%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM512+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 : n005.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 08:39:40 AM UTC 2026 % Result : Theorem 21.40s 21.69s % Output : Proof 21.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM512+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 % 0.17/0.34 % Computer : n005.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 11:26:03 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 21.40/21.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 21.40/21.69 --- Run --no-e-matching --full-saturate-quant at 6... % 21.40/21.69 % SZS status Theorem % 21.40/21.69 % SZS output start Proof % 21.40/21.69 ( % 21.40/21.69 (declare-sort $$unsorted 0) % 21.40/21.69 (declare-const tptp.xr $$unsorted) % 21.40/21.69 (declare-const tptp.xk $$unsorted) % 21.40/21.69 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 21.40/21.69 (declare-const tptp.xm $$unsorted) % 21.40/21.69 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 21.40/21.69 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 21.40/21.69 (declare-const tptp.xn $$unsorted) % 21.40/21.69 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 21.40/21.69 (declare-const tptp.sz00 $$unsorted) % 21.40/21.69 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 21.40/21.69 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 21.40/21.69 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 21.40/21.69 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 21.40/21.69 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 21.40/21.69 (declare-const tptp.sz10 $$unsorted) % 21.40/21.69 (declare-const tptp.xp $$unsorted) % 21.40/21.69 (define @t1 () (@var "W0" $$unsorted)) % 21.40/21.69 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 21.40/21.69 (define @t3 () (@list @t1)) % 21.40/21.69 (define @t4 () (@var "W1" $$unsorted)) % 21.40/21.69 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 21.40/21.69 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 21.40/21.69 (define @t7 () (and @t2 @t6)) % 21.40/21.69 (define @t8 () (@list @t1 @t4)) % 21.40/21.69 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 21.40/21.69 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 21.40/21.69 (define @t11 () (@var "W2" $$unsorted)) % 21.40/21.69 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 21.40/21.69 (define @t13 () (tptp.sdtpldt0 @t5 @t11)) % 21.40/21.69 (define @t14 () (tptp.aNaturalNumber0 @t11)) % 21.40/21.69 (define @t15 () (and @t2 @t6 @t14)) % 21.40/21.69 (define @t16 () (@list @t1 @t4 @t11)) % 21.40/21.69 (define @t17 () (tptp.sdtasdt0 @t4 @t1)) % 21.40/21.69 (define @t18 () (= @t9 @t17)) % 21.40/21.69 (define @t19 () (forall @t8 (=> @t7 @t18))) % 21.40/21.69 (define @t20 () (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))) % 21.40/21.69 (define @t21 () (forall @t16 (=> @t15 @t20))) % 21.40/21.69 (define @t22 () (tptp.sdtasdt0 @t11 @t1)) % 21.40/21.69 (define @t23 () (tptp.sdtasdt0 @t1 @t11)) % 21.40/21.69 (define @t24 () (= @t4 @t11)) % 21.40/21.69 (define @t25 () (tptp.sdtpldt0 @t11 @t1)) % 21.40/21.69 (define @t26 () (tptp.sdtpldt0 @t1 @t11)) % 21.40/21.69 (define @t27 () (= @t17 @t22)) % 21.40/21.69 (define @t28 () (= @t9 @t23)) % 21.40/21.69 (define @t29 () (and @t6 @t14)) % 21.40/21.69 (define @t30 () (= @t1 tptp.sz00)) % 21.40/21.69 (define @t31 () (not @t30)) % 21.40/21.69 (define @t32 () (= @t4 tptp.sz00)) % 21.40/21.69 (define @t33 () (and @t14 (= @t26 @t4))) % 21.40/21.69 (define @t34 () (@list @t11)) % 21.40/21.69 (define @t35 () (tptp.sdtlseqdt0 @t1 @t4)) % 21.40/21.69 (define @t36 () (= @t1 @t4)) % 21.40/21.69 (define @t37 () (tptp.sdtlseqdt0 @t4 @t1)) % 21.40/21.69 (define @t38 () (tptp.sdtlseqdt0 @t4 @t11)) % 21.40/21.69 (define @t39 () (= @t4 @t1)) % 21.40/21.69 (define @t40 () (tptp.sdtpldt0 @t11 @t4)) % 21.40/21.69 (define @t41 () (and (not @t36) @t35)) % 21.40/21.69 (define @t42 () (= @t1 tptp.sz10)) % 21.40/21.69 (define @t43 () (tptp.iLess0 @t1 @t4)) % 21.40/21.69 (define @t44 () (and @t14 (= @t4 @t23))) % 21.40/21.69 (define @t45 () (tptp.doDivides0 @t1 @t4)) % 21.40/21.69 (define @t46 () (tptp.sdtsldt0 @t4 @t1)) % 21.40/21.69 (define @t47 () (and @t31 @t45)) % 21.40/21.69 (define @t48 () (tptp.doDivides0 @t1 @t11)) % 21.40/21.69 (define @t49 () (tptp.doDivides0 @t1 @t12)) % 21.40/21.69 (define @t50 () (tptp.doDivides0 @t4 @t1)) % 21.40/21.69 (define @t51 () (@list @t4)) % 21.40/21.69 (define @t52 () (not @t42)) % 21.40/21.69 (define @t53 () (tptp.aNaturalNumber0 tptp.xm)) % 21.40/21.69 (define @t54 () (tptp.aNaturalNumber0 tptp.xn)) % 21.40/21.69 (define @t55 () (@var "W3" $$unsorted)) % 21.40/21.69 (define @t56 () (tptp.sdtasdt0 @t11 @t55)) % 21.40/21.69 (define @t57 () (tptp.aNaturalNumber0 @t55)) % 21.40/21.69 (define @t58 () (@list @t55)) % 21.40/21.69 (define @t59 () (@var "W4" $$unsorted)) % 21.40/21.69 (define @t60 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 21.40/21.69 (define @t61 () (tptp.sdtpldt0 tptp.xp @t1)) % 21.40/21.69 (define @t62 () (tptp.sdtsldt0 @t60 tptp.xp)) % 21.40/21.69 (define @t63 () (tptp.sdtasdt0 tptp.xp tptp.xk)) % 21.40/21.69 (define @t64 () (= @t60 @t63)) % 21.40/21.69 (define @t65 () (= tptp.xk tptp.sz10)) % 21.40/21.69 (define @t66 () (= tptp.xk tptp.sz00)) % 21.40/21.69 (define @t67 () (tptp.sdtasdt0 tptp.xr @t1)) % 21.40/21.69 (define @t68 () (tptp.aNaturalNumber0 tptp.xr)) % 21.40/21.69 (define @t69 () (and (exists @t3 (and @t2 (= tptp.xn @t67))) (tptp.doDivides0 tptp.xr tptp.xn))) % 21.40/21.69 (define @t70 () (tptp.sdtsldt0 tptp.xn tptp.xr)) % 21.40/21.69 (define @t71 () (tptp.sdtasdt0 tptp.xr @t70)) % 21.40/21.69 (define @t72 () (= tptp.xn @t71)) % 21.40/21.69 (define @t73 () (tptp.aNaturalNumber0 @t70)) % 21.40/21.69 (define @t74 () (and @t73 @t72)) % 21.40/21.69 (define @t75 () (=> @t74 (= @t70 tptp.xn))) % 21.40/21.69 (define @t76 () (not @t75)) % 21.40/21.69 (define @t77 () (tptp.sdtsldt0 @t63 tptp.xr)) % 21.40/21.69 (define @t78 () (tptp.sdtasdt0 @t77 tptp.xr)) % 21.40/21.69 (define @t79 () (= @t60 @t78)) % 21.40/21.69 (define @t80 () (tptp.sdtasdt0 tptp.xr @t77)) % 21.40/21.69 (define @t81 () (= @t63 @t80)) % 21.40/21.69 (define @t82 () (tptp.aNaturalNumber0 @t77)) % 21.40/21.69 (define @t83 () (and @t82 @t81)) % 21.40/21.69 (define @t84 () (=> @t83 @t79)) % 21.40/21.69 (define @t85 () (tptp.sdtasdt0 @t70 tptp.xm)) % 21.40/21.69 (define @t86 () (tptp.sdtasdt0 @t85 tptp.xr)) % 21.40/21.69 (define @t87 () (=> @t74 (= @t86 @t60))) % 21.40/21.69 (define @t88 () (and @t87 @t84)) % 21.40/21.69 (define @t89 () (not @t88)) % 21.40/21.69 (define @t90 () (not @t6)) % 21.40/21.69 (define @t91 () (not @t2)) % 21.40/21.69 (define @t92 () (or @t91 @t90 @t18)) % 21.40/21.69 (define @t93 () (tptp.sdtasdt0 tptp.xm @t70)) % 21.40/21.69 (define @t94 () (not @t73)) % 21.40/21.69 (define @t95 () (not @t53)) % 21.40/21.69 (define @t96 () (or @t95 @t94 (= @t93 @t85))) % 21.40/21.69 (define @t97 () (forall @t8 @t92)) % 21.40/21.69 (define @t98 () (= @t85 @t93)) % 21.40/21.69 (define @t99 () (or @t95 @t94 @t98)) % 21.40/21.69 (define @t100 () (@list false)) % 21.40/21.69 (define @t101 () (@list @t97)) % 21.40/21.69 (define @t102 () (@list false false false)) % 21.40/21.69 (define @t103 () (tptp.sdtasdt0 @t93 tptp.xr)) % 21.40/21.69 (define @t104 () (not @t14)) % 21.40/21.69 (define @t105 () (or @t91 @t90 @t104)) % 21.40/21.69 (define @t106 () (tptp.sdtasdt0 @t70 tptp.xr)) % 21.40/21.69 (define @t107 () (= @t103 (tptp.sdtasdt0 tptp.xm @t106))) % 21.40/21.69 (define @t108 () (not @t68)) % 21.40/21.69 (define @t109 () (or @t95 @t94 @t108 @t107)) % 21.40/21.69 (define @t110 () (= @t71 @t106)) % 21.40/21.69 (define @t111 () (or @t108 @t94 @t110)) % 21.40/21.69 (define @t112 () (tptp.sdtasdt0 tptp.xm tptp.xn)) % 21.40/21.69 (define @t113 () (= @t60 @t112)) % 21.40/21.69 (define @t114 () (not @t54)) % 21.40/21.69 (define @t115 () (or @t114 @t95 @t113)) % 21.40/21.69 (define @t116 () (= @t60 @t86)) % 21.40/21.69 (define @t117 () (=> @t74 @t116)) % 21.40/21.69 (define @t118 () (and @t117 @t84)) % 21.40/21.69 (define @t119 () (tptp.sdtasdt0 tptp.xp @t62)) % 21.40/21.69 (define @t120 () (tptp.sdtsldt0 @t119 tptp.xr)) % 21.40/21.69 (define @t121 () (tptp.sdtasdt0 @t120 tptp.xr)) % 21.40/21.69 (define @t122 () (= @t60 @t121)) % 21.40/21.69 (define @t123 () (tptp.sdtasdt0 tptp.xr @t120)) % 21.40/21.69 (define @t124 () (= @t119 @t123)) % 21.40/21.69 (define @t125 () (tptp.aNaturalNumber0 @t120)) % 21.40/21.69 (define @t126 () (and @t125 @t124)) % 21.40/21.69 (define @t127 () (=> @t126 @t122)) % 21.40/21.69 (define @t128 () (@list true)) % 21.40/21.69 (define @t129 () (@list @t127)) % 21.40/21.69 (define @t130 () (not @t126)) % 21.40/21.69 (define @t131 () (@list @t126)) % 21.40/21.69 (define @t132 () (not @t125)) % 21.40/21.69 (define @t133 () (or @t108 @t132 (= @t123 @t121))) % 21.40/21.69 (define @t134 () (= @t121 @t123)) % 21.40/21.69 (define @t135 () (or @t108 @t132 @t134)) % 21.40/21.69 (assume @p1 (forall @t3 (=> @t2 true))) % 21.40/21.69 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 21.40/21.69 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 21.40/21.69 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 21.40/21.69 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 21.40/21.69 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 21.40/21.69 (assume @p7 (forall @t16 (=> @t15 (= @t13 (tptp.sdtpldt0 @t1 @t12))))) % 21.40/21.69 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 21.40/21.69 (assume @p9 @t19) % 21.40/21.69 (assume @p10 @t21) % 21.40/21.69 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 21.40/21.69 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 21.40/21.69 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t23)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t17 @t22)))))) % 21.40/21.69 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t5 @t26) (= @t10 @t25)) @t24)))) % 21.40/21.69 (assume @p15 (forall @t3 (=> @t2 (=> @t31 (forall (@list @t4 @t11) (=> @t29 (=> (or @t28 @t27) @t24))))))) % 21.40/21.69 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t30 @t32))))) % 21.40/21.69 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t30 @t32))))) % 21.40/21.69 (assume @p18 (forall @t8 (=> @t7 (= @t35 (exists @t34 @t33))))) % 21.40/21.69 (assume @p19 (forall @t8 (=> @t7 (=> @t35 (forall @t34 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t33)))))) % 21.40/21.69 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 21.40/21.69 (assume @p21 (forall @t8 (=> @t7 (=> (and @t35 @t37) @t36)))) % 21.40/21.69 (assume @p22 (forall @t16 (=> @t15 (=> (and @t35 @t38) (tptp.sdtlseqdt0 @t1 @t11))))) % 21.40/21.69 (assume @p23 (forall @t8 (=> @t7 (or @t35 (and (not @t39) @t37))))) % 21.40/21.69 (assume @p24 (forall @t8 (=> @t7 (=> @t41 (forall @t34 (=> @t14 (and (not (= @t25 @t40)) (tptp.sdtlseqdt0 @t25 @t40) (not (= @t26 @t12)) (tptp.sdtlseqdt0 @t26 @t12)))))))) % 21.40/21.69 (assume @p25 (forall @t16 (=> @t15 (=> (and @t31 (not @t24) @t38) (and (not @t28) (tptp.sdtlseqdt0 @t9 @t23) (not @t27) (tptp.sdtlseqdt0 @t17 @t22)))))) % 21.40/21.69 (assume @p26 (forall @t3 (=> @t2 (or @t30 @t42 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 21.40/21.69 (assume @p27 (forall @t8 (=> @t7 (=> @t31 (tptp.sdtlseqdt0 @t4 @t17))))) % 21.40/21.69 (assume @p28 (forall @t8 (=> @t7 (=> @t43 true)))) % 21.40/21.69 (assume @p29 (forall @t8 (=> @t7 (=> @t41 @t43)))) % 21.40/21.69 (assume @p30 (forall @t8 (=> @t7 (= @t45 (exists @t34 @t44))))) % 21.40/21.69 (assume @p31 (forall @t8 (=> @t7 (=> @t47 (forall @t34 (= (= @t11 @t46) @t44)))))) % 21.40/21.69 (assume @p32 (forall @t16 (=> @t15 (=> (and @t45 (tptp.doDivides0 @t4 @t11)) @t48)))) % 21.40/21.69 (assume @p33 (forall @t16 (=> @t15 (=> (and @t45 @t48) @t49)))) % 21.40/21.69 (assume @p34 (forall @t16 (=> @t15 (=> (and @t45 @t49) @t48)))) % 21.40/21.69 (assume @p35 (forall @t8 (=> @t7 (=> (and @t45 (not @t32)) @t35)))) % 21.40/21.69 (assume @p36 (forall @t8 (=> @t7 (=> @t47 (forall @t34 (=> @t14 (= (tptp.sdtasdt0 @t11 @t46) (tptp.sdtsldt0 (tptp.sdtasdt0 @t11 @t4) @t1)))))))) % 21.40/21.69 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t31 @t52 (forall @t51 (=> (and @t6 @t50) (or (= @t4 tptp.sz10) @t39)))))))) % 21.40/21.69 (assume @p38 (forall @t3 (=> (and @t2 @t31 @t52) (exists @t51 (and @t6 @t50 (tptp.isPrime0 @t4)))))) % 21.40/21.69 (assume @p39 (and @t54 @t53 (tptp.aNaturalNumber0 tptp.xp))) % 21.40/21.69 (assume @p40 (forall @t16 (=> @t15 (=> (and (or (and (not (= @t11 tptp.sz00)) (not (= @t11 tptp.sz10)) (forall @t58 (=> (and @t57 (exists (@list @t59) (and (tptp.aNaturalNumber0 @t59) (= @t11 (tptp.sdtasdt0 @t55 @t59)))) (tptp.doDivides0 @t55 @t11)) (or (= @t55 tptp.sz10) (= @t55 @t11))))) (tptp.isPrime0 @t11)) (or (exists @t58 (and @t57 (= @t9 @t56))) (tptp.doDivides0 @t11 @t9))) (=> (tptp.iLess0 @t13 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t58 (and @t57 (= @t1 @t56))) (tptp.doDivides0 @t11 @t1)) (and (exists @t58 (and @t57 (= @t4 @t56))) (tptp.doDivides0 @t11 @t4)))))))) % 21.40/21.69 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t51 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t42 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t60 (tptp.sdtasdt0 tptp.xp @t1)))) (tptp.doDivides0 tptp.xp @t60))) % 21.40/21.69 (assume @p42 (not (or (exists @t3 (and @t2 (= @t61 tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)))) % 21.40/21.69 (assume @p43 (not (or (exists @t3 (and @t2 (= @t61 tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm)))) % 21.40/21.69 (assume @p44 (and (not (= tptp.xn tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xn @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xm @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 21.40/21.69 (assume @p45 (and (tptp.aNaturalNumber0 tptp.xk) @t64 (= tptp.xk @t62))) % 21.40/21.69 (assume @p46 (not (or @t66 @t65))) % 21.40/21.69 (assume @p47 (and (not @t66) (not @t65))) % 21.40/21.69 (assume @p48 (and @t68 (exists @t3 (and @t2 (= tptp.xk @t67))) (tptp.doDivides0 tptp.xr tptp.xk) (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t51 (and @t6 (= tptp.xr @t9))) (tptp.doDivides0 @t1 tptp.xr))) (or @t42 (= @t1 tptp.xr)))) (tptp.isPrime0 tptp.xr))) % 21.40/21.69 (assume @p49 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xk))) (exists @t3 (and @t2 (= @t60 @t67))) (tptp.doDivides0 tptp.xr @t60))) % 21.40/21.69 (assume @p50 (and (not (= tptp.xk tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xk @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xk tptp.xp))) % 21.40/21.69 (assume @p51 (or @t69 (and (exists @t3 (and @t2 (= tptp.xm @t67))) (tptp.doDivides0 tptp.xr tptp.xm)))) % 21.40/21.69 (assume @p52 @t69) % 21.40/21.69 (assume @p53 (and @t76 @t73 @t72 (exists @t3 (and @t2 (= (tptp.sdtpldt0 @t70 @t1) tptp.xn))) (tptp.sdtlseqdt0 @t70 tptp.xn))) % 21.40/21.69 (assume @p54 @t89) % 21.40/21.69 (assume @p55 true) % 21.40/21.69 (step @p56 :rule evaluate :args ((= false true))) % 21.40/21.69 (step @p57 :rule refl :args (tptp.xr)) % 21.40/21.69 (step @p58 :rule aci_norm :args ((= (or (or @t91 @t90) @t18) @t92))) % 21.40/21.69 (step @p59 :rule refl :args (@t18)) % 21.40/21.69 (step @p60 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 21.40/21.69 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or (not @t7) @t18))) % 21.40/21.69 (step @p62 :rule trans :premises (@p61 @p58)) % 21.40/21.69 (step @p63 :rule bool-impl-elim :args (@t7 @t18)) % 21.40/21.69 (step @p64 :rule trans :premises (@p63 @p62)) % 21.40/21.69 (step @p65 :rule cong :premises (@p64) :args (@t19)) % 21.40/21.69 (step @p66 :rule eq_resolve :premises (@p9 @p65)) % 21.40/21.69 (step @p67 :rule eq-symm :args (@t93 @t85)) % 21.40/21.69 (step @p68 :rule refl :args (@t94)) % 21.40/21.69 (step @p69 :rule refl :args (@t95)) % 21.40/21.69 (step @p70 :rule nary_cong :premises (@p69 @p68 @p67) :args (@t96)) % 21.40/21.69 (step @p71 :rule refl :args (@t97)) % 21.40/21.69 (step @p72 :rule cong :premises (@p71 @p70) :args ((=> @t97 @t96))) % 21.40/21.69 (assume-push @p193 @t97) % 21.40/21.69 (step @p74 :rule instantiate :premises (@p66) :args ((@list tptp.xm @t70))) % 21.40/21.69 (step-pop @p194 :rule scope :premises (@p74)) % 21.40/21.69 (step @p75 :rule process_scope :premises (@p194) :args (@t96)) % 21.40/21.69 (step @p77 :rule eq_resolve :premises (@p75 @p72)) % 21.40/21.69 (step @p78 :rule implies_elim :premises (@p77)) % 21.40/21.69 (step @p79 :rule chain_m_resolution :premises (@p78 @p66) :args (@t99 @t100 @t101)) % 21.40/21.69 (step @p80 :rule eq-symm :args (@t70 tptp.xn)) % 21.40/21.69 (step @p81 :rule refl :args (@t74)) % 21.40/21.69 (step @p82 :rule cong :premises (@p81 @p80) :args (@t75)) % 21.40/21.69 (step @p83 :rule cong :premises (@p82) :args (@t76)) % 21.40/21.69 (step @p84 :rule and_elim :premises (@p53) :args (0)) % 21.40/21.69 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 21.40/21.69 (step @p86 :rule not_implies_elim1 :premises (@p85)) % 21.40/21.69 (step @p87 :rule and_elim :premises (@p86) :args (0)) % 21.40/21.69 (step @p88 :rule and_elim :premises (@p39) :args (1)) % 21.40/21.69 (step @p89 :rule cnf_or_pos :args (@t99)) % 21.40/21.69 (step @p90 :rule reordering :premises (@p89) :args ((or @t95 @t94 @t98 (not @t99)))) % 21.40/21.69 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p87 @p79) :args (@t98 @t102 (@list @t53 @t73 @t99))) % 21.40/21.69 (step @p92 :rule symm :premises (@p91)) % 21.40/21.69 (step @p93 :rule cong :premises (@p92 @p57) :args (@t103)) % 21.40/21.69 (step @p94 :rule aci_norm :args ((= (or @t105 @t20) (or @t91 @t90 @t104 @t20)))) % 21.40/21.69 (step @p95 :rule refl :args (@t20)) % 21.40/21.69 (step @p96 :rule aci_norm :args ((= (or @t91 (or @t90 @t104)) @t105))) % 21.40/21.69 (step @p97 :rule bool-and-de-morgan :args (@t6 @t14 true)) % 21.40/21.69 (step @p98 :rule refl :args (@t91)) % 21.40/21.69 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or @t91 (not @t29)))) % 21.40/21.69 (step @p100 :rule bool-and-de-morgan :args (@t2 @t6 (and @t14))) % 21.40/21.69 (step @p101 :rule trans :premises (@p100 @p99)) % 21.40/21.69 (step @p102 :rule trans :premises (@p101 @p96)) % 21.40/21.69 (step @p103 :rule nary_cong :premises (@p102 @p95) :args ((or (not @t15) @t20))) % 21.40/21.69 (step @p104 :rule trans :premises (@p103 @p94)) % 21.40/21.69 (step @p105 :rule bool-impl-elim :args (@t15 @t20)) % 21.40/21.69 (step @p106 :rule trans :premises (@p105 @p104)) % 21.40/21.69 (step @p107 :rule cong :premises (@p106) :args (@t21)) % 21.40/21.69 (step @p108 :rule eq_resolve :premises (@p10 @p107)) % 21.40/21.69 (step @p109 :rule instantiate :premises (@p108) :args ((@list tptp.xm @t70 tptp.xr))) % 21.40/21.69 (step @p110 :rule and_elim :premises (@p48) :args (0)) % 21.40/21.69 (step @p111 :rule cnf_or_pos :args (@t109)) % 21.40/21.69 (step @p112 :rule reordering :premises (@p111) :args ((or @t95 @t108 @t94 @t107 (not @t109)))) % 21.40/21.69 (step @p113 :rule chain_m_resolution :premises (@p112 @p88 @p110 @p87 @p109) :args (@t107 (@list false false false false) (@list @t53 @t68 @t73 @t109))) % 21.40/21.69 (step @p114 :rule symm :premises (@p113)) % 21.40/21.69 (step @p115 :rule instantiate :premises (@p66) :args ((@list tptp.xr @t70))) % 21.40/21.69 (step @p116 :rule cnf_or_pos :args (@t111)) % 21.40/21.69 (step @p117 :rule reordering :premises (@p116) :args ((or @t108 @t94 @t110 (not @t111)))) % 21.40/21.69 (step @p118 :rule chain_m_resolution :premises (@p117 @p110 @p87 @p115) :args (@t110 @t102 (@list @t68 @t73 @t111))) % 21.40/21.69 (step @p119 :rule and_elim :premises (@p86) :args (1)) % 21.40/21.69 (step @p120 :rule trans :premises (@p119 @p118)) % 21.40/21.69 (step @p121 :rule refl :args (tptp.xm)) % 21.40/21.69 (step @p122 :rule cong :premises (@p121 @p120) :args (@t112)) % 21.40/21.69 (step @p123 :rule instantiate :premises (@p66) :args ((@list tptp.xn tptp.xm))) % 21.40/21.69 (step @p124 :rule and_elim :premises (@p39) :args (0)) % 21.40/21.69 (step @p125 :rule cnf_or_pos :args (@t115)) % 21.40/21.69 (step @p126 :rule reordering :premises (@p125) :args ((or @t114 @t95 @t113 (not @t115)))) % 21.40/21.69 (step @p127 :rule chain_m_resolution :premises (@p126 @p124 @p88 @p123) :args (@t113 @t102 (@list @t54 @t53 @t115))) % 21.40/21.69 (step @p128 :rule trans :premises (@p127 @p122 @p114 @p93)) % 21.40/21.70 (step @p129 :rule cnf_implies_neg2 :args (@t117)) % 21.40/21.70 (step @p130 :rule chain_m_resolution :premises (@p129 @p128) :args (@t117 @t100 (@list @t116))) % 21.40/21.70 (step @p131 :rule and_elim :premises (@p45) :args (2)) % 21.40/21.70 (step @p132 :rule refl :args (tptp.xp)) % 21.40/21.70 (step @p133 :rule cong :premises (@p132 @p131) :args (@t63)) % 21.40/21.70 (step @p134 :rule cong :premises (@p133 @p57) :args (@t77)) % 21.40/21.70 (step @p135 :rule cong :premises (@p134 @p57) :args (@t78)) % 21.40/21.70 (step @p136 :rule refl :args (@t60)) % 21.40/21.70 (step @p137 :rule cong :premises (@p136 @p135) :args (@t79)) % 21.40/21.70 (step @p138 :rule cong :premises (@p57 @p134) :args (@t80)) % 21.40/21.70 (step @p139 :rule cong :premises (@p133 @p138) :args (@t81)) % 21.40/21.70 (step @p140 :rule cong :premises (@p134) :args (@t82)) % 21.40/21.70 (step @p141 :rule nary_cong :premises (@p140 @p139) :args (@t83)) % 21.40/21.70 (step @p142 :rule cong :premises (@p141 @p137) :args (@t84)) % 21.40/21.70 (step @p143 :rule refl :args (@t117)) % 21.40/21.70 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t118)) % 21.40/21.70 (step @p145 :rule cong :premises (@p144) :args ((not @t118))) % 21.40/21.70 (step @p146 :rule refl :args (@t84)) % 21.40/21.70 (step @p147 :rule eq-symm :args (@t86 @t60)) % 21.40/21.70 (step @p148 :rule cong :premises (@p81 @p147) :args (@t87)) % 21.40/21.70 (step @p149 :rule nary_cong :premises (@p148 @p146) :args (@t88)) % 21.40/21.70 (step @p150 :rule cong :premises (@p149) :args (@t89)) % 21.40/21.70 (step @p151 :rule trans :premises (@p150 @p145)) % 21.40/21.70 (step @p152 :rule eq_resolve :premises (@p54 @p151)) % 21.40/21.70 (step @p153 :rule not_and :premises (@p152)) % 21.40/21.70 (step @p154 :rule chain_m_resolution :premises (@p153 @p130) :args ((not @t127) @t100 (@list @t117))) % 21.40/21.70 (step @p155 :rule cnf_implies_neg1 :args (@t127)) % 21.40/21.70 (step @p156 :rule reordering :premises (@p155) :args ((or @t126 @t127))) % 21.40/21.70 (step @p157 :rule chain_m_resolution :premises (@p156 @p154) :args (@t126 @t128 @t129)) % 21.40/21.70 (step @p158 :rule cnf_and_pos :args (@t126 1)) % 21.40/21.70 (step @p159 :rule reordering :premises (@p158) :args ((or @t124 @t130))) % 21.40/21.70 (step @p160 :rule chain_m_resolution :premises (@p159 @p157) :args (@t124 @t100 @t131)) % 21.40/21.70 (step @p161 :rule symm :premises (@p160)) % 21.40/21.70 (step @p162 :rule eq-symm :args (@t123 @t121)) % 21.40/21.70 (step @p163 :rule refl :args (@t132)) % 21.40/21.70 (step @p164 :rule refl :args (@t108)) % 21.40/21.70 (step @p165 :rule nary_cong :premises (@p164 @p163 @p162) :args (@t133)) % 21.40/21.70 (step @p166 :rule cong :premises (@p71 @p165) :args ((=> @t97 @t133))) % 21.40/21.70 (assume-push @p195 @t97) % 21.40/21.70 (step @p168 :rule instantiate :premises (@p66) :args ((@list tptp.xr @t120))) % 21.40/21.70 (step-pop @p196 :rule scope :premises (@p168)) % 21.40/21.70 (step @p169 :rule process_scope :premises (@p196) :args (@t133)) % 21.40/21.70 (step @p171 :rule eq_resolve :premises (@p169 @p166)) % 21.40/21.70 (step @p172 :rule implies_elim :premises (@p171)) % 21.40/21.70 (step @p173 :rule chain_m_resolution :premises (@p172 @p66) :args (@t135 @t100 @t101)) % 21.40/21.70 (step @p174 :rule cnf_and_pos :args (@t126 0)) % 21.40/21.70 (step @p175 :rule reordering :premises (@p174) :args ((or @t125 @t130))) % 21.40/21.70 (step @p176 :rule chain_m_resolution :premises (@p175 @p157) :args (@t125 @t100 @t131)) % 21.40/21.70 (step @p177 :rule cnf_or_pos :args (@t135)) % 21.40/21.70 (step @p178 :rule reordering :premises (@p177) :args ((or @t108 @t132 @t134 (not @t135)))) % 21.40/21.70 (step @p179 :rule chain_m_resolution :premises (@p178 @p110 @p176 @p173) :args (@t134 @t102 (@list @t68 @t125 @t135))) % 21.55/21.70 (step @p180 :rule trans :premises (@p179 @p161)) % 21.55/21.70 (step @p181 :rule symm :premises (@p180)) % 21.55/21.70 (step @p182 :rule cong :premises (@p136 @p133) :args (@t64)) % 21.55/21.70 (step @p183 :rule and_elim :premises (@p45) :args (1)) % 21.55/21.70 (step @p184 :rule eq_resolve :premises (@p183 @p182)) % 21.55/21.70 (step @p185 :rule trans :premises (@p184 @p181)) % 21.55/21.70 (step @p186 :rule true_intro :premises (@p185)) % 21.55/21.70 (step @p187 :rule cnf_implies_neg2 :args (@t127)) % 21.55/21.70 (step @p188 :rule chain_m_resolution :premises (@p187 @p154) :args ((not @t122) @t128 @t129)) % 21.55/21.70 (step @p189 :rule false_intro :premises (@p188)) % 21.55/21.70 (step @p190 :rule symm :premises (@p189)) % 21.55/21.70 (step @p191 :rule trans :premises (@p190 @p186)) % 21.55/21.70 (step @p192 false :rule eq_resolve :premises (@p191 @p56)) % 21.55/21.70 ) % 21.55/21.70 % SZS output end Proof % 21.55/21.70 % cvc5 exiting %------------------------------------------------------------------------------