%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM473+2 : 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 : n012.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 08:39:32 AM UTC 2026 % Result : Theorem 4.12s 4.33s % Output : Proof 4.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM473+2 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 11:22:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.33 %----Proving TF0_NAR, FOF, or CNF % 4.12/4.33 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 4.12/4.33 % SZS status Theorem % 4.12/4.33 % SZS output start Proof % 4.12/4.33 ( % 4.12/4.33 (declare-sort $$unsorted 0) % 4.12/4.33 (declare-const tptp.xq $$unsorted) % 4.12/4.33 (declare-const tptp.xp $$unsorted) % 4.12/4.33 (declare-const tptp.sz10 $$unsorted) % 4.12/4.33 (declare-const tptp.xl $$unsorted) % 4.12/4.33 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 4.12/4.33 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 4.12/4.33 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 4.12/4.33 (declare-const tptp.sz00 $$unsorted) % 4.12/4.33 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 4.12/4.33 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 4.12/4.33 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 4.12/4.33 (declare-const tptp.xn $$unsorted) % 4.12/4.33 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 4.12/4.33 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 4.12/4.33 (declare-const tptp.xm $$unsorted) % 4.12/4.33 (define @t1 () (@var "W0" $$unsorted)) % 4.12/4.33 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 4.12/4.33 (define @t3 () (@list @t1)) % 4.12/4.33 (define @t4 () (@var "W1" $$unsorted)) % 4.12/4.33 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 4.12/4.33 (define @t6 () (tptp.aNaturalNumber0 @t5)) % 4.12/4.33 (define @t7 () (tptp.aNaturalNumber0 @t4)) % 4.12/4.33 (define @t8 () (and @t2 @t7)) % 4.12/4.33 (define @t9 () (@list @t1 @t4)) % 4.12/4.33 (define @t10 () (forall @t9 (=> @t8 @t6))) % 4.12/4.33 (define @t11 () (tptp.sdtasdt0 @t1 @t4)) % 4.12/4.33 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 4.12/4.33 (define @t13 () (@var "W2" $$unsorted)) % 4.12/4.33 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 4.12/4.33 (define @t15 () (tptp.aNaturalNumber0 @t13)) % 4.12/4.33 (define @t16 () (and @t2 @t7 @t15)) % 4.12/4.33 (define @t17 () (@list @t1 @t4 @t13)) % 4.12/4.33 (define @t18 () (tptp.sdtasdt0 @t4 @t1)) % 4.12/4.33 (define @t19 () (= @t11 @t18)) % 4.12/4.33 (define @t20 () (forall @t9 (=> @t8 @t19))) % 4.12/4.33 (define @t21 () (tptp.sdtasdt0 @t13 @t1)) % 4.12/4.33 (define @t22 () (tptp.sdtasdt0 @t1 @t13)) % 4.12/4.33 (define @t23 () (= @t4 @t13)) % 4.12/4.33 (define @t24 () (tptp.sdtpldt0 @t13 @t1)) % 4.12/4.33 (define @t25 () (tptp.sdtpldt0 @t1 @t13)) % 4.12/4.33 (define @t26 () (= @t18 @t21)) % 4.12/4.33 (define @t27 () (= @t11 @t22)) % 4.12/4.33 (define @t28 () (and @t7 @t15)) % 4.12/4.33 (define @t29 () (= @t1 tptp.sz00)) % 4.12/4.33 (define @t30 () (not @t29)) % 4.12/4.33 (define @t31 () (= @t4 tptp.sz00)) % 4.12/4.33 (define @t32 () (and @t15 (= @t25 @t4))) % 4.12/4.33 (define @t33 () (@list @t13)) % 4.12/4.33 (define @t34 () (tptp.sdtlseqdt0 @t1 @t4)) % 4.12/4.33 (define @t35 () (= @t1 @t4)) % 4.12/4.33 (define @t36 () (tptp.sdtlseqdt0 @t4 @t1)) % 4.12/4.33 (define @t37 () (and @t34 @t36)) % 4.12/4.33 (define @t38 () (=> @t37 @t35)) % 4.12/4.33 (define @t39 () (forall @t9 (=> @t8 @t38))) % 4.12/4.33 (define @t40 () (tptp.sdtlseqdt0 @t4 @t13)) % 4.12/4.33 (define @t41 () (not (= @t4 @t1))) % 4.12/4.33 (define @t42 () (and @t41 @t36)) % 4.12/4.33 (define @t43 () (or @t34 @t42)) % 4.12/4.33 (define @t44 () (=> @t8 @t43)) % 4.12/4.33 (define @t45 () (forall @t9 @t44)) % 4.12/4.33 (define @t46 () (tptp.sdtpldt0 @t13 @t4)) % 4.12/4.33 (define @t47 () (not @t35)) % 4.12/4.33 (define @t48 () (and @t47 @t34)) % 4.12/4.33 (define @t49 () (and (not @t27) (tptp.sdtlseqdt0 @t11 @t22) (not @t26) (tptp.sdtlseqdt0 @t18 @t21))) % 4.12/4.33 (define @t50 () (not @t23)) % 4.12/4.33 (define @t51 () (and @t30 @t50 @t40)) % 4.12/4.33 (define @t52 () (=> @t51 @t49)) % 4.12/4.33 (define @t53 () (forall @t17 (=> @t16 @t52))) % 4.12/4.33 (define @t54 () (tptp.iLess0 @t1 @t4)) % 4.12/4.33 (define @t55 () (and @t15 (= @t4 @t22))) % 4.12/4.33 (define @t56 () (tptp.doDivides0 @t1 @t4)) % 4.12/4.33 (define @t57 () (tptp.doDivides0 @t1 @t13)) % 4.12/4.33 (define @t58 () (tptp.aNaturalNumber0 tptp.xn)) % 4.12/4.33 (define @t59 () (tptp.aNaturalNumber0 tptp.xm)) % 4.12/4.33 (define @t60 () (tptp.aNaturalNumber0 tptp.xl)) % 4.12/4.33 (define @t61 () (tptp.sdtpldt0 tptp.xm tptp.xn)) % 4.12/4.33 (define @t62 () (tptp.sdtasdt0 tptp.xl @t1)) % 4.12/4.33 (define @t63 () (and @t2 (= @t61 @t62))) % 4.12/4.33 (define @t64 () (exists @t3 @t63)) % 4.12/4.33 (define @t65 () (= tptp.xl tptp.sz00)) % 4.12/4.33 (define @t66 () (tptp.sdtsldt0 tptp.xm tptp.xl)) % 4.12/4.33 (define @t67 () (= tptp.xp @t66)) % 4.12/4.33 (define @t68 () (tptp.sdtasdt0 tptp.xl tptp.xp)) % 4.12/4.33 (define @t69 () (= tptp.xm @t68)) % 4.12/4.33 (define @t70 () (tptp.aNaturalNumber0 tptp.xp)) % 4.12/4.33 (define @t71 () (= tptp.xq (tptp.sdtsldt0 @t61 tptp.xl))) % 4.12/4.33 (define @t72 () (tptp.sdtasdt0 tptp.xl tptp.xq)) % 4.12/4.33 (define @t73 () (= @t61 @t72)) % 4.12/4.33 (define @t74 () (tptp.aNaturalNumber0 tptp.xq)) % 4.12/4.33 (define @t75 () (tptp.sdtlseqdt0 tptp.xm @t61)) % 4.12/4.33 (define @t76 () (tptp.sdtlseqdt0 tptp.xp tptp.xq)) % 4.12/4.33 (define @t77 () (tptp.sdtpldt0 tptp.xp @t1)) % 4.12/4.33 (define @t78 () (and @t2 (= @t77 tptp.xq))) % 4.12/4.33 (define @t79 () (exists @t3 @t78)) % 4.12/4.33 (define @t80 () (or @t79 @t76)) % 4.12/4.33 (define @t81 () (not @t80)) % 4.12/4.33 (define @t82 () (= @t62 @t61)) % 4.12/4.33 (define @t83 () (and @t2 @t82)) % 4.12/4.33 (define @t84 () (forall @t3 (not @t83))) % 4.12/4.33 (define @t85 () (not @t84)) % 4.12/4.33 (define @t86 () (not @t2)) % 4.12/4.33 (define @t87 () (forall @t3 (or @t86 (not @t82)))) % 4.12/4.33 (define @t88 () (@quantifiers_skolemize @t87 0)) % 4.12/4.33 (define @t89 () (tptp.sdtasdt0 tptp.xl @t88)) % 4.12/4.33 (define @t90 () (= @t61 @t89)) % 4.12/4.33 (define @t91 () (not @t90)) % 4.12/4.33 (define @t92 () (tptp.aNaturalNumber0 @t88)) % 4.12/4.33 (define @t93 () (not @t92)) % 4.12/4.33 (define @t94 () (or @t93 @t91)) % 4.12/4.33 (define @t95 () (not @t94)) % 4.12/4.33 (define @t96 () (not @t87)) % 4.12/4.33 (define @t97 () (not (= @t89 @t61))) % 4.12/4.33 (define @t98 () (or @t93 @t97)) % 4.12/4.33 (define @t99 () (not @t98)) % 4.12/4.33 (define @t100 () (@list true)) % 4.12/4.33 (define @t101 () (@list @t94)) % 4.12/4.33 (define @t102 () (not @t7)) % 4.12/4.33 (define @t103 () (or @t86 @t102)) % 4.12/4.33 (define @t104 () (not @t8)) % 4.12/4.33 (define @t105 () (tptp.sdtasdt0 tptp.xp tptp.xl)) % 4.12/4.33 (define @t106 () (= @t68 @t105)) % 4.12/4.33 (define @t107 () (not @t70)) % 4.12/4.33 (define @t108 () (not @t60)) % 4.12/4.33 (define @t109 () (or @t108 @t107 @t106)) % 4.12/4.33 (define @t110 () (@list false false false)) % 4.12/4.33 (define @t111 () (tptp.sdtasdt0 @t88 tptp.xl)) % 4.12/4.33 (define @t112 () (= @t89 @t111)) % 4.12/4.33 (define @t113 () (or @t108 @t93 @t112)) % 4.12/4.33 (define @t114 () (not @t36)) % 4.12/4.33 (define @t115 () (not @t34)) % 4.12/4.33 (define @t116 () (or @t115 @t114 @t35)) % 4.12/4.33 (define @t117 () (and @t47 @t36)) % 4.12/4.33 (define @t118 () (or @t86 @t102 @t34 @t117)) % 4.12/4.33 (define @t119 () (or @t34 @t117)) % 4.12/4.33 (define @t120 () (= tptp.xq @t77)) % 4.12/4.33 (define @t121 () (and @t2 @t120)) % 4.12/4.33 (define @t122 () (forall @t3 (not @t121))) % 4.12/4.33 (define @t123 () (not @t122)) % 4.12/4.33 (define @t124 () (tptp.sdtlseqdt0 tptp.xq tptp.xp)) % 4.12/4.33 (define @t125 () (= tptp.xp tptp.xq)) % 4.12/4.33 (define @t126 () (not @t125)) % 4.12/4.33 (define @t127 () (and @t126 @t124)) % 4.12/4.33 (define @t128 () (not @t74)) % 4.12/4.33 (define @t129 () (or @t107 @t128 @t76 @t127)) % 4.12/4.33 (define @t130 () (@list false)) % 4.12/4.33 (define @t131 () (= tptp.xm @t61)) % 4.12/4.33 (define @t132 () (and @t67 @t71 @t131)) % 4.12/4.33 (define @t133 () (not @t131)) % 4.12/4.33 (define @t134 () (tptp.aNaturalNumber0 @t61)) % 4.12/4.33 (define @t135 () (not @t58)) % 4.12/4.33 (define @t136 () (not @t59)) % 4.12/4.33 (define @t137 () (or @t136 @t135 @t134)) % 4.12/4.33 (define @t138 () (tptp.sdtlseqdt0 @t61 tptp.xm)) % 4.12/4.33 (define @t139 () (not @t138)) % 4.12/4.33 (define @t140 () (not @t75)) % 4.12/4.33 (define @t141 () (not @t134)) % 4.12/4.33 (define @t142 () (or @t136 @t141 @t140 @t139 @t131)) % 4.12/4.33 (define @t143 () (not @t40)) % 4.12/4.33 (define @t144 () (not @t15)) % 4.12/4.33 (define @t145 () (or @t86 @t102 @t144 @t29 @t23 @t143 @t49)) % 4.12/4.33 (define @t146 () (or @t29 @t23 @t143 @t49)) % 4.12/4.33 (define @t147 () (or @t86 @t102 @t144)) % 4.12/4.33 (define @t148 () (not @t50)) % 4.12/4.33 (define @t149 () (not @t30)) % 4.12/4.33 (define @t150 () (or @t149 @t148 @t143)) % 4.12/4.33 (define @t151 () (tptp.sdtasdt0 tptp.xq tptp.xl)) % 4.12/4.33 (define @t152 () (tptp.sdtlseqdt0 @t151 @t105)) % 4.12/4.33 (define @t153 () (not (= @t151 @t105))) % 4.12/4.33 (define @t154 () (tptp.sdtlseqdt0 @t72 @t68)) % 4.12/4.33 (define @t155 () (not (= @t72 @t68))) % 4.12/4.33 (define @t156 () (and @t155 @t154 @t153 @t152)) % 4.12/4.33 (define @t157 () (not @t124)) % 4.12/4.33 (define @t158 () (= tptp.xq tptp.xp)) % 4.12/4.33 (define @t159 () (or @t108 @t128 @t107 @t65 @t158 @t157 @t156)) % 4.12/4.33 (define @t160 () (forall @t17 @t145)) % 4.12/4.33 (define @t161 () (and (not (= @t68 @t72)) @t154 (not (= @t105 @t151)) @t152)) % 4.12/4.33 (define @t162 () (= tptp.sz00 tptp.xl)) % 4.12/4.33 (define @t163 () (or @t108 @t128 @t107 @t162 @t125 @t157 @t161)) % 4.12/4.33 (define @t164 () (not @t158)) % 4.12/4.33 (define @t165 () (and @t164 @t76)) % 4.12/4.33 (define @t166 () (or @t128 @t107 @t124 @t165)) % 4.12/4.33 (define @t167 () (forall @t9 @t118)) % 4.12/4.33 (define @t168 () (and @t126 @t76)) % 4.12/4.33 (define @t169 () (or @t128 @t107 @t124 @t168)) % 4.12/4.33 (define @t170 () (not @t168)) % 4.12/4.33 (define @t171 () (not @t154)) % 4.12/4.33 (define @t172 () (not @t112)) % 4.12/4.33 (define @t173 () (not @t106)) % 4.12/4.33 (define @t174 () (not @t73)) % 4.12/4.33 (define @t175 () (not @t69)) % 4.12/4.33 (define @t176 () (and @t154 @t73 @t90 @t112 @t106 @t69 @t139)) % 4.12/4.33 (assume @p1 (forall @t3 (=> @t2 true))) % 4.12/4.33 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 4.12/4.33 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 4.12/4.33 (assume @p4 @t10) % 4.12/4.33 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t11)))) % 4.12/4.33 (assume @p6 (forall @t9 (=> @t8 (= @t5 @t12)))) % 4.12/4.33 (assume @p7 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t5 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 4.12/4.33 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 4.12/4.33 (assume @p9 @t20) % 4.12/4.33 (assume @p10 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t11 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 4.12/4.33 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 4.12/4.33 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 4.12/4.33 (assume @p13 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t11 @t22)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t18 @t21)))))) % 4.12/4.33 (assume @p14 (forall @t17 (=> @t16 (=> (or (= @t5 @t25) (= @t12 @t24)) @t23)))) % 4.12/4.33 (assume @p15 (forall @t3 (=> @t2 (=> @t30 (forall (@list @t4 @t13) (=> @t28 (=> (or @t27 @t26) @t23))))))) % 4.12/4.33 (assume @p16 (forall @t9 (=> @t8 (=> (= @t5 tptp.sz00) (and @t29 @t31))))) % 4.12/4.33 (assume @p17 (forall @t9 (=> @t8 (=> (= @t11 tptp.sz00) (or @t29 @t31))))) % 4.12/4.33 (assume @p18 (forall @t9 (=> @t8 (= @t34 (exists @t33 @t32))))) % 4.12/4.33 (assume @p19 (forall @t9 (=> @t8 (=> @t34 (forall @t33 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t32)))))) % 4.12/4.33 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 4.12/4.33 (assume @p21 @t39) % 4.12/4.33 (assume @p22 (forall @t17 (=> @t16 (=> (and @t34 @t40) (tptp.sdtlseqdt0 @t1 @t13))))) % 4.12/4.33 (assume @p23 @t45) % 4.12/4.33 (assume @p24 (forall @t9 (=> @t8 (=> @t48 (forall @t33 (=> @t15 (and (not (= @t24 @t46)) (tptp.sdtlseqdt0 @t24 @t46) (not (= @t25 @t14)) (tptp.sdtlseqdt0 @t25 @t14)))))))) % 4.12/4.33 (assume @p25 @t53) % 4.12/4.33 (assume @p26 (forall @t3 (=> @t2 (or @t29 (= @t1 tptp.sz10) (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 4.12/4.33 (assume @p27 (forall @t9 (=> @t8 (=> @t30 (tptp.sdtlseqdt0 @t4 @t18))))) % 4.12/4.33 (assume @p28 (forall @t9 (=> @t8 (=> @t54 true)))) % 4.12/4.33 (assume @p29 (forall @t9 (=> @t8 (=> @t48 @t54)))) % 4.12/4.33 (assume @p30 (forall @t9 (=> @t8 (= @t56 (exists @t33 @t55))))) % 4.12/4.33 (assume @p31 (forall @t9 (=> @t8 (=> (and @t30 @t56) (forall @t33 (= (= @t13 (tptp.sdtsldt0 @t4 @t1)) @t55)))))) % 4.12/4.33 (assume @p32 (forall @t17 (=> @t16 (=> (and @t56 (tptp.doDivides0 @t4 @t13)) @t57)))) % 4.12/4.33 (assume @p33 (forall @t17 (=> @t16 (=> (and @t56 @t57) (tptp.doDivides0 @t1 @t14))))) % 4.12/4.33 (assume @p34 (and @t60 @t59 @t58)) % 4.12/4.33 (assume @p35 (and (exists @t3 (and @t2 (= tptp.xm @t62))) (tptp.doDivides0 tptp.xl tptp.xm) @t64 (tptp.doDivides0 tptp.xl @t61))) % 4.12/4.33 (assume @p36 (not @t65)) % 4.12/4.33 (assume @p37 (and @t70 @t69 @t67)) % 4.12/4.33 (assume @p38 (and @t74 @t73 @t71)) % 4.12/4.33 (assume @p39 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xm @t1) @t61))) @t75)) % 4.12/4.33 (assume @p40 @t81) % 4.12/4.33 (assume @p41 true) % 4.12/4.33 (step @p42 :rule and_elim :premises (@p37) :args (1)) % 4.12/4.33 (step @p43 :rule and_elim :premises (@p38) :args (1)) % 4.12/4.33 (step @p44 :rule bool-and-de-morgan :args (@t2 @t82 true)) % 4.12/4.33 (step @p45 :rule cong :premises (@p44) :args (@t84)) % 4.12/4.33 (step @p46 :rule cong :premises (@p45) :args (@t85)) % 4.12/4.33 (step @p47 :rule exists-elim :args ((= (exists @t3 @t83) @t85))) % 4.12/4.33 (step @p48 :rule trans :premises (@p47 @p46)) % 4.12/4.33 (step @p49 :rule eq-symm :args (@t61 @t62)) % 4.12/4.33 (step @p50 :rule refl :args (@t2)) % 4.12/4.33 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t63)) % 4.12/4.33 (step @p52 :rule cong :premises (@p51) :args (@t64)) % 4.12/4.33 (step @p53 :rule trans :premises (@p52 @p48)) % 4.12/4.33 (step @p54 :rule and_elim :premises (@p35) :args (2)) % 4.12/4.33 (step @p55 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@p108) :args ((or (not @t37) @t35))) % 4.12/4.33 (step @p111 :rule trans :premises (@p110 @p107)) % 4.12/4.33 (step @p112 :rule bool-impl-elim :args (@t37 @t35)) % 4.12/4.33 (step @p113 :rule trans :premises (@p112 @p111)) % 4.12/4.33 (step @p114 :rule nary_cong :premises (@p83 @p113) :args ((or @t104 @t38))) % 4.12/4.33 (step @p115 :rule trans :premises (@p114 @p106)) % 4.12/4.33 (step @p116 :rule bool-impl-elim :args (@t8 @t38)) % 4.12/4.33 (step @p117 :rule trans :premises (@p116 @p115)) % 4.12/4.33 (step @p118 :rule cong :premises (@p117) :args (@t39)) % 4.12/4.33 (step @p119 :rule eq_resolve :premises (@p21 @p118)) % 4.12/4.33 (step @p120 :rule instantiate :premises (@p119) :args ((@list tptp.xm @t61))) % 4.12/4.33 (step @p121 :rule and_elim :premises (@p37) :args (2)) % 4.12/4.33 (step @p122 :rule and_elim :premises (@p38) :args (2)) % 4.12/4.33 (step @p123 :rule aci_norm :args ((= (or @t103 @t119) @t118))) % 4.12/4.33 (step @p124 :rule refl :args (@t119)) % 4.12/4.33 (step @p125 :rule nary_cong :premises (@p83 @p124) :args ((or @t104 @t119))) % 4.12/4.33 (step @p126 :rule trans :premises (@p125 @p123)) % 4.12/4.33 (step @p127 :rule bool-impl-elim :args (@t8 @t119)) % 4.12/4.33 (step @p128 :rule trans :premises (@p127 @p126)) % 4.12/4.33 (step @p129 :rule cong :premises (@p128) :args ((forall @t9 (=> @t8 @t119)))) % 4.12/4.33 (step @p130 :rule refl :args (@t36)) % 4.12/4.33 (step @p131 :rule eq-symm :args (@t4 @t1)) % 4.12/4.33 (step @p132 :rule cong :premises (@p131) :args (@t41)) % 4.12/4.33 (step @p133 :rule nary_cong :premises (@p132 @p130) :args (@t42)) % 4.12/4.33 (step @p134 :rule refl :args (@t34)) % 4.12/4.33 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t43)) % 4.12/4.33 (step @p136 :rule refl :args (@t8)) % 4.12/4.33 (step @p137 :rule cong :premises (@p136 @p135) :args (@t44)) % 4.12/4.33 (step @p138 :rule cong :premises (@p137) :args (@t45)) % 4.12/4.33 (step @p139 :rule trans :premises (@p138 @p129)) % 4.12/4.33 (step @p140 :rule 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(@t81)) % 4.12/4.33 (step @p155 :rule eq_resolve :premises (@p40 @p154)) % 4.12/4.33 (step @p156 :rule not_or_elim :premises (@p155) :args (1)) % 4.12/4.33 (step @p157 :rule cnf_or_pos :args (@t129)) % 4.12/4.33 (step @p158 :rule reordering :premises (@p157) :args ((or @t76 @t107 @t128 @t127 (not @t129)))) % 4.12/4.33 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p91 @p142 @p141) :args (@t127 (@list true false false false) (@list @t76 @t70 @t74 @t129))) % 4.12/4.33 (step @p160 :rule cnf_and_pos :args (@t127 0)) % 4.12/4.33 (step @p161 :rule reordering :premises (@p160) :args ((or @t126 (not @t127)))) % 4.12/4.33 (step @p162 :rule chain_m_resolution :premises (@p161 @p159) :args (@t126 @t130 (@list @t127))) % 4.12/4.33 (assume-push @p349 @t67) % 4.12/4.33 (assume-push @p350 @t71) % 4.12/4.33 (assume-push @p351 @t131) % 4.12/4.33 (assume-push @p352 @t71) % 4.12/4.33 (assume-push @p353 @t131) % 4.12/4.33 (assume-push @p354 @t67) % 4.12/4.33 (step @p169 :rule symm :premises (@p122)) % 4.12/4.33 (step @p170 :rule refl :args (tptp.xl)) % 4.12/4.33 (step @p171 :rule cong :premises (@p351 @p170) :args (@t66)) % 4.12/4.33 (step @p172 :rule trans :premises (@p121 @p171 @p169)) % 4.12/4.33 (step-pop @p355 :rule scope :premises (@p172)) % 4.12/4.33 (step-pop @p356 :rule scope :premises (@p355)) % 4.12/4.33 (step-pop @p357 :rule scope :premises (@p356)) % 4.12/4.33 (step @p173 :rule process_scope :premises (@p357) :args (@t125)) % 4.12/4.33 (step @p177 :rule and_intro :premises (@p122 @p351 @p121)) % 4.12/4.33 (step @p178 :rule modus_ponens :premises (@p177 @p173)) % 4.12/4.33 (step-pop @p358 :rule scope :premises (@p178)) % 4.12/4.33 (step-pop @p359 :rule scope :premises (@p358)) % 4.12/4.33 (step-pop @p360 :rule scope :premises (@p359)) % 4.12/4.33 (step @p179 :rule process_scope :premises (@p360) :args (@t125)) % 4.12/4.33 (step @p183 :rule implies_elim :premises (@p179)) % 4.12/4.33 (step @p184 :rule cnf_and_neg :args (@t132)) % 4.12/4.33 (step @p185 :rule resolution :premises (@p184 @p183) :args (true @t132)) % 4.12/4.33 (step @p186 :rule reordering :premises (@p185) :args ((or (not @t67) (not @t71) @t125 @t133))) % 4.12/4.33 (step @p187 :rule chain_m_resolution :premises (@p186 @p162 @p122 @p121) :args (@t133 (@list true false false) (@list @t125 @t71 @t67))) % 4.12/4.33 (step @p188 :rule aci_norm :args ((= (or @t103 @t6) (or @t86 @t102 @t6)))) % 4.12/4.33 (step @p189 :rule refl :args (@t6)) % 4.12/4.33 (step @p190 :rule nary_cong :premises (@p83 @p189) :args ((or @t104 @t6))) % 4.12/4.33 (step @p191 :rule trans :premises (@p190 @p188)) % 4.12/4.33 (step @p192 :rule bool-impl-elim :args (@t8 @t6)) % 4.12/4.33 (step @p193 :rule trans :premises (@p192 @p191)) % 4.12/4.33 (step @p194 :rule cong :premises (@p193) :args (@t10)) % 4.12/4.33 (step @p195 :rule eq_resolve :premises (@p4 @p194)) % 4.12/4.33 (step @p196 :rule instantiate :premises (@p195) :args ((@list tptp.xm tptp.xn))) % 4.12/4.33 (step @p197 :rule and_elim :premises (@p34) :args (2)) % 4.12/4.33 (step @p198 :rule and_elim :premises (@p34) :args (1)) % 4.12/4.33 (step @p199 :rule cnf_or_pos :args (@t137)) % 4.12/4.33 (step @p200 :rule reordering :premises (@p199) :args ((or @t136 @t135 @t134 (not @t137)))) % 4.12/4.33 (step @p201 :rule chain_m_resolution :premises (@p200 @p198 @p197 @p196) :args (@t134 @t110 (@list @t59 @t58 @t137))) % 4.12/4.33 (step @p202 :rule and_elim :premises (@p39) :args (1)) % 4.12/4.33 (step @p203 :rule cnf_or_pos :args (@t142)) % 4.12/4.33 (step @p204 :rule reordering :premises (@p203) :args ((or @t136 @t140 @t141 @t139 @t131 (not @t142)))) % 4.12/4.33 (step @p205 :rule chain_m_resolution :premises (@p204 @p198 @p202 @p201 @p187 @p120) :args (@t139 (@list false false false true false) (@list @t59 @t75 @t134 @t131 @t142))) % 4.12/4.33 (step @p206 :rule aci_norm :args ((= (or @t147 @t146) @t145))) % 4.12/4.33 (step @p207 :rule aci_norm :args ((= (or (or @t29 @t23 @t143) @t49) @t146))) % 4.12/4.33 (step @p208 :rule refl :args 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@p207)) % 4.12/4.33 (step @p223 :rule bool-impl-elim :args (@t51 @t49)) % 4.12/4.33 (step @p224 :rule trans :premises (@p223 @p222)) % 4.12/4.33 (step @p225 :rule aci_norm :args ((= (or @t86 (or @t102 @t144)) @t147))) % 4.12/4.33 (step @p226 :rule bool-and-de-morgan :args (@t7 @t15 true)) % 4.12/4.33 (step @p227 :rule refl :args (@t86)) % 4.12/4.33 (step @p228 :rule nary_cong :premises (@p227 @p226) :args ((or @t86 (not @t28)))) % 4.12/4.33 (step @p229 :rule bool-and-de-morgan :args (@t2 @t7 (and @t15))) % 4.12/4.33 (step @p230 :rule trans :premises (@p229 @p228)) % 4.12/4.33 (step @p231 :rule trans :premises (@p230 @p225)) % 4.12/4.33 (step @p232 :rule nary_cong :premises (@p231 @p224) :args ((or (not @t16) @t52))) % 4.12/4.33 (step @p233 :rule trans :premises (@p232 @p206)) % 4.12/4.33 (step @p234 :rule bool-impl-elim :args (@t16 @t52)) % 4.12/4.33 (step @p235 :rule trans :premises (@p234 @p233)) % 4.12/4.33 (step @p236 :rule cong :premises (@p235) :args (@t53)) % 4.12/4.33 (step @p237 :rule eq_resolve :premises (@p25 @p236)) % 4.12/4.33 (step @p238 :rule refl :args (@t152)) % 4.12/4.33 (step @p239 :rule eq-symm :args (@t151 @t105)) % 4.12/4.33 (step @p240 :rule cong :premises (@p239) :args (@t153)) % 4.12/4.33 (step @p241 :rule refl :args (@t154)) % 4.12/4.33 (step @p242 :rule eq-symm :args (@t72 @t68)) % 4.12/4.33 (step @p243 :rule cong :premises (@p242) :args (@t155)) % 4.12/4.33 (step @p244 :rule nary_cong :premises (@p243 @p241 @p240 @p238) :args (@t156)) % 4.12/4.33 (step @p245 :rule refl :args (@t157)) % 4.12/4.33 (step @p246 :rule eq-symm :args (tptp.xq tptp.xp)) % 4.12/4.33 (step @p247 :rule eq-symm :args (tptp.xl tptp.sz00)) % 4.12/4.33 (step @p248 :rule refl :args (@t107)) % 4.12/4.33 (step @p249 :rule refl :args (@t128)) % 4.12/4.33 (step @p250 :rule refl :args (@t108)) % 4.12/4.33 (step @p251 :rule nary_cong :premises (@p250 @p249 @p248 @p247 @p246 @p245 @p244) :args (@t159)) % 4.12/4.33 (step @p252 :rule refl :args (@t160)) % 4.12/4.33 (step @p253 :rule cong :premises (@p252 @p251) :args ((=> @t160 @t159))) % 4.12/4.33 (assume-push @p361 @t160) % 4.12/4.33 (step @p255 :rule instantiate :premises (@p237) :args ((@list tptp.xl tptp.xq tptp.xp))) % 4.12/4.33 (step-pop @p362 :rule scope :premises (@p255)) % 4.12/4.33 (step @p256 :rule process_scope :premises (@p362) :args (@t159)) % 4.12/4.33 (step @p258 :rule eq_resolve :premises (@p256 @p253)) % 4.12/4.33 (step @p259 :rule implies_elim :premises (@p258)) % 4.12/4.33 (step @p260 :rule chain_m_resolution :premises (@p259 @p237) :args (@t163 @t130 (@list @t160))) % 4.12/4.33 (step @p261 :rule cong :premises (@p246) :args (@t164)) % 4.12/4.33 (step @p262 :rule nary_cong :premises (@p261 @p143) :args (@t165)) % 4.12/4.33 (step @p263 :rule refl :args (@t124)) % 4.12/4.33 (step @p264 :rule nary_cong :premises (@p249 @p248 @p263 @p262) :args (@t166)) % 4.12/4.33 (step @p265 :rule refl :args (@t167)) % 4.12/4.33 (step @p266 :rule cong :premises (@p265 @p264) :args ((=> @t167 @t166))) % 4.12/4.33 (assume-push @p363 @t167) % 4.12/4.33 (step @p268 :rule instantiate :premises (@p140) :args ((@list tptp.xq tptp.xp))) % 4.12/4.33 (step-pop @p364 :rule scope :premises (@p268)) % 4.12/4.33 (step @p269 :rule process_scope :premises (@p364) :args (@t166)) % 4.12/4.33 (step @p271 :rule eq_resolve :premises (@p269 @p266)) % 4.12/4.33 (step @p272 :rule implies_elim :premises (@p271)) % 4.12/4.33 (step @p273 :rule chain_m_resolution :premises (@p272 @p140) :args (@t169 @t130 (@list @t167))) % 4.12/4.33 (step @p274 :rule cnf_and_pos :args (@t168 1)) % 4.12/4.33 (step @p275 :rule reordering :premises (@p274) :args ((or @t76 @t170))) % 4.12/4.33 (step @p276 :rule chain_m_resolution :premises (@p275 @p156) :args (@t170 @t100 (@list @t76))) % 4.12/4.33 (step @p277 :rule cnf_or_pos :args (@t169)) % 4.12/4.33 (step @p278 :rule reordering :premises (@p277) :args ((or @t107 @t128 @t124 @t168 (not @t169)))) % 4.12/4.35 (step @p279 :rule chain_m_resolution :premises (@p278 @p91 @p142 @p276 @p273) :args (@t124 (@list false false true false) (@list @t70 @t74 @t168 @t169))) % 4.12/4.35 (step @p280 :rule symm :premises (@p36)) % 4.12/4.35 (step @p281 :rule cnf_or_pos :args (@t163)) % 4.12/4.35 (step @p282 :rule reordering :premises (@p281) :args ((or @t162 @t108 @t107 @t128 @t125 @t157 @t161 (not @t163)))) % 4.12/4.35 (step @p283 :rule chain_m_resolution :premises (@p282 @p280 @p92 @p91 @p142 @p162 @p279 @p260) :args (@t161 (@list true false false false true false false) (@list @t162 @t60 @t70 @t74 @t125 @t124 @t163))) % 4.12/4.35 (step @p284 :rule cnf_and_pos :args (@t161 1)) % 4.12/4.35 (step @p285 :rule reordering :premises (@p284) :args ((or @t154 (not @t161)))) % 4.12/4.35 (step @p286 :rule chain_m_resolution :premises (@p285 @p283) :args (@t154 @t130 (@list @t161))) % 4.12/4.35 (step @p287 :rule refl :args (@t171)) % 4.12/4.35 (step @p288 :rule bool-double-not-elim :args (@t138)) % 4.12/4.35 (step @p289 :rule refl :args (@t172)) % 4.12/4.35 (step @p290 :rule refl :args (@t173)) % 4.12/4.35 (step @p291 :rule refl :args (@t91)) % 4.12/4.35 (step @p292 :rule refl :args (@t174)) % 4.12/4.35 (step @p293 :rule refl :args (@t175)) % 4.12/4.35 (step @p294 :rule nary_cong :premises (@p293 @p292 @p291 @p290 @p289 @p288 @p287) :args ((or @t175 @t174 @t91 @t173 @t172 (not @t139) @t171))) % 4.12/4.35 (assume-push @p365 @t154) % 4.12/4.35 (assume-push @p366 @t73) % 4.12/4.35 (assume-push @p367 @t90) % 4.12/4.35 (assume-push @p368 @t112) % 4.12/4.35 (assume-push @p369 @t106) % 4.12/4.35 (assume-push @p370 @t69) % 4.12/4.35 (assume-push @p371 @t139) % 4.12/4.35 (step @p302 :rule evaluate :args ((= false true))) % 4.12/4.35 (step @p303 :rule true_intro :premises (@p286)) % 4.12/4.35 (step @p304 :rule symm :premises (@p95)) % 4.12/4.35 (step @p305 :rule symm :premises (@p80)) % 4.12/4.35 (step @p306 :rule symm :premises (@p105)) % 4.12/4.35 (step @p307 :rule trans :premises (@p306 @p305)) % 4.12/4.35 (step @p308 :rule trans :premises (@p307 @p43)) % 4.12/4.35 (step @p309 :rule cong :premises (@p308 @p304) :args ((tptp.sdtlseqdt0 @t111 @t105))) % 4.12/4.35 (step @p310 :rule trans :premises (@p42 @p95)) % 4.12/4.35 (step @p311 :rule symm :premises (@p307)) % 4.12/4.35 (step @p312 :rule cong :premises (@p311 @p310) :args (@t138)) % 4.12/4.35 (step @p313 :rule false_intro :premises (@p371)) % 4.12/4.35 (step @p314 :rule symm :premises (@p313)) % 4.12/4.35 (step @p315 :rule trans :premises (@p314 @p312 @p309 @p303)) % 4.12/4.35 (step @p316 false :rule eq_resolve :premises (@p315 @p302)) % 4.12/4.35 (step-pop @p372 :rule scope :premises (@p316)) % 4.12/4.35 (step-pop @p373 :rule scope :premises (@p372)) % 4.12/4.35 (step-pop @p374 :rule scope :premises (@p373)) % 4.12/4.35 (step-pop @p375 :rule scope :premises (@p374)) % 4.12/4.35 (step-pop @p376 :rule scope :premises (@p375)) % 4.12/4.35 (step-pop @p377 :rule scope :premises (@p376)) % 4.12/4.35 (step-pop @p378 :rule scope :premises (@p377)) % 4.12/4.35 (step @p317 :rule process_scope :premises (@p378) :args (false)) % 4.12/4.35 (assume-push @p379 @t69) % 4.12/4.35 (assume-push @p380 @t73) % 4.12/4.35 (assume-push @p381 @t90) % 4.12/4.35 (assume-push @p382 @t106) % 4.12/4.35 (assume-push @p383 @t112) % 4.12/4.35 (assume-push @p384 @t139) % 4.12/4.35 (assume-push @p385 @t154) % 4.12/4.35 (step @p332 :rule and_intro :premises (@p286 @p43 @p80 @p105 @p95 @p42 @p384)) % 4.12/4.35 (step-pop @p386 :rule scope :premises (@p332)) % 4.12/4.35 (step-pop @p387 :rule scope :premises (@p386)) % 4.12/4.35 (step-pop @p388 :rule scope :premises (@p387)) % 4.12/4.35 (step-pop @p389 :rule scope :premises (@p388)) % 4.12/4.35 (step-pop @p390 :rule scope :premises (@p389)) % 4.12/4.35 (step-pop @p391 :rule scope :premises (@p390)) % 4.12/4.35 (step-pop @p392 :rule scope :premises (@p391)) % 4.12/4.35 (step @p333 :rule process_scope :premises (@p392) :args (@t176)) % 4.12/4.35 (step @p341 :rule implies_elim :premises (@p333)) % 4.12/4.35 (step @p342 :rule resolution :premises (@p341 @p317) :args (true @t176)) % 4.12/4.35 (step @p343 :rule not_and :premises (@p342)) % 4.12/4.35 (step @p344 :rule eq_resolve :premises (@p343 @p294)) % 4.12/4.35 (step @p345 :rule reordering :premises (@p344) :args ((or @t175 @t174 @t91 @t138 @t173 @t172 @t171))) % 4.12/4.35 (step @p346 false :rule chain_m_resolution :premises (@p345 @p286 @p205 @p105 @p95 @p80 @p43 @p42) :args (false (@list false true false false false false false) (@list @t154 @t138 @t112 @t106 @t90 @t73 @t69))) % 4.12/4.35 ) % 4.12/4.35 % SZS output end Proof % 4.12/4.35 % cvc5 exiting %------------------------------------------------------------------------------