%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM504+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 : n027.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 08:39:38 AM UTC 2026 % Result : Theorem 28.21s 28.51s % Output : Proof 28.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM504+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 % 0.16/0.34 % Computer : n027.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 11:25:06 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 28.21/28.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 28.21/28.51 --- Run --no-e-matching --full-saturate-quant at 6... % 28.21/28.51 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 28.21/28.51 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 28.21/28.51 % SZS status Theorem % 28.21/28.51 % SZS output start Proof % 28.21/28.51 ( % 28.21/28.51 (declare-sort $$unsorted 0) % 28.21/28.51 (declare-const tptp.xr $$unsorted) % 28.21/28.51 (declare-const tptp.xk $$unsorted) % 28.21/28.51 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 28.21/28.51 (declare-const tptp.xm $$unsorted) % 28.21/28.51 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.21/28.51 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 28.21/28.51 (declare-const tptp.xn $$unsorted) % 28.21/28.51 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 28.21/28.51 (declare-const tptp.sz00 $$unsorted) % 28.21/28.51 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.21/28.51 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.21/28.51 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 28.21/28.51 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 28.21/28.51 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 28.21/28.51 (declare-const tptp.sz10 $$unsorted) % 28.21/28.51 (declare-const tptp.xp $$unsorted) % 28.21/28.51 (define @t1 () (@var "W0" $$unsorted)) % 28.21/28.51 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 28.21/28.51 (define @t3 () (@list @t1)) % 28.21/28.51 (define @t4 () (@var "W1" $$unsorted)) % 28.21/28.51 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 28.21/28.51 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 28.21/28.51 (define @t7 () (and @t2 @t6)) % 28.21/28.51 (define @t8 () (@list @t1 @t4)) % 28.21/28.51 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 28.21/28.51 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 28.21/28.51 (define @t11 () (forall @t8 (=> @t7 @t10))) % 28.21/28.51 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 28.21/28.51 (define @t13 () (@var "W2" $$unsorted)) % 28.21/28.51 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 28.21/28.51 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 28.21/28.51 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 28.21/28.51 (define @t17 () (and @t2 @t6 @t16)) % 28.21/28.51 (define @t18 () (@list @t1 @t4 @t13)) % 28.21/28.51 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 28.21/28.51 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 28.21/28.51 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 28.21/28.51 (define @t22 () (= @t4 @t13)) % 28.21/28.51 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 28.21/28.51 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 28.21/28.51 (define @t25 () (= @t19 @t20)) % 28.21/28.51 (define @t26 () (= @t9 @t21)) % 28.21/28.51 (define @t27 () (= @t1 tptp.sz00)) % 28.21/28.51 (define @t28 () (not @t27)) % 28.21/28.51 (define @t29 () (= @t4 tptp.sz00)) % 28.21/28.51 (define @t30 () (and @t16 (= @t24 @t4))) % 28.21/28.51 (define @t31 () (@list @t13)) % 28.21/28.51 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 28.21/28.51 (define @t33 () (= @t1 @t4)) % 28.21/28.51 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 28.21/28.51 (define @t35 () (and @t32 @t34)) % 28.21/28.51 (define @t36 () (=> @t35 @t33)) % 28.21/28.51 (define @t37 () (forall @t8 (=> @t7 @t36))) % 28.21/28.51 (define @t38 () (tptp.sdtlseqdt0 @t4 @t13)) % 28.21/28.51 (define @t39 () (= @t4 @t1)) % 28.21/28.51 (define @t40 () (tptp.sdtpldt0 @t13 @t4)) % 28.21/28.51 (define @t41 () (and (not @t33) @t32)) % 28.21/28.51 (define @t42 () (= @t1 tptp.sz10)) % 28.21/28.51 (define @t43 () (tptp.iLess0 @t1 @t4)) % 28.21/28.51 (define @t44 () (and @t16 (= @t4 @t21))) % 28.21/28.51 (define @t45 () (tptp.doDivides0 @t1 @t4)) % 28.21/28.51 (define @t46 () (tptp.sdtsldt0 @t4 @t1)) % 28.21/28.51 (define @t47 () (= @t13 @t46)) % 28.21/28.51 (define @t48 () (forall @t31 (= @t47 @t44))) % 28.21/28.51 (define @t49 () (and @t28 @t45)) % 28.21/28.51 (define @t50 () (=> @t49 @t48)) % 28.21/28.51 (define @t51 () (=> @t7 @t50)) % 28.21/28.51 (define @t52 () (forall @t8 @t51)) % 28.21/28.51 (define @t53 () (tptp.doDivides0 @t1 @t13)) % 28.21/28.51 (define @t54 () (tptp.doDivides0 @t1 @t14)) % 28.21/28.51 (define @t55 () (or (= @t4 tptp.sz10) @t39)) % 28.21/28.51 (define @t56 () (tptp.doDivides0 @t4 @t1)) % 28.21/28.51 (define @t57 () (and @t6 @t56)) % 28.21/28.51 (define @t58 () (=> @t57 @t55)) % 28.21/28.51 (define @t59 () (@list @t4)) % 28.21/28.51 (define @t60 () (forall @t59 @t58)) % 28.21/28.51 (define @t61 () (not @t42)) % 28.21/28.51 (define @t62 () (and @t28 @t61 @t60)) % 28.21/28.51 (define @t63 () (tptp.isPrime0 @t1)) % 28.21/28.51 (define @t64 () (= @t63 @t62)) % 28.21/28.51 (define @t65 () (=> @t2 @t64)) % 28.21/28.51 (define @t66 () (forall @t3 @t65)) % 28.21/28.51 (define @t67 () (tptp.aNaturalNumber0 tptp.xp)) % 28.21/28.51 (define @t68 () (tptp.aNaturalNumber0 tptp.xm)) % 28.21/28.51 (define @t69 () (tptp.aNaturalNumber0 tptp.xn)) % 28.21/28.51 (define @t70 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 28.21/28.51 (define @t71 () (tptp.doDivides0 tptp.xp @t70)) % 28.21/28.51 (define @t72 () (tptp.isPrime0 tptp.xp)) % 28.21/28.51 (define @t73 () (tptp.sdtsldt0 @t70 tptp.xp)) % 28.21/28.51 (define @t74 () (= tptp.xk tptp.sz10)) % 28.21/28.51 (define @t75 () (= tptp.xk tptp.sz00)) % 28.21/28.51 (define @t76 () (tptp.sdtasdt0 tptp.xp tptp.xk)) % 28.21/28.51 (define @t77 () (tptp.sdtasdt0 tptp.xp tptp.xm)) % 28.21/28.51 (define @t78 () (tptp.sdtlseqdt0 @t77 @t76)) % 28.21/28.51 (define @t79 () (tptp.sdtlseqdt0 @t70 @t77)) % 28.21/28.51 (define @t80 () (= @t70 @t77)) % 28.21/28.51 (define @t81 () (= tptp.sz10 @t4)) % 28.21/28.51 (define @t82 () (not @t56)) % 28.21/28.51 (define @t83 () (not @t6)) % 28.21/28.51 (define @t84 () (or @t83 @t82 @t81 @t33)) % 28.21/28.51 (define @t85 () (= @t63 (and @t28 @t61 (forall @t59 @t84)))) % 28.21/28.51 (define @t86 () (or @t81 @t33)) % 28.21/28.51 (define @t87 () (not (tptp.doDivides0 @t4 tptp.xp))) % 28.21/28.51 (define @t88 () (or @t83 @t87 @t81 (= tptp.xp @t4))) % 28.21/28.51 (define @t89 () (forall @t59 @t88)) % 28.21/28.51 (define @t90 () (not (= tptp.xp tptp.sz10))) % 28.21/28.51 (define @t91 () (= tptp.xp tptp.sz00)) % 28.21/28.51 (define @t92 () (not @t91)) % 28.21/28.51 (define @t93 () (and @t92 @t90 @t89)) % 28.21/28.51 (define @t94 () (= @t72 @t93)) % 28.21/28.51 (define @t95 () (not @t67)) % 28.21/28.51 (define @t96 () (or @t95 @t94)) % 28.21/28.51 (define @t97 () (not @t2)) % 28.21/28.51 (define @t98 () (forall @t3 (or @t97 @t85))) % 28.21/28.51 (define @t99 () (= tptp.sz00 tptp.xp)) % 28.21/28.51 (define @t100 () (not @t99)) % 28.21/28.51 (define @t101 () (and @t100 (not (= tptp.sz10 tptp.xp)) (forall @t59 (or @t83 @t87 @t81 (= @t4 tptp.xp))))) % 28.21/28.51 (define @t102 () (= @t72 @t101)) % 28.21/28.51 (define @t103 () (or @t95 @t102)) % 28.21/28.51 (define @t104 () (@list false)) % 28.21/28.51 (define @t105 () (@list false false)) % 28.21/28.51 (define @t106 () (or @t97 @t83)) % 28.21/28.51 (define @t107 () (not @t7)) % 28.21/28.51 (define @t108 () (tptp.aNaturalNumber0 @t70)) % 28.21/28.51 (define @t109 () (not @t68)) % 28.21/28.51 (define @t110 () (not @t69)) % 28.21/28.51 (define @t111 () (or @t110 @t109 @t108)) % 28.21/28.51 (define @t112 () (@list false false false)) % 28.21/28.51 (define @t113 () (not @t34)) % 28.21/28.51 (define @t114 () (not @t32)) % 28.21/28.51 (define @t115 () (or @t97 @t83 @t114 @t113 @t33)) % 28.21/28.51 (define @t116 () (or @t114 @t113 @t33)) % 28.21/28.51 (define @t117 () (not @t79)) % 28.21/28.51 (define @t118 () (tptp.sdtlseqdt0 @t77 @t70)) % 28.21/28.51 (define @t119 () (not @t118)) % 28.21/28.51 (define @t120 () (not @t108)) % 28.21/28.51 (define @t121 () (tptp.aNaturalNumber0 @t77)) % 28.21/28.51 (define @t122 () (not @t121)) % 28.21/28.51 (define @t123 () (or @t122 @t120 @t119 @t117 (= @t77 @t70))) % 28.21/28.51 (define @t124 () (forall @t8 @t115)) % 28.21/28.51 (define @t125 () (or @t122 @t120 @t119 @t117 @t80)) % 28.21/28.51 (define @t126 () (or @t95 @t109 @t121)) % 28.21/28.51 (define @t127 () (tptp.sdtasdt0 tptp.xp @t73)) % 28.21/28.51 (define @t128 () (= @t70 @t127)) % 28.21/28.51 (define @t129 () (not @t128)) % 28.21/28.51 (define @t130 () (tptp.sdtlseqdt0 @t77 @t127)) % 28.21/28.51 (define @t131 () (not @t130)) % 28.21/28.51 (define @t132 () (and (tptp.aNaturalNumber0 @t73) @t128)) % 28.21/28.51 (define @t133 () (not @t132)) % 28.21/28.51 (define @t134 () (@var "BOUND_VARIABLE_8025" $$unsorted)) % 28.21/28.51 (define @t135 () (and (tptp.aNaturalNumber0 @t134) (= @t4 (tptp.sdtasdt0 @t1 @t134)))) % 28.21/28.51 (define @t136 () (= @t135 (= @t134 @t46))) % 28.21/28.51 (define @t137 () (not @t45)) % 28.21/28.51 (define @t138 () (or @t97 @t83 @t27 @t137 @t136)) % 28.21/28.51 (define @t139 () (@list @t1 @t4 @t134)) % 28.21/28.51 (define @t140 () (forall @t139 @t138)) % 28.21/28.51 (define @t141 () (@list @t134)) % 28.21/28.51 (define @t142 () (forall @t141 @t138)) % 28.21/28.51 (define @t143 () (forall @t141 @t136)) % 28.21/28.51 (define @t144 () (or @t97 @t83 @t27 @t137 @t143)) % 28.21/28.51 (define @t145 () (forall @t31 (= @t44 @t47))) % 28.21/28.51 (define @t146 () (or @t97 @t83 @t27 @t137 @t145)) % 28.21/28.51 (define @t147 () (or @t27 @t137 @t145)) % 28.21/28.51 (define @t148 () (=> @t49 @t145)) % 28.21/28.51 (define @t149 () (= @t73 @t73)) % 28.21/28.51 (define @t150 () (not @t71)) % 28.21/28.51 (define @t151 () (or @t95 @t120 @t91 @t150 (= @t132 @t149))) % 28.21/28.51 (define @t152 () (forall @t139 (or @t97 @t83 @t27 @t137 (= @t135 (= @t46 @t134))))) % 28.21/28.51 (define @t153 () (or @t95 @t120 @t99 @t150 @t132)) % 28.21/28.51 (assume @p1 (forall @t3 (=> @t2 true))) % 28.21/28.51 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 28.21/28.51 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 28.21/28.51 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 28.21/28.51 (assume @p5 @t11) % 28.21/28.51 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 28.21/28.51 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 28.21/28.51 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 28.21/28.51 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t19)))) % 28.21/28.51 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 28.21/28.51 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 28.21/28.51 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 28.21/28.51 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 28.21/28.51 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 28.21/28.51 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> (and @t6 @t16) (=> (or @t26 @t25) @t22))))))) % 28.21/28.51 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 28.21/28.51 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t27 @t29))))) % 28.21/28.51 (assume @p18 (forall @t8 (=> @t7 (= @t32 (exists @t31 @t30))))) % 28.21/28.51 (assume @p19 (forall @t8 (=> @t7 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 28.21/28.51 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 28.21/28.51 (assume @p21 @t37) % 28.21/28.51 (assume @p22 (forall @t18 (=> @t17 (=> (and @t32 @t38) (tptp.sdtlseqdt0 @t1 @t13))))) % 28.21/28.51 (assume @p23 (forall @t8 (=> @t7 (or @t32 (and (not @t39) @t34))))) % 28.21/28.51 (assume @p24 (forall @t8 (=> @t7 (=> @t41 (forall @t31 (=> @t16 (and (not (= @t23 @t40)) (tptp.sdtlseqdt0 @t23 @t40) (not (= @t24 @t14)) (tptp.sdtlseqdt0 @t24 @t14)))))))) % 28.21/28.51 (assume @p25 (forall @t18 (=> @t17 (=> (and @t28 (not @t22) @t38) (and (not @t26) (tptp.sdtlseqdt0 @t9 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 28.21/28.51 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t42 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 28.21/28.51 (assume @p27 (forall @t8 (=> @t7 (=> @t28 (tptp.sdtlseqdt0 @t4 @t19))))) % 28.21/28.51 (assume @p28 (forall @t8 (=> @t7 (=> @t43 true)))) % 28.21/28.51 (assume @p29 (forall @t8 (=> @t7 (=> @t41 @t43)))) % 28.21/28.51 (assume @p30 (forall @t8 (=> @t7 (= @t45 (exists @t31 @t44))))) % 28.21/28.51 (assume @p31 @t52) % 28.21/28.51 (assume @p32 (forall @t18 (=> @t17 (=> (and @t45 (tptp.doDivides0 @t4 @t13)) @t53)))) % 28.21/28.51 (assume @p33 (forall @t18 (=> @t17 (=> (and @t45 @t53) @t54)))) % 28.21/28.51 (assume @p34 (forall @t18 (=> @t17 (=> (and @t45 @t54) @t53)))) % 28.21/28.51 (assume @p35 (forall @t8 (=> @t7 (=> (and @t45 (not @t29)) @t32)))) % 28.21/28.51 (assume @p36 (forall @t8 (=> @t7 (=> @t49 (forall @t31 (=> @t16 (= (tptp.sdtasdt0 @t13 @t46) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 28.21/28.51 (assume @p37 @t66) % 28.21/28.51 (assume @p38 (forall @t3 (=> (and @t2 @t28 @t61) (exists @t59 (and @t6 @t56 (tptp.isPrime0 @t4)))))) % 28.21/28.51 (assume @p39 (and @t69 @t68 @t67)) % 28.21/28.51 (assume @p40 (forall @t18 (=> @t17 (=> (and (tptp.isPrime0 @t13) (tptp.doDivides0 @t13 @t9)) (=> (tptp.iLess0 @t15 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 @t13 @t1) (tptp.doDivides0 @t13 @t4))))))) % 28.21/28.51 (assume @p41 (and @t72 @t71)) % 28.21/28.51 (assume @p42 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 28.21/28.51 (assume @p43 (not (tptp.sdtlseqdt0 tptp.xp tptp.xm))) % 28.21/28.51 (assume @p44 (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 28.21/28.51 (assume @p45 (= tptp.xk @t73)) % 28.21/28.51 (assume @p46 (not (or @t75 @t74))) % 28.21/28.51 (assume @p47 (and (not @t75) (not @t74))) % 28.21/28.51 (assume @p48 (and (tptp.aNaturalNumber0 tptp.xr) (tptp.doDivides0 tptp.xr tptp.xk) (tptp.isPrime0 tptp.xr))) % 28.21/28.51 (assume @p49 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr @t70))) % 28.21/28.51 (assume @p50 (tptp.sdtlseqdt0 tptp.xp tptp.xk)) % 28.21/28.51 (assume @p51 (and (not @t80) @t79 (not (= @t77 @t76)) @t78)) % 28.21/28.51 (assume @p52 (not false)) % 28.21/28.51 (assume @p53 true) % 28.21/28.51 (step @p54 :rule and_elim :premises (@p39) :args (2)) % 28.21/28.51 (step @p55 :rule and_elim :premises (@p41) :args (1)) % 28.21/28.51 (step @p56 :rule bool-impl-elim :args (@t2 @t85)) % 28.21/28.51 (step @p57 :rule cong :premises (@p56) :args ((forall @t3 (=> @t2 @t85)))) % 28.21/28.51 (step @p58 :rule aci_norm :args ((= (or (or @t83 @t82) @t86) @t84))) % 28.21/28.51 (step @p59 :rule refl :args (@t86)) % 28.21/28.51 (step @p60 :rule bool-and-de-morgan :args (@t6 @t56 true)) % 28.21/28.51 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or (not @t57) @t86))) % 28.21/28.51 (step @p62 :rule trans :premises (@p61 @p58)) % 28.21/28.51 (step @p63 :rule bool-impl-elim :args (@t57 @t86)) % 28.21/28.51 (step @p64 :rule trans :premises (@p63 @p62)) % 28.21/28.51 (step @p65 :rule cong :premises (@p64) :args ((forall @t59 (=> @t57 @t86)))) % 28.21/28.51 (step @p66 :rule eq-symm :args (@t4 @t1)) % 28.21/28.51 (step @p67 :rule eq-symm :args (@t4 tptp.sz10)) % 28.21/28.51 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t55)) % 28.21/28.51 (step @p69 :rule refl :args (@t57)) % 28.21/28.51 (step @p70 :rule cong :premises (@p69 @p68) :args (@t58)) % 28.21/28.51 (step @p71 :rule cong :premises (@p70) :args (@t60)) % 28.21/28.51 (step @p72 :rule trans :premises (@p71 @p65)) % 28.21/28.51 (step @p73 :rule refl :args (@t61)) % 28.21/28.51 (step @p74 :rule refl :args (@t28)) % 28.21/28.51 (step @p75 :rule nary_cong :premises (@p74 @p73 @p72) :args (@t62)) % 28.21/28.51 (step @p76 :rule refl :args (@t63)) % 28.21/28.51 (step @p77 :rule cong :premises (@p76 @p75) :args (@t64)) % 28.21/28.51 (step @p78 :rule refl :args (@t2)) % 28.21/28.51 (step @p79 :rule cong :premises (@p78 @p77) :args (@t65)) % 28.21/28.51 (step @p80 :rule cong :premises (@p79) :args (@t66)) % 28.21/28.51 (step @p81 :rule trans :premises (@p80 @p57)) % 28.21/28.51 (step @p82 :rule eq_resolve :premises (@p37 @p81)) % 28.21/28.51 (step @p83 :rule eq-symm :args (tptp.xp @t4)) % 28.21/28.51 (step @p84 :rule refl :args (@t81)) % 28.21/28.51 (step @p85 :rule refl :args (@t87)) % 28.21/28.51 (step @p86 :rule refl :args (@t83)) % 28.21/28.51 (step @p87 :rule nary_cong :premises (@p86 @p85 @p84 @p83) :args (@t88)) % 28.21/28.51 (step @p88 :rule cong :premises (@p87) :args (@t89)) % 28.21/28.51 (step @p89 :rule eq-symm :args (tptp.xp tptp.sz10)) % 28.21/28.51 (step @p90 :rule cong :premises (@p89) :args (@t90)) % 28.21/28.51 (step @p91 :rule eq-symm :args (tptp.xp tptp.sz00)) % 28.21/28.51 (step @p92 :rule cong :premises (@p91) :args (@t92)) % 28.21/28.51 (step @p93 :rule nary_cong :premises (@p92 @p90 @p88) :args (@t93)) % 28.21/28.51 (step @p94 :rule refl :args (@t72)) % 28.21/28.51 (step @p95 :rule cong :premises (@p94 @p93) :args (@t94)) % 28.21/28.51 (step @p96 :rule refl :args (@t95)) % 28.21/28.51 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t96)) % 28.21/28.51 (step @p98 :rule refl :args (@t98)) % 28.21/28.51 (step @p99 :rule cong :premises (@p98 @p97) :args ((=> @t98 @t96))) % 28.21/28.51 (assume-push @p270 @t98) % 28.21/28.51 (step @p101 :rule instantiate :premises (@p82) :args ((@list tptp.xp))) % 28.21/28.51 (step-pop @p271 :rule scope :premises (@p101)) % 28.21/28.51 (step @p102 :rule process_scope :premises (@p271) :args (@t96)) % 28.21/28.51 (step @p104 :rule eq_resolve :premises (@p102 @p99)) % 28.21/28.51 (step @p105 :rule implies_elim :premises (@p104)) % 28.21/28.51 (step @p106 :rule chain_m_resolution :premises (@p105 @p82) :args (@t103 @t104 (@list @t98))) % 28.21/28.51 (step @p107 :rule cnf_or_pos :args (@t103)) % 28.21/28.51 (step @p108 :rule reordering :premises (@p107) :args ((or @t95 @t102 (not @t103)))) % 28.21/28.51 (step @p109 :rule chain_m_resolution :premises (@p108 @p54 @p106) :args (@t102 @t105 (@list @t67 @t103))) % 28.21/28.51 (step @p110 :rule and_elim :premises (@p41) :args (0)) % 28.21/28.51 (step @p111 :rule cnf_equiv_pos1 :args (@t102)) % 28.21/28.51 (step @p112 :rule reordering :premises (@p111) :args ((or (not @t72) @t101 (not @t102)))) % 28.21/28.51 (step @p113 :rule chain_m_resolution :premises (@p112 @p110 @p109) :args (@t101 @t105 (@list @t72 @t102))) % 28.21/28.51 (step @p114 :rule cnf_and_pos :args (@t101 0)) % 28.21/28.51 (step @p115 :rule reordering :premises (@p114) :args ((or @t100 (not @t101)))) % 28.21/28.51 (step @p116 :rule chain_m_resolution :premises (@p115 @p113) :args (@t100 @t104 (@list @t101))) % 28.21/28.51 (step @p117 :rule aci_norm :args ((= (or @t106 @t10) (or @t97 @t83 @t10)))) % 28.21/28.51 (step @p118 :rule refl :args (@t10)) % 28.21/28.51 (step @p119 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 28.21/28.51 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or @t107 @t10))) % 28.21/28.51 (step @p121 :rule trans :premises (@p120 @p117)) % 28.21/28.51 (step @p122 :rule bool-impl-elim :args (@t7 @t10)) % 28.21/28.51 (step @p123 :rule trans :premises (@p122 @p121)) % 28.21/28.51 (step @p124 :rule cong :premises (@p123) :args (@t11)) % 28.21/28.51 (step @p125 :rule eq_resolve :premises (@p5 @p124)) % 28.21/28.51 (step @p126 :rule instantiate :premises (@p125) :args ((@list tptp.xn tptp.xm))) % 28.21/28.51 (step @p127 :rule and_elim :premises (@p39) :args (1)) % 28.21/28.51 (step @p128 :rule and_elim :premises (@p39) :args (0)) % 28.21/28.51 (step @p129 :rule cnf_or_pos :args (@t111)) % 28.21/28.51 (step @p130 :rule reordering :premises (@p129) :args ((or @t110 @t109 @t108 (not @t111)))) % 28.21/28.51 (step @p131 :rule chain_m_resolution :premises (@p130 @p128 @p127 @p126) :args (@t108 @t112 (@list @t69 @t68 @t111))) % 28.21/28.51 (step @p132 :rule aci_norm :args ((= (or @t106 @t116) @t115))) % 28.21/28.51 (step @p133 :rule aci_norm :args ((= (or (or @t114 @t113) @t33) @t116))) % 28.21/28.51 (step @p134 :rule refl :args (@t33)) % 28.21/28.51 (step @p135 :rule bool-and-de-morgan :args (@t32 @t34 true)) % 28.21/28.51 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or (not @t35) @t33))) % 28.21/28.51 (step @p137 :rule trans :premises (@p136 @p133)) % 28.21/28.51 (step @p138 :rule bool-impl-elim :args (@t35 @t33)) % 28.21/28.51 (step @p139 :rule trans :premises (@p138 @p137)) % 28.21/28.51 (step @p140 :rule nary_cong :premises (@p119 @p139) :args ((or @t107 @t36))) % 28.21/28.51 (step @p141 :rule trans :premises (@p140 @p132)) % 28.21/28.51 (step @p142 :rule bool-impl-elim :args (@t7 @t36)) % 28.21/28.51 (step @p143 :rule trans :premises (@p142 @p141)) % 28.21/28.51 (step @p144 :rule cong :premises (@p143) :args (@t37)) % 28.21/28.51 (step @p145 :rule eq_resolve :premises (@p21 @p144)) % 28.21/28.51 (step @p146 :rule eq-symm :args (@t77 @t70)) % 28.21/28.51 (step @p147 :rule refl :args (@t117)) % 28.21/28.51 (step @p148 :rule refl :args (@t119)) % 28.21/28.51 (step @p149 :rule refl :args (@t120)) % 28.21/28.51 (step @p150 :rule refl :args (@t122)) % 28.21/28.51 (step @p151 :rule nary_cong :premises (@p150 @p149 @p148 @p147 @p146) :args (@t123)) % 28.21/28.51 (step @p152 :rule refl :args (@t124)) % 28.21/28.51 (step @p153 :rule cong :premises (@p152 @p151) :args ((=> @t124 @t123))) % 28.21/28.51 (assume-push @p272 @t124) % 28.21/28.51 (step @p155 :rule instantiate :premises (@p145) :args ((@list @t77 @t70))) % 28.21/28.51 (step-pop @p273 :rule scope :premises (@p155)) % 28.21/28.51 (step @p156 :rule process_scope :premises (@p273) :args (@t123)) % 28.21/28.51 (step @p158 :rule eq_resolve :premises (@p156 @p153)) % 28.21/28.51 (step @p159 :rule implies_elim :premises (@p158)) % 28.21/28.51 (step @p160 :rule chain_m_resolution :premises (@p159 @p145) :args (@t125 @t104 (@list @t124))) % 28.21/28.51 (step @p161 :rule instantiate :premises (@p125) :args ((@list tptp.xp tptp.xm))) % 28.21/28.51 (step @p162 :rule cnf_or_pos :args (@t126)) % 28.21/28.51 (step @p163 :rule reordering :premises (@p162) :args ((or @t109 @t95 @t121 (not @t126)))) % 28.21/28.51 (step @p164 :rule chain_m_resolution :premises (@p163 @p127 @p54 @p161) :args (@t121 @t112 (@list @t68 @t67 @t126))) % 28.21/28.51 (step @p165 :rule and_elim :premises (@p51) :args (1)) % 28.21/28.51 (step @p166 :rule and_elim :premises (@p51) :args (0)) % 28.21/28.51 (step @p167 :rule cnf_or_pos :args (@t125)) % 28.21/28.51 (step @p168 :rule reordering :premises (@p167) :args ((or @t80 @t117 @t122 @t120 @t119 (not @t125)))) % 28.21/28.51 (step @p169 :rule chain_m_resolution :premises (@p168 @p166 @p165 @p164 @p131 @p160) :args (@t119 (@list true false false false false) (@list @t80 @t79 @t121 @t108 @t125))) % 28.21/28.51 (step @p170 :rule refl :args (tptp.xp)) % 28.21/28.51 (step @p171 :rule cong :premises (@p170 @p45) :args (@t76)) % 28.21/28.51 (step @p172 :rule refl :args (@t77)) % 28.21/28.51 (step @p173 :rule cong :premises (@p172 @p171) :args (@t78)) % 28.21/28.51 (step @p174 :rule and_elim :premises (@p51) :args (3)) % 28.21/28.51 (step @p175 :rule eq_resolve :premises (@p174 @p173)) % 28.21/28.51 (step @p176 :rule bool-double-not-elim :args (@t118)) % 28.21/28.51 (step @p177 :rule refl :args (@t129)) % 28.21/28.51 (step @p178 :rule refl :args (@t131)) % 28.21/28.51 (step @p179 :rule nary_cong :premises (@p178 @p177 @p176) :args ((or @t131 @t129 (not @t119)))) % 28.21/28.51 (assume-push @p274 @t130) % 28.21/28.51 (assume-push @p275 @t128) % 28.21/28.51 (assume-push @p276 @t119) % 28.21/28.51 (step @p183 :rule evaluate :args ((= false true))) % 28.21/28.51 (step @p184 :rule true_intro :premises (@p175)) % 28.21/28.51 (step @p185 :rule cong :premises (@p172 @p275) :args (@t118)) % 28.21/28.51 (step @p186 :rule false_intro :premises (@p169)) % 28.21/28.51 (step @p187 :rule symm :premises (@p186)) % 28.21/28.51 (step @p188 :rule trans :premises (@p187 @p185 @p184)) % 28.21/28.51 (step @p189 false :rule eq_resolve :premises (@p188 @p183)) % 28.21/28.51 (step-pop @p277 :rule scope :premises (@p189)) % 28.21/28.51 (step-pop @p278 :rule scope :premises (@p277)) % 28.21/28.51 (step-pop @p279 :rule scope :premises (@p278)) % 28.21/28.51 (step @p190 :rule process_scope :premises (@p279) :args (false)) % 28.21/28.51 (step @p194 :rule not_and :premises (@p190)) % 28.21/28.51 (step @p195 :rule eq_resolve :premises (@p194 @p179)) % 28.21/28.51 (step @p196 :rule chain_m_resolution :premises (@p195 @p175 @p169) :args (@t129 (@list false true) (@list @t130 @t118))) % 28.21/28.51 (step @p197 :rule cnf_and_pos :args (@t132 1)) % 28.21/28.51 (step @p198 :rule reordering :premises (@p197) :args ((or @t128 @t133))) % 28.21/28.51 (step @p199 :rule chain_m_resolution :premises (@p198 @p196) :args (@t133 (@list true) (@list @t128))) % 28.21/28.51 (step @p200 :rule eq-symm :args (@t134 @t46)) % 28.21/28.51 (step @p201 :rule refl :args (@t135)) % 28.21/28.51 (step @p202 :rule cong :premises (@p201 @p200) :args (@t136)) % 28.21/28.51 (step @p203 :rule refl :args (@t137)) % 28.21/28.51 (step @p204 :rule refl :args (@t27)) % 28.21/28.51 (step @p205 :rule refl :args (@t97)) % 28.21/28.51 (step @p206 :rule nary_cong :premises (@p205 @p86 @p204 @p203 @p202) :args (@t138)) % 28.21/28.51 (step @p207 :rule cong :premises (@p206) :args (@t140)) % 28.21/28.51 (step @p208 :rule quant-merge-prenex :args ((= (forall @t8 @t142) @t140))) % 28.21/28.51 (step @p209 :rule alpha_equiv :args (@t143 (@list @t134) (@list @t13))) % 28.21/28.51 (step @p210 :rule refl :args (@t137)) % 28.21/28.51 (step @p211 :rule refl :args (@t27)) % 28.21/28.51 (step @p212 :rule refl :args (@t83)) % 28.21/28.51 (step @p213 :rule refl :args (@t97)) % 28.21/28.51 (step @p214 :rule nary_cong :premises (@p213 @p212 @p211 @p210 @p209) :args (@t144)) % 28.21/28.51 (step @p215 :rule quant-miniscope-or :args ((= @t142 @t144))) % 28.21/28.51 (step @p216 :rule trans :premises (@p215 @p214)) % 28.21/28.51 (step @p217 :rule symm :premises (@p216)) % 28.21/28.51 (step @p218 :rule cong :premises (@p217) :args ((forall @t8 @t146))) % 28.21/28.51 (step @p219 :rule trans :premises (@p218 @p208)) % 28.21/28.51 (step @p220 :rule trans :premises (@p219 @p207)) % 28.21/28.51 (step @p221 :rule aci_norm :args ((= (or @t106 @t147) @t146))) % 28.21/28.51 (step @p222 :rule aci_norm :args ((= (or (or @t27 @t137) @t145) @t147))) % 28.21/28.51 (step @p223 :rule refl :args (@t145)) % 28.21/28.51 (step @p224 :rule bool-double-not-elim :args (@t27)) % 28.21/28.51 (step @p225 :rule nary_cong :premises (@p224 @p210) :args ((or (not @t28) @t137))) % 28.21/28.51 (step @p226 :rule bool-and-de-morgan :args (@t28 @t45 true)) % 28.21/28.51 (step @p227 :rule trans :premises (@p226 @p225)) % 28.21/28.51 (step @p228 :rule nary_cong :premises (@p227 @p223) :args ((or (not @t49) @t145))) % 28.21/28.51 (step @p229 :rule trans :premises (@p228 @p222)) % 28.21/28.51 (step @p230 :rule bool-impl-elim :args (@t49 @t145)) % 28.21/28.51 (step @p231 :rule trans :premises (@p230 @p229)) % 28.21/28.51 (step @p232 :rule nary_cong :premises (@p119 @p231) :args ((or @t107 @t148))) % 28.21/28.51 (step @p233 :rule trans :premises (@p232 @p221)) % 28.21/28.51 (step @p234 :rule bool-impl-elim :args (@t7 @t148)) % 28.21/28.51 (step @p235 :rule trans :premises (@p234 @p233)) % 28.21/28.51 (step @p236 :rule cong :premises (@p235) :args ((forall @t8 (=> @t7 @t148)))) % 28.21/28.51 (step @p237 :rule trans :premises (@p236 @p220)) % 28.21/28.51 (step @p238 :rule eq-symm :args (@t47 @t44)) % 28.21/28.51 (step @p239 :rule cong :premises (@p238) :args (@t48)) % 28.21/28.51 (step @p240 :rule refl :args (@t49)) % 28.21/28.51 (step @p241 :rule cong :premises (@p240 @p239) :args (@t50)) % 28.21/28.51 (step @p242 :rule refl :args (@t7)) % 28.21/28.51 (step @p243 :rule cong :premises (@p242 @p241) :args (@t51)) % 28.21/28.51 (step @p244 :rule cong :premises (@p243) :args (@t52)) % 28.21/28.51 (step @p245 :rule trans :premises (@p244 @p237)) % 28.21/28.51 (step @p246 :rule eq_resolve :premises (@p31 @p245)) % 28.21/28.51 (step @p247 :rule bool-eq-true :args (@t132)) % 28.21/28.51 (step @p248 :rule eq-symm :args (true @t132)) % 28.21/28.51 (step @p249 :rule trans :premises (@p248 @p247)) % 28.21/28.51 (step @p250 :rule refl :args (@t132)) % 28.21/28.51 (step @p251 :rule eq-refl :args (@t73)) % 28.21/28.51 (step @p252 :rule cong :premises (@p251 @p250) :args ((= @t149 @t132))) % 28.21/28.51 (step @p253 :rule trans :premises (@p252 @p249)) % 28.21/28.51 (step @p254 :rule eq-symm :args (@t132 @t149)) % 28.21/28.51 (step @p255 :rule trans :premises (@p254 @p253)) % 28.21/28.51 (step @p256 :rule refl :args (@t150)) % 28.21/28.51 (step @p257 :rule nary_cong :premises (@p96 @p149 @p91 @p256 @p255) :args (@t151)) % 28.21/28.51 (step @p258 :rule refl :args (@t152)) % 28.21/28.51 (step @p259 :rule cong :premises (@p258 @p257) :args ((=> @t152 @t151))) % 28.21/28.51 (assume-push @p280 @t152) % 28.21/28.51 (step @p261 :rule instantiate :premises (@p246) :args ((@list tptp.xp @t70 @t73))) % 28.21/28.51 (step-pop @p281 :rule scope :premises (@p261)) % 28.21/28.51 (step @p262 :rule process_scope :premises (@p281) :args (@t151)) % 28.21/28.51 (step @p264 :rule eq_resolve :premises (@p262 @p259)) % 28.21/28.51 (step @p265 :rule implies_elim :premises (@p264)) % 28.21/28.51 (step @p266 :rule chain_m_resolution :premises (@p265 @p246) :args (@t153 @t104 (@list @t152))) % 28.21/28.51 (step @p267 :rule cnf_or_pos :args (@t153)) % 28.21/28.51 (step @p268 :rule reordering :premises (@p267) :args ((or @t95 @t150 @t99 @t120 @t132 (not @t153)))) % 28.21/28.51 (step @p269 false :rule chain_m_resolution :premises (@p268 @p266 @p199 @p131 @p116 @p55 @p54) :args (false (@list false true false true false false) (@list @t153 @t132 @t108 @t99 @t71 @t67))) % 28.21/28.51 ) % 28.21/28.51 % SZS output end Proof % 28.21/28.51 % cvc5 exiting %------------------------------------------------------------------------------