%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM462+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 : n001.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 08:39:29 AM UTC 2026 % Result : Theorem 1.04s 1.22s % Output : Proof 1.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM462+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 : n001.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 11:22:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 1.04/1.22 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.04/1.22 % SZS status Theorem % 1.04/1.22 % SZS output start Proof % 1.04/1.22 ( % 1.04/1.22 (declare-sort $$unsorted 0) % 1.04/1.22 (declare-const tptp.xm $$unsorted) % 1.04/1.22 (declare-const tptp.xl $$unsorted) % 1.04/1.22 (declare-const tptp.xn $$unsorted) % 1.04/1.22 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.04/1.22 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.04/1.22 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 1.04/1.22 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.04/1.22 (declare-const tptp.sz10 $$unsorted) % 1.04/1.22 (declare-const tptp.sz00 $$unsorted) % 1.04/1.22 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 1.04/1.22 (define @t1 () (@var "W0" $$unsorted)) % 1.04/1.22 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 1.04/1.22 (define @t3 () (@list @t1)) % 1.04/1.22 (define @t4 () (@var "W1" $$unsorted)) % 1.04/1.22 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 1.04/1.22 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 1.04/1.22 (define @t7 () (and @t2 @t6)) % 1.04/1.22 (define @t8 () (@list @t1 @t4)) % 1.04/1.22 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 1.04/1.22 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 1.04/1.22 (define @t11 () (forall @t8 (=> @t7 @t10))) % 1.04/1.22 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 1.04/1.22 (define @t13 () (@var "W2" $$unsorted)) % 1.04/1.22 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 1.04/1.22 (define @t15 () (tptp.aNaturalNumber0 @t13)) % 1.04/1.22 (define @t16 () (and @t2 @t6 @t15)) % 1.04/1.22 (define @t17 () (@list @t1 @t4 @t13)) % 1.04/1.22 (define @t18 () (tptp.sdtasdt0 @t4 @t1)) % 1.04/1.22 (define @t19 () (= @t9 @t18)) % 1.04/1.22 (define @t20 () (forall @t8 (=> @t7 @t19))) % 1.04/1.22 (define @t21 () (tptp.sdtasdt0 @t13 @t1)) % 1.04/1.22 (define @t22 () (tptp.sdtasdt0 @t1 @t13)) % 1.04/1.22 (define @t23 () (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t22)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t18 @t21)))) % 1.04/1.22 (define @t24 () (forall @t17 (=> @t16 @t23))) % 1.04/1.22 (define @t25 () (= @t4 @t13)) % 1.04/1.22 (define @t26 () (tptp.sdtpldt0 @t13 @t1)) % 1.04/1.22 (define @t27 () (tptp.sdtpldt0 @t1 @t13)) % 1.04/1.22 (define @t28 () (= @t18 @t21)) % 1.04/1.22 (define @t29 () (= @t9 @t22)) % 1.04/1.22 (define @t30 () (or @t29 @t28)) % 1.04/1.22 (define @t31 () (=> @t30 @t25)) % 1.04/1.22 (define @t32 () (and @t6 @t15)) % 1.04/1.22 (define @t33 () (@list @t4 @t13)) % 1.04/1.22 (define @t34 () (forall @t33 (=> @t32 @t31))) % 1.04/1.22 (define @t35 () (= @t1 tptp.sz00)) % 1.04/1.22 (define @t36 () (not @t35)) % 1.04/1.22 (define @t37 () (=> @t36 @t34)) % 1.04/1.22 (define @t38 () (=> @t2 @t37)) % 1.04/1.22 (define @t39 () (forall @t3 @t38)) % 1.04/1.22 (define @t40 () (= @t4 tptp.sz00)) % 1.04/1.22 (define @t41 () (and @t15 (= @t27 @t4))) % 1.04/1.22 (define @t42 () (@list @t13)) % 1.04/1.22 (define @t43 () (exists @t42 @t41)) % 1.04/1.22 (define @t44 () (tptp.sdtlseqdt0 @t1 @t4)) % 1.04/1.22 (define @t45 () (= @t44 @t43)) % 1.04/1.22 (define @t46 () (=> @t7 @t45)) % 1.04/1.22 (define @t47 () (forall @t8 @t46)) % 1.04/1.22 (define @t48 () (= @t1 @t4)) % 1.04/1.22 (define @t49 () (tptp.sdtlseqdt0 @t4 @t1)) % 1.04/1.22 (define @t50 () (tptp.sdtpldt0 @t13 @t4)) % 1.04/1.22 (define @t51 () (tptp.aNaturalNumber0 tptp.xn)) % 1.04/1.22 (define @t52 () (tptp.aNaturalNumber0 tptp.xl)) % 1.04/1.22 (define @t53 () (tptp.aNaturalNumber0 tptp.xm)) % 1.04/1.22 (define @t54 () (tptp.sdtlseqdt0 tptp.xl tptp.xn)) % 1.04/1.22 (define @t55 () (= tptp.xl tptp.xn)) % 1.04/1.22 (define @t56 () (= tptp.xm tptp.sz00)) % 1.04/1.22 (define @t57 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 1.04/1.22 (define @t58 () (tptp.sdtasdt0 tptp.xl tptp.xm)) % 1.04/1.22 (define @t59 () (tptp.sdtlseqdt0 @t58 @t57)) % 1.04/1.22 (define @t60 () (not (= @t58 @t57))) % 1.04/1.22 (define @t61 () (tptp.sdtasdt0 tptp.xm tptp.xn)) % 1.04/1.22 (define @t62 () (tptp.sdtasdt0 tptp.xm tptp.xl)) % 1.04/1.22 (define @t63 () (tptp.sdtlseqdt0 @t62 @t61)) % 1.04/1.22 (define @t64 () (not (= @t62 @t61))) % 1.04/1.22 (define @t65 () (and @t64 @t63 @t60 @t59)) % 1.04/1.22 (define @t66 () (not @t65)) % 1.04/1.22 (define @t67 () (= @t4 @t27)) % 1.04/1.22 (define @t68 () (not @t15)) % 1.04/1.22 (define @t69 () (= @t44 (not (forall @t42 (or @t68 (not @t67)))))) % 1.04/1.22 (define @t70 () (not @t6)) % 1.04/1.22 (define @t71 () (not @t2)) % 1.04/1.22 (define @t72 () (or @t71 @t70)) % 1.04/1.22 (define @t73 () (not @t7)) % 1.04/1.22 (define @t74 () (and @t15 @t67)) % 1.04/1.22 (define @t75 () (forall @t42 (not @t74))) % 1.04/1.22 (define @t76 () (not @t75)) % 1.04/1.22 (define @t77 () (@list tptp.xm tptp.xn)) % 1.04/1.22 (define @t78 () (tptp.aNaturalNumber0 @t61)) % 1.04/1.22 (define @t79 () (not @t51)) % 1.04/1.22 (define @t80 () (not @t53)) % 1.04/1.22 (define @t81 () (or @t80 @t79 @t78)) % 1.04/1.22 (define @t82 () (@list false false false)) % 1.04/1.22 (define @t83 () (@list tptp.xm tptp.xl)) % 1.04/1.22 (define @t84 () (tptp.aNaturalNumber0 @t62)) % 1.04/1.22 (define @t85 () (not @t52)) % 1.04/1.22 (define @t86 () (or @t80 @t85 @t84)) % 1.04/1.22 (define @t87 () (forall @t42 (or @t68 (not (= @t61 (tptp.sdtpldt0 @t62 @t13)))))) % 1.04/1.22 (define @t88 () (not @t87)) % 1.04/1.22 (define @t89 () (= @t63 @t88)) % 1.04/1.22 (define @t90 () (not @t78)) % 1.04/1.22 (define @t91 () (not @t84)) % 1.04/1.22 (define @t92 () (or @t91 @t90 @t89)) % 1.04/1.22 (define @t93 () (forall @t42 (or @t68 (not (= tptp.xn (tptp.sdtpldt0 tptp.xl @t13)))))) % 1.04/1.22 (define @t94 () (@quantifiers_skolemize @t93 0)) % 1.04/1.22 (define @t95 () (tptp.sdtasdt0 @t94 tptp.xm)) % 1.04/1.22 (define @t96 () (or @t71 @t70 @t19)) % 1.04/1.22 (define @t97 () (or @t80 @t85 (= @t62 @t58))) % 1.04/1.22 (define @t98 () (forall @t8 @t96)) % 1.04/1.22 (define @t99 () (= @t58 @t62)) % 1.04/1.22 (define @t100 () (or @t80 @t85 @t99)) % 1.04/1.22 (define @t101 () (@list false)) % 1.04/1.22 (define @t102 () (@list @t98)) % 1.04/1.22 (define @t103 () (tptp.sdtpldt0 @t58 @t95)) % 1.04/1.22 (define @t104 () (or @t71 @t70 @t68)) % 1.04/1.22 (define @t105 () (or @t70 @t68)) % 1.04/1.22 (define @t106 () (not @t32)) % 1.04/1.22 (define @t107 () (not @t93)) % 1.04/1.22 (define @t108 () (= @t54 @t107)) % 1.04/1.22 (define @t109 () (or @t85 @t79 @t108)) % 1.04/1.22 (define @t110 () (@list false false)) % 1.04/1.22 (define @t111 () (tptp.aNaturalNumber0 @t94)) % 1.04/1.22 (define @t112 () (tptp.sdtpldt0 tptp.xl @t94)) % 1.04/1.22 (define @t113 () (= tptp.xn @t112)) % 1.04/1.22 (define @t114 () (not @t113)) % 1.04/1.22 (define @t115 () (not @t111)) % 1.04/1.22 (define @t116 () (or @t115 @t114)) % 1.04/1.22 (define @t117 () (@list true)) % 1.04/1.22 (define @t118 () (@list @t116)) % 1.04/1.22 (define @t119 () (= (tptp.sdtasdt0 @t112 tptp.xm) @t103)) % 1.04/1.22 (define @t120 () (and (= (tptp.sdtasdt0 tptp.xm @t112) (tptp.sdtpldt0 @t62 (tptp.sdtasdt0 tptp.xm @t94))) @t119)) % 1.04/1.22 (define @t121 () (or @t80 @t85 @t115 @t120)) % 1.04/1.22 (define @t122 () (or @t80 @t79 (= @t61 @t57))) % 1.04/1.22 (define @t123 () (= @t57 @t61)) % 1.04/1.22 (define @t124 () (or @t80 @t79 @t123)) % 1.04/1.22 (define @t125 () (tptp.aNaturalNumber0 @t95)) % 1.04/1.22 (define @t126 () (or @t115 @t80 @t125)) % 1.04/1.22 (define @t127 () (= @t61 (tptp.sdtpldt0 @t62 @t95))) % 1.04/1.22 (define @t128 () (not @t127)) % 1.04/1.22 (define @t129 () (not @t125)) % 1.04/1.22 (define @t130 () (or @t129 @t128)) % 1.04/1.22 (define @t131 () (not @t130)) % 1.04/1.22 (define @t132 () (@list @t95)) % 1.04/1.22 (define @t133 () (not @t89)) % 1.04/1.22 (define @t134 () (@list true false)) % 1.04/1.22 (define @t135 () (tptp.aNaturalNumber0 @t57)) % 1.04/1.22 (define @t136 () (or @t79 @t80 @t135)) % 1.04/1.22 (define @t137 () (tptp.aNaturalNumber0 @t58)) % 1.04/1.22 (define @t138 () (or @t85 @t80 @t137)) % 1.04/1.22 (define @t139 () (forall @t42 (or @t68 (not (= @t57 (tptp.sdtpldt0 @t58 @t13)))))) % 1.04/1.22 (define @t140 () (not @t139)) % 1.04/1.22 (define @t141 () (= @t59 @t140)) % 1.04/1.22 (define @t142 () (not @t135)) % 1.04/1.22 (define @t143 () (not @t137)) % 1.04/1.22 (define @t144 () (or @t143 @t142 @t141)) % 1.04/1.22 (define @t145 () (= @t57 @t103)) % 1.04/1.22 (define @t146 () (not @t145)) % 1.04/1.22 (define @t147 () (or @t129 @t146)) % 1.04/1.22 (define @t148 () (not @t147)) % 1.04/1.22 (define @t149 () (not @t141)) % 1.04/1.22 (define @t150 () (not @t59)) % 1.04/1.22 (define @t151 () (= @t57 @t58)) % 1.04/1.22 (define @t152 () (not @t63)) % 1.04/1.22 (define @t153 () (= @t61 @t62)) % 1.04/1.22 (define @t154 () (not @t151)) % 1.04/1.22 (define @t155 () (not @t153)) % 1.04/1.22 (define @t156 () (not @t155)) % 1.04/1.22 (define @t157 () (not @t123)) % 1.04/1.22 (define @t158 () (not @t99)) % 1.04/1.22 (define @t159 () (and @t155 @t99 @t123)) % 1.04/1.22 (define @t160 () (and @t155 @t154)) % 1.04/1.22 (define @t161 () (not @t160)) % 1.04/1.22 (define @t162 () (@var "BOUND_VARIABLE_7687" $$unsorted)) % 1.04/1.22 (define @t163 () (@var "BOUND_VARIABLE_7685" $$unsorted)) % 1.04/1.22 (define @t164 () (= @t163 @t162)) % 1.04/1.22 (define @t165 () (and (not (= (tptp.sdtasdt0 @t1 @t163) (tptp.sdtasdt0 @t1 @t162))) (not (= (tptp.sdtasdt0 @t163 @t1) (tptp.sdtasdt0 @t162 @t1))))) % 1.04/1.22 (define @t166 () (not (tptp.aNaturalNumber0 @t162))) % 1.04/1.22 (define @t167 () (not (tptp.aNaturalNumber0 @t163))) % 1.04/1.22 (define @t168 () (or @t71 @t35 @t167 @t166 @t165 @t164)) % 1.04/1.22 (define @t169 () (or @t167 @t166 @t165 @t164)) % 1.04/1.22 (define @t170 () (or @t71 @t35 @t169)) % 1.04/1.22 (define @t171 () (@list @t1 @t163 @t162)) % 1.04/1.22 (define @t172 () (forall @t171 @t170)) % 1.04/1.22 (define @t173 () (@list @t163 @t162)) % 1.04/1.22 (define @t174 () (forall @t173 @t170)) % 1.04/1.22 (define @t175 () (forall @t173 @t169)) % 1.04/1.22 (define @t176 () (or @t71 @t35 @t175)) % 1.04/1.22 (define @t177 () (and (not @t29) (not @t28))) % 1.04/1.22 (define @t178 () (or @t70 @t68 @t177 @t25)) % 1.04/1.22 (define @t179 () (forall @t33 @t178)) % 1.04/1.22 (define @t180 () (or @t71 @t35 @t179)) % 1.04/1.22 (define @t181 () (=> @t36 @t179)) % 1.04/1.22 (define @t182 () (and @t64 @t60)) % 1.04/1.22 (define @t183 () (or @t80 @t56 @t85 @t79 @t182 @t55)) % 1.04/1.22 (define @t184 () (forall @t171 @t168)) % 1.04/1.22 (define @t185 () (= tptp.sz00 tptp.xm)) % 1.04/1.22 (define @t186 () (or @t80 @t185 @t85 @t79 @t160 @t55)) % 1.04/1.22 (assume @p1 (forall @t3 (=> @t2 true))) % 1.04/1.22 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 1.04/1.22 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 1.04/1.22 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 1.04/1.22 (assume @p5 @t11) % 1.04/1.22 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 1.04/1.22 (assume @p7 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t5 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 1.04/1.22 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 1.04/1.22 (assume @p9 @t20) % 1.04/1.22 (assume @p10 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 1.04/1.22 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 1.04/1.22 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 1.04/1.22 (assume @p13 @t24) % 1.04/1.22 (assume @p14 (forall @t17 (=> @t16 (=> (or (= @t5 @t27) (= @t12 @t26)) @t25)))) % 1.04/1.22 (assume @p15 @t39) % 1.04/1.22 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t35 @t40))))) % 1.04/1.22 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t35 @t40))))) % 1.04/1.22 (assume @p18 @t47) % 1.04/1.22 (assume @p19 (forall @t8 (=> @t7 (=> @t44 (forall @t42 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t41)))))) % 1.04/1.22 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 1.04/1.22 (assume @p21 (forall @t8 (=> @t7 (=> (and @t44 @t49) @t48)))) % 1.04/1.22 (assume @p22 (forall @t17 (=> @t16 (=> (and @t44 (tptp.sdtlseqdt0 @t4 @t13)) (tptp.sdtlseqdt0 @t1 @t13))))) % 1.04/1.22 (assume @p23 (forall @t8 (=> @t7 (or @t44 (and (not (= @t4 @t1)) @t49))))) % 1.04/1.22 (assume @p24 (forall @t8 (=> @t7 (=> (and (not @t48) @t44) (forall @t42 (=> @t15 (and (not (= @t26 @t50)) (tptp.sdtlseqdt0 @t26 @t50) (not (= @t27 @t14)) (tptp.sdtlseqdt0 @t27 @t14)))))))) % 1.04/1.22 (assume @p25 (and @t53 @t52 @t51)) % 1.04/1.22 (assume @p26 (and (not @t56) (not @t55) @t54)) % 1.04/1.22 (assume @p27 @t66) % 1.04/1.22 (assume @p28 true) % 1.04/1.22 (step @p29 :rule and_elim :premises (@p25) :args (0)) % 1.04/1.22 (step @p30 :rule and_elim :premises (@p25) :args (1)) % 1.04/1.22 (step @p31 :rule and_elim :premises (@p25) :args (2)) % 1.04/1.22 (step @p32 :rule and_elim :premises (@p26) :args (0)) % 1.04/1.22 (step @p33 :rule symm :premises (@p32)) % 1.04/1.22 (step @p34 :rule and_elim :premises (@p26) :args (1)) % 1.04/1.22 (step @p35 :rule aci_norm :args ((= (or @t72 @t69) (or @t71 @t70 @t69)))) % 1.04/1.22 (step @p36 :rule refl :args (@t69)) % 1.04/1.22 (step @p37 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 1.04/1.22 (step @p38 :rule nary_cong :premises (@p37 @p36) :args ((or @t73 @t69))) % 1.04/1.22 (step @p39 :rule trans :premises (@p38 @p35)) % 1.04/1.22 (step @p40 :rule bool-impl-elim :args (@t7 @t69)) % 1.04/1.22 (step @p41 :rule trans :premises (@p40 @p39)) % 1.04/1.22 (step @p42 :rule cong :premises (@p41) :args ((forall @t8 (=> @t7 @t69)))) % 1.04/1.22 (step @p43 :rule bool-and-de-morgan :args (@t15 @t67 true)) % 1.04/1.22 (step @p44 :rule cong :premises (@p43) :args (@t75)) % 1.04/1.22 (step @p45 :rule cong :premises (@p44) :args (@t76)) % 1.04/1.22 (step @p46 :rule exists-elim :args ((= (exists @t42 @t74) @t76))) % 1.04/1.22 (step @p47 :rule trans :premises (@p46 @p45)) % 1.04/1.22 (step @p48 :rule eq-symm :args (@t27 @t4)) % 1.04/1.22 (step @p49 :rule refl :args (@t15)) % 1.04/1.22 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t41)) % 1.04/1.22 (step @p51 :rule cong :premises (@p50) :args (@t43)) % 1.04/1.22 (step @p52 :rule trans :premises (@p51 @p47)) % 1.04/1.22 (step @p53 :rule refl :args (@t44)) % 1.04/1.22 (step @p54 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(assume-push @p335 @t123) % 1.04/1.23 (assume-push @p336 @t155) % 1.04/1.23 (assume-push @p337 @t123) % 1.04/1.23 (assume-push @p338 @t99) % 1.04/1.23 (step @p244 :rule false_intro :premises (@p333)) % 1.04/1.23 (step @p245 :rule cong :premises (@p165 @p104) :args (@t151)) % 1.04/1.23 (step @p246 :rule trans :premises (@p245 @p244)) % 1.04/1.23 (step @p247 :rule false_elim :premises (@p246)) % 1.04/1.23 (step-pop @p339 :rule scope :premises (@p247)) % 1.04/1.23 (step-pop @p340 :rule scope :premises (@p339)) % 1.04/1.23 (step-pop @p341 :rule scope :premises (@p340)) % 1.04/1.23 (step @p248 :rule process_scope :premises (@p341) :args (@t154)) % 1.04/1.23 (step @p252 :rule and_intro :premises (@p333 @p165 @p104)) % 1.04/1.23 (step @p253 :rule modus_ponens :premises (@p252 @p248)) % 1.04/1.23 (step-pop @p342 :rule scope :premises (@p253)) % 1.04/1.23 (step-pop @p343 :rule scope :premises (@p342)) % 1.04/1.23 (step-pop @p344 :rule scope :premises (@p343)) % 1.04/1.23 (step @p254 :rule process_scope :premises (@p344) :args (@t154)) % 1.04/1.23 (step @p258 :rule implies_elim :premises (@p254)) % 1.04/1.23 (step @p259 :rule cnf_and_neg :args (@t159)) % 1.04/1.23 (step @p260 :rule resolution :premises (@p259 @p258) :args (true @t159)) % 1.04/1.23 (step @p261 :rule eq_resolve :premises (@p260 @p237)) % 1.04/1.23 (step @p262 :rule reordering :premises (@p261) :args ((or @t153 @t154 @t158 @t157))) % 1.04/1.23 (step @p263 :rule chain_m_resolution :premises (@p262 @p165 @p104 @p233 @p218 @p188) :args (@t153 (@list false false false false false) (@list @t123 @t99 @t151 @t59 @t63))) % 1.04/1.23 (step @p264 :rule cnf_and_pos :args (@t160 0)) % 1.04/1.23 (step @p265 :rule reordering :premises (@p264) :args ((or @t155 @t161))) % 1.04/1.23 (step @p266 :rule chain_m_resolution :premises (@p265 @p263) :args (@t161 @t101 (@list @t153))) % 1.04/1.23 (step @p267 :rule aci_norm :args ((= @t170 @t168))) % 1.04/1.23 (step @p268 :rule cong :premises (@p267) :args (@t172)) % 1.04/1.23 (step @p269 :rule quant-merge-prenex :args ((= (forall @t3 @t174) @t172))) % 1.04/1.23 (step @p270 :rule alpha_equiv :args (@t175 (@list @t163 @t162) (@list @t4 @t13))) % 1.04/1.23 (step @p271 :rule refl :args (@t35)) % 1.04/1.23 (step @p272 :rule nary_cong :premises (@p110 @p271 @p270) :args (@t176)) % 1.04/1.23 (step @p273 :rule quant-miniscope-or :args ((= @t174 @t176))) % 1.04/1.23 (step @p274 :rule trans :premises (@p273 @p272)) % 1.04/1.23 (step @p275 :rule symm :premises (@p274)) % 1.04/1.23 (step @p276 :rule cong :premises (@p275) :args ((forall @t3 @t180))) % 1.04/1.23 (step @p277 :rule trans :premises (@p276 @p269)) % 1.04/1.23 (step @p278 :rule trans :premises (@p277 @p268)) % 1.04/1.23 (step @p279 :rule aci_norm :args ((= (or @t71 (or @t35 @t179)) @t180))) % 1.04/1.23 (step @p280 :rule refl :args (@t179)) % 1.04/1.23 (step @p281 :rule bool-double-not-elim :args (@t35)) % 1.04/1.23 (step @p282 :rule nary_cong :premises (@p281 @p280) :args ((or (not @t36) @t179))) % 1.04/1.23 (step @p283 :rule bool-impl-elim :args (@t36 @t179)) % 1.04/1.23 (step @p284 :rule trans :premises (@p283 @p282)) % 1.04/1.23 (step @p285 :rule nary_cong :premises (@p110 @p284) :args ((or @t71 @t181))) % 1.04/1.23 (step @p286 :rule trans :premises (@p285 @p279)) % 1.04/1.23 (step @p287 :rule bool-impl-elim :args (@t2 @t181)) % 1.04/1.23 (step @p288 :rule trans :premises (@p287 @p286)) % 1.04/1.23 (step @p289 :rule cong :premises (@p288) :args ((forall @t3 (=> @t2 @t181)))) % 1.04/1.23 (step @p290 :rule trans :premises (@p289 @p278)) % 1.04/1.23 (step @p291 :rule aci_norm :args ((= (or @t105 (or @t177 @t25)) @t178))) % 1.04/1.23 (step @p292 :rule refl :args (@t25)) % 1.04/1.23 (step @p293 :rule bool-or-de-morgan :args (@t29 @t28 false)) % 1.04/1.23 (step @p294 :rule nary_cong :premises (@p293 @p292) :args ((or (not @t30) @t25))) % 1.04/1.23 (step @p295 :rule bool-impl-elim :args (@t30 @t25)) % 1.04/1.23 (step @p296 :rule trans :premises (@p295 @p294)) % 1.04/1.23 (step @p297 :rule nary_cong :premises (@p109 @p296) :args ((or @t106 @t31))) % 1.04/1.23 (step @p298 :rule trans :premises (@p297 @p291)) % 1.04/1.23 (step @p299 :rule bool-impl-elim :args (@t32 @t31)) % 1.04/1.23 (step @p300 :rule trans :premises (@p299 @p298)) % 1.04/1.23 (step @p301 :rule cong :premises (@p300) :args (@t34)) % 1.04/1.23 (step @p302 :rule refl :args (@t36)) % 1.04/1.23 (step @p303 :rule cong :premises (@p302 @p301) :args (@t37)) % 1.04/1.23 (step @p304 :rule refl :args (@t2)) % 1.04/1.23 (step @p305 :rule cong :premises (@p304 @p303) :args (@t38)) % 1.04/1.23 (step @p306 :rule cong :premises (@p305) :args (@t39)) % 1.04/1.23 (step @p307 :rule trans :premises (@p306 @p290)) % 1.04/1.23 (step @p308 :rule eq_resolve :premises (@p15 @p307)) % 1.04/1.23 (step @p309 :rule refl :args (@t55)) % 1.04/1.23 (step @p310 :rule nary_cong :premises (@p227 @p225) :args (@t182)) % 1.04/1.23 (step @p311 :rule eq-symm :args (tptp.xm tptp.sz00)) % 1.04/1.23 (step @p312 :rule nary_cong :premises (@p91 @p311 @p90 @p153 @p310 @p309) :args (@t183)) % 1.04/1.23 (step @p313 :rule refl :args (@t184)) % 1.04/1.23 (step @p314 :rule cong :premises (@p313 @p312) :args ((=> @t184 @t183))) % 1.04/1.23 (assume-push @p345 @t184) % 1.04/1.23 (step @p316 :rule instantiate :premises (@p308) :args ((@list tptp.xm tptp.xl tptp.xn))) % 1.04/1.23 (step-pop @p346 :rule scope :premises (@p316)) % 1.04/1.23 (step @p317 :rule process_scope :premises (@p346) :args (@t183)) % 1.04/1.23 (step @p319 :rule eq_resolve :premises (@p317 @p314)) % 1.04/1.23 (step @p320 :rule implies_elim :premises (@p319)) % 1.04/1.23 (step @p321 :rule chain_m_resolution :premises (@p320 @p308) :args (@t186 @t101 (@list @t184))) % 1.04/1.23 (step @p322 :rule cnf_or_pos :args (@t186)) % 1.04/1.23 (step @p323 :rule reordering :premises (@p322) :args ((or @t55 @t185 @t80 @t85 @t79 @t160 (not @t186)))) % 1.04/1.23 (step @p324 false :rule chain_m_resolution :premises (@p323 @p321 @p266 @p34 @p33 @p31 @p30 @p29) :args (false (@list false true true true false false false) (@list @t186 @t160 @t55 @t185 @t51 @t52 @t53))) % 1.04/1.23 ) % 1.04/1.23 % SZS output end Proof % 1.04/1.23 % cvc5 exiting %------------------------------------------------------------------------------