%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM513+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 1.33s 1.54s % Output : Proof 1.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM513+3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n015.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 11:26:34 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 1.33/1.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.33/1.54 % SZS status Theorem % 1.33/1.54 % SZS output start Proof % 1.33/1.54 ( % 1.33/1.54 (declare-sort $$unsorted 0) % 1.33/1.54 (declare-const tptp.xr $$unsorted) % 1.33/1.54 (declare-const tptp.xk $$unsorted) % 1.33/1.54 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 1.33/1.54 (declare-const tptp.xm $$unsorted) % 1.33/1.54 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.33/1.54 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 1.33/1.54 (declare-const tptp.xn $$unsorted) % 1.33/1.54 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 1.33/1.54 (declare-const tptp.sz00 $$unsorted) % 1.33/1.54 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.33/1.54 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.33/1.54 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.33/1.54 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 1.33/1.54 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 1.33/1.54 (declare-const tptp.sz10 $$unsorted) % 1.33/1.54 (declare-const tptp.xp $$unsorted) % 1.33/1.54 (define @t1 () (@var "W0" $$unsorted)) % 1.33/1.54 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 1.33/1.54 (define @t3 () (@list @t1)) % 1.33/1.54 (define @t4 () (@var "W1" $$unsorted)) % 1.33/1.54 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 1.33/1.54 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 1.33/1.54 (define @t7 () (and @t2 @t6)) % 1.33/1.54 (define @t8 () (@list @t1 @t4)) % 1.33/1.54 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 1.33/1.54 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 1.33/1.54 (define @t11 () (@var "W2" $$unsorted)) % 1.33/1.54 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 1.33/1.54 (define @t13 () (tptp.sdtpldt0 @t5 @t11)) % 1.33/1.54 (define @t14 () (tptp.aNaturalNumber0 @t11)) % 1.33/1.54 (define @t15 () (and @t2 @t6 @t14)) % 1.33/1.54 (define @t16 () (@list @t1 @t4 @t11)) % 1.33/1.54 (define @t17 () (tptp.sdtasdt0 @t4 @t1)) % 1.33/1.54 (define @t18 () (= @t9 @t17)) % 1.33/1.54 (define @t19 () (forall @t8 (=> @t7 @t18))) % 1.33/1.54 (define @t20 () (tptp.sdtasdt0 @t11 @t1)) % 1.33/1.54 (define @t21 () (tptp.sdtasdt0 @t1 @t11)) % 1.33/1.54 (define @t22 () (= @t4 @t11)) % 1.33/1.54 (define @t23 () (tptp.sdtpldt0 @t11 @t1)) % 1.33/1.54 (define @t24 () (tptp.sdtpldt0 @t1 @t11)) % 1.33/1.54 (define @t25 () (= @t17 @t20)) % 1.33/1.54 (define @t26 () (= @t9 @t21)) % 1.33/1.54 (define @t27 () (= @t1 tptp.sz00)) % 1.33/1.54 (define @t28 () (not @t27)) % 1.33/1.54 (define @t29 () (= @t4 tptp.sz00)) % 1.33/1.54 (define @t30 () (and @t14 (= @t24 @t4))) % 1.33/1.54 (define @t31 () (@list @t11)) % 1.33/1.54 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 1.33/1.54 (define @t33 () (= @t1 @t4)) % 1.33/1.54 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 1.33/1.54 (define @t35 () (tptp.sdtlseqdt0 @t4 @t11)) % 1.33/1.54 (define @t36 () (= @t4 @t1)) % 1.33/1.54 (define @t37 () (tptp.sdtpldt0 @t11 @t4)) % 1.33/1.54 (define @t38 () (and (not @t33) @t32)) % 1.33/1.54 (define @t39 () (= @t1 tptp.sz10)) % 1.33/1.54 (define @t40 () (tptp.iLess0 @t1 @t4)) % 1.33/1.54 (define @t41 () (and @t14 (= @t4 @t21))) % 1.33/1.54 (define @t42 () (tptp.doDivides0 @t1 @t4)) % 1.33/1.54 (define @t43 () (tptp.sdtsldt0 @t4 @t1)) % 1.33/1.54 (define @t44 () (and @t28 @t42)) % 1.33/1.54 (define @t45 () (tptp.doDivides0 @t1 @t11)) % 1.33/1.54 (define @t46 () (tptp.doDivides0 @t1 @t12)) % 1.33/1.54 (define @t47 () (= (tptp.sdtasdt0 @t11 @t43) (tptp.sdtsldt0 (tptp.sdtasdt0 @t11 @t4) @t1))) % 1.33/1.54 (define @t48 () (forall @t31 (=> @t14 @t47))) % 1.33/1.54 (define @t49 () (=> @t44 @t48)) % 1.33/1.54 (define @t50 () (=> @t7 @t49)) % 1.33/1.54 (define @t51 () (forall @t8 @t50)) % 1.33/1.54 (define @t52 () (tptp.doDivides0 @t4 @t1)) % 1.33/1.54 (define @t53 () (@list @t4)) % 1.33/1.54 (define @t54 () (not @t39)) % 1.33/1.54 (define @t55 () (tptp.aNaturalNumber0 tptp.xp)) % 1.33/1.54 (define @t56 () (tptp.aNaturalNumber0 tptp.xm)) % 1.33/1.54 (define @t57 () (tptp.aNaturalNumber0 tptp.xn)) % 1.33/1.54 (define @t58 () (@var "W3" $$unsorted)) % 1.33/1.54 (define @t59 () (tptp.sdtasdt0 @t11 @t58)) % 1.33/1.54 (define @t60 () (tptp.aNaturalNumber0 @t58)) % 1.33/1.54 (define @t61 () (@list @t58)) % 1.33/1.54 (define @t62 () (@var "W4" $$unsorted)) % 1.33/1.54 (define @t63 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 1.33/1.54 (define @t64 () (tptp.sdtpldt0 tptp.xp @t1)) % 1.33/1.54 (define @t65 () (tptp.sdtasdt0 tptp.xp tptp.xk)) % 1.33/1.54 (define @t66 () (= @t63 @t65)) % 1.33/1.54 (define @t67 () (tptp.aNaturalNumber0 tptp.xk)) % 1.33/1.54 (define @t68 () (= tptp.xk tptp.sz10)) % 1.33/1.54 (define @t69 () (= tptp.xk tptp.sz00)) % 1.33/1.54 (define @t70 () (= tptp.xr tptp.sz00)) % 1.33/1.54 (define @t71 () (tptp.doDivides0 tptp.xr tptp.xk)) % 1.33/1.54 (define @t72 () (tptp.sdtasdt0 tptp.xr @t1)) % 1.33/1.54 (define @t73 () (tptp.aNaturalNumber0 tptp.xr)) % 1.33/1.54 (define @t74 () (tptp.doDivides0 tptp.xr tptp.xn)) % 1.33/1.54 (define @t75 () (and (exists @t3 (and @t2 (= tptp.xn @t72))) @t74)) % 1.33/1.54 (define @t76 () (tptp.sdtsldt0 tptp.xn tptp.xr)) % 1.33/1.54 (define @t77 () (= tptp.xn (tptp.sdtasdt0 tptp.xr @t76))) % 1.33/1.54 (define @t78 () (tptp.aNaturalNumber0 @t76)) % 1.33/1.54 (define @t79 () (and @t78 @t77)) % 1.33/1.54 (define @t80 () (=> @t79 (= @t76 tptp.xn))) % 1.33/1.54 (define @t81 () (not @t80)) % 1.33/1.54 (define @t82 () (tptp.sdtsldt0 @t65 tptp.xr)) % 1.33/1.54 (define @t83 () (tptp.sdtasdt0 @t76 tptp.xm)) % 1.33/1.54 (define @t84 () (tptp.sdtsldt0 tptp.xk tptp.xr)) % 1.33/1.54 (define @t85 () (tptp.sdtasdt0 tptp.xp @t84)) % 1.33/1.54 (define @t86 () (=> @t79 (= @t85 @t83))) % 1.33/1.54 (define @t87 () (and (tptp.aNaturalNumber0 @t84) (= tptp.xk (tptp.sdtasdt0 tptp.xr @t84)))) % 1.33/1.54 (define @t88 () (=> @t87 @t86)) % 1.33/1.54 (define @t89 () (not @t88)) % 1.33/1.54 (define @t90 () (not @t6)) % 1.33/1.54 (define @t91 () (not @t2)) % 1.33/1.54 (define @t92 () (or @t91 @t90)) % 1.33/1.54 (define @t93 () (not @t7)) % 1.33/1.54 (define @t94 () (tptp.sdtasdt0 tptp.xm tptp.xn)) % 1.33/1.54 (define @t95 () (= @t63 @t94)) % 1.33/1.54 (define @t96 () (not @t56)) % 1.33/1.54 (define @t97 () (not @t57)) % 1.33/1.54 (define @t98 () (or @t97 @t96 @t95)) % 1.33/1.54 (define @t99 () (@list false false false)) % 1.33/1.54 (define @t100 () (tptp.sdtasdt0 tptp.xm @t76)) % 1.33/1.54 (define @t101 () (= @t83 @t100)) % 1.33/1.54 (define @t102 () (not @t78)) % 1.33/1.54 (define @t103 () (or @t102 @t96 @t101)) % 1.33/1.54 (define @t104 () (@var "BOUND_VARIABLE_8238" $$unsorted)) % 1.33/1.54 (define @t105 () (= (tptp.sdtasdt0 @t104 @t43) (tptp.sdtsldt0 (tptp.sdtasdt0 @t104 @t4) @t1))) % 1.33/1.54 (define @t106 () (not (tptp.aNaturalNumber0 @t104))) % 1.33/1.54 (define @t107 () (not @t42)) % 1.33/1.54 (define @t108 () (or @t91 @t90 @t27 @t107 @t106 @t105)) % 1.33/1.54 (define @t109 () (or @t106 @t105)) % 1.33/1.54 (define @t110 () (or @t91 @t90 @t27 @t107 @t109)) % 1.33/1.54 (define @t111 () (@list @t1 @t4 @t104)) % 1.33/1.54 (define @t112 () (forall @t111 @t110)) % 1.33/1.54 (define @t113 () (@list @t104)) % 1.33/1.54 (define @t114 () (forall @t113 @t110)) % 1.33/1.54 (define @t115 () (forall @t113 @t109)) % 1.33/1.54 (define @t116 () (or @t91 @t90 @t27 @t107 @t115)) % 1.33/1.54 (define @t117 () (forall @t31 (or (not @t14) @t47))) % 1.33/1.54 (define @t118 () (or @t91 @t90 @t27 @t107 @t117)) % 1.33/1.54 (define @t119 () (or @t27 @t107 @t117)) % 1.33/1.54 (define @t120 () (=> @t44 @t117)) % 1.33/1.54 (define @t121 () (not @t55)) % 1.33/1.54 (define @t122 () (not @t71)) % 1.33/1.54 (define @t123 () (not @t67)) % 1.33/1.54 (define @t124 () (not @t73)) % 1.33/1.54 (define @t125 () (or @t124 @t123 @t70 @t122 @t121 (= @t85 @t82))) % 1.33/1.54 (define @t126 () (forall @t111 @t108)) % 1.33/1.54 (define @t127 () (= @t82 @t85)) % 1.33/1.54 (define @t128 () (= tptp.sz00 tptp.xr)) % 1.33/1.54 (define @t129 () (or @t124 @t123 @t128 @t122 @t121 @t127)) % 1.33/1.54 (define @t130 () (@list false)) % 1.33/1.54 (define @t131 () (@list @t126)) % 1.33/1.54 (define @t132 () (@list true false false false false false)) % 1.33/1.54 (define @t133 () (tptp.sdtsldt0 @t94 tptp.xr)) % 1.33/1.54 (define @t134 () (= @t100 @t133)) % 1.33/1.54 (define @t135 () (not @t74)) % 1.33/1.54 (define @t136 () (or @t124 @t97 @t70 @t135 @t96 @t134)) % 1.33/1.54 (define @t137 () (or @t124 @t97 @t128 @t135 @t96 @t134)) % 1.33/1.54 (define @t138 () (not @t134)) % 1.33/1.54 (define @t139 () (not @t127)) % 1.33/1.54 (define @t140 () (not @t101)) % 1.33/1.54 (define @t141 () (not @t95)) % 1.33/1.54 (define @t142 () (= @t83 @t85)) % 1.33/1.54 (define @t143 () (not @t66)) % 1.33/1.54 (define @t144 () (not @t142)) % 1.33/1.54 (define @t145 () (and @t138 @t134)) % 1.33/1.54 (assume @p1 (forall @t3 (=> @t2 true))) % 1.33/1.54 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 1.33/1.54 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 1.33/1.54 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 1.33/1.54 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 1.33/1.54 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 1.33/1.54 (assume @p7 (forall @t16 (=> @t15 (= @t13 (tptp.sdtpldt0 @t1 @t12))))) % 1.33/1.54 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 1.33/1.54 (assume @p9 @t19) % 1.33/1.54 (assume @p10 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))))) % 1.33/1.54 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 1.33/1.54 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 1.33/1.54 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t21)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t17 @t20)))))) % 1.33/1.54 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t5 @t24) (= @t10 @t23)) @t22)))) % 1.33/1.54 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t11) (=> (and @t6 @t14) (=> (or @t26 @t25) @t22))))))) % 1.33/1.54 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 1.33/1.54 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t27 @t29))))) % 1.33/1.54 (assume @p18 (forall @t8 (=> @t7 (= @t32 (exists @t31 @t30))))) % 1.33/1.54 (assume @p19 (forall @t8 (=> @t7 (=> @t32 (forall @t31 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 1.33/1.54 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 1.33/1.54 (assume @p21 (forall @t8 (=> @t7 (=> (and @t32 @t34) @t33)))) % 1.33/1.54 (assume @p22 (forall @t16 (=> @t15 (=> (and @t32 @t35) (tptp.sdtlseqdt0 @t1 @t11))))) % 1.33/1.54 (assume @p23 (forall @t8 (=> @t7 (or @t32 (and (not @t36) @t34))))) % 1.33/1.54 (assume @p24 (forall @t8 (=> @t7 (=> @t38 (forall @t31 (=> @t14 (and (not (= @t23 @t37)) (tptp.sdtlseqdt0 @t23 @t37) (not (= @t24 @t12)) (tptp.sdtlseqdt0 @t24 @t12)))))))) % 1.33/1.54 (assume @p25 (forall @t16 (=> @t15 (=> (and @t28 (not @t22) @t35) (and (not @t26) (tptp.sdtlseqdt0 @t9 @t21) (not @t25) (tptp.sdtlseqdt0 @t17 @t20)))))) % 1.33/1.54 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t39 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 1.33/1.54 (assume @p27 (forall @t8 (=> @t7 (=> @t28 (tptp.sdtlseqdt0 @t4 @t17))))) % 1.33/1.54 (assume @p28 (forall @t8 (=> @t7 (=> @t40 true)))) % 1.33/1.54 (assume @p29 (forall @t8 (=> @t7 (=> @t38 @t40)))) % 1.33/1.54 (assume @p30 (forall @t8 (=> @t7 (= @t42 (exists @t31 @t41))))) % 1.33/1.54 (assume @p31 (forall @t8 (=> @t7 (=> @t44 (forall @t31 (= (= @t11 @t43) @t41)))))) % 1.33/1.54 (assume @p32 (forall @t16 (=> @t15 (=> (and @t42 (tptp.doDivides0 @t4 @t11)) @t45)))) % 1.33/1.54 (assume @p33 (forall @t16 (=> @t15 (=> (and @t42 @t45) @t46)))) % 1.33/1.54 (assume @p34 (forall @t16 (=> @t15 (=> (and @t42 @t46) @t45)))) % 1.33/1.54 (assume @p35 (forall @t8 (=> @t7 (=> (and @t42 (not @t29)) @t32)))) % 1.33/1.54 (assume @p36 @t51) % 1.33/1.54 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t28 @t54 (forall @t53 (=> (and @t6 @t52) (or (= @t4 tptp.sz10) @t36)))))))) % 1.33/1.54 (assume @p38 (forall @t3 (=> (and @t2 @t28 @t54) (exists @t53 (and @t6 @t52 (tptp.isPrime0 @t4)))))) % 1.33/1.54 (assume @p39 (and @t57 @t56 @t55)) % 1.33/1.54 (assume @p40 (forall @t16 (=> @t15 (=> (and (or (and (not (= @t11 tptp.sz00)) (not (= @t11 tptp.sz10)) (forall @t61 (=> (and @t60 (exists (@list @t62) (and (tptp.aNaturalNumber0 @t62) (= @t11 (tptp.sdtasdt0 @t58 @t62)))) (tptp.doDivides0 @t58 @t11)) (or (= @t58 tptp.sz10) (= @t58 @t11))))) (tptp.isPrime0 @t11)) (or (exists @t61 (and @t60 (= @t9 @t59))) (tptp.doDivides0 @t11 @t9))) (=> (tptp.iLess0 @t13 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t61 (and @t60 (= @t1 @t59))) (tptp.doDivides0 @t11 @t1)) (and (exists @t61 (and @t60 (= @t4 @t59))) (tptp.doDivides0 @t11 @t4)))))))) % 1.33/1.54 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t53 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t39 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t63 (tptp.sdtasdt0 tptp.xp @t1)))) (tptp.doDivides0 tptp.xp @t63))) % 1.33/1.54 (assume @p42 (not (or (exists @t3 (and @t2 (= @t64 tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)))) % 1.33/1.54 (assume @p43 (not (or (exists @t3 (and @t2 (= @t64 tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm)))) % 1.33/1.54 (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))) % 1.33/1.54 (assume @p45 (and @t67 @t66 (= tptp.xk (tptp.sdtsldt0 @t63 tptp.xp)))) % 1.33/1.54 (assume @p46 (not (or @t69 @t68))) % 1.33/1.54 (assume @p47 (and (not @t69) (not @t68))) % 1.33/1.54 (assume @p48 (and @t73 (exists @t3 (and @t2 (= tptp.xk @t72))) @t71 (not @t70) (not (= tptp.xr tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t53 (and @t6 (= tptp.xr @t9))) (tptp.doDivides0 @t1 tptp.xr))) (or @t39 (= @t1 tptp.xr)))) (tptp.isPrime0 tptp.xr))) % 1.33/1.54 (assume @p49 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xk))) (exists @t3 (and @t2 (= @t63 @t72))) (tptp.doDivides0 tptp.xr @t63))) % 1.33/1.54 (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))) % 1.33/1.54 (assume @p51 (or @t75 (and (exists @t3 (and @t2 (= tptp.xm @t72))) (tptp.doDivides0 tptp.xr tptp.xm)))) % 1.33/1.54 (assume @p52 @t75) % 1.33/1.54 (assume @p53 (and @t81 @t78 @t77 (exists @t3 (and @t2 (= (tptp.sdtpldt0 @t76 @t1) tptp.xn))) (tptp.sdtlseqdt0 @t76 tptp.xn))) % 1.33/1.54 (assume @p54 (and @t78 @t77 (= (tptp.sdtasdt0 @t83 tptp.xr) @t63) (tptp.aNaturalNumber0 @t82) (= @t65 (tptp.sdtasdt0 tptp.xr @t82)) (= @t63 (tptp.sdtasdt0 @t82 tptp.xr)))) % 1.33/1.54 (assume @p55 @t89) % 1.33/1.54 (assume @p56 true) % 1.33/1.54 (step @p57 :rule and_elim :premises (@p45) :args (1)) % 1.33/1.54 (step @p58 :rule eq-symm :args (@t85 @t83)) % 1.33/1.54 (step @p59 :rule refl :args (@t79)) % 1.33/1.54 (step @p60 :rule cong :premises (@p59 @p58) :args (@t86)) % 1.33/1.54 (step @p61 :rule refl :args (@t87)) % 1.33/1.54 (step @p62 :rule cong :premises (@p61 @p60) :args (@t88)) % 1.33/1.54 (step @p63 :rule cong :premises (@p62) :args (@t89)) % 1.33/1.54 (step @p64 :rule eq_resolve :premises (@p55 @p63)) % 1.33/1.54 (step @p65 :rule not_implies_elim2 :premises (@p64)) % 1.33/1.54 (step @p66 :rule not_implies_elim2 :premises (@p65)) % 1.33/1.54 (step @p67 :rule aci_norm :args ((= (or @t92 @t18) (or @t91 @t90 @t18)))) % 1.33/1.54 (step @p68 :rule refl :args (@t18)) % 1.33/1.54 (step @p69 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 1.33/1.54 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or @t93 @t18))) % 1.33/1.54 (step @p71 :rule trans :premises (@p70 @p67)) % 1.33/1.54 (step @p72 :rule bool-impl-elim :args (@t7 @t18)) % 1.33/1.54 (step @p73 :rule trans :premises (@p72 @p71)) % 1.33/1.54 (step @p74 :rule cong :premises (@p73) :args (@t19)) % 1.33/1.54 (step @p75 :rule eq_resolve :premises (@p9 @p74)) % 1.33/1.54 (step @p76 :rule instantiate :premises (@p75) :args ((@list tptp.xn tptp.xm))) % 1.33/1.54 (step @p77 :rule and_elim :premises (@p39) :args (1)) % 1.33/1.54 (step @p78 :rule and_elim :premises (@p39) :args (0)) % 1.33/1.54 (step @p79 :rule cnf_or_pos :args (@t98)) % 1.33/1.54 (step @p80 :rule reordering :premises (@p79) :args ((or @t97 @t96 @t95 (not @t98)))) % 1.33/1.54 (step @p81 :rule chain_m_resolution :premises (@p80 @p78 @p77 @p76) :args (@t95 @t99 (@list @t57 @t56 @t98))) % 1.33/1.54 (step @p82 :rule instantiate :premises (@p75) :args ((@list @t76 tptp.xm))) % 1.33/1.54 (step @p83 :rule eq-symm :args (@t76 tptp.xn)) % 1.33/1.54 (step @p84 :rule cong :premises (@p59 @p83) :args (@t80)) % 1.33/1.54 (step @p85 :rule cong :premises (@p84) :args (@t81)) % 1.33/1.54 (step @p86 :rule and_elim :premises (@p53) :args (0)) % 1.33/1.54 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 1.33/1.54 (step @p88 :rule not_implies_elim1 :premises (@p87)) % 1.33/1.54 (step @p89 :rule and_elim :premises (@p88) :args (0)) % 1.33/1.54 (step @p90 :rule cnf_or_pos :args (@t103)) % 1.33/1.54 (step @p91 :rule reordering :premises (@p90) :args ((or @t96 @t102 @t101 (not @t103)))) % 1.33/1.54 (step @p92 :rule chain_m_resolution :premises (@p91 @p77 @p89 @p82) :args (@t101 @t99 (@list @t56 @t78 @t103))) % 1.33/1.54 (step @p93 :rule aci_norm :args ((= @t110 @t108))) % 1.33/1.54 (step @p94 :rule cong :premises (@p93) :args (@t112)) % 1.33/1.54 (step @p95 :rule quant-merge-prenex :args ((= (forall @t8 @t114) @t112))) % 1.33/1.54 (step @p96 :rule alpha_equiv :args (@t115 (@list @t104) (@list @t11))) % 1.33/1.54 (step @p97 :rule refl :args (@t107)) % 1.33/1.54 (step @p98 :rule refl :args (@t27)) % 1.33/1.54 (step @p99 :rule refl :args (@t90)) % 1.33/1.54 (step @p100 :rule refl :args (@t91)) % 1.33/1.54 (step @p101 :rule nary_cong :premises (@p100 @p99 @p98 @p97 @p96) :args (@t116)) % 1.33/1.54 (step @p102 :rule quant-miniscope-or :args ((= @t114 @t116))) % 1.33/1.54 (step @p103 :rule trans :premises (@p102 @p101)) % 1.33/1.54 (step @p104 :rule symm :premises (@p103)) % 1.33/1.54 (step @p105 :rule cong :premises (@p104) :args ((forall @t8 @t118))) % 1.33/1.54 (step @p106 :rule trans :premises (@p105 @p95)) % 1.33/1.54 (step @p107 :rule trans :premises (@p106 @p94)) % 1.33/1.54 (step @p108 :rule aci_norm :args ((= (or @t92 @t119) @t118))) % 1.33/1.54 (step @p109 :rule aci_norm :args ((= (or (or @t27 @t107) @t117) @t119))) % 1.33/1.54 (step @p110 :rule refl :args (@t117)) % 1.33/1.54 (step @p111 :rule bool-double-not-elim :args (@t27)) % 1.33/1.54 (step @p112 :rule nary_cong :premises (@p111 @p97) :args ((or (not @t28) @t107))) % 1.33/1.54 (step @p113 :rule bool-and-de-morgan :args (@t28 @t42 true)) % 1.33/1.54 (step @p114 :rule trans :premises (@p113 @p112)) % 1.33/1.54 (step @p115 :rule nary_cong :premises (@p114 @p110) :args ((or (not @t44) @t117))) % 1.33/1.54 (step @p116 :rule trans :premises (@p115 @p109)) % 1.33/1.54 (step @p117 :rule bool-impl-elim :args (@t44 @t117)) % 1.33/1.54 (step @p118 :rule trans :premises (@p117 @p116)) % 1.33/1.54 (step @p119 :rule nary_cong :premises (@p69 @p118) :args ((or @t93 @t120))) % 1.33/1.54 (step @p120 :rule trans :premises (@p119 @p108)) % 1.33/1.54 (step @p121 :rule bool-impl-elim :args (@t7 @t120)) % 1.33/1.54 (step @p122 :rule trans :premises (@p121 @p120)) % 1.33/1.54 (step @p123 :rule cong :premises (@p122) :args ((forall @t8 (=> @t7 @t120)))) % 1.33/1.54 (step @p124 :rule trans :premises (@p123 @p107)) % 1.33/1.54 (step @p125 :rule bool-impl-elim :args (@t14 @t47)) % 1.33/1.54 (step @p126 :rule cong :premises (@p125) :args (@t48)) % 1.33/1.54 (step @p127 :rule refl :args (@t44)) % 1.33/1.54 (step @p128 :rule cong :premises (@p127 @p126) :args (@t49)) % 1.33/1.54 (step @p129 :rule refl :args (@t7)) % 1.33/1.54 (step @p130 :rule cong :premises (@p129 @p128) :args (@t50)) % 1.33/1.54 (step @p131 :rule cong :premises (@p130) :args (@t51)) % 1.33/1.54 (step @p132 :rule trans :premises (@p131 @p124)) % 1.33/1.54 (step @p133 :rule eq_resolve :premises (@p36 @p132)) % 1.33/1.54 (step @p134 :rule eq-symm :args (@t85 @t82)) % 1.33/1.54 (step @p135 :rule refl :args (@t121)) % 1.33/1.54 (step @p136 :rule refl :args (@t122)) % 1.33/1.54 (step @p137 :rule eq-symm :args (tptp.xr tptp.sz00)) % 1.33/1.54 (step @p138 :rule refl :args (@t123)) % 1.33/1.54 (step @p139 :rule refl :args (@t124)) % 1.33/1.54 (step @p140 :rule nary_cong :premises (@p139 @p138 @p137 @p136 @p135 @p134) :args (@t125)) % 1.33/1.54 (step @p141 :rule refl :args (@t126)) % 1.33/1.54 (step @p142 :rule cong :premises (@p141 @p140) :args ((=> @t126 @t125))) % 1.33/1.54 (assume-push @p224 @t126) % 1.33/1.54 (step @p144 :rule instantiate :premises (@p133) :args ((@list tptp.xr tptp.xk tptp.xp))) % 1.33/1.54 (step-pop @p225 :rule scope :premises (@p144)) % 1.33/1.54 (step @p145 :rule process_scope :premises (@p225) :args (@t125)) % 1.33/1.54 (step @p147 :rule eq_resolve :premises (@p145 @p142)) % 1.33/1.54 (step @p148 :rule implies_elim :premises (@p147)) % 1.33/1.54 (step @p149 :rule chain_m_resolution :premises (@p148 @p133) :args (@t129 @t130 @t131)) % 1.33/1.54 (step @p150 :rule and_elim :premises (@p48) :args (2)) % 1.33/1.54 (step @p151 :rule and_elim :premises (@p48) :args (0)) % 1.33/1.54 (step @p152 :rule and_elim :premises (@p45) :args (0)) % 1.33/1.54 (step @p153 :rule and_elim :premises (@p39) :args (2)) % 1.33/1.54 (step @p154 :rule and_elim :premises (@p48) :args (3)) % 1.33/1.54 (step @p155 :rule symm :premises (@p154)) % 1.33/1.54 (step @p156 :rule cnf_or_pos :args (@t129)) % 1.33/1.54 (step @p157 :rule reordering :premises (@p156) :args ((or @t128 @t121 @t123 @t124 @t122 @t127 (not @t129)))) % 1.33/1.54 (step @p158 :rule chain_m_resolution :premises (@p157 @p155 @p153 @p152 @p151 @p150 @p149) :args (@t127 @t132 (@list @t128 @t55 @t67 @t73 @t71 @t129))) % 1.33/1.54 (step @p159 :rule refl :args (@t134)) % 1.33/1.54 (step @p160 :rule refl :args (@t96)) % 1.33/1.54 (step @p161 :rule refl :args (@t135)) % 1.33/1.54 (step @p162 :rule refl :args (@t97)) % 1.33/1.54 (step @p163 :rule nary_cong :premises (@p139 @p162 @p137 @p161 @p160 @p159) :args (@t136)) % 1.33/1.54 (step @p164 :rule cong :premises (@p141 @p163) :args ((=> @t126 @t136))) % 1.33/1.54 (assume-push @p226 @t126) % 1.33/1.54 (step @p166 :rule instantiate :premises (@p133) :args ((@list tptp.xr tptp.xn tptp.xm))) % 1.33/1.54 (step-pop @p227 :rule scope :premises (@p166)) % 1.33/1.54 (step @p167 :rule process_scope :premises (@p227) :args (@t136)) % 1.33/1.54 (step @p169 :rule eq_resolve :premises (@p167 @p164)) % 1.33/1.54 (step @p170 :rule implies_elim :premises (@p169)) % 1.33/1.54 (step @p171 :rule chain_m_resolution :premises (@p170 @p133) :args (@t137 @t130 @t131)) % 1.33/1.54 (step @p172 :rule and_elim :premises (@p52) :args (1)) % 1.33/1.54 (step @p173 :rule cnf_or_pos :args (@t137)) % 1.33/1.54 (step @p174 :rule reordering :premises (@p173) :args ((or @t128 @t97 @t96 @t124 @t135 @t134 (not @t137)))) % 1.33/1.54 (step @p175 :rule chain_m_resolution :premises (@p174 @p155 @p78 @p77 @p151 @p172 @p171) :args (@t134 @t132 (@list @t128 @t57 @t56 @t73 @t74 @t137))) % 1.33/1.54 (step @p176 :rule refl :args (@t138)) % 1.33/1.54 (step @p177 :rule refl :args (@t139)) % 1.33/1.54 (step @p178 :rule refl :args (@t140)) % 1.33/1.54 (step @p179 :rule refl :args (@t141)) % 1.33/1.54 (step @p180 :rule bool-double-not-elim :args (@t142)) % 1.33/1.54 (step @p181 :rule refl :args (@t143)) % 1.33/1.54 (step @p182 :rule nary_cong :premises (@p181 @p180 @p179 @p178 @p177 @p176) :args ((or @t143 (not @t144) @t141 @t140 @t139 @t138))) % 1.33/1.54 (assume-push @p228 @t138) % 1.33/1.54 (assume-push @p229 @t134) % 1.33/1.54 (step @p185 :rule evaluate :args ((= false true))) % 1.33/1.54 (step @p186 :rule true_intro :premises (@p175)) % 1.33/1.54 (step @p187 :rule false_intro :premises (@p66)) % 1.33/1.54 (step @p188 :rule refl :args (tptp.xr)) % 1.33/1.54 (step @p189 :rule symm :premises (@p81)) % 1.33/1.54 (step @p190 :rule trans :premises (@p189 @p57)) % 1.33/1.54 (step @p191 :rule cong :premises (@p190 @p188) :args (@t133)) % 1.33/1.54 (step @p192 :rule trans :premises (@p191 @p158)) % 1.33/1.54 (step @p193 :rule symm :premises (@p92)) % 1.33/1.54 (step @p194 :rule cong :premises (@p193 @p192) :args (@t134)) % 1.33/1.55 (step @p195 :rule trans :premises (@p194 @p187)) % 1.33/1.55 (step @p196 :rule symm :premises (@p195)) % 1.33/1.55 (step @p197 :rule trans :premises (@p196 @p186)) % 1.33/1.55 (step @p198 false :rule eq_resolve :premises (@p197 @p185)) % 1.33/1.55 (step-pop @p230 :rule scope :premises (@p198)) % 1.33/1.55 (step-pop @p231 :rule scope :premises (@p230)) % 1.33/1.55 (step @p199 :rule process_scope :premises (@p231) :args (false)) % 1.33/1.55 (assume-push @p232 @t66) % 1.33/1.55 (assume-push @p233 @t144) % 1.33/1.55 (assume-push @p234 @t95) % 1.33/1.55 (assume-push @p235 @t101) % 1.33/1.55 (assume-push @p236 @t127) % 1.33/1.55 (assume-push @p237 @t134) % 1.33/1.55 (step @p187 :rule false_intro :premises (@p66)) % 1.33/1.55 (step @p188 :rule refl :args (tptp.xr)) % 1.33/1.55 (step @p189 :rule symm :premises (@p81)) % 1.33/1.55 (step @p190 :rule trans :premises (@p189 @p57)) % 1.33/1.55 (step @p191 :rule cong :premises (@p190 @p188) :args (@t133)) % 1.33/1.55 (step @p192 :rule trans :premises (@p191 @p158)) % 1.33/1.55 (step @p193 :rule symm :premises (@p92)) % 1.33/1.55 (step @p194 :rule cong :premises (@p193 @p192) :args (@t134)) % 1.33/1.55 (step @p208 :rule trans :premises (@p194 @p187)) % 1.33/1.55 (step @p209 :rule false_elim :premises (@p208)) % 1.33/1.55 (step @p210 :rule and_intro :premises (@p209 @p175)) % 1.33/1.55 (step-pop @p238 :rule scope :premises (@p210)) % 1.33/1.55 (step-pop @p239 :rule scope :premises (@p238)) % 1.33/1.55 (step-pop @p240 :rule scope :premises (@p239)) % 1.33/1.55 (step-pop @p241 :rule scope :premises (@p240)) % 1.33/1.55 (step-pop @p242 :rule scope :premises (@p241)) % 1.33/1.55 (step-pop @p243 :rule scope :premises (@p242)) % 1.33/1.55 (step @p211 :rule process_scope :premises (@p243) :args (@t145)) % 1.33/1.55 (step @p218 :rule implies_elim :premises (@p211)) % 1.33/1.55 (step @p219 :rule resolution :premises (@p218 @p199) :args (true @t145)) % 1.33/1.55 (step @p220 :rule not_and :premises (@p219)) % 1.33/1.55 (step @p221 :rule eq_resolve :premises (@p220 @p182)) % 1.33/1.55 (step @p222 :rule reordering :premises (@p221) :args ((or @t142 @t143 @t141 @t140 @t139 @t138))) % 1.33/1.55 (step @p223 false :rule chain_m_resolution :premises (@p222 @p175 @p158 @p92 @p81 @p66 @p57) :args (false (@list false false false false true false) (@list @t134 @t127 @t101 @t95 @t142 @t66))) % 1.33/1.55 ) % 1.33/1.55 % SZS output end Proof % 1.33/1.55 % cvc5 exiting %------------------------------------------------------------------------------