0.64 (step @p51 :rule trans :premises (@p50 @p47)) % 0.45/0.64 (step @p52 :rule bool-impl-elim :args (@t7 @t95)) % 0.45/0.64 (step @p53 :rule trans :premises (@p52 @p51)) % 0.45/0.64 (step @p54 :rule cong :premises (@p53) :args ((forall @t8 (=> @t7 @t95)))) % 0.45/0.64 (step @p55 :rule refl :args (@t32)) % 0.45/0.64 (step @p56 :rule eq-symm :args (@t4 @t1)) % 0.45/0.64 (step @p57 :rule cong :premises (@p56) :args (@t35)) % 0.45/0.64 (step @p58 :rule nary_cong :premises (@p57 @p55) :args (@t36)) % 0.45/0.64 (step @p59 :rule refl :args (@t30)) % 0.45/0.64 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t37)) % 0.45/0.64 (step @p61 :rule refl :args (@t7)) % 0.45/0.64 (step @p62 :rule cong :premises (@p61 @p60) :args (@t38)) % 0.45/0.64 (step @p63 :rule cong :premises (@p62) :args (@t39)) % 0.45/0.64 (step @p64 :rule trans :premises (@p63 @p54)) % 0.45/0.64 (step @p65 :rule eq_resolve :premises (@p23 @p64)) % 0.45/0.64 (step @p66 :rule refl :args (@t75)) % 0.45/0.64 (step @p67 :rule eq-symm :args (tptp.xp tptp.xm)) % 0.45/0.64 (step @p68 :rule cong :premises (@p67) :args (@t96)) % 0.45/0.64 (step @p69 :rule nary_cong :premises (@p68 @p66) :args (@t97)) % 0.45/0.64 (step @p70 :rule refl :args (@t70)) % 0.45/0.64 (step @p71 :rule refl :args (@t98)) % 0.45/0.64 (step @p72 :rule refl :args (@t99)) % 0.45/0.64 (step @p73 :rule nary_cong :premises (@p72 @p71 @p70 @p69) :args (@t100)) % 0.45/0.64 (step @p74 :rule refl :args (@t101)) % 0.45/0.64 (step @p75 :rule cong :premises (@p74 @p73) :args ((=> @t101 @t100))) % 0.45/0.64 (assume-push @p192 @t101) % 0.45/0.64 (step @p77 :rule instantiate :premises (@p65) :args ((@list tptp.xp tptp.xm))) % 0.45/0.64 (step-pop @p193 :rule scope :premises (@p77)) % 0.45/0.64 (step @p78 :rule process_scope :premises (@p193) :args (@t100)) % 0.45/0.64 (step @p80 :rule eq_resolve :premises (@p78 @p75)) % 0.45/0.64 (step @p81 :rule implies_elim :premises (@p80)) % 0.45/0.64 (step @p82 :rule chain_m_resolution :premises (@p81 @p65) :args (@t103 @t104 @t105)) % 0.45/0.64 (step @p83 :rule and_elim :premises (@p39) :args (2)) % 0.45/0.64 (step @p84 :rule and_elim :premises (@p39) :args (1)) % 0.45/0.64 (step @p85 :rule bool-and-de-morgan :args (@t2 @t106 true)) % 0.45/0.64 (step @p86 :rule cong :premises (@p85) :args (@t108)) % 0.45/0.64 (step @p87 :rule cong :premises (@p86) :args (@t109)) % 0.45/0.64 (step @p88 :rule exists-elim :args ((= (exists @t3 @t107) @t109))) % 0.45/0.64 (step @p89 :rule trans :premises (@p88 @p87)) % 0.45/0.64 (step @p90 :rule eq-symm :args (@t65 tptp.xm)) % 0.45/0.64 (step @p91 :rule refl :args (@t2)) % 0.45/0.64 (step @p92 :rule nary_cong :premises (@p91 @p90) :args (@t71)) % 0.45/0.64 (step @p93 :rule cong :premises (@p92) :args (@t72)) % 0.45/0.64 (step @p94 :rule trans :premises (@p93 @p89)) % 0.45/0.64 (step @p95 :rule nary_cong :premises (@p94 @p70) :args (@t73)) % 0.45/0.64 (step @p96 :rule cong :premises (@p95) :args (@t74)) % 0.45/0.64 (step @p97 :rule eq_resolve :premises (@p43 @p96)) % 0.45/0.64 (step @p98 :rule not_or_elim :premises (@p97) :args (1)) % 0.45/0.64 (step @p99 :rule cnf_or_pos :args (@t103)) % 0.45/0.64 (step @p100 :rule reordering :premises (@p99) :args ((or @t70 @t98 @t99 @t102 (not @t103)))) % 0.45/0.64 (step @p101 :rule chain_m_resolution :premises (@p100 @p98 @p84 @p83 @p82) :args (@t102 @t110 (@list @t70 @t55 @t54 @t103))) % 0.45/0.64 (step @p102 :rule cnf_and_pos :args (@t102 0)) % 0.45/0.64 (step @p103 :rule reordering :premises (@p102) :args ((or @t81 (not @t102)))) % 0.45/0.64 (step @p104 :rule chain_m_resolution :premises (@p103 @p101) :args (@t81 @t104 (@list @t102))) % 0.45/0.64 (step @p105 :rule refl :args (@t82)) % 0.45/0.64 (step @p106 :rule eq-symm :args (tptp.xp tptp.xn)) % 0.45/0.64 (step @p107 :rule cong :premises (@p106) :args (@t111)) % 0.45/0.64 (step @p108 :rule nary_cong :premises (@p107 @p105) :args (@t112)) % 0.45/0.64 (step @p109 :rule refl :args (@t64)) % 0.45/0.64 (step @p110 :rule refl :args (@t113)) % 0.45/0.64 (step @p111 :rule nary_cong :premises (@p72 @p110 @p109 @p108) :args (@t114)) % 0.45/0.64 (step @p112 :rule cong :premises (@p74 @p111) :args ((=> @t101 @t114))) % 0.45/0.64 (assume-push @p194 @t101) % 0.45/0.64 (step @p114 :rule instantiate :premises (@p65) :args ((@list tptp.xp tptp.xn))) % 0.45/0.64 (step-pop @p195 :rule scope :premises (@p114)) % 0.45/0.64 (step @p115 :rule process_scope :premises (@p195) :args (@t114)) % 0.45/0.64 (step @p117 :rule eq_resolve :premises (@p115 @p112)) % 0.45/0.64 (step @p118 :rule implies_elim :premises (@p117)) % 0.45/0.64 (step @p119 :rule chain_m_resolution :premises (@p118 @p65) :args (@t116 @t104 @t105)) % 0.45/0.64 (step @p120 :rule and_elim :premises (@p39) :args (0)) % 0.45/0.64 (step @p121 :rule bool-and-de-morgan :args (@t2 @t117 true)) % 0.45/0.64 (step @p122 :rule cong :premises (@p121) :args (@t119)) % 0.45/0.64 (step @p123 :rule cong :premises (@p122) :args (@t120)) % 0.45/0.64 (step @p124 :rule exists-elim :args ((= (exists @t3 @t118) @t120))) % 0.45/0.64 (step @p125 :rule trans :premises (@p124 @p123)) % 0.45/0.64 (step @p126 :rule eq-symm :args (@t65 tptp.xn)) % 0.45/0.64 (step @p127 :rule nary_cong :premises (@p91 @p126) :args (@t66)) % 0.45/0.64 (step @p128 :rule cong :premises (@p127) :args (@t67)) % 0.45/0.64 (step @p129 :rule trans :premises (@p128 @p125)) % 0.45/0.64 (step @p130 :rule nary_cong :premises (@p129 @p109) :args (@t68)) % 0.45/0.64 (step @p131 :rule cong :premises (@p130) :args (@t69)) % 0.45/0.64 (step @p132 :rule eq_resolve :premises (@p42 @p131)) % 0.45/0.64 (step @p133 :rule not_or_elim :premises (@p132) :args (1)) % 0.45/0.64 (step @p134 :rule cnf_or_pos :args (@t116)) % 0.45/0.64 (step @p135 :rule reordering :premises (@p134) :args ((or @t64 @t113 @t99 @t115 (not @t116)))) % 0.45/0.64 (step @p136 :rule chain_m_resolution :premises (@p135 @p133 @p120 @p83 @p119) :args (@t115 @t110 (@list @t64 @t56 @t54 @t116))) % 0.45/0.64 (step @p137 :rule cnf_and_pos :args (@t115 0)) % 0.45/0.64 (step @p138 :rule reordering :premises (@p137) :args ((or @t88 (not @t115)))) % 0.45/0.64 (step @p139 :rule chain_m_resolution :premises (@p138 @p136) :args (@t88 @t104 (@list @t115))) % 0.45/0.64 (step @p140 :rule instantiate :premises (@p65) :args ((@list tptp.xn tptp.xp))) % 0.45/0.64 (step @p141 :rule cnf_and_pos :args (@t121 1)) % 0.45/0.64 (step @p142 :rule reordering :premises (@p141) :args ((or @t64 @t122))) % 0.45/0.64 (step @p143 :rule chain_m_resolution :premises (@p142 @p133) :args (@t122 @t123 (@list @t64))) % 0.45/0.64 (step @p144 :rule cnf_or_pos :args (@t124)) % 0.45/0.64 (step @p145 :rule reordering :premises (@p144) :args ((or @t82 @t113 @t99 @t121 (not @t124)))) % 0.45/0.64 (step @p146 :rule chain_m_resolution :premises (@p145 @p120 @p83 @p143 @p140) :args (@t82 @t125 (@list @t56 @t54 @t121 @t124))) % 0.45/0.64 (step @p147 :rule cnf_or_neg :args (@t127 1)) % 0.45/0.64 (step @p148 :rule chain_m_resolution :premises (@p147 @p146) :args (@t127 @t104 (@list @t82))) % 0.45/0.64 (step @p149 :rule instantiate :premises (@p65) :args ((@list tptp.xm tptp.xp))) % 0.45/0.64 (step @p150 :rule cnf_and_pos :args (@t128 1)) % 0.45/0.64 (step @p151 :rule reordering :premises (@p150) :args ((or @t70 @t129))) % 0.45/0.64 (step @p152 :rule chain_m_resolution :premises (@p151 @p98) :args (@t129 @t123 (@list @t70))) % 0.45/0.64 (step @p153 :rule cnf_or_pos :args (@t130)) % 0.45/0.64 (step @p154 :rule reordering :premises (@p153) :args ((or @t75 @t98 @t99 @t128 (not @t130)))) % 0.45/0.64 (step @p155 :rule chain_m_resolution :premises (@p154 @p84 @p83 @p152 @p149) :args (@t75 @t125 (@list @t55 @t54 @t128 @t130))) % 0.45/0.64 (step @p156 :rule cnf_or_neg :args (@t132 1)) % 0.45/0.64 (step @p157 :rule chain_m_resolution :premises (@p156 @p155) :args (@t132 @t104 (@list @t75))) % 0.45/0.64 (step @p158 :rule refl :args (@t133)) % 0.45/0.64 (step @p159 :rule bool-double-not-elim :args (@t80)) % 0.45/0.64 (step @p160 :rule refl :args (@t134)) % 0.45/0.64 (step @p161 :rule bool-double-not-elim :args (@t87)) % 0.45/0.64 (step @p162 :rule nary_cong :premises (@p161 @p160 @p159 @p158) :args ((or (not @t88) @t134 (not @t81) @t133))) % 0.45/0.64 (step @p163 :rule bool-and-de-morgan :args (@t2 @t131 true)) % 0.45/0.64 (step @p164 :rule cong :premises (@p163) :args (@t136)) % 0.45/0.64 (step @p165 :rule cong :premises (@p164) :args (@t137)) % 0.45/0.64 (step @p166 :rule exists-elim :args ((= (exists @t3 @t135) @t137))) % 0.45/0.64 (step @p167 :rule trans :premises (@p166 @p165)) % 0.45/0.64 (step @p168 :rule eq-symm :args (@t76 tptp.xp)) % 0.45/0.64 (step @p169 :rule nary_cong :premises (@p91 @p168) :args (@t77)) % 0.45/0.64 (step @p170 :rule cong :premises (@p169) :args (@t78)) % 0.45/0.64 (step @p171 :rule trans :premises (@p170 @p167)) % 0.45/0.64 (step @p172 :rule nary_cong :premises (@p171 @p66) :args (@t79)) % 0.45/0.64 (step @p173 :rule refl :args (@t81)) % 0.45/0.64 (step @p174 :rule bool-and-de-morgan :args (@t2 @t126 true)) % 0.45/0.64 (step @p175 :rule cong :premises (@p174) :args (@t139)) % 0.45/0.64 (step @p176 :rule cong :premises (@p175) :args (@t140)) % 0.45/0.64 (step @p177 :rule exists-elim :args ((= (exists @t3 @t138) @t140))) % 0.45/0.64 (step @p178 :rule trans :premises (@p177 @p176)) % 0.45/0.64 (step @p179 :rule eq-symm :args (@t83 tptp.xp)) % 0.45/0.64 (step @p180 :rule nary_cong :premises (@p91 @p179) :args (@t84)) % 0.45/0.64 (step @p181 :rule cong :premises (@p180) :args (@t85)) % 0.45/0.64 (step @p182 :rule trans :premises (@p181 @p178)) % 0.45/0.64 (step @p183 :rule nary_cong :premises (@p182 @p105) :args (@t86)) % 0.45/0.64 (step @p184 :rule refl :args (@t88)) % 0.45/0.64 (step @p185 :rule nary_cong :premises (@p184 @p183 @p173 @p172) :args (@t89)) % 0.45/0.64 (step @p186 :rule cong :premises (@p185) :args (@t90)) % 0.45/0.64 (step @p187 :rule eq_resolve :premises (@p44 @p186)) % 0.45/0.64 (step @p188 :rule not_and :premises (@p187)) % 0.45/0.64 (step @p189 :rule eq_resolve :premises (@p188 @p162)) % 0.45/0.64 (step @p190 :rule reordering :premises (@p189) :args ((or @t87 @t80 @t134 @t133))) % 0.45/0.64 (step @p191 false :rule chain_m_resolution :premises (@p190 @p157 @p148 @p139 @p104) :args (false (@list false false true true) (@list @t132 @t127 @t87 @t80))) % 0.45/0.64 ) % 0.45/0.64 % SZS output end Proof % 0.45/0.64 % cvc5 exiting %------------------------------------------------------------------------------