%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM525+1 : 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 : n003.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 08:39:43 AM UTC 2026 % Result : Theorem 28.15s 28.34s % Output : Proof 28.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM525+1 : 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 : n003.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 11:27:59 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 28.15/28.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 28.15/28.34 --- Run --no-e-matching --full-saturate-quant at 6... % 28.15/28.34 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 28.15/28.34 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 28.15/28.34 % SZS status Theorem % 28.15/28.34 % SZS output start Proof % 28.15/28.34 ( % 28.15/28.34 (declare-sort $$unsorted 0) % 28.15/28.34 (declare-const tptp.xq $$unsorted) % 28.15/28.34 (declare-const tptp.xp $$unsorted) % 28.15/28.34 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 28.15/28.34 (declare-const tptp.sz10 $$unsorted) % 28.15/28.34 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.15/28.34 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 28.15/28.34 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 28.15/28.34 (declare-const tptp.sz00 $$unsorted) % 28.15/28.34 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.15/28.34 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.15/28.34 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.15/28.34 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 28.15/28.34 (declare-const tptp.xn $$unsorted) % 28.15/28.34 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 28.15/28.34 (declare-const tptp.xm $$unsorted) % 28.15/28.34 (define @t1 () (@var "W0" $$unsorted)) % 28.15/28.34 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 28.15/28.34 (define @t3 () (@list @t1)) % 28.15/28.34 (define @t4 () (@var "W1" $$unsorted)) % 28.15/28.34 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 28.15/28.34 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 28.15/28.34 (define @t7 () (and @t2 @t6)) % 28.15/28.34 (define @t8 () (@list @t1 @t4)) % 28.15/28.34 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 28.15/28.34 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 28.15/28.34 (define @t11 () (@var "W2" $$unsorted)) % 28.15/28.34 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 28.15/28.34 (define @t13 () (tptp.aNaturalNumber0 @t11)) % 28.15/28.34 (define @t14 () (and @t2 @t6 @t13)) % 28.15/28.34 (define @t15 () (@list @t1 @t4 @t11)) % 28.15/28.34 (define @t16 () (tptp.sdtasdt0 @t4 @t1)) % 28.15/28.34 (define @t17 () (= @t9 @t16)) % 28.15/28.34 (define @t18 () (forall @t8 (=> @t7 @t17))) % 28.15/28.34 (define @t19 () (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))) % 28.15/28.34 (define @t20 () (forall @t15 (=> @t14 @t19))) % 28.15/28.34 (define @t21 () (tptp.sdtasdt0 @t11 @t1)) % 28.15/28.34 (define @t22 () (tptp.sdtasdt0 @t1 @t11)) % 28.15/28.34 (define @t23 () (= @t4 @t11)) % 28.15/28.34 (define @t24 () (tptp.sdtpldt0 @t11 @t1)) % 28.15/28.34 (define @t25 () (tptp.sdtpldt0 @t1 @t11)) % 28.15/28.34 (define @t26 () (= @t16 @t21)) % 28.15/28.34 (define @t27 () (= @t9 @t22)) % 28.15/28.34 (define @t28 () (and @t6 @t13)) % 28.15/28.34 (define @t29 () (= @t1 tptp.sz00)) % 28.15/28.34 (define @t30 () (not @t29)) % 28.15/28.34 (define @t31 () (= @t4 tptp.sz00)) % 28.15/28.34 (define @t32 () (and @t13 (= @t25 @t4))) % 28.15/28.34 (define @t33 () (@list @t11)) % 28.15/28.34 (define @t34 () (tptp.sdtlseqdt0 @t1 @t4)) % 28.15/28.34 (define @t35 () (= @t1 @t4)) % 28.15/28.34 (define @t36 () (tptp.sdtlseqdt0 @t4 @t1)) % 28.15/28.34 (define @t37 () (tptp.sdtlseqdt0 @t4 @t11)) % 28.15/28.34 (define @t38 () (= @t4 @t1)) % 28.15/28.34 (define @t39 () (tptp.sdtpldt0 @t11 @t4)) % 28.15/28.34 (define @t40 () (and (not @t35) @t34)) % 28.15/28.34 (define @t41 () (= @t1 tptp.sz10)) % 28.15/28.34 (define @t42 () (tptp.iLess0 @t1 @t4)) % 28.15/28.34 (define @t43 () (and @t13 (= @t4 @t22))) % 28.15/28.34 (define @t44 () (tptp.doDivides0 @t1 @t4)) % 28.15/28.34 (define @t45 () (tptp.sdtsldt0 @t4 @t1)) % 28.15/28.34 (define @t46 () (= @t11 @t45)) % 28.15/28.34 (define @t47 () (forall @t33 (= @t46 @t43))) % 28.15/28.34 (define @t48 () (and @t30 @t44)) % 28.15/28.34 (define @t49 () (=> @t48 @t47)) % 28.15/28.34 (define @t50 () (=> @t7 @t49)) % 28.15/28.34 (define @t51 () (forall @t8 @t50)) % 28.15/28.34 (define @t52 () (tptp.doDivides0 @t1 @t11)) % 28.15/28.34 (define @t53 () (tptp.doDivides0 @t1 @t12)) % 28.15/28.34 (define @t54 () (not @t31)) % 28.15/28.34 (define @t55 () (tptp.doDivides0 @t4 @t1)) % 28.15/28.34 (define @t56 () (@list @t4)) % 28.15/28.34 (define @t57 () (not @t41)) % 28.15/28.34 (define @t58 () (tptp.isPrime0 @t11)) % 28.15/28.34 (define @t59 () (= tptp.xp tptp.sz00)) % 28.15/28.34 (define @t60 () (tptp.aNaturalNumber0 tptp.xp)) % 28.15/28.34 (define @t61 () (tptp.aNaturalNumber0 tptp.xn)) % 28.15/28.34 (define @t62 () (tptp.sdtasdt0 tptp.xn tptp.xn)) % 28.15/28.34 (define @t63 () (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))) % 28.15/28.34 (define @t64 () (= @t63 @t62)) % 28.15/28.34 (define @t65 () (tptp.doDivides0 tptp.xp tptp.xn)) % 28.15/28.34 (define @t66 () (tptp.sdtsldt0 tptp.xn tptp.xp)) % 28.15/28.34 (define @t67 () (tptp.sdtasdt0 tptp.xq tptp.xq)) % 28.15/28.34 (define @t68 () (tptp.sdtasdt0 tptp.xp @t67)) % 28.15/28.34 (define @t69 () (tptp.sdtasdt0 tptp.xp @t68)) % 28.15/28.34 (define @t70 () (= @t63 @t69)) % 28.15/28.34 (define @t71 () (not @t70)) % 28.15/28.34 (define @t72 () (@var "BOUND_VARIABLE_8009" $$unsorted)) % 28.15/28.34 (define @t73 () (and (tptp.aNaturalNumber0 @t72) (= @t4 (tptp.sdtasdt0 @t1 @t72)))) % 28.15/28.34 (define @t74 () (= @t73 (= @t72 @t45))) % 28.15/28.34 (define @t75 () (not @t44)) % 28.15/28.34 (define @t76 () (not @t6)) % 28.15/28.34 (define @t77 () (not @t2)) % 28.15/28.34 (define @t78 () (or @t77 @t76 @t29 @t75 @t74)) % 28.15/28.34 (define @t79 () (@list @t1 @t4 @t72)) % 28.15/28.34 (define @t80 () (forall @t79 @t78)) % 28.15/28.34 (define @t81 () (@list @t72)) % 28.15/28.34 (define @t82 () (forall @t81 @t78)) % 28.15/28.34 (define @t83 () (forall @t81 @t74)) % 28.15/28.34 (define @t84 () (or @t77 @t76 @t29 @t75 @t83)) % 28.15/28.34 (define @t85 () (forall @t33 (= @t43 @t46))) % 28.15/28.34 (define @t86 () (or @t77 @t76 @t29 @t75 @t85)) % 28.15/28.34 (define @t87 () (or @t29 @t75 @t85)) % 28.15/28.34 (define @t88 () (or @t77 @t76)) % 28.15/28.34 (define @t89 () (=> @t48 @t85)) % 28.15/28.34 (define @t90 () (not @t7)) % 28.15/28.34 (define @t91 () (tptp.sdtasdt0 tptp.xp @t66)) % 28.15/28.34 (define @t92 () (= tptp.xn @t91)) % 28.15/28.34 (define @t93 () (tptp.aNaturalNumber0 @t66)) % 28.15/28.34 (define @t94 () (and @t93 @t92)) % 28.15/28.34 (define @t95 () (= @t66 @t66)) % 28.15/28.34 (define @t96 () (not @t65)) % 28.15/28.34 (define @t97 () (not @t61)) % 28.15/28.34 (define @t98 () (not @t60)) % 28.15/28.34 (define @t99 () (or @t98 @t97 @t59 @t96 (= @t94 @t95))) % 28.15/28.34 (define @t100 () (forall @t79 (or @t77 @t76 @t29 @t75 (= @t73 (= @t45 @t72))))) % 28.15/28.34 (define @t101 () (= tptp.sz00 tptp.xp)) % 28.15/28.34 (define @t102 () (or @t98 @t97 @t101 @t96 @t94)) % 28.15/28.34 (define @t103 () (@list false)) % 28.15/28.34 (define @t104 () (not @t94)) % 28.15/28.34 (define @t105 () (@list @t94)) % 28.15/28.34 (define @t106 () (not @t13)) % 28.15/28.34 (define @t107 () (or @t77 @t76 @t106 @t19)) % 28.15/28.34 (define @t108 () (or @t77 @t76 @t106)) % 28.15/28.34 (define @t109 () (tptp.sdtasdt0 @t91 @t66)) % 28.15/28.34 (define @t110 () (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 @t66 @t66))) % 28.15/28.34 (define @t111 () (not @t93)) % 28.15/28.34 (define @t112 () (or @t98 @t111 @t111 (= @t109 @t110))) % 28.15/28.34 (define @t113 () (forall @t15 @t107)) % 28.15/28.34 (define @t114 () (= @t110 @t109)) % 28.15/28.34 (define @t115 () (or @t98 @t111 @t111 @t114)) % 28.15/28.34 (define @t116 () (@list false false false)) % 28.15/28.34 (define @t117 () (tptp.sdtasdt0 @t66 tptp.xn)) % 28.15/28.34 (define @t118 () (tptp.sdtasdt0 tptp.xn @t66)) % 28.15/28.34 (define @t119 () (= @t118 @t117)) % 28.15/28.34 (define @t120 () (or @t97 @t111 @t119)) % 28.15/28.34 (define @t121 () (tptp.sdtasdt0 tptp.xp @t117)) % 28.15/28.34 (define @t122 () (tptp.sdtasdt0 @t91 tptp.xn)) % 28.15/28.34 (define @t123 () (= @t122 @t121)) % 28.15/28.34 (define @t124 () (or @t98 @t111 @t97 @t123)) % 28.15/28.34 (define @t125 () (not @t123)) % 28.15/28.34 (define @t126 () (not @t119)) % 28.15/28.34 (define @t127 () (not @t92)) % 28.15/28.34 (define @t128 () (not @t114)) % 28.15/28.34 (define @t129 () (= @t63 (tptp.sdtasdt0 tptp.xp @t110))) % 28.15/28.34 (define @t130 () (not @t64)) % 28.15/28.34 (define @t131 () (not @t129)) % 28.15/28.34 (define @t132 () (and @t123 @t125)) % 28.15/28.34 (assume @p1 (forall @t3 (=> @t2 true))) % 28.15/28.34 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 28.15/28.34 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 28.15/28.34 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 28.15/28.34 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 28.15/28.34 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 28.15/28.34 (assume @p7 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t5 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 28.15/28.34 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 28.15/28.34 (assume @p9 @t18) % 28.15/28.34 (assume @p10 @t20) % 28.15/28.34 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 28.15/28.34 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 28.15/28.34 (assume @p13 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t22)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 @t21)))))) % 28.15/28.34 (assume @p14 (forall @t15 (=> @t14 (=> (or (= @t5 @t25) (= @t10 @t24)) @t23)))) % 28.15/28.34 (assume @p15 (forall @t3 (=> @t2 (=> @t30 (forall (@list @t4 @t11) (=> @t28 (=> (or @t27 @t26) @t23))))))) % 28.15/28.34 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t29 @t31))))) % 28.15/28.34 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t29 @t31))))) % 28.15/28.34 (assume @p18 (forall @t8 (=> @t7 (= @t34 (exists @t33 @t32))))) % 28.15/28.34 (assume @p19 (forall @t8 (=> @t7 (=> @t34 (forall @t33 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t32)))))) % 28.15/28.34 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 28.15/28.34 (assume @p21 (forall @t8 (=> @t7 (=> (and @t34 @t36) @t35)))) % 28.15/28.34 (assume @p22 (forall @t15 (=> @t14 (=> (and @t34 @t37) (tptp.sdtlseqdt0 @t1 @t11))))) % 28.15/28.34 (assume @p23 (forall @t8 (=> @t7 (or @t34 (and (not @t38) @t36))))) % 28.15/28.34 (assume @p24 (forall @t8 (=> @t7 (=> @t40 (forall @t33 (=> @t13 (and (not (= @t24 @t39)) (tptp.sdtlseqdt0 @t24 @t39) (not (= @t25 @t12)) (tptp.sdtlseqdt0 @t25 @t12)))))))) % 28.15/28.34 (assume @p25 (forall @t15 (=> @t14 (=> (and @t30 (not @t23) @t37) (and (not @t27) (tptp.sdtlseqdt0 @t9 @t22) (not @t26) (tptp.sdtlseqdt0 @t16 @t21)))))) % 28.15/28.34 (assume @p26 (forall @t3 (=> @t2 (or @t29 @t41 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 28.15/28.34 (assume @p27 (forall @t8 (=> @t7 (=> @t30 (tptp.sdtlseqdt0 @t4 @t16))))) % 28.15/28.34 (assume @p28 (forall @t8 (=> @t7 (=> @t42 true)))) % 28.15/28.34 (assume @p29 (forall @t8 (=> @t7 (=> @t40 @t42)))) % 28.15/28.34 (assume @p30 (forall @t8 (=> @t7 (= @t44 (exists @t33 @t43))))) % 28.15/28.34 (assume @p31 @t51) % 28.15/28.34 (assume @p32 (forall @t15 (=> @t14 (=> (and @t44 (tptp.doDivides0 @t4 @t11)) @t52)))) % 28.15/28.34 (assume @p33 (forall @t15 (=> @t14 (=> (and @t44 @t52) @t53)))) % 28.15/28.34 (assume @p34 (forall @t15 (=> @t14 (=> (and @t44 @t53) @t52)))) % 28.15/28.34 (assume @p35 (forall @t8 (=> @t7 (=> (and @t44 @t54) @t34)))) % 28.15/28.34 (assume @p36 (forall @t8 (=> @t7 (=> @t48 (forall @t33 (=> @t13 (= (tptp.sdtasdt0 @t11 @t45) (tptp.sdtsldt0 (tptp.sdtasdt0 @t11 @t4) @t1)))))))) % 28.15/28.34 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t30 @t57 (forall @t56 (=> (and @t6 @t55) (or (= @t4 tptp.sz10) @t38)))))))) % 28.15/28.34 (assume @p38 (forall @t3 (=> (and @t2 @t30 @t57) (exists @t56 (and @t6 @t55 (tptp.isPrime0 @t4)))))) % 28.15/28.34 (assume @p39 (forall @t15 (=> @t14 (=> (and @t58 (tptp.doDivides0 @t11 @t9)) (or (tptp.doDivides0 @t11 @t1) (tptp.doDivides0 @t11 @t4)))))) % 28.15/28.34 (assume @p40 (and @t61 (tptp.aNaturalNumber0 tptp.xm) @t60 (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not @t59))) % 28.15/28.34 (assume @p41 (forall @t15 (=> (and @t2 @t6 @t13 @t30 @t54 (not (= @t11 tptp.sz00))) (=> (= (tptp.sdtasdt0 @t11 (tptp.sdtasdt0 @t4 @t4)) (tptp.sdtasdt0 @t1 @t1)) (=> (tptp.iLess0 @t1 tptp.xn) (not @t58)))))) % 28.15/28.34 (assume @p42 @t64) % 28.15/28.34 (assume @p43 (tptp.isPrime0 tptp.xp)) % 28.15/28.34 (assume @p44 (and (tptp.doDivides0 tptp.xp @t62) @t65)) % 28.15/28.34 (assume @p45 (= tptp.xq @t66)) % 28.15/28.34 (assume @p46 @t71) % 28.15/28.34 (assume @p47 true) % 28.15/28.34 (step @p48 :rule cong :premises (@p45 @p45) :args (@t67)) % 28.15/28.34 (step @p49 :rule refl :args (tptp.xp)) % 28.15/28.34 (step @p50 :rule cong :premises (@p49 @p48) :args (@t68)) % 28.15/28.34 (step @p51 :rule cong :premises (@p49 @p50) :args (@t69)) % 28.15/28.34 (step @p52 :rule refl :args (@t63)) % 28.15/28.34 (step @p53 :rule cong :premises (@p52 @p51) :args (@t70)) % 28.15/28.34 (step @p54 :rule cong :premises (@p53) :args (@t71)) % 28.15/28.34 (step @p55 :rule eq_resolve :premises (@p46 @p54)) % 28.15/28.34 (step @p56 :rule eq-symm :args (@t72 @t45)) % 28.15/28.34 (step @p57 :rule refl :args (@t73)) % 28.15/28.34 (step @p58 :rule cong :premises (@p57 @p56) :args (@t74)) % 28.15/28.34 (step @p59 :rule refl :args (@t75)) % 28.15/28.34 (step @p60 :rule refl :args (@t29)) % 28.15/28.34 (step @p61 :rule refl :args (@t76)) % 28.15/28.34 (step @p62 :rule refl :args (@t77)) % 28.15/28.34 (step @p63 :rule nary_cong :premises (@p62 @p61 @p60 @p59 @p58) :args (@t78)) % 28.15/28.34 (step @p64 :rule cong :premises (@p63) :args (@t80)) % 28.15/28.34 (step @p65 :rule quant-merge-prenex :args ((= (forall @t8 @t82) @t80))) % 28.15/28.34 (step @p66 :rule alpha_equiv :args (@t83 (@list @t72) (@list @t11))) % 28.15/28.34 (step @p67 :rule refl :args (@t75)) % 28.15/28.34 (step @p68 :rule refl :args (@t29)) % 28.15/28.34 (step @p69 :rule refl :args (@t76)) % 28.15/28.34 (step @p70 :rule refl :args (@t77)) % 28.15/28.34 (step @p71 :rule nary_cong :premises (@p70 @p69 @p68 @p67 @p66) :args (@t84)) % 28.15/28.34 (step @p72 :rule quant-miniscope-or :args ((= @t82 @t84))) % 28.15/28.34 (step @p73 :rule trans :premises (@p72 @p71)) % 28.15/28.34 (step @p74 :rule symm :premises (@p73)) % 28.15/28.34 (step @p75 :rule cong :premises (@p74) :args ((forall @t8 @t86))) % 28.15/28.34 (step @p76 :rule trans :premises (@p75 @p65)) % 28.15/28.34 (step @p77 :rule trans :premises (@p76 @p64)) % 28.15/28.34 (step @p78 :rule aci_norm :args ((= (or @t88 @t87) @t86))) % 28.15/28.34 (step @p79 :rule aci_norm :args ((= (or (or @t29 @t75) @t85) @t87))) % 28.15/28.34 (step @p80 :rule refl :args (@t85)) % 28.15/28.34 (step @p81 :rule bool-double-not-elim :args (@t29)) % 28.15/28.34 (step @p82 :rule nary_cong :premises (@p81 @p67) :args ((or (not @t30) @t75))) % 28.15/28.34 (step @p83 :rule bool-and-de-morgan :args (@t30 @t44 true)) % 28.15/28.34 (step @p84 :rule trans :premises (@p83 @p82)) % 28.15/28.34 (step @p85 :rule nary_cong :premises (@p84 @p80) :args ((or (not @t48) @t85))) % 28.15/28.34 (step @p86 :rule trans :premises (@p85 @p79)) % 28.15/28.34 (step @p87 :rule bool-impl-elim :args (@t48 @t85)) % 28.15/28.34 (step @p88 :rule trans :premises (@p87 @p86)) % 28.15/28.34 (step @p89 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 28.15/28.34 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t90 @t89))) % 28.15/28.34 (step @p91 :rule trans :premises (@p90 @p78)) % 28.15/28.34 (step @p92 :rule bool-impl-elim :args (@t7 @t89)) % 28.15/28.34 (step @p93 :rule trans :premises (@p92 @p91)) % 28.15/28.34 (step @p94 :rule cong :premises (@p93) :args ((forall @t8 (=> @t7 @t89)))) % 28.15/28.34 (step @p95 :rule trans :premises (@p94 @p77)) % 28.15/28.34 (step @p96 :rule eq-symm :args (@t46 @t43)) % 28.15/28.34 (step @p97 :rule cong :premises (@p96) :args (@t47)) % 28.15/28.34 (step @p98 :rule refl :args (@t48)) % 28.15/28.34 (step @p99 :rule cong :premises (@p98 @p97) :args (@t49)) % 28.15/28.34 (step @p100 :rule refl :args (@t7)) % 28.15/28.34 (step @p101 :rule cong :premises (@p100 @p99) :args (@t50)) % 28.15/28.34 (step @p102 :rule cong :premises (@p101) :args (@t51)) % 28.15/28.34 (step @p103 :rule trans :premises (@p102 @p95)) % 28.15/28.34 (step @p104 :rule eq_resolve :premises (@p31 @p103)) % 28.15/28.34 (step @p105 :rule bool-eq-true :args (@t94)) % 28.15/28.34 (step @p106 :rule eq-symm :args (true @t94)) % 28.15/28.34 (step @p107 :rule trans :premises (@p106 @p105)) % 28.15/28.34 (step @p108 :rule refl :args (@t94)) % 28.15/28.34 (step @p109 :rule eq-refl :args (@t66)) % 28.15/28.34 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t95 @t94))) % 28.15/28.34 (step @p111 :rule trans :premises (@p110 @p107)) % 28.15/28.34 (step @p112 :rule eq-symm :args (@t94 @t95)) % 28.15/28.34 (step @p113 :rule trans :premises (@p112 @p111)) % 28.15/28.34 (step @p114 :rule refl :args (@t96)) % 28.15/28.34 (step @p115 :rule eq-symm :args (tptp.xp tptp.sz00)) % 28.15/28.34 (step @p116 :rule refl :args (@t97)) % 28.15/28.34 (step @p117 :rule refl :args (@t98)) % 28.15/28.34 (step @p118 :rule nary_cong :premises (@p117 @p116 @p115 @p114 @p113) :args (@t99)) % 28.15/28.34 (step @p119 :rule refl :args (@t100)) % 28.15/28.34 (step @p120 :rule cong :premises (@p119 @p118) :args ((=> @t100 @t99))) % 28.15/28.34 (assume-push @p241 @t100) % 28.15/28.34 (step @p122 :rule instantiate :premises (@p104) :args ((@list tptp.xp tptp.xn @t66))) % 28.15/28.34 (step-pop @p242 :rule scope :premises (@p122)) % 28.15/28.34 (step @p123 :rule process_scope :premises (@p242) :args (@t99)) % 28.15/28.34 (step @p125 :rule eq_resolve :premises (@p123 @p120)) % 28.15/28.34 (step @p126 :rule implies_elim :premises (@p125)) % 28.15/28.34 (step @p127 :rule chain_m_resolution :premises (@p126 @p104) :args (@t102 @t103 (@list @t100))) % 28.15/28.34 (step @p128 :rule and_elim :premises (@p44) :args (1)) % 28.15/28.34 (step @p129 :rule and_elim :premises (@p40) :args (2)) % 28.15/28.34 (step @p130 :rule and_elim :premises (@p40) :args (0)) % 28.15/28.34 (step @p131 :rule and_elim :premises (@p40) :args (5)) % 28.15/28.34 (step @p132 :rule symm :premises (@p131)) % 28.15/28.34 (step @p133 :rule cnf_or_pos :args (@t102)) % 28.15/28.34 (step @p134 :rule reordering :premises (@p133) :args ((or @t101 @t97 @t98 @t96 @t94 (not @t102)))) % 28.15/28.34 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p130 @p129 @p128 @p127) :args (@t94 (@list true false false false false) (@list @t101 @t61 @t60 @t65 @t102))) % 28.15/28.34 (step @p136 :rule cnf_and_pos :args (@t94 1)) % 28.15/28.34 (step @p137 :rule reordering :premises (@p136) :args ((or @t92 @t104))) % 28.15/28.34 (step @p138 :rule chain_m_resolution :premises (@p137 @p135) :args (@t92 @t103 @t105)) % 28.15/28.34 (step @p139 :rule aci_norm :args ((= (or @t108 @t19) @t107))) % 28.15/28.34 (step @p140 :rule refl :args (@t19)) % 28.15/28.34 (step @p141 :rule aci_norm :args ((= (or @t77 (or @t76 @t106)) @t108))) % 28.15/28.34 (step @p142 :rule bool-and-de-morgan :args (@t6 @t13 true)) % 28.15/28.34 (step @p143 :rule nary_cong :premises (@p70 @p142) :args ((or @t77 (not @t28)))) % 28.15/28.34 (step @p144 :rule bool-and-de-morgan :args (@t2 @t6 (and @t13))) % 28.15/28.34 (step @p145 :rule trans :premises (@p144 @p143)) % 28.15/28.34 (step @p146 :rule trans :premises (@p145 @p141)) % 28.15/28.34 (step @p147 :rule nary_cong :premises (@p146 @p140) :args ((or (not @t14) @t19))) % 28.15/28.34 (step @p148 :rule trans :premises (@p147 @p139)) % 28.15/28.34 (step @p149 :rule bool-impl-elim :args (@t14 @t19)) % 28.15/28.34 (step @p150 :rule trans :premises (@p149 @p148)) % 28.15/28.34 (step @p151 :rule cong :premises (@p150) :args (@t20)) % 28.15/28.34 (step @p152 :rule eq_resolve :premises (@p10 @p151)) % 28.15/28.34 (step @p153 :rule eq-symm :args (@t109 @t110)) % 28.15/28.34 (step @p154 :rule refl :args (@t111)) % 28.15/28.34 (step @p155 :rule nary_cong :premises (@p117 @p154 @p154 @p153) :args (@t112)) % 28.15/28.34 (step @p156 :rule refl :args (@t113)) % 28.15/28.34 (step @p157 :rule cong :premises (@p156 @p155) :args ((=> @t113 @t112))) % 28.15/28.34 (assume-push @p243 @t113) % 28.15/28.34 (step @p159 :rule instantiate :premises (@p152) :args ((@list tptp.xp @t66 @t66))) % 28.15/28.34 (step-pop @p244 :rule scope :premises (@p159)) % 28.15/28.34 (step @p160 :rule process_scope :premises (@p244) :args (@t112)) % 28.15/28.34 (step @p162 :rule eq_resolve :premises (@p160 @p157)) % 28.15/28.34 (step @p163 :rule implies_elim :premises (@p162)) % 28.15/28.34 (step @p164 :rule chain_m_resolution :premises (@p163 @p152) :args (@t115 @t103 (@list @t113))) % 28.15/28.34 (step @p165 :rule cnf_and_pos :args (@t94 0)) % 28.15/28.34 (step @p166 :rule reordering :premises (@p165) :args ((or @t93 @t104))) % 28.15/28.34 (step @p167 :rule chain_m_resolution :premises (@p166 @p135) :args (@t93 @t103 @t105)) % 28.15/28.34 (step @p168 :rule cnf_or_pos :args (@t115)) % 28.15/28.34 (step @p169 :rule factoring :premises (@p168)) % 28.15/28.34 (step @p170 :rule reordering :premises (@p169) :args ((or @t98 @t111 @t114 (not @t115)))) % 28.15/28.34 (step @p171 :rule chain_m_resolution :premises (@p170 @p129 @p167 @p164) :args (@t114 @t116 (@list @t60 @t93 @t115))) % 28.15/28.34 (step @p172 :rule aci_norm :args ((= (or @t88 @t17) (or @t77 @t76 @t17)))) % 28.15/28.34 (step @p173 :rule refl :args (@t17)) % 28.15/28.34 (step @p174 :rule nary_cong :premises (@p89 @p173) :args ((or @t90 @t17))) % 28.15/28.34 (step @p175 :rule trans :premises (@p174 @p172)) % 28.15/28.34 (step @p176 :rule bool-impl-elim :args (@t7 @t17)) % 28.15/28.34 (step @p177 :rule trans :premises (@p176 @p175)) % 28.15/28.34 (step @p178 :rule cong :premises (@p177) :args (@t18)) % 28.15/28.34 (step @p179 :rule eq_resolve :premises (@p9 @p178)) % 28.15/28.34 (step @p180 :rule instantiate :premises (@p179) :args ((@list tptp.xn @t66))) % 28.15/28.34 (step @p181 :rule cnf_or_pos :args (@t120)) % 28.15/28.34 (step @p182 :rule reordering :premises (@p181) :args ((or @t97 @t111 @t119 (not @t120)))) % 28.15/28.34 (step @p183 :rule chain_m_resolution :premises (@p182 @p130 @p167 @p180) :args (@t119 @t116 (@list @t61 @t93 @t120))) % 28.15/28.34 (step @p184 :rule instantiate :premises (@p152) :args ((@list tptp.xp @t66 tptp.xn))) % 28.15/28.34 (step @p185 :rule cnf_or_pos :args (@t124)) % 28.15/28.34 (step @p186 :rule reordering :premises (@p185) :args ((or @t97 @t98 @t111 @t123 (not @t124)))) % 28.15/28.34 (step @p187 :rule chain_m_resolution :premises (@p186 @p130 @p129 @p167 @p184) :args (@t123 (@list false false false false) (@list @t61 @t60 @t93 @t124))) % 28.15/28.34 (step @p188 :rule refl :args (@t125)) % 28.15/28.34 (step @p189 :rule refl :args (@t126)) % 28.15/28.34 (step @p190 :rule refl :args (@t127)) % 28.15/28.34 (step @p191 :rule refl :args (@t128)) % 28.15/28.34 (step @p192 :rule bool-double-not-elim :args (@t129)) % 28.15/28.34 (step @p193 :rule refl :args (@t130)) % 28.15/28.34 (step @p194 :rule nary_cong :premises (@p193 @p192 @p191 @p190 @p189 @p188) :args ((or @t130 (not @t131) @t128 @t127 @t126 @t125))) % 28.15/28.34 (assume-push @p245 @t123) % 28.15/28.34 (assume-push @p246 @t125) % 28.15/28.34 (step @p197 :rule evaluate :args ((= false true))) % 28.15/28.34 (step @p198 :rule true_intro :premises (@p187)) % 28.15/28.34 (step @p199 :rule false_intro :premises (@p55)) % 28.15/28.34 (step @p200 :rule symm :premises (@p171)) % 28.15/28.34 (step @p201 :rule refl :args (@t66)) % 28.15/28.34 (step @p202 :rule cong :premises (@p138 @p201) :args (@t118)) % 28.15/28.34 (step @p203 :rule symm :premises (@p183)) % 28.15/28.34 (step @p204 :rule trans :premises (@p203 @p202 @p200)) % 28.15/28.34 (step @p205 :rule cong :premises (@p49 @p204) :args (@t121)) % 28.15/28.34 (step @p206 :rule symm :premises (@p42)) % 28.15/28.34 (step @p207 :rule refl :args (tptp.xn)) % 28.15/28.34 (step @p208 :rule symm :premises (@p138)) % 28.15/28.34 (step @p209 :rule cong :premises (@p208 @p207) :args (@t122)) % 28.15/28.34 (step @p210 :rule trans :premises (@p209 @p206)) % 28.15/28.34 (step @p211 :rule cong :premises (@p210 @p205) :args (@t123)) % 28.15/28.34 (step @p212 :rule trans :premises (@p211 @p199)) % 28.15/28.34 (step @p213 :rule symm :premises (@p212)) % 28.15/28.34 (step @p214 :rule trans :premises (@p213 @p198)) % 28.15/28.34 (step @p215 false :rule eq_resolve :premises (@p214 @p197)) % 28.15/28.34 (step-pop @p247 :rule scope :premises (@p215)) % 28.15/28.34 (step-pop @p248 :rule scope :premises (@p247)) % 28.15/28.34 (step @p216 :rule process_scope :premises (@p248) :args (false)) % 28.15/28.34 (assume-push @p249 @t64) % 28.15/28.34 (assume-push @p250 @t131) % 28.15/28.34 (assume-push @p251 @t114) % 28.15/28.34 (assume-push @p252 @t92) % 28.15/28.34 (assume-push @p253 @t119) % 28.15/28.34 (assume-push @p254 @t123) % 28.15/28.34 (step @p199 :rule false_intro :premises (@p55)) % 28.15/28.34 (step @p200 :rule symm :premises (@p171)) % 28.15/28.34 (step @p201 :rule refl :args (@t66)) % 28.15/28.34 (step @p202 :rule cong :premises (@p138 @p201) :args (@t118)) % 28.15/28.34 (step @p203 :rule symm :premises (@p183)) % 28.15/28.34 (step @p204 :rule trans :premises (@p203 @p202 @p200)) % 28.15/28.34 (step @p205 :rule cong :premises (@p49 @p204) :args (@t121)) % 28.15/28.34 (step @p206 :rule symm :premises (@p42)) % 28.15/28.34 (step @p207 :rule refl :args (tptp.xn)) % 28.15/28.34 (step @p208 :rule symm :premises (@p138)) % 28.15/28.34 (step @p209 :rule cong :premises (@p208 @p207) :args (@t122)) % 28.15/28.35 (step @p210 :rule trans :premises (@p209 @p206)) % 28.15/28.35 (step @p211 :rule cong :premises (@p210 @p205) :args (@t123)) % 28.15/28.35 (step @p225 :rule trans :premises (@p211 @p199)) % 28.15/28.35 (step @p226 :rule false_elim :premises (@p225)) % 28.15/28.35 (step @p227 :rule and_intro :premises (@p187 @p226)) % 28.15/28.35 (step-pop @p255 :rule scope :premises (@p227)) % 28.15/28.35 (step-pop @p256 :rule scope :premises (@p255)) % 28.15/28.35 (step-pop @p257 :rule scope :premises (@p256)) % 28.15/28.35 (step-pop @p258 :rule scope :premises (@p257)) % 28.15/28.35 (step-pop @p259 :rule scope :premises (@p258)) % 28.15/28.35 (step-pop @p260 :rule scope :premises (@p259)) % 28.15/28.35 (step @p228 :rule process_scope :premises (@p260) :args (@t132)) % 28.15/28.35 (step @p235 :rule implies_elim :premises (@p228)) % 28.15/28.35 (step @p236 :rule resolution :premises (@p235 @p216) :args (true @t132)) % 28.15/28.35 (step @p237 :rule not_and :premises (@p236)) % 28.15/28.35 (step @p238 :rule eq_resolve :premises (@p237 @p194)) % 28.15/28.35 (step @p239 :rule reordering :premises (@p238) :args ((or @t129 @t130 @t128 @t127 @t126 @t125))) % 28.15/28.35 (step @p240 false :rule chain_m_resolution :premises (@p239 @p187 @p183 @p171 @p138 @p55 @p42) :args (false (@list false false false false true false) (@list @t123 @t119 @t114 @t92 @t129 @t64))) % 28.15/28.35 ) % 28.15/28.35 % SZS output end Proof % 28.15/28.35 % cvc5 exiting %------------------------------------------------------------------------------