%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM523+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 : n009.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 34.26s 34.54s % Output : Proof 34.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM523+3 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n009.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 11:27:14 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 34.26/34.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 34.26/34.54 --- Run --no-e-matching --full-saturate-quant at 6... % 34.26/34.54 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 34.26/34.54 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 34.26/34.54 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 34.26/34.54 % SZS status Theorem % 34.26/34.54 % SZS output start Proof % 34.26/34.54 ( % 34.26/34.54 (declare-sort $$unsorted 0) % 34.26/34.54 (declare-const tptp.xp $$unsorted) % 34.26/34.54 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 34.26/34.54 (declare-const tptp.sz10 $$unsorted) % 34.26/34.54 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.26/34.54 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 34.26/34.54 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 34.26/34.54 (declare-const tptp.sz00 $$unsorted) % 34.26/34.54 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.26/34.54 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.26/34.54 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 34.26/34.54 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 34.26/34.54 (declare-const tptp.xn $$unsorted) % 34.26/34.54 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 34.26/34.54 (declare-const tptp.xm $$unsorted) % 34.26/34.54 (define @t1 () (@var "W0" $$unsorted)) % 34.26/34.54 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 34.26/34.54 (define @t3 () (@list @t1)) % 34.26/34.54 (define @t4 () (@var "W1" $$unsorted)) % 34.26/34.54 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 34.26/34.54 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 34.26/34.54 (define @t7 () (and @t2 @t6)) % 34.26/34.54 (define @t8 () (@list @t1 @t4)) % 34.26/34.54 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 34.26/34.54 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 34.26/34.54 (define @t11 () (forall @t8 (=> @t7 @t10))) % 34.26/34.54 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 34.26/34.54 (define @t13 () (@var "W2" $$unsorted)) % 34.26/34.54 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 34.26/34.54 (define @t15 () (tptp.aNaturalNumber0 @t13)) % 34.26/34.54 (define @t16 () (and @t2 @t6 @t15)) % 34.26/34.54 (define @t17 () (@list @t1 @t4 @t13)) % 34.26/34.54 (define @t18 () (tptp.sdtasdt0 @t4 @t1)) % 34.26/34.54 (define @t19 () (tptp.sdtasdt0 @t13 @t1)) % 34.26/34.54 (define @t20 () (tptp.sdtasdt0 @t1 @t13)) % 34.26/34.54 (define @t21 () (= @t4 @t13)) % 34.26/34.54 (define @t22 () (tptp.sdtpldt0 @t13 @t1)) % 34.26/34.54 (define @t23 () (tptp.sdtpldt0 @t1 @t13)) % 34.26/34.54 (define @t24 () (= @t18 @t19)) % 34.26/34.54 (define @t25 () (= @t9 @t20)) % 34.26/34.54 (define @t26 () (and @t6 @t15)) % 34.26/34.54 (define @t27 () (= @t1 tptp.sz00)) % 34.26/34.54 (define @t28 () (not @t27)) % 34.26/34.54 (define @t29 () (= @t4 tptp.sz00)) % 34.26/34.54 (define @t30 () (and @t15 (= @t23 @t4))) % 34.26/34.54 (define @t31 () (@list @t13)) % 34.26/34.54 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 34.26/34.54 (define @t33 () (= @t1 @t4)) % 34.26/34.54 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 34.26/34.54 (define @t35 () (tptp.sdtlseqdt0 @t4 @t13)) % 34.26/34.54 (define @t36 () (= @t4 @t1)) % 34.26/34.54 (define @t37 () (tptp.sdtpldt0 @t13 @t4)) % 34.26/34.54 (define @t38 () (and (not @t33) @t32)) % 34.26/34.54 (define @t39 () (= @t1 tptp.sz10)) % 34.26/34.54 (define @t40 () (tptp.iLess0 @t1 @t4)) % 34.26/34.54 (define @t41 () (= @t4 @t20)) % 34.26/34.54 (define @t42 () (and @t15 @t41)) % 34.26/34.54 (define @t43 () (exists @t31 @t42)) % 34.26/34.54 (define @t44 () (tptp.doDivides0 @t1 @t4)) % 34.26/34.54 (define @t45 () (= @t44 @t43)) % 34.26/34.54 (define @t46 () (=> @t7 @t45)) % 34.26/34.54 (define @t47 () (forall @t8 @t46)) % 34.26/34.54 (define @t48 () (tptp.sdtsldt0 @t4 @t1)) % 34.26/34.54 (define @t49 () (and @t28 @t44)) % 34.26/34.54 (define @t50 () (tptp.doDivides0 @t1 @t13)) % 34.26/34.54 (define @t51 () (tptp.doDivides0 @t1 @t14)) % 34.26/34.54 (define @t52 () (not @t29)) % 34.26/34.54 (define @t53 () (tptp.doDivides0 @t4 @t1)) % 34.26/34.54 (define @t54 () (@list @t4)) % 34.26/34.54 (define @t55 () (not @t39)) % 34.26/34.54 (define @t56 () (tptp.doDivides0 @t13 @t4)) % 34.26/34.54 (define @t57 () (tptp.doDivides0 @t13 @t1)) % 34.26/34.54 (define @t58 () (or @t57 @t56)) % 34.26/34.54 (define @t59 () (tptp.doDivides0 @t13 @t9)) % 34.26/34.54 (define @t60 () (tptp.isPrime0 @t13)) % 34.26/34.54 (define @t61 () (and @t60 @t59)) % 34.26/34.54 (define @t62 () (=> @t61 @t58)) % 34.26/34.54 (define @t63 () (forall @t17 (=> @t16 @t62))) % 34.26/34.54 (define @t64 () (tptp.aNaturalNumber0 tptp.xp)) % 34.26/34.54 (define @t65 () (tptp.aNaturalNumber0 tptp.xm)) % 34.26/34.54 (define @t66 () (tptp.aNaturalNumber0 tptp.xn)) % 34.26/34.54 (define @t67 () (@var "W3" $$unsorted)) % 34.26/34.54 (define @t68 () (@var "W4" $$unsorted)) % 34.26/34.54 (define @t69 () (tptp.sdtasdt0 tptp.xn tptp.xn)) % 34.26/34.54 (define @t70 () (tptp.sdtasdt0 tptp.xm tptp.xm)) % 34.26/34.54 (define @t71 () (tptp.sdtasdt0 tptp.xp @t70)) % 34.26/34.54 (define @t72 () (= @t71 @t69)) % 34.26/34.54 (define @t73 () (tptp.isPrime0 tptp.xp)) % 34.26/34.54 (define @t74 () (tptp.doDivides0 tptp.xp tptp.xn)) % 34.26/34.54 (define @t75 () (tptp.sdtasdt0 tptp.xp @t1)) % 34.26/34.54 (define @t76 () (= tptp.xn @t75)) % 34.26/34.54 (define @t77 () (and @t2 @t76)) % 34.26/34.54 (define @t78 () (exists @t3 @t77)) % 34.26/34.54 (define @t79 () (or @t78 @t74)) % 34.26/34.54 (define @t80 () (tptp.doDivides0 tptp.xp @t69)) % 34.26/34.54 (define @t81 () (= @t69 @t75)) % 34.26/34.54 (define @t82 () (and @t2 @t81)) % 34.26/34.54 (define @t83 () (exists @t3 @t82)) % 34.26/34.54 (define @t84 () (or @t83 @t80)) % 34.26/34.54 (define @t85 () (and @t84 @t79)) % 34.26/34.54 (define @t86 () (not @t85)) % 34.26/34.54 (define @t87 () (not @t59)) % 34.26/34.54 (define @t88 () (not @t60)) % 34.26/34.54 (define @t89 () (not @t15)) % 34.26/34.54 (define @t90 () (not @t6)) % 34.26/34.54 (define @t91 () (not @t2)) % 34.26/34.54 (define @t92 () (or @t91 @t90 @t89 @t88 @t87 @t57 @t56)) % 34.26/34.54 (define @t93 () (or @t88 @t87 @t57 @t56)) % 34.26/34.54 (define @t94 () (or @t91 @t90 @t89)) % 34.26/34.54 (define @t95 () (= @t44 (not (forall @t31 (or @t89 (not @t41)))))) % 34.26/34.54 (define @t96 () (or @t91 @t90)) % 34.26/34.54 (define @t97 () (not @t7)) % 34.26/34.54 (define @t98 () (forall @t31 (not @t42))) % 34.26/34.54 (define @t99 () (not @t98)) % 34.26/34.54 (define @t100 () (tptp.aNaturalNumber0 @t69)) % 34.26/34.54 (define @t101 () (not @t66)) % 34.26/34.54 (define @t102 () (or @t101 @t101 @t100)) % 34.26/34.54 (define @t103 () (@list false false)) % 34.26/34.54 (define @t104 () (forall @t31 (or @t89 (not (= @t69 (tptp.sdtasdt0 tptp.xp @t13)))))) % 34.26/34.54 (define @t105 () (not @t104)) % 34.26/34.54 (define @t106 () (= @t80 @t105)) % 34.26/34.54 (define @t107 () (not @t100)) % 34.26/34.54 (define @t108 () (not @t64)) % 34.26/34.54 (define @t109 () (or @t108 @t107 @t106)) % 34.26/34.54 (define @t110 () (tptp.aNaturalNumber0 @t70)) % 34.26/34.54 (define @t111 () (not @t65)) % 34.26/34.54 (define @t112 () (or @t111 @t111 @t110)) % 34.26/34.54 (define @t113 () (not @t72)) % 34.26/34.54 (define @t114 () (not @t110)) % 34.26/34.54 (define @t115 () (or @t114 @t113)) % 34.26/34.54 (define @t116 () (not @t115)) % 34.26/34.54 (define @t117 () (not (= @t69 @t71))) % 34.26/34.54 (define @t118 () (or @t114 @t117)) % 34.26/34.54 (define @t119 () (forall @t3 (or @t91 (not @t81)))) % 34.26/34.54 (define @t120 () (not @t119)) % 34.26/34.54 (define @t121 () (@list true)) % 34.26/34.54 (define @t122 () (@list @t119)) % 34.26/34.54 (define @t123 () (not @t106)) % 34.26/34.54 (define @t124 () (@list true false)) % 34.26/34.54 (define @t125 () (or @t120 @t80)) % 34.26/34.54 (define @t126 () (forall @t3 (not @t77))) % 34.26/34.54 (define @t127 () (not @t126)) % 34.26/34.54 (define @t128 () (forall @t3 (not @t82))) % 34.26/34.54 (define @t129 () (not @t128)) % 34.26/34.54 (define @t130 () (or (not (forall @t3 (or @t91 (not @t76)))) @t74)) % 34.26/34.54 (define @t131 () (not @t80)) % 34.26/34.54 (define @t132 () (not @t73)) % 34.26/34.54 (define @t133 () (or @t101 @t101 @t108 @t132 @t131 @t74 @t74)) % 34.26/34.54 (define @t134 () (not @t133)) % 34.26/34.54 (define @t135 () (forall @t17 @t92)) % 34.26/34.54 (assume @p1 (forall @t3 (=> @t2 true))) % 34.26/34.54 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 34.26/34.54 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 34.26/34.54 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 34.26/34.54 (assume @p5 @t11) % 34.26/34.54 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 34.26/34.54 (assume @p7 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t5 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 34.26/34.54 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 34.26/34.54 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t18)))) % 34.26/34.54 (assume @p10 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 34.26/34.54 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 34.26/34.54 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 34.26/34.54 (assume @p13 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t20)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t18 @t19)))))) % 34.26/34.54 (assume @p14 (forall @t17 (=> @t16 (=> (or (= @t5 @t23) (= @t12 @t22)) @t21)))) % 34.26/34.54 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> @t26 (=> (or @t25 @t24) @t21))))))) % 34.26/34.54 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 34.26/34.54 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t27 @t29))))) % 34.26/34.54 (assume @p18 (forall @t8 (=> @t7 (= @t32 (exists @t31 @t30))))) % 34.26/34.54 (assume @p19 (forall @t8 (=> @t7 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 34.26/34.54 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 34.26/34.54 (assume @p21 (forall @t8 (=> @t7 (=> (and @t32 @t34) @t33)))) % 34.26/34.54 (assume @p22 (forall @t17 (=> @t16 (=> (and @t32 @t35) (tptp.sdtlseqdt0 @t1 @t13))))) % 34.26/34.54 (assume @p23 (forall @t8 (=> @t7 (or @t32 (and (not @t36) @t34))))) % 34.26/34.54 (assume @p24 (forall @t8 (=> @t7 (=> @t38 (forall @t31 (=> @t15 (and (not (= @t22 @t37)) (tptp.sdtlseqdt0 @t22 @t37) (not (= @t23 @t14)) (tptp.sdtlseqdt0 @t23 @t14)))))))) % 34.26/34.54 (assume @p25 (forall @t17 (=> @t16 (=> (and @t28 (not @t21) @t35) (and (not @t25) (tptp.sdtlseqdt0 @t9 @t20) (not @t24) (tptp.sdtlseqdt0 @t18 @t19)))))) % 34.26/34.54 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t39 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 34.26/34.54 (assume @p27 (forall @t8 (=> @t7 (=> @t28 (tptp.sdtlseqdt0 @t4 @t18))))) % 34.26/34.54 (assume @p28 (forall @t8 (=> @t7 (=> @t40 true)))) % 34.26/34.54 (assume @p29 (forall @t8 (=> @t7 (=> @t38 @t40)))) % 34.26/34.54 (assume @p30 @t47) % 34.26/34.54 (assume @p31 (forall @t8 (=> @t7 (=> @t49 (forall @t31 (= (= @t13 @t48) @t42)))))) % 34.26/34.54 (assume @p32 (forall @t17 (=> @t16 (=> (and @t44 (tptp.doDivides0 @t4 @t13)) @t50)))) % 34.26/34.54 (assume @p33 (forall @t17 (=> @t16 (=> (and @t44 @t50) @t51)))) % 34.26/34.54 (assume @p34 (forall @t17 (=> @t16 (=> (and @t44 @t51) @t50)))) % 34.26/34.54 (assume @p35 (forall @t8 (=> @t7 (=> (and @t44 @t52) @t32)))) % 34.26/34.54 (assume @p36 (forall @t8 (=> @t7 (=> @t49 (forall @t31 (=> @t15 (= (tptp.sdtasdt0 @t13 @t48) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 34.26/34.54 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t28 @t55 (forall @t54 (=> (and @t6 @t53) (or (= @t4 tptp.sz10) @t36)))))))) % 34.26/34.54 (assume @p38 (forall @t3 (=> (and @t2 @t28 @t55) (exists @t54 (and @t6 @t53 (tptp.isPrime0 @t4)))))) % 34.26/34.54 (assume @p39 @t63) % 34.26/34.54 (assume @p40 (and @t66 @t65 @t64 (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00)))) % 34.26/34.54 (assume @p41 (forall @t17 (=> (and @t2 @t6 @t15 @t28 @t52 (not (= @t13 tptp.sz00))) (=> (= (tptp.sdtasdt0 @t13 (tptp.sdtasdt0 @t4 @t4)) (tptp.sdtasdt0 @t1 @t1)) (=> (tptp.iLess0 @t1 tptp.xn) (not (or (and (not (= @t13 tptp.sz10)) (forall (@list @t67) (=> (and (tptp.aNaturalNumber0 @t67) (exists (@list @t68) (and (tptp.aNaturalNumber0 @t68) (= @t13 (tptp.sdtasdt0 @t67 @t68)))) (tptp.doDivides0 @t67 @t13)) (or (= @t67 tptp.sz10) (= @t67 @t13))))) @t60))))))) % 34.26/34.54 (assume @p42 @t72) % 34.26/34.54 (assume @p43 (and (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t54 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t39 (= @t1 tptp.xp)))) @t73)) % 34.26/34.54 (assume @p44 @t86) % 34.26/34.54 (assume @p45 true) % 34.26/34.54 (step @p46 :rule aci_norm :args ((= (or @t94 @t93) @t92))) % 34.26/34.54 (step @p47 :rule aci_norm :args ((= (or (or @t88 @t87) @t58) @t93))) % 34.26/34.54 (step @p48 :rule refl :args (@t58)) % 34.26/34.54 (step @p49 :rule bool-and-de-morgan :args (@t60 @t59 true)) % 34.26/34.54 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t61) @t58))) % 34.26/34.54 (step @p51 :rule trans :premises (@p50 @p47)) % 34.26/34.54 (step @p52 :rule bool-impl-elim :args (@t61 @t58)) % 34.26/34.54 (step @p53 :rule trans :premises (@p52 @p51)) % 34.26/34.54 (step @p54 :rule aci_norm :args ((= (or @t91 (or @t90 @t89)) @t94))) % 34.26/34.54 (step @p55 :rule bool-and-de-morgan :args (@t6 @t15 true)) % 34.26/34.54 (step @p56 :rule refl :args (@t91)) % 34.26/34.54 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or @t91 (not @t26)))) % 34.26/34.54 (step @p58 :rule bool-and-de-morgan :args (@t2 @t6 (and @t15))) % 34.26/34.54 (step @p59 :rule trans :premises (@p58 @p57)) % 34.26/34.54 (step @p60 :rule trans :premises (@p59 @p54)) % 34.26/34.54 (step @p61 :rule nary_cong :premises (@p60 @p53) :args ((or (not @t16) @t62))) % 34.26/34.54 (step @p62 :rule trans :premises (@p61 @p46)) % 34.26/34.54 (step @p63 :rule bool-impl-elim :args (@t16 @t62)) % 34.26/34.54 (step @p64 :rule trans :premises (@p63 @p62)) % 34.26/34.54 (step @p65 :rule cong :premises (@p64) :args (@t63)) % 34.26/34.54 (step @p66 :rule eq_resolve :premises (@p39 @p65)) % 34.26/34.54 (step @p67 :rule aci_norm :args ((= (or @t96 @t95) (or @t91 @t90 @t95)))) % 34.26/34.54 (step @p68 :rule refl :args (@t95)) % 34.26/34.54 (step @p69 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 34.26/34.54 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or @t97 @t95))) % 34.26/34.54 (step @p71 :rule trans :premises (@p70 @p67)) % 34.26/34.54 (step @p72 :rule bool-impl-elim :args (@t7 @t95)) % 34.26/34.54 (step @p73 :rule trans :premises (@p72 @p71)) % 34.26/34.54 (step @p74 :rule cong :premises (@p73) :args ((forall @t8 (=> @t7 @t95)))) % 34.26/34.54 (step @p75 :rule bool-and-de-morgan :args (@t15 @t41 true)) % 34.26/34.54 (step @p76 :rule cong :premises (@p75) :args (@t98)) % 34.26/34.54 (step @p77 :rule cong :premises (@p76) :args (@t99)) % 34.26/34.54 (step @p78 :rule exists-elim :args ((= @t43 @t99))) % 34.26/34.54 (step @p79 :rule trans :premises (@p78 @p77)) % 34.26/34.54 (step @p80 :rule refl :args (@t44)) % 34.26/34.54 (step @p81 :rule cong :premises (@p80 @p79) :args (@t45)) % 34.26/34.54 (step @p82 :rule refl :args (@t7)) % 34.26/34.54 (step @p83 :rule cong :premises (@p82 @p81) :args (@t46)) % 34.26/34.54 (step @p84 :rule cong :premises (@p83) :args (@t47)) % 34.26/34.54 (step @p85 :rule trans :premises (@p84 @p74)) % 34.26/34.54 (step @p86 :rule eq_resolve :premises (@p30 @p85)) % 34.26/34.54 (step @p87 :rule instantiate :premises (@p86) :args ((@list tptp.xp @t69))) % 34.26/34.54 (step @p88 :rule aci_norm :args ((= (or @t96 @t10) (or @t91 @t90 @t10)))) % 34.26/34.54 (step @p89 :rule refl :args (@t10)) % 34.26/34.54 (step @p90 :rule nary_cong :premises (@p69 @p89) :args ((or @t97 @t10))) % 34.26/34.54 (step @p91 :rule trans :premises (@p90 @p88)) % 34.26/34.54 (step @p92 :rule bool-impl-elim :args (@t7 @t10)) % 34.26/34.54 (step @p93 :rule trans :premises (@p92 @p91)) % 34.26/34.54 (step @p94 :rule cong :premises (@p93) :args (@t11)) % 34.26/34.54 (step @p95 :rule eq_resolve :premises (@p5 @p94)) % 34.26/34.54 (step @p96 :rule instantiate :premises (@p95) :args ((@list tptp.xn tptp.xn))) % 34.26/34.54 (step @p97 :rule and_elim :premises (@p40) :args (0)) % 34.26/34.54 (step @p98 :rule cnf_or_pos :args (@t102)) % 34.26/34.54 (step @p99 :rule factoring :premises (@p98)) % 34.26/34.54 (step @p100 :rule reordering :premises (@p99) :args ((or @t101 @t100 (not @t102)))) % 34.26/34.54 (step @p101 :rule chain_m_resolution :premises (@p100 @p97 @p96) :args (@t100 @t103 (@list @t66 @t102))) % 34.26/34.54 (step @p102 :rule and_elim :premises (@p40) :args (2)) % 34.26/34.54 (step @p103 :rule cnf_or_pos :args (@t109)) % 34.26/34.54 (step @p104 :rule reordering :premises (@p103) :args ((or @t108 @t107 @t106 (not @t109)))) % 34.26/34.54 (step @p105 :rule chain_m_resolution :premises (@p104 @p102 @p101 @p87) :args (@t106 (@list false false false) (@list @t64 @t100 @t109))) % 34.26/34.54 (step @p106 :rule instantiate :premises (@p95) :args ((@list tptp.xm tptp.xm))) % 34.26/34.54 (step @p107 :rule and_elim :premises (@p40) :args (1)) % 34.26/34.54 (step @p108 :rule cnf_or_pos :args (@t112)) % 34.26/34.54 (step @p109 :rule factoring :premises (@p108)) % 34.26/34.54 (step @p110 :rule reordering :premises (@p109) :args ((or @t111 @t110 (not @t112)))) % 34.26/34.54 (step @p111 :rule chain_m_resolution :premises (@p110 @p107 @p106) :args (@t110 @t103 (@list @t65 @t112))) % 34.26/34.54 (step @p112 :rule cnf_or_pos :args (@t115)) % 34.26/34.54 (step @p113 :rule reordering :premises (@p112) :args ((or @t113 @t114 @t116))) % 34.26/34.54 (step @p114 :rule chain_m_resolution :premises (@p113 @p42 @p111) :args (@t116 @t103 (@list @t72 @t110))) % 34.26/34.54 (step @p115 :rule eq-symm :args (@t69 @t71)) % 34.26/34.54 (step @p116 :rule cong :premises (@p115) :args (@t117)) % 34.26/34.54 (step @p117 :rule refl :args (@t114)) % 34.26/34.54 (step @p118 :rule nary_cong :premises (@p117 @p116) :args (@t118)) % 34.26/34.54 (step @p119 :rule refl :args (@t119)) % 34.26/34.54 (step @p120 :rule cong :premises (@p119 @p118) :args ((=> @t119 @t118))) % 34.26/34.54 (assume-push @p177 @t119) % 34.26/34.54 (step @p122 :rule instantiate :premises (@p177) :args ((@list @t70))) % 34.26/34.54 (step-pop @p178 :rule scope :premises (@p122)) % 34.26/34.54 (step @p123 :rule process_scope :premises (@p178) :args (@t118)) % 34.26/34.54 (step @p125 :rule eq_resolve :premises (@p123 @p120)) % 34.26/34.54 (step @p126 :rule implies_elim :premises (@p125)) % 34.26/34.54 (step @p127 :rule chain_m_resolution :premises (@p126 @p114) :args (@t120 @t121 (@list @t115))) % 34.26/34.54 (step @p128 :rule alpha_equiv :args (@t119 (@list @t1) (@list @t13))) % 34.26/34.54 (step @p129 :rule equiv_elim2 :premises (@p128)) % 34.26/34.54 (step @p130 :rule chain_m_resolution :premises (@p129 @p127) :args (@t105 @t121 @t122)) % 34.26/34.54 (step @p131 :rule bool-double-not-elim :args (@t104)) % 34.26/34.54 (step @p132 :rule refl :args (@t80)) % 34.26/34.54 (step @p133 :rule refl :args (@t123)) % 34.26/34.54 (step @p134 :rule nary_cong :premises (@p133 @p132 @p131) :args ((or @t123 @t80 (not @t105)))) % 34.26/34.54 (step @p135 :rule cnf_equiv_pos2 :args (@t106)) % 34.26/34.54 (step @p136 :rule eq_resolve :premises (@p135 @p134)) % 34.26/34.54 (step @p137 :rule reordering :premises (@p136) :args ((or @t80 @t104 @t123))) % 34.26/34.54 (step @p138 :rule chain_m_resolution :premises (@p137 @p130 @p105) :args (@t80 @t124 (@list @t104 @t106))) % 34.26/34.54 (step @p139 :rule and_elim :premises (@p43) :args (2)) % 34.26/34.54 (step @p140 :rule bool-double-not-elim :args (@t119)) % 34.26/34.54 (step @p141 :rule refl :args (@t125)) % 34.26/34.54 (step @p142 :rule nary_cong :premises (@p141 @p140) :args ((or @t125 (not @t120)))) % 34.26/34.54 (step @p143 :rule cnf_or_neg :args (@t125 0)) % 34.26/34.54 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 34.26/34.54 (step @p145 :rule reordering :premises (@p144) :args ((or @t119 @t125))) % 34.26/34.54 (step @p146 :rule chain_m_resolution :premises (@p145 @p127) :args (@t125 @t121 @t122)) % 34.26/34.54 (step @p147 :rule refl :args (@t74)) % 34.26/34.54 (step @p148 :rule bool-and-de-morgan :args (@t2 @t76 true)) % 34.26/34.54 (step @p149 :rule cong :premises (@p148) :args (@t126)) % 34.26/34.54 (step @p150 :rule cong :premises (@p149) :args (@t127)) % 34.26/34.54 (step @p151 :rule exists-elim :args ((= @t78 @t127))) % 34.26/34.54 (step @p152 :rule trans :premises (@p151 @p150)) % 34.26/34.54 (step @p153 :rule nary_cong :premises (@p152 @p147) :args (@t79)) % 34.26/34.54 (step @p154 :rule bool-and-de-morgan :args (@t2 @t81 true)) % 34.26/34.54 (step @p155 :rule cong :premises (@p154) :args (@t128)) % 34.26/34.54 (step @p156 :rule cong :premises (@p155) :args (@t129)) % 34.26/34.54 (step @p157 :rule exists-elim :args ((= @t83 @t129))) % 34.26/34.54 (step @p158 :rule trans :premises (@p157 @p156)) % 34.26/34.54 (step @p159 :rule nary_cong :premises (@p158 @p132) :args (@t84)) % 34.26/34.54 (step @p160 :rule nary_cong :premises (@p159 @p153) :args (@t85)) % 34.26/34.54 (step @p161 :rule cong :premises (@p160) :args (@t86)) % 34.26/34.54 (step @p162 :rule eq_resolve :premises (@p44 @p161)) % 34.26/34.54 (step @p163 :rule not_and :premises (@p162)) % 34.26/34.54 (step @p164 :rule chain_m_resolution :premises (@p163 @p146) :args ((not @t130) (@list false) (@list @t125))) % 34.26/34.54 (step @p165 :rule cnf_or_neg :args (@t130 1)) % 34.26/34.54 (step @p166 :rule chain_m_resolution :premises (@p165 @p164) :args ((not @t74) @t121 (@list @t130))) % 34.26/34.54 (step @p167 :rule cnf_or_pos :args (@t133)) % 34.26/34.54 (step @p168 :rule factoring :premises (@p167)) % 34.26/34.54 (step @p169 :rule reordering :premises (@p168) :args ((or @t74 @t101 @t108 @t132 @t131 @t134))) % 34.26/34.54 (step @p170 :rule chain_m_resolution :premises (@p169 @p166 @p97 @p102 @p139 @p138) :args (@t134 (@list true false false false false) (@list @t74 @t66 @t64 @t73 @t80))) % 34.26/34.54 (assume-push @p179 @t135) % 34.26/34.54 (step @p172 :rule instantiate :premises (@p66) :args ((@list tptp.xn tptp.xn tptp.xp))) % 34.26/34.54 (step-pop @p180 :rule scope :premises (@p172)) % 34.26/34.54 (step @p173 :rule process_scope :premises (@p180) :args (@t133)) % 34.26/34.54 (step @p175 :rule implies_elim :premises (@p173)) % 34.26/34.54 (step @p176 false :rule chain_m_resolution :premises (@p175 @p170 @p66) :args (false @t124 (@list @t133 @t135))) % 34.26/34.54 ) % 34.26/34.54 % SZS output end Proof % 34.26/34.54 % cvc5 exiting %------------------------------------------------------------------------------