%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM487+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 : n024.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 08:39:35 AM UTC 2026 % Result : Theorem 15.41s 15.79s % Output : Proof 15.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM487+3 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.25 % Computer : n024.cluster.edu % 0.09/0.25 % Model : x86_64 x86_64 % 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.25 % Memory : 8042.1875MB % 0.09/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.25 % CPULimit : 300 % 0.09/0.25 % WCLimit : 300 % 0.09/0.25 % DateTime : Tue Jun 2 06:23:15 EDT 2026 % 0.09/0.25 % CPUTime : % 0.16/0.34 %----Proving TF0_NAR, FOF, or CNF % 15.41/15.79 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.41/15.79 --- Run --no-e-matching --full-saturate-quant at 6... % 15.41/15.79 % SZS status Theorem % 15.41/15.79 % SZS output start Proof % 15.41/15.79 ( % 15.41/15.79 (declare-sort $$unsorted 0) % 15.41/15.79 (declare-const tptp.xr $$unsorted) % 15.41/15.79 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 15.41/15.79 (declare-const tptp.xm $$unsorted) % 15.41/15.79 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.41/15.79 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 15.41/15.79 (declare-const tptp.xn $$unsorted) % 15.41/15.79 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 15.41/15.79 (declare-const tptp.sz00 $$unsorted) % 15.41/15.79 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.41/15.79 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.41/15.79 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.41/15.79 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 15.41/15.79 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 15.41/15.79 (declare-const tptp.sz10 $$unsorted) % 15.41/15.79 (declare-const tptp.xp $$unsorted) % 15.41/15.79 (define @t1 () (@var "W0" $$unsorted)) % 15.41/15.79 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 15.41/15.79 (define @t3 () (@list @t1)) % 15.41/15.79 (define @t4 () (tptp.aNaturalNumber0 tptp.sz00)) % 15.41/15.79 (define @t5 () (@var "W1" $$unsorted)) % 15.41/15.79 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 15.41/15.79 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 15.41/15.79 (define @t8 () (and @t2 @t7)) % 15.41/15.79 (define @t9 () (@list @t1 @t5)) % 15.41/15.79 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 15.41/15.79 (define @t11 () (tptp.sdtpldt0 @t5 @t1)) % 15.41/15.79 (define @t12 () (= @t6 @t11)) % 15.41/15.79 (define @t13 () (forall @t9 (=> @t8 @t12))) % 15.41/15.79 (define @t14 () (@var "W2" $$unsorted)) % 15.41/15.79 (define @t15 () (tptp.sdtpldt0 @t5 @t14)) % 15.41/15.79 (define @t16 () (tptp.sdtpldt0 @t6 @t14)) % 15.41/15.79 (define @t17 () (tptp.aNaturalNumber0 @t14)) % 15.41/15.79 (define @t18 () (and @t2 @t7 @t17)) % 15.41/15.79 (define @t19 () (@list @t1 @t5 @t14)) % 15.41/15.79 (define @t20 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 15.41/15.79 (define @t21 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 15.41/15.79 (define @t22 () (and (= @t21 @t1) @t20)) % 15.41/15.79 (define @t23 () (=> @t2 @t22)) % 15.41/15.79 (define @t24 () (forall @t3 @t23)) % 15.41/15.79 (define @t25 () (tptp.sdtasdt0 @t5 @t1)) % 15.41/15.79 (define @t26 () (tptp.sdtasdt0 @t14 @t1)) % 15.41/15.79 (define @t27 () (tptp.sdtasdt0 @t1 @t14)) % 15.41/15.79 (define @t28 () (= @t5 @t14)) % 15.41/15.79 (define @t29 () (tptp.sdtpldt0 @t14 @t1)) % 15.41/15.79 (define @t30 () (= @t11 @t29)) % 15.41/15.79 (define @t31 () (tptp.sdtpldt0 @t1 @t14)) % 15.41/15.79 (define @t32 () (= @t6 @t31)) % 15.41/15.79 (define @t33 () (or @t32 @t30)) % 15.41/15.79 (define @t34 () (=> @t33 @t28)) % 15.41/15.79 (define @t35 () (forall @t19 (=> @t18 @t34))) % 15.41/15.79 (define @t36 () (= @t25 @t26)) % 15.41/15.79 (define @t37 () (= @t10 @t27)) % 15.41/15.79 (define @t38 () (and @t7 @t17)) % 15.41/15.79 (define @t39 () (= @t1 tptp.sz00)) % 15.41/15.79 (define @t40 () (not @t39)) % 15.41/15.79 (define @t41 () (= @t5 tptp.sz00)) % 15.41/15.79 (define @t42 () (and @t17 (= @t31 @t5))) % 15.41/15.79 (define @t43 () (@list @t14)) % 15.41/15.79 (define @t44 () (tptp.sdtlseqdt0 @t1 @t5)) % 15.41/15.79 (define @t45 () (= @t1 @t5)) % 15.41/15.79 (define @t46 () (tptp.sdtlseqdt0 @t5 @t1)) % 15.41/15.79 (define @t47 () (tptp.sdtlseqdt0 @t5 @t14)) % 15.41/15.79 (define @t48 () (= @t5 @t1)) % 15.41/15.79 (define @t49 () (tptp.sdtpldt0 @t14 @t5)) % 15.41/15.79 (define @t50 () (and (not @t45) @t44)) % 15.41/15.79 (define @t51 () (= @t1 tptp.sz10)) % 15.41/15.79 (define @t52 () (tptp.iLess0 @t1 @t5)) % 15.41/15.79 (define @t53 () (and @t17 (= @t5 @t27))) % 15.41/15.79 (define @t54 () (tptp.doDivides0 @t1 @t5)) % 15.41/15.79 (define @t55 () (tptp.sdtsldt0 @t5 @t1)) % 15.41/15.79 (define @t56 () (and @t40 @t54)) % 15.41/15.79 (define @t57 () (tptp.doDivides0 @t1 @t14)) % 15.41/15.79 (define @t58 () (tptp.doDivides0 @t1 @t15)) % 15.41/15.79 (define @t59 () (tptp.doDivides0 @t5 @t1)) % 15.41/15.79 (define @t60 () (@list @t5)) % 15.41/15.79 (define @t61 () (not @t51)) % 15.41/15.79 (define @t62 () (tptp.aNaturalNumber0 tptp.xp)) % 15.41/15.79 (define @t63 () (tptp.aNaturalNumber0 tptp.xn)) % 15.41/15.79 (define @t64 () (@var "W3" $$unsorted)) % 15.41/15.79 (define @t65 () (tptp.sdtasdt0 @t14 @t64)) % 15.41/15.79 (define @t66 () (tptp.aNaturalNumber0 @t64)) % 15.41/15.79 (define @t67 () (@list @t64)) % 15.41/15.79 (define @t68 () (@var "W4" $$unsorted)) % 15.41/15.79 (define @t69 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 15.41/15.79 (define @t70 () (tptp.sdtpldt0 tptp.xp tptp.xr)) % 15.41/15.79 (define @t71 () (tptp.aNaturalNumber0 tptp.xr)) % 15.41/15.79 (define @t72 () (tptp.sdtlseqdt0 tptp.xr tptp.xn)) % 15.41/15.79 (define @t73 () (tptp.sdtpldt0 tptp.xr @t1)) % 15.41/15.79 (define @t74 () (and @t2 (= @t73 tptp.xn))) % 15.41/15.79 (define @t75 () (exists @t3 @t74)) % 15.41/15.79 (define @t76 () (or @t75 @t72)) % 15.41/15.79 (define @t77 () (not (= tptp.xr tptp.xn))) % 15.41/15.79 (define @t78 () (and @t77 @t76)) % 15.41/15.79 (define @t79 () (not @t78)) % 15.41/15.79 (define @t80 () (and (not @t32) (not @t30))) % 15.41/15.79 (define @t81 () (not @t17)) % 15.41/15.79 (define @t82 () (not @t7)) % 15.41/15.79 (define @t83 () (not @t2)) % 15.41/15.79 (define @t84 () (or @t83 @t82 @t81 @t80 @t28)) % 15.41/15.79 (define @t85 () (or @t83 @t82 @t81)) % 15.41/15.79 (define @t86 () (= tptp.sz00 tptp.xp)) % 15.41/15.79 (define @t87 () (tptp.sdtpldt0 tptp.sz00 @t70)) % 15.41/15.79 (define @t88 () (tptp.sdtpldt0 tptp.xp @t70)) % 15.41/15.79 (define @t89 () (not (= @t87 @t88))) % 15.41/15.79 (define @t90 () (tptp.sdtpldt0 @t70 tptp.sz00)) % 15.41/15.79 (define @t91 () (tptp.sdtpldt0 @t70 tptp.xp)) % 15.41/15.79 (define @t92 () (not (= @t90 @t91))) % 15.41/15.79 (define @t93 () (and @t92 @t89)) % 15.41/15.79 (define @t94 () (not @t62)) % 15.41/15.79 (define @t95 () (not @t4)) % 15.41/15.79 (define @t96 () (tptp.aNaturalNumber0 @t70)) % 15.41/15.79 (define @t97 () (not @t96)) % 15.41/15.79 (define @t98 () (or @t97 @t95 @t94 @t93 @t86)) % 15.41/15.79 (define @t99 () (forall @t19 @t84)) % 15.41/15.79 (define @t100 () (= @t91 @t90)) % 15.41/15.79 (define @t101 () (not @t100)) % 15.41/15.79 (define @t102 () (and @t101 (not (= @t88 @t87)))) % 15.41/15.79 (define @t103 () (or @t97 @t95 @t94 @t102 @t86)) % 15.41/15.79 (define @t104 () (@list false)) % 15.41/15.79 (define @t105 () (and (= @t1 @t21) @t20)) % 15.41/15.79 (define @t106 () (= @t70 @t90)) % 15.41/15.79 (define @t107 () (and @t106 (= @t70 @t87))) % 15.41/15.79 (define @t108 () (or @t97 @t107)) % 15.41/15.79 (define @t109 () (or @t83 @t82 @t12)) % 15.41/15.79 (define @t110 () (= @t88 @t91)) % 15.41/15.79 (define @t111 () (or @t94 @t97 @t110)) % 15.41/15.79 (define @t112 () (@list false false false)) % 15.41/15.79 (define @t113 () (= tptp.xr @t70)) % 15.41/15.79 (define @t114 () (and @t113 @t110 @t106)) % 15.41/15.79 (define @t115 () (not @t113)) % 15.41/15.79 (define @t116 () (forall @t3 (or @t83 (not (= @t70 @t73))))) % 15.41/15.79 (define @t117 () (not @t116)) % 15.41/15.79 (define @t118 () (or @t117 (tptp.sdtlseqdt0 tptp.xr @t70))) % 15.41/15.79 (define @t119 () (not @t118)) % 15.41/15.79 (define @t120 () (not (= @t70 tptp.xr))) % 15.41/15.79 (define @t121 () (and @t120 @t118)) % 15.41/15.79 (define @t122 () (= tptp.xn @t73)) % 15.41/15.79 (define @t123 () (not @t122)) % 15.41/15.79 (define @t124 () (or @t83 @t123)) % 15.41/15.79 (define @t125 () (forall @t3 @t124)) % 15.41/15.79 (define @t126 () (not @t125)) % 15.41/15.79 (define @t127 () (or @t126 @t72)) % 15.41/15.79 (define @t128 () (= tptp.xn tptp.xr)) % 15.41/15.79 (define @t129 () (not @t128)) % 15.41/15.79 (define @t130 () (and @t129 @t127)) % 15.41/15.79 (define @t131 () (and @t2 @t122)) % 15.41/15.79 (define @t132 () (forall @t3 (not @t131))) % 15.41/15.79 (define @t133 () (not @t132)) % 15.41/15.79 (define @t134 () (@list true)) % 15.41/15.79 (define @t135 () (tptp.sdtpldt0 tptp.xr tptp.xp)) % 15.41/15.79 (define @t136 () (= @t70 @t135)) % 15.41/15.79 (define @t137 () (not @t136)) % 15.41/15.79 (define @t138 () (or @t94 @t137)) % 15.41/15.79 (define @t139 () (not @t71)) % 15.41/15.79 (define @t140 () (or @t139 @t94 (= @t135 @t70))) % 15.41/15.79 (define @t141 () (forall @t9 @t109)) % 15.41/15.79 (define @t142 () (or @t139 @t94 @t136)) % 15.41/15.79 (assume @p1 (forall @t3 (=> @t2 true))) % 15.41/15.79 (assume @p2 @t4) % 15.41/15.79 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 15.41/15.79 (assume @p4 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t6)))) % 15.41/15.79 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t10)))) % 15.41/15.79 (assume @p6 @t13) % 15.41/15.79 (assume @p7 (forall @t19 (=> @t18 (= @t16 (tptp.sdtpldt0 @t1 @t15))))) % 15.41/15.79 (assume @p8 @t24) % 15.41/15.79 (assume @p9 (forall @t9 (=> @t8 (= @t10 @t25)))) % 15.41/15.79 (assume @p10 (forall @t19 (=> @t18 (= (tptp.sdtasdt0 @t10 @t14) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t14)))))) % 15.41/15.79 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 15.41/15.79 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 15.41/15.79 (assume @p13 (forall @t19 (=> @t18 (and (= (tptp.sdtasdt0 @t1 @t15) (tptp.sdtpldt0 @t10 @t27)) (= (tptp.sdtasdt0 @t15 @t1) (tptp.sdtpldt0 @t25 @t26)))))) % 15.41/15.79 (assume @p14 @t35) % 15.41/15.79 (assume @p15 (forall @t3 (=> @t2 (=> @t40 (forall (@list @t5 @t14) (=> @t38 (=> (or @t37 @t36) @t28))))))) % 15.41/15.79 (assume @p16 (forall @t9 (=> @t8 (=> (= @t6 tptp.sz00) (and @t39 @t41))))) % 15.41/15.79 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t39 @t41))))) % 15.41/15.79 (assume @p18 (forall @t9 (=> @t8 (= @t44 (exists @t43 @t42))))) % 15.41/15.79 (assume @p19 (forall @t9 (=> @t8 (=> @t44 (forall @t43 (= (= @t14 (tptp.sdtmndt0 @t5 @t1)) @t42)))))) % 15.41/15.79 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 15.41/15.79 (assume @p21 (forall @t9 (=> @t8 (=> (and @t44 @t46) @t45)))) % 15.41/15.79 (assume @p22 (forall @t19 (=> @t18 (=> (and @t44 @t47) (tptp.sdtlseqdt0 @t1 @t14))))) % 15.41/15.79 (assume @p23 (forall @t9 (=> @t8 (or @t44 (and (not @t48) @t46))))) % 15.41/15.79 (assume @p24 (forall @t9 (=> @t8 (=> @t50 (forall @t43 (=> @t17 (and (not (= @t29 @t49)) (tptp.sdtlseqdt0 @t29 @t49) (not (= @t31 @t15)) (tptp.sdtlseqdt0 @t31 @t15)))))))) % 15.41/15.79 (assume @p25 (forall @t19 (=> @t18 (=> (and @t40 (not @t28) @t47) (and (not @t37) (tptp.sdtlseqdt0 @t10 @t27) (not @t36) (tptp.sdtlseqdt0 @t25 @t26)))))) % 15.41/15.79 (assume @p26 (forall @t3 (=> @t2 (or @t39 @t51 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 15.41/15.79 (assume @p27 (forall @t9 (=> @t8 (=> @t40 (tptp.sdtlseqdt0 @t5 @t25))))) % 15.41/15.79 (assume @p28 (forall @t9 (=> @t8 (=> @t52 true)))) % 15.41/15.79 (assume @p29 (forall @t9 (=> @t8 (=> @t50 @t52)))) % 15.41/15.79 (assume @p30 (forall @t9 (=> @t8 (= @t54 (exists @t43 @t53))))) % 15.41/15.79 (assume @p31 (forall @t9 (=> @t8 (=> @t56 (forall @t43 (= (= @t14 @t55) @t53)))))) % 15.41/15.79 (assume @p32 (forall @t19 (=> @t18 (=> (and @t54 (tptp.doDivides0 @t5 @t14)) @t57)))) % 15.41/15.79 (assume @p33 (forall @t19 (=> @t18 (=> (and @t54 @t57) @t58)))) % 15.41/15.79 (assume @p34 (forall @t19 (=> @t18 (=> (and @t54 @t58) @t57)))) % 15.41/15.79 (assume @p35 (forall @t9 (=> @t8 (=> (and @t54 (not @t41)) @t44)))) % 15.41/15.79 (assume @p36 (forall @t9 (=> @t8 (=> @t56 (forall @t43 (=> @t17 (= (tptp.sdtasdt0 @t14 @t55) (tptp.sdtsldt0 (tptp.sdtasdt0 @t14 @t5) @t1)))))))) % 15.41/15.79 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t40 @t61 (forall @t60 (=> (and @t7 @t59) (or (= @t5 tptp.sz10) @t48)))))))) % 15.41/15.79 (assume @p38 (forall @t3 (=> (and @t2 @t40 @t61) (exists @t60 (and @t7 @t59 (tptp.isPrime0 @t5)))))) % 15.41/15.79 (assume @p39 (and @t63 (tptp.aNaturalNumber0 tptp.xm) @t62)) % 15.41/15.79 (assume @p40 (forall @t19 (=> @t18 (=> (and (or (and (not (= @t14 tptp.sz00)) (not (= @t14 tptp.sz10)) (forall @t67 (=> (and @t66 (exists (@list @t68) (and (tptp.aNaturalNumber0 @t68) (= @t14 (tptp.sdtasdt0 @t64 @t68)))) (tptp.doDivides0 @t64 @t14)) (or (= @t64 tptp.sz10) (= @t64 @t14))))) (tptp.isPrime0 @t14)) (or (exists @t67 (and @t66 (= @t10 @t65))) (tptp.doDivides0 @t14 @t10))) (=> (tptp.iLess0 @t16 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t67 (and @t66 (= @t1 @t65))) (tptp.doDivides0 @t14 @t1)) (and (exists @t67 (and @t66 (= @t5 @t65))) (tptp.doDivides0 @t14 @t5)))))))) % 15.41/15.79 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t60 (and @t7 (= tptp.xp @t10))) (tptp.doDivides0 @t1 tptp.xp))) (or @t51 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t69 (tptp.sdtasdt0 tptp.xp @t1)))) (tptp.doDivides0 tptp.xp @t69))) % 15.41/15.79 (assume @p42 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xp @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 15.41/15.79 (assume @p43 (and @t71 (= @t70 tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) % 15.41/15.79 (assume @p44 @t79) % 15.41/15.79 (assume @p45 true) % 15.41/15.79 (step @p46 :rule and_elim :premises (@p39) :args (2)) % 15.41/15.79 (step @p47 :rule aci_norm :args ((= (or @t85 (or @t80 @t28)) @t84))) % 15.41/15.79 (step @p48 :rule refl :args (@t28)) % 15.41/15.79 (step @p49 :rule bool-or-de-morgan :args (@t32 @t30 false)) % 15.41/15.79 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t33) @t28))) % 15.41/15.79 (step @p51 :rule bool-impl-elim :args (@t33 @t28)) % 15.41/15.79 (step @p52 :rule trans :premises (@p51 @p50)) % 15.41/15.79 (step @p53 :rule aci_norm :args ((= (or @t83 (or @t82 @t81)) @t85))) % 15.41/15.79 (step @p54 :rule bool-and-de-morgan :args (@t7 @t17 true)) % 15.41/15.79 (step @p55 :rule refl :args (@t83)) % 15.41/15.79 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or @t83 (not @t38)))) % 15.41/15.79 (step @p57 :rule bool-and-de-morgan :args (@t2 @t7 (and @t17))) % 15.41/15.79 (step @p58 :rule trans :premises (@p57 @p56)) % 15.41/15.79 (step @p59 :rule trans :premises (@p58 @p53)) % 15.41/15.79 (step @p60 :rule nary_cong :premises (@p59 @p52) :args ((or (not @t18) @t34))) % 15.41/15.79 (step @p61 :rule trans :premises (@p60 @p47)) % 15.41/15.79 (step @p62 :rule bool-impl-elim :args (@t18 @t34)) % 15.41/15.79 (step @p63 :rule trans :premises (@p62 @p61)) % 15.41/15.79 (step @p64 :rule cong :premises (@p63) :args (@t35)) % 15.41/15.79 (step @p65 :rule eq_resolve :premises (@p14 @p64)) % 15.41/15.79 (step @p66 :rule refl :args (@t86)) % 15.41/15.79 (step @p67 :rule eq-symm :args (@t87 @t88)) % 15.41/15.79 (step @p68 :rule cong :premises (@p67) :args (@t89)) % 15.41/15.79 (step @p69 :rule eq-symm :args (@t90 @t91)) % 15.41/15.79 (step @p70 :rule cong :premises (@p69) :args (@t92)) % 15.41/15.79 (step @p71 :rule nary_cong :premises (@p70 @p68) :args (@t93)) % 15.41/15.79 (step @p72 :rule refl :args (@t94)) % 15.41/15.79 (step @p73 :rule refl :args (@t95)) % 15.41/15.79 (step @p74 :rule refl :args (@t97)) % 15.41/15.79 (step @p75 :rule nary_cong :premises (@p74 @p73 @p72 @p71 @p66) :args (@t98)) % 15.41/15.79 (step @p76 :rule refl :args (@t99)) % 15.41/15.79 (step @p77 :rule cong :premises (@p76 @p75) :args ((=> @t99 @t98))) % 15.41/15.79 (assume-push @p227 @t99) % 15.41/15.79 (step @p79 :rule instantiate :premises (@p65) :args ((@list @t70 tptp.sz00 tptp.xp))) % 15.41/15.79 (step-pop @p228 :rule scope :premises (@p79)) % 15.41/15.79 (step @p80 :rule process_scope :premises (@p228) :args (@t98)) % 15.41/15.79 (step @p82 :rule eq_resolve :premises (@p80 @p77)) % 15.41/15.79 (step @p83 :rule implies_elim :premises (@p82)) % 15.41/15.79 (step @p84 :rule chain_m_resolution :premises (@p83 @p65) :args (@t103 @t104 (@list @t99))) % 15.41/15.79 (step @p85 :rule and_elim :premises (@p43) :args (1)) % 15.41/15.79 (step @p86 :rule symm :premises (@p85)) % 15.41/15.79 (step @p87 :rule cong :premises (@p86) :args (@t63)) % 15.41/15.79 (step @p88 :rule and_elim :premises (@p39) :args (0)) % 15.41/15.79 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 15.41/15.79 (step @p90 :rule and_elim :premises (@p41) :args (0)) % 15.41/15.79 (step @p91 :rule symm :premises (@p90)) % 15.41/15.79 (step @p92 :rule cnf_or_pos :args (@t103)) % 15.41/15.79 (step @p93 :rule reordering :premises (@p92) :args ((or @t86 @t95 @t97 @t94 @t102 (not @t103)))) % 15.41/15.79 (step @p94 :rule chain_m_resolution :premises (@p93 @p91 @p2 @p89 @p46 @p84) :args (@t102 (@list true false false false false) (@list @t86 @t4 @t96 @t62 @t103))) % 15.41/15.79 (step @p95 :rule cnf_and_pos :args (@t102 0)) % 15.41/15.79 (step @p96 :rule reordering :premises (@p95) :args ((or @t101 (not @t102)))) % 15.41/15.79 (step @p97 :rule chain_m_resolution :premises (@p96 @p94) :args (@t101 @t104 (@list @t102))) % 15.41/15.79 (step @p98 :rule bool-impl-elim :args (@t2 @t105)) % 15.41/15.79 (step @p99 :rule cong :premises (@p98) :args ((forall @t3 (=> @t2 @t105)))) % 15.41/15.79 (step @p100 :rule refl :args (@t20)) % 15.41/15.79 (step @p101 :rule eq-symm :args (@t21 @t1)) % 15.41/15.79 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t22)) % 15.41/15.79 (step @p103 :rule refl :args (@t2)) % 15.41/15.79 (step @p104 :rule cong :premises (@p103 @p102) :args (@t23)) % 15.41/15.79 (step @p105 :rule cong :premises (@p104) :args (@t24)) % 15.41/15.79 (step @p106 :rule trans :premises (@p105 @p99)) % 15.41/15.79 (step @p107 :rule eq_resolve :premises (@p8 @p106)) % 15.41/15.79 (step @p108 :rule instantiate :premises (@p107) :args ((@list @t70))) % 15.41/15.79 (step @p109 :rule cnf_or_pos :args (@t108)) % 15.41/15.79 (step @p110 :rule reordering :premises (@p109) :args ((or @t97 @t107 (not @t108)))) % 15.41/15.79 (step @p111 :rule chain_m_resolution :premises (@p110 @p89 @p108) :args (@t107 (@list false false) (@list @t96 @t108))) % 15.41/15.79 (step @p112 :rule cnf_and_pos :args (@t107 0)) % 15.41/15.79 (step @p113 :rule reordering :premises (@p112) :args ((or @t106 (not @t107)))) % 15.41/15.79 (step @p114 :rule chain_m_resolution :premises (@p113 @p111) :args (@t106 @t104 (@list @t107))) % 15.41/15.79 (step @p115 :rule aci_norm :args ((= (or (or @t83 @t82) @t12) @t109))) % 15.41/15.79 (step @p116 :rule refl :args (@t12)) % 15.41/15.79 (step @p117 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 15.41/15.79 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or (not @t8) @t12))) % 15.41/15.79 (step @p119 :rule trans :premises (@p118 @p115)) % 15.41/15.79 (step @p120 :rule bool-impl-elim :args (@t8 @t12)) % 15.41/15.79 (step @p121 :rule trans :premises (@p120 @p119)) % 15.41/15.79 (step @p122 :rule cong :premises (@p121) :args (@t13)) % 15.41/15.79 (step @p123 :rule eq_resolve :premises (@p6 @p122)) % 15.41/15.79 (step @p124 :rule instantiate :premises (@p123) :args ((@list tptp.xp @t70))) % 15.41/15.79 (step @p125 :rule cnf_or_pos :args (@t111)) % 15.41/15.79 (step @p126 :rule reordering :premises (@p125) :args ((or @t97 @t94 @t110 (not @t111)))) % 15.41/15.79 (step @p127 :rule chain_m_resolution :premises (@p126 @p89 @p46 @p124) :args (@t110 @t112 (@list @t96 @t62 @t111))) % 15.41/15.79 (assume-push @p229 @t113) % 15.41/15.79 (assume-push @p230 @t110) % 15.41/15.79 (assume-push @p231 @t106) % 15.41/15.79 (assume-push @p232 @t106) % 15.41/15.79 (assume-push @p233 @t113) % 15.41/15.79 (assume-push @p234 @t110) % 15.41/15.79 (step @p134 :rule symm :premises (@p229)) % 15.41/15.79 (step @p135 :rule refl :args (tptp.xp)) % 15.41/15.79 (step @p136 :rule cong :premises (@p135 @p134) :args (@t88)) % 15.41/15.79 (step @p137 :rule symm :premises (@p127)) % 15.41/15.79 (step @p138 :rule trans :premises (@p137 @p136 @p114)) % 15.41/15.79 (step-pop @p235 :rule scope :premises (@p138)) % 15.41/15.79 (step-pop @p236 :rule scope :premises (@p235)) % 15.41/15.79 (step-pop @p237 :rule scope :premises (@p236)) % 15.41/15.79 (step @p139 :rule process_scope :premises (@p237) :args (@t100)) % 15.41/15.79 (step @p143 :rule and_intro :premises (@p114 @p229 @p127)) % 15.41/15.79 (step @p144 :rule modus_ponens :premises (@p143 @p139)) % 15.41/15.79 (step-pop @p238 :rule scope :premises (@p144)) % 15.41/15.79 (step-pop @p239 :rule scope :premises (@p238)) % 15.41/15.79 (step-pop @p240 :rule scope :premises (@p239)) % 15.41/15.79 (step @p145 :rule process_scope :premises (@p240) :args (@t100)) % 15.41/15.79 (step @p149 :rule implies_elim :premises (@p145)) % 15.41/15.79 (step @p150 :rule cnf_and_neg :args (@t114)) % 15.41/15.79 (step @p151 :rule resolution :premises (@p150 @p149) :args (true @t114)) % 15.41/15.79 (step @p152 :rule chain_m_resolution :premises (@p151 @p127 @p114 @p97) :args (@t115 (@list false false true) (@list @t110 @t106 @t100))) % 15.41/15.79 (step @p153 :rule refl :args (@t119)) % 15.41/15.79 (step @p154 :rule bool-double-not-elim :args (@t113)) % 15.41/15.79 (step @p155 :rule nary_cong :premises (@p154 @p153) :args ((or (not @t115) @t119))) % 15.41/15.79 (step @p156 :rule refl :args (@t118)) % 15.41/15.79 (step @p157 :rule eq-symm :args (@t70 tptp.xr)) % 15.41/15.79 (step @p158 :rule cong :premises (@p157) :args (@t120)) % 15.41/15.79 (step @p159 :rule nary_cong :premises (@p158 @p156) :args (@t121)) % 15.41/15.79 (step @p160 :rule cong :premises (@p159) :args ((not @t121))) % 15.41/15.79 (step @p161 :rule refl :args (tptp.xr)) % 15.41/15.79 (step @p162 :rule cong :premises (@p161 @p86) :args (@t72)) % 15.41/15.79 (step @p163 :rule refl :args (@t73)) % 15.41/15.79 (step @p164 :rule cong :premises (@p86 @p163) :args (@t122)) % 15.41/15.79 (step @p165 :rule cong :premises (@p164) :args (@t123)) % 15.41/15.79 (step @p166 :rule refl :args (@t83)) % 15.41/15.79 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t124)) % 15.41/15.79 (step @p168 :rule cong :premises (@p167) :args (@t125)) % 15.41/15.79 (step @p169 :rule cong :premises (@p168) :args (@t126)) % 15.41/15.79 (step @p170 :rule nary_cong :premises (@p169 @p162) :args (@t127)) % 15.41/15.79 (step @p171 :rule cong :premises (@p86 @p161) :args (@t128)) % 15.41/15.79 (step @p172 :rule cong :premises (@p171) :args (@t129)) % 15.41/15.79 (step @p173 :rule nary_cong :premises (@p172 @p170) :args (@t130)) % 15.41/15.79 (step @p174 :rule cong :premises (@p173) :args ((not @t130))) % 15.41/15.79 (step @p175 :rule trans :premises (@p174 @p160)) % 15.41/15.79 (step @p176 :rule refl :args (@t72)) % 15.41/15.79 (step @p177 :rule bool-and-de-morgan :args (@t2 @t122 true)) % 15.41/15.79 (step @p178 :rule cong :premises (@p177) :args (@t132)) % 15.41/15.79 (step @p179 :rule cong :premises (@p178) :args (@t133)) % 15.41/15.79 (step @p180 :rule exists-elim :args ((= (exists @t3 @t131) @t133))) % 15.41/15.79 (step @p181 :rule trans :premises (@p180 @p179)) % 15.41/15.79 (step @p182 :rule eq-symm :args (@t73 tptp.xn)) % 15.41/15.79 (step @p183 :rule nary_cong :premises (@p103 @p182) :args (@t74)) % 15.41/15.79 (step @p184 :rule cong :premises (@p183) :args (@t75)) % 15.41/15.79 (step @p185 :rule trans :premises (@p184 @p181)) % 15.41/15.79 (step @p186 :rule nary_cong :premises (@p185 @p176) :args (@t76)) % 15.41/15.79 (step @p187 :rule eq-symm :args (tptp.xr tptp.xn)) % 15.41/15.79 (step @p188 :rule cong :premises (@p187) :args (@t77)) % 15.41/15.79 (step @p189 :rule nary_cong :premises (@p188 @p186) :args (@t78)) % 15.41/15.79 (step @p190 :rule cong :premises (@p189) :args (@t79)) % 15.41/15.79 (step @p191 :rule trans :premises (@p190 @p175)) % 15.41/15.79 (step @p192 :rule eq_resolve :premises (@p44 @p191)) % 15.41/15.79 (step @p193 :rule not_and :premises (@p192)) % 15.41/15.79 (step @p194 :rule eq_resolve :premises (@p193 @p155)) % 15.41/15.79 (step @p195 :rule chain_m_resolution :premises (@p194 @p152) :args (@t119 @t134 (@list @t113))) % 15.41/15.79 (step @p196 :rule bool-double-not-elim :args (@t116)) % 15.41/15.79 (step @p197 :rule nary_cong :premises (@p156 @p196) :args ((or @t118 (not @t117)))) % 15.41/15.79 (step @p198 :rule cnf_or_neg :args (@t118 0)) % 15.41/15.79 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 15.41/15.79 (step @p200 :rule reordering :premises (@p199) :args ((or @t116 @t118))) % 15.41/15.79 (step @p201 :rule chain_m_resolution :premises (@p200 @p195) :args (@t116 @t134 (@list @t118))) % 15.41/15.79 (assume-push @p241 @t116) % 15.41/15.79 (step @p203 :rule instantiate :premises (@p241) :args ((@list tptp.xp))) % 15.41/15.79 (step-pop @p242 :rule scope :premises (@p203)) % 15.41/15.79 (step @p204 :rule process_scope :premises (@p242) :args (@t138)) % 15.41/15.79 (step @p206 :rule implies_elim :premises (@p204)) % 15.41/15.79 (step @p207 :rule chain_m_resolution :premises (@p206 @p201) :args (@t138 @t104 (@list @t116))) % 15.41/15.79 (step @p208 :rule eq-symm :args (@t135 @t70)) % 15.41/15.79 (step @p209 :rule refl :args (@t139)) % 15.41/15.79 (step @p210 :rule nary_cong :premises (@p209 @p72 @p208) :args (@t140)) % 15.41/15.79 (step @p211 :rule refl :args (@t141)) % 15.41/15.79 (step @p212 :rule cong :premises (@p211 @p210) :args ((=> @t141 @t140))) % 15.41/15.79 (assume-push @p243 @t141) % 15.41/15.79 (step @p214 :rule instantiate :premises (@p123) :args ((@list tptp.xr tptp.xp))) % 15.41/15.79 (step-pop @p244 :rule scope :premises (@p214)) % 15.41/15.79 (step @p215 :rule process_scope :premises (@p244) :args (@t140)) % 15.63/15.80 (step @p217 :rule eq_resolve :premises (@p215 @p212)) % 15.63/15.80 (step @p218 :rule implies_elim :premises (@p217)) % 15.63/15.80 (step @p219 :rule chain_m_resolution :premises (@p218 @p123) :args (@t142 @t104 (@list @t141))) % 15.63/15.80 (step @p220 :rule and_elim :premises (@p43) :args (0)) % 15.63/15.80 (step @p221 :rule cnf_or_pos :args (@t142)) % 15.63/15.80 (step @p222 :rule reordering :premises (@p221) :args ((or @t94 @t139 @t136 (not @t142)))) % 15.63/15.80 (step @p223 :rule chain_m_resolution :premises (@p222 @p46 @p220 @p219) :args (@t136 @t112 (@list @t62 @t71 @t142))) % 15.63/15.80 (step @p224 :rule cnf_or_pos :args (@t138)) % 15.63/15.80 (step @p225 :rule reordering :premises (@p224) :args ((or @t94 @t137 (not @t138)))) % 15.63/15.80 (step @p226 false :rule chain_m_resolution :premises (@p225 @p223 @p207 @p46) :args (false @t112 (@list @t136 @t138 @t62))) % 15.63/15.80 ) % 15.63/15.80 % SZS output end Proof % 15.63/15.80 % cvc5 exiting %------------------------------------------------------------------------------