%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM545+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n020.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 08:39:47 AM UTC 2026 % Result : Theorem 0.71s 0.92s % Output : Proof 0.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : NUM545+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.14/0.32 % Computer : n020.cluster.edu % 0.14/0.32 % Model : x86_64 x86_64 % 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.32 % Memory : 8042.1875MB % 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.32 % CPULimit : 300 % 0.14/0.32 % WCLimit : 300 % 0.14/0.32 % DateTime : Tue Jun 2 11:28:55 EDT 2026 % 0.14/0.32 % CPUTime : % 0.29/0.48 %----Proving TF0_NAR, FOF, or CNF % 0.71/0.92 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.71/0.92 % SZS status Theorem % 0.71/0.92 % SZS output start Proof % 0.71/0.92 ( % 0.71/0.92 (declare-sort $$unsorted 0) % 0.71/0.92 (declare-const tptp.xS $$unsorted) % 0.71/0.92 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.71/0.92 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.71/0.92 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.71/0.92 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.71/0.92 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.slcrc0 $$unsorted) % 0.71/0.92 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.92 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.71/0.92 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.71/0.92 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.71/0.92 (declare-const tptp.szNzAzT0 $$unsorted) % 0.71/0.92 (declare-const tptp.sz00 $$unsorted) % 0.71/0.92 (define @t1 () (@var "W0" $$unsorted)) % 0.71/0.92 (define @t2 () (tptp.aSet0 @t1)) % 0.71/0.92 (define @t3 () (@list @t1)) % 0.71/0.92 (define @t4 () (tptp.aElement0 @t1)) % 0.71/0.92 (define @t5 () (@var "W1" $$unsorted)) % 0.71/0.92 (define @t6 () (tptp.aElement0 @t5)) % 0.71/0.92 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.71/0.92 (define @t8 () (@list @t5)) % 0.71/0.92 (define @t9 () (tptp.isFinite0 @t1)) % 0.71/0.92 (define @t10 () (exists @t8 @t7)) % 0.71/0.92 (define @t11 () (not @t10)) % 0.71/0.92 (define @t12 () (and @t2 @t11)) % 0.71/0.92 (define @t13 () (= @t1 tptp.slcrc0)) % 0.71/0.92 (define @t14 () (= @t13 @t12)) % 0.71/0.92 (define @t15 () (forall @t3 @t14)) % 0.71/0.92 (define @t16 () (tptp.isCountable0 @t1)) % 0.71/0.92 (define @t17 () (not @t9)) % 0.71/0.92 (define @t18 () (and @t2 @t16)) % 0.71/0.92 (define @t19 () (not @t13)) % 0.71/0.92 (define @t20 () (@var "W2" $$unsorted)) % 0.71/0.92 (define @t21 () (tptp.aElementOf0 @t20 @t1)) % 0.71/0.92 (define @t22 () (tptp.aElementOf0 @t20 @t5)) % 0.71/0.92 (define @t23 () (@list @t20)) % 0.71/0.92 (define @t24 () (forall @t23 (=> @t22 @t21))) % 0.71/0.92 (define @t25 () (tptp.aSet0 @t5)) % 0.71/0.92 (define @t26 () (and @t25 @t24)) % 0.71/0.92 (define @t27 () (tptp.aSubsetOf0 @t5 @t1)) % 0.71/0.92 (define @t28 () (= @t27 @t26)) % 0.71/0.92 (define @t29 () (forall @t8 @t28)) % 0.71/0.92 (define @t30 () (=> @t2 @t29)) % 0.71/0.92 (define @t31 () (forall @t3 @t30)) % 0.71/0.92 (define @t32 () (tptp.isFinite0 @t5)) % 0.71/0.92 (define @t33 () (and @t2 @t9)) % 0.71/0.92 (define @t34 () (= @t1 @t5)) % 0.71/0.92 (define @t35 () (tptp.aSubsetOf0 @t1 @t5)) % 0.71/0.92 (define @t36 () (@list @t1 @t5)) % 0.71/0.92 (define @t37 () (tptp.aSet0 @t20)) % 0.71/0.92 (define @t38 () (@list @t1 @t5 @t20)) % 0.71/0.92 (define @t39 () (@var "W3" $$unsorted)) % 0.71/0.92 (define @t40 () (= @t39 @t5)) % 0.71/0.92 (define @t41 () (tptp.aElementOf0 @t39 @t1)) % 0.71/0.92 (define @t42 () (tptp.aElement0 @t39)) % 0.71/0.92 (define @t43 () (tptp.aElementOf0 @t39 @t20)) % 0.71/0.92 (define @t44 () (@list @t39)) % 0.71/0.92 (define @t45 () (tptp.sdtpldt0 @t1 @t5)) % 0.71/0.92 (define @t46 () (and @t2 @t6)) % 0.71/0.92 (define @t47 () (tptp.sdtmndt0 @t1 @t5)) % 0.71/0.92 (define @t48 () (tptp.sdtpldt0 @t5 @t1)) % 0.71/0.92 (define @t49 () (and @t25 (tptp.isCountable0 @t5))) % 0.71/0.92 (define @t50 () (tptp.sdtmndt0 @t5 @t1)) % 0.71/0.92 (define @t51 () (and @t25 @t32)) % 0.71/0.92 (define @t52 () (tptp.aSet0 tptp.szNzAzT0)) % 0.71/0.92 (define @t53 () (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.71/0.92 (define @t54 () (tptp.szszuzczcdt0 @t1)) % 0.71/0.92 (define @t55 () (not (= @t54 tptp.sz00))) % 0.71/0.92 (define @t56 () (tptp.aElementOf0 @t54 tptp.szNzAzT0)) % 0.71/0.92 (define @t57 () (and @t56 @t55)) % 0.71/0.92 (define @t58 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.71/0.92 (define @t59 () (=> @t58 @t57)) % 0.71/0.92 (define @t60 () (forall @t3 @t59)) % 0.71/0.92 (define @t61 () (tptp.szszuzczcdt0 @t5)) % 0.71/0.92 (define @t62 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.71/0.92 (define @t63 () (and @t58 @t62)) % 0.71/0.92 (define @t64 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.71/0.92 (define @t65 () (tptp.sdtlseqdt0 @t5 @t20)) % 0.71/0.92 (define @t66 () (tptp.aElementOf0 @t20 tptp.szNzAzT0)) % 0.71/0.92 (define @t67 () (tptp.sbrdtbr0 @t1)) % 0.71/0.92 (define @t68 () (not @t7)) % 0.71/0.92 (define @t69 () (tptp.szmzizndt0 @t1)) % 0.71/0.92 (define @t70 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.71/0.92 (define @t71 () (tptp.sdtlseqdt0 @t20 @t5)) % 0.71/0.92 (define @t72 () (forall @t23 (=> @t21 @t71))) % 0.71/0.92 (define @t73 () (and @t7 @t72)) % 0.71/0.92 (define @t74 () (tptp.szmzazxdt0 @t1)) % 0.71/0.92 (define @t75 () (= @t5 @t74)) % 0.71/0.92 (define @t76 () (= @t75 @t73)) % 0.71/0.92 (define @t77 () (forall @t8 @t76)) % 0.71/0.92 (define @t78 () (and @t70 @t9 @t19)) % 0.71/0.92 (define @t79 () (=> @t78 @t77)) % 0.71/0.92 (define @t80 () (forall @t3 @t79)) % 0.71/0.92 (define @t81 () (tptp.szmzizndt0 @t5)) % 0.71/0.92 (define @t82 () (tptp.slbdtrb0 @t1)) % 0.71/0.92 (define @t83 () (tptp.slbdtrb0 tptp.sz00)) % 0.71/0.92 (define @t84 () (tptp.slbdtrb0 @t5)) % 0.71/0.92 (define @t85 () (tptp.isFinite0 tptp.xS)) % 0.71/0.92 (define @t86 () (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0)) % 0.71/0.92 (define @t87 () (tptp.szmzazxdt0 tptp.xS)) % 0.71/0.92 (define @t88 () (tptp.szszuzczcdt0 @t87)) % 0.71/0.92 (define @t89 () (tptp.aSubsetOf0 tptp.xS (tptp.slbdtrb0 @t88))) % 0.71/0.92 (define @t90 () (= tptp.xS tptp.slcrc0)) % 0.71/0.92 (define @t91 () (not @t90)) % 0.71/0.92 (define @t92 () (=> @t91 @t89)) % 0.71/0.92 (define @t93 () (tptp.aSubsetOf0 tptp.xS @t82)) % 0.71/0.92 (define @t94 () (and @t58 @t93)) % 0.71/0.92 (define @t95 () (exists @t3 @t94)) % 0.71/0.92 (define @t96 () (not @t95)) % 0.71/0.92 (define @t97 () (forall @t3 (or (not @t58) (not @t93)))) % 0.71/0.92 (define @t98 () (forall @t3 (not @t94))) % 0.71/0.92 (define @t99 () (not @t98)) % 0.71/0.92 (define @t100 () (and @t56 (not (= tptp.sz00 @t54)))) % 0.71/0.92 (define @t101 () (@list @t87)) % 0.71/0.92 (define @t102 () (@var "BOUND_VARIABLE_7833" $$unsorted)) % 0.71/0.92 (define @t103 () (= (tptp.aSubsetOf0 @t102 @t1) (and (tptp.aSet0 @t102) (forall @t23 (or (not (tptp.aElementOf0 @t20 @t102)) @t21))))) % 0.71/0.92 (define @t104 () (not @t2)) % 0.71/0.92 (define @t105 () (or @t104 @t103)) % 0.71/0.92 (define @t106 () (@list @t102)) % 0.71/0.92 (define @t107 () (forall @t106 @t105)) % 0.71/0.92 (define @t108 () (forall @t106 @t103)) % 0.71/0.92 (define @t109 () (@list @t5)) % 0.71/0.92 (define @t110 () (or @t104 @t108)) % 0.71/0.92 (define @t111 () (forall @t8 (= @t27 (and @t25 (forall @t23 (or (not @t22) @t21)))))) % 0.71/0.92 (define @t112 () (not (tptp.aElementOf0 @t20 tptp.xS))) % 0.71/0.92 (define @t113 () (forall @t23 (or @t112 @t66))) % 0.71/0.92 (define @t114 () (tptp.aSet0 tptp.xS)) % 0.71/0.92 (define @t115 () (and @t114 @t113)) % 0.71/0.92 (define @t116 () (= @t86 @t115)) % 0.71/0.92 (define @t117 () (not @t52)) % 0.71/0.92 (define @t118 () (or @t117 @t116)) % 0.71/0.92 (define @t119 () (@list false false)) % 0.71/0.92 (define @t120 () (not @t86)) % 0.71/0.92 (define @t121 () (not @t115)) % 0.71/0.92 (define @t122 () (@list false)) % 0.71/0.92 (define @t123 () (@list @t115)) % 0.71/0.92 (define @t124 () (@var "BOUND_VARIABLE_8316" $$unsorted)) % 0.71/0.92 (define @t125 () (= @t74 @t124)) % 0.71/0.92 (define @t126 () (not @t21)) % 0.71/0.92 (define @t127 () (and (tptp.aElementOf0 @t124 @t1) (forall @t23 (or @t126 (tptp.sdtlseqdt0 @t20 @t124))))) % 0.71/0.92 (define @t128 () (= (= @t124 @t74) @t127)) % 0.71/0.92 (define @t129 () (not @t70)) % 0.71/0.92 (define @t130 () (or @t129 @t17 @t13 @t128)) % 0.71/0.92 (define @t131 () (@list @t1 @t124)) % 0.71/0.92 (define @t132 () (forall @t131 @t130)) % 0.71/0.92 (define @t133 () (@list @t124)) % 0.71/0.92 (define @t134 () (forall @t133 @t130)) % 0.71/0.92 (define @t135 () (forall @t133 @t128)) % 0.71/0.92 (define @t136 () (or @t129 @t17 @t13 @t135)) % 0.71/0.92 (define @t137 () (forall @t8 (= @t75 (and @t7 (forall @t23 (or @t126 @t71)))))) % 0.71/0.92 (define @t138 () (or @t129 @t17 @t13 @t137)) % 0.71/0.92 (define @t139 () (not @t19)) % 0.71/0.92 (define @t140 () (or @t129 @t17 @t139)) % 0.71/0.92 (define @t141 () (tptp.aElementOf0 @t87 tptp.xS)) % 0.71/0.92 (define @t142 () (and @t141 (forall @t23 (or @t112 (tptp.sdtlseqdt0 @t20 @t87))))) % 0.71/0.92 (define @t143 () (= @t142 (= @t87 @t87))) % 0.71/0.92 (define @t144 () (not @t85)) % 0.71/0.92 (define @t145 () (or @t120 @t144 @t90 @t143)) % 0.71/0.92 (define @t146 () (forall @t131 (or @t129 @t17 @t13 (= @t127 @t125)))) % 0.71/0.92 (define @t147 () (= tptp.slcrc0 tptp.xS)) % 0.71/0.92 (define @t148 () (or @t120 @t144 @t147 @t142)) % 0.71/0.92 (define @t149 () (forall @t8 @t68)) % 0.71/0.92 (define @t150 () (tptp.aSet0 tptp.slcrc0)) % 0.71/0.92 (define @t151 () (and @t150 (forall @t8 (not (tptp.aElementOf0 @t5 tptp.slcrc0))))) % 0.71/0.92 (define @t152 () (= (= tptp.slcrc0 tptp.slcrc0) @t151)) % 0.71/0.92 (define @t153 () (forall @t3 (= @t13 (and @t2 @t149)))) % 0.71/0.92 (define @t154 () (tptp.aSet0 @t83)) % 0.71/0.92 (define @t155 () (forall @t23 (or @t112 (tptp.aElementOf0 @t20 @t83)))) % 0.71/0.92 (define @t156 () (and @t114 @t155)) % 0.71/0.92 (define @t157 () (tptp.aSubsetOf0 tptp.xS @t83)) % 0.71/0.92 (define @t158 () (= @t157 @t156)) % 0.71/0.92 (define @t159 () (not @t154)) % 0.71/0.92 (define @t160 () (or @t159 @t158)) % 0.71/0.92 (define @t161 () (not @t157)) % 0.71/0.92 (define @t162 () (not @t53)) % 0.71/0.92 (define @t163 () (or @t162 @t161)) % 0.71/0.92 (define @t164 () (not @t156)) % 0.71/0.92 (define @t165 () (@list true false)) % 0.71/0.92 (define @t166 () (not @t155)) % 0.71/0.92 (define @t167 () (@quantifiers_skolemize @t155 0)) % 0.71/0.92 (define @t168 () (tptp.aElementOf0 @t167 @t83)) % 0.71/0.92 (define @t169 () (tptp.aElementOf0 @t167 tptp.xS)) % 0.71/0.92 (define @t170 () (not @t169)) % 0.71/0.92 (define @t171 () (or @t170 @t168)) % 0.71/0.92 (define @t172 () (not @t168)) % 0.71/0.92 (define @t173 () (@list true)) % 0.71/0.92 (define @t174 () (@list @t171)) % 0.71/0.92 (define @t175 () (not @t147)) % 0.71/0.92 (define @t176 () (= tptp.slcrc0 @t83)) % 0.71/0.92 (define @t177 () (not @t176)) % 0.71/0.92 (define @t178 () (and @t172 @t176 @t147 @t169)) % 0.71/0.92 (define @t179 () (tptp.aElementOf0 @t87 tptp.szNzAzT0)) % 0.71/0.92 (define @t180 () (not @t141)) % 0.71/0.92 (define @t181 () (or @t180 @t179)) % 0.71/0.92 (define @t182 () (tptp.aElementOf0 @t88 tptp.szNzAzT0)) % 0.71/0.92 (define @t183 () (and @t182 (not (= tptp.sz00 @t88)))) % 0.71/0.92 (define @t184 () (not @t179)) % 0.71/0.92 (define @t185 () (or @t184 @t183)) % 0.71/0.92 (define @t186 () (not @t89)) % 0.71/0.92 (define @t187 () (not @t182)) % 0.71/0.92 (define @t188 () (or @t187 @t186)) % 0.71/0.92 (define @t189 () (not @t188)) % 0.71/0.92 (assume @p1 (forall @t3 (=> @t2 true))) % 0.71/0.92 (assume @p2 (forall @t3 (=> @t4 true))) % 0.71/0.92 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.71/0.92 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.71/0.92 (assume @p5 @t15) % 0.71/0.92 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.71/0.92 (assume @p7 (forall @t3 (=> @t2 (=> @t16 true)))) % 0.71/0.92 (assume @p8 (forall @t3 (=> @t18 @t17))) % 0.71/0.92 (assume @p9 (forall @t3 (=> @t18 @t19))) % 0.71/0.92 (assume @p10 @t31) % 0.71/0.92 (assume @p11 (forall @t3 (=> @t33 (forall @t8 (=> @t27 @t32))))) % 0.71/0.92 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.71/0.92 (assume @p13 (forall @t36 (=> (and @t2 @t25) (=> (and @t35 @t27) @t34)))) % 0.71/0.92 (assume @p14 (forall @t38 (=> (and @t2 @t25 @t37) (=> (and @t35 (tptp.aSubsetOf0 @t5 @t20)) (tptp.aSubsetOf0 @t1 @t20))))) % 0.71/0.92 (assume @p15 (forall @t36 (=> @t46 (forall @t23 (= (= @t20 @t45) (and @t37 (forall @t44 (= @t43 (and @t42 (or @t41 @t40)))))))))) % 0.71/0.92 (assume @p16 (forall @t36 (=> @t46 (forall @t23 (= (= @t20 @t47) (and @t37 (forall @t44 (= @t43 (and @t42 @t41 (not @t40)))))))))) % 0.71/0.92 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t47 @t5) @t1)))))) % 0.71/0.92 (assume @p18 (forall @t36 (=> (and @t4 @t25) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t48 @t1) @t5))))) % 0.71/0.92 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t49 (tptp.isCountable0 @t48)))))) % 0.71/0.92 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t49 (tptp.isCountable0 @t50)))))) % 0.71/0.92 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t51 (tptp.isFinite0 @t48)))))) % 0.71/0.92 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t51 (tptp.isFinite0 @t50)))))) % 0.71/0.92 (assume @p23 (and @t52 (tptp.isCountable0 tptp.szNzAzT0))) % 0.71/0.92 (assume @p24 @t53) % 0.71/0.92 (assume @p25 @t60) % 0.71/0.92 (assume @p26 (forall @t36 (=> @t63 (=> (= @t54 @t61) @t34)))) % 0.71/0.92 (assume @p27 (forall @t3 (=> @t58 (or (= @t1 tptp.sz00) (exists @t8 (and @t62 (= @t1 @t61))))))) % 0.71/0.92 (assume @p28 (forall @t3 (=> @t58 (not (= @t1 @t54))))) % 0.71/0.92 (assume @p29 (forall @t36 (=> @t63 (=> @t64 true)))) % 0.71/0.92 (assume @p30 (forall @t3 (=> @t58 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.71/0.92 (assume @p31 (forall @t3 (=> @t58 (not (tptp.sdtlseqdt0 @t54 tptp.sz00))))) % 0.71/0.92 (assume @p32 (forall @t36 (=> @t63 (= @t64 (tptp.sdtlseqdt0 @t54 @t61))))) % 0.71/0.92 (assume @p33 (forall @t3 (=> @t58 (tptp.sdtlseqdt0 @t1 @t54)))) % 0.71/0.92 (assume @p34 (forall @t3 (=> @t58 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.71/0.92 (assume @p35 (forall @t36 (=> @t63 (=> (and @t64 (tptp.sdtlseqdt0 @t5 @t1)) @t34)))) % 0.71/0.92 (assume @p36 (forall @t38 (=> (and @t58 @t62 @t66) (=> (and @t64 @t65) (tptp.sdtlseqdt0 @t1 @t20))))) % 0.71/0.92 (assume @p37 (forall @t36 (=> @t63 (or @t64 (tptp.sdtlseqdt0 @t61 @t1))))) % 0.71/0.92 (assume @p38 (forall @t36 (=> @t63 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.71/0.92 (assume @p39 (forall @t3 (=> @t58 (tptp.iLess0 @t1 @t54)))) % 0.71/0.92 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t67)))) % 0.71/0.92 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t67 tptp.szNzAzT0) @t9)))) % 0.71/0.92 (assume @p42 (forall @t3 (=> @t2 (= (= @t67 tptp.sz00) @t13)))) % 0.71/0.92 (assume @p43 (forall @t3 (=> @t33 (forall @t8 (=> @t6 (=> @t68 (= (tptp.sbrdtbr0 @t45) (tptp.szszuzczcdt0 @t67)))))))) % 0.71/0.92 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t47)) @t67)))))) % 0.71/0.92 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t27) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t67)))))) % 0.71/0.92 (assume @p46 (forall @t36 (=> (and @t2 @t62) (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t67)) (exists @t23 (and (tptp.aSubsetOf0 @t20 @t1) (= (tptp.sbrdtbr0 @t20) @t5))))))) % 0.71/0.92 (assume @p47 (forall @t3 (=> (and @t70 @t19) (forall @t8 (= (= @t5 @t69) (and @t7 (forall @t23 (=> @t21 @t65)))))))) % 0.71/0.92 (assume @p48 @t80) % 0.71/0.92 (assume @p49 (forall @t36 (=> (and @t70 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t19 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t69 @t5) (tptp.aElementOf0 @t81 @t1)) (= @t69 @t81))))) % 0.71/0.92 (assume @p50 (forall @t3 (=> @t58 (forall @t8 (= (= @t5 @t82) (and @t25 (forall @t23 (= @t22 (and @t66 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t20) @t1)))))))))) % 0.71/0.92 (assume @p51 (forall @t3 (=> @t58 (tptp.isFinite0 @t82)))) % 0.71/0.92 (assume @p52 (= @t83 tptp.slcrc0)) % 0.71/0.92 (assume @p53 (forall @t36 (=> @t63 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t61)) (or (tptp.aElementOf0 @t1 @t84) @t34))))) % 0.71/0.92 (assume @p54 (forall @t36 (=> @t63 (= @t64 (tptp.aSubsetOf0 @t82 @t84))))) % 0.71/0.92 (assume @p55 (and @t86 @t85)) % 0.71/0.92 (assume @p56 @t92) % 0.71/0.92 (assume @p57 @t96) % 0.71/0.92 (assume @p58 true) % 0.71/0.92 (step @p59 :rule bool-double-not-elim :args 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cong :premises (@p74 @p73) :args (@t59)) % 0.71/0.92 (step @p76 :rule cong :premises (@p75) :args (@t60)) % 0.71/0.92 (step @p77 :rule trans :premises (@p76 @p69)) % 0.71/0.92 (step @p78 :rule eq_resolve :premises (@p25 @p77)) % 0.71/0.92 (step @p79 :rule instantiate :premises (@p78) :args (@t101)) % 0.71/0.92 (step @p80 :rule quant-merge-prenex :args ((= (forall @t3 @t107) (forall (@list @t1 @t102) @t105)))) % 0.71/0.92 (step @p81 :rule alpha_equiv :args (@t108 (@list @t102) @t109)) % 0.71/0.92 (step @p82 :rule refl :args (@t104)) % 0.71/0.92 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t110)) % 0.71/0.92 (step @p84 :rule quant-miniscope-or :args ((= @t107 @t110))) % 0.71/0.92 (step @p85 :rule trans :premises (@p84 @p83)) % 0.71/0.92 (step @p86 :rule symm :premises (@p85)) % 0.71/0.92 (step @p87 :rule cong :premises (@p86) :args ((forall @t3 (or @t104 @t111)))) % 0.71/0.92 (step @p88 :rule trans :premises (@p87 @p80)) % 0.71/0.92 (step @p89 :rule bool-impl-elim :args (@t2 @t111)) % 0.71/0.92 (step @p90 :rule cong :premises (@p89) :args ((forall @t3 (=> @t2 @t111)))) % 0.71/0.92 (step @p91 :rule trans :premises (@p90 @p88)) % 0.71/0.92 (step @p92 :rule bool-impl-elim :args (@t22 @t21)) % 0.71/0.92 (step @p93 :rule cong :premises (@p92) :args (@t24)) % 0.71/0.92 (step @p94 :rule refl :args (@t25)) % 0.71/0.92 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t26)) % 0.71/0.92 (step @p96 :rule refl :args (@t27)) % 0.71/0.92 (step @p97 :rule cong :premises (@p96 @p95) :args (@t28)) % 0.71/0.92 (step @p98 :rule cong :premises (@p97) :args (@t29)) % 0.71/0.92 (step @p99 :rule refl :args (@t2)) % 0.71/0.92 (step @p100 :rule cong :premises (@p99 @p98) :args (@t30)) % 0.71/0.92 (step @p101 :rule cong :premises (@p100) :args (@t31)) % 0.71/0.92 (step @p102 :rule trans :premises (@p101 @p91)) % 0.71/0.92 (step @p103 :rule eq_resolve :premises (@p10 @p102)) % 0.71/0.92 (step @p104 :rule instantiate :premises (@p103) :args ((@list tptp.szNzAzT0 tptp.xS))) % 0.71/0.92 (step @p105 :rule and_elim :premises (@p23) :args (0)) % 0.71/0.92 (step @p106 :rule cnf_or_pos :args (@t118)) % 0.71/0.92 (step @p107 :rule reordering :premises (@p106) :args ((or @t117 @t116 (not @t118)))) % 0.71/0.92 (step @p108 :rule chain_m_resolution :premises (@p107 @p105 @p104) :args (@t116 @t119 (@list @t52 @t118))) % 0.71/0.92 (step @p109 :rule and_elim :premises (@p55) :args (0)) % 0.71/0.92 (step @p110 :rule cnf_equiv_pos1 :args (@t116)) % 0.71/0.92 (step @p111 :rule reordering :premises (@p110) :args ((or @t120 @t115 (not @t116)))) % 0.71/0.92 (step @p112 :rule chain_m_resolution :premises (@p111 @p109 @p108) :args (@t115 @t119 (@list @t86 @t116))) % 0.71/0.92 (step @p113 :rule cnf_and_pos :args (@t115 1)) % 0.71/0.92 (step @p114 :rule reordering :premises (@p113) :args ((or @t113 @t121))) % 0.71/0.92 (step @p115 :rule chain_m_resolution :premises (@p114 @p112) :args (@t113 @t122 @t123)) % 0.71/0.92 (step @p116 :rule instantiate :premises (@p115) :args (@t101)) % 0.71/0.92 (step @p117 :rule eq-symm :args (@t125 @t127)) % 0.71/0.92 (step @p118 :rule refl :args (@t127)) % 0.71/0.92 (step @p119 :rule eq-symm :args (@t124 @t74)) % 0.71/0.92 (step @p120 :rule cong :premises (@p119 @p118) :args (@t128)) % 0.71/0.92 (step @p121 :rule trans :premises (@p120 @p117)) % 0.71/0.92 (step @p122 :rule refl :args (@t13)) % 0.71/0.92 (step @p123 :rule refl :args (@t17)) % 0.71/0.92 (step @p124 :rule refl :args (@t129)) % 0.71/0.92 (step @p125 :rule nary_cong :premises (@p124 @p123 @p122 @p121) :args (@t130)) % 0.71/0.92 (step @p126 :rule cong :premises (@p125) :args (@t132)) % 0.71/0.92 (step @p127 :rule quant-merge-prenex :args ((= (forall @t3 @t134) @t132))) % 0.71/0.92 (step @p128 :rule alpha_equiv :args (@t135 (@list @t124) @t109)) % 0.71/0.92 (step @p129 :rule refl :args (@t13)) % 0.71/0.92 (step @p130 :rule refl :args (@t17)) % 0.71/0.92 (step @p131 :rule refl :args (@t129)) % 0.71/0.92 (step @p132 :rule nary_cong :premises (@p131 @p130 @p129 @p128) :args (@t136)) % 0.71/0.92 (step @p133 :rule quant-miniscope-or :args ((= @t134 @t136))) % 0.71/0.92 (step @p134 :rule trans :premises (@p133 @p132)) % 0.71/0.92 (step @p135 :rule symm :premises (@p134)) % 0.71/0.92 (step @p136 :rule cong :premises (@p135) :args ((forall @t3 @t138))) % 0.71/0.92 (step @p137 :rule trans :premises (@p136 @p127)) % 0.71/0.92 (step @p138 :rule trans :premises (@p137 @p126)) % 0.71/0.92 (step @p139 :rule aci_norm :args ((= (or (or @t129 @t17 @t13) @t137) @t138))) % 0.71/0.92 (step @p140 :rule refl :args (@t137)) % 0.71/0.92 (step @p141 :rule bool-double-not-elim :args (@t13)) % 0.71/0.92 (step @p142 :rule nary_cong :premises (@p131 @p130 @p141) :args (@t140)) % 0.71/0.92 (step @p143 :rule aci_norm :args ((= (or @t129 (or @t17 @t139)) @t140))) % 0.71/0.92 (step @p144 :rule trans :premises (@p143 @p142)) % 0.71/0.92 (step @p145 :rule bool-and-de-morgan :args (@t9 @t19 true)) % 0.71/0.92 (step @p146 :rule nary_cong :premises (@p131 @p145) :args ((or @t129 (not (and @t9 @t19))))) % 0.71/0.92 (step @p147 :rule bool-and-de-morgan :args (@t70 @t9 (and @t19))) % 0.71/0.92 (step @p148 :rule trans :premises (@p147 @p146)) % 0.71/0.92 (step @p149 :rule trans :premises (@p148 @p144)) % 0.71/0.92 (step @p150 :rule nary_cong :premises (@p149 @p140) :args ((or (not @t78) @t137))) % 0.71/0.92 (step @p151 :rule trans :premises (@p150 @p139)) % 0.71/0.92 (step @p152 :rule bool-impl-elim :args (@t78 @t137)) % 0.71/0.92 (step @p153 :rule trans :premises (@p152 @p151)) % 0.71/0.92 (step @p154 :rule cong :premises (@p153) :args ((forall @t3 (=> @t78 @t137)))) % 0.71/0.92 (step @p155 :rule trans :premises (@p154 @p138)) % 0.71/0.92 (step @p156 :rule bool-impl-elim :args (@t21 @t71)) % 0.71/0.92 (step @p157 :rule cong :premises (@p156) :args (@t72)) % 0.71/0.92 (step @p158 :rule refl :args (@t7)) % 0.71/0.92 (step @p159 :rule nary_cong :premises (@p158 @p157) :args (@t73)) % 0.71/0.92 (step @p160 :rule refl :args (@t75)) % 0.71/0.92 (step @p161 :rule cong :premises 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(step-pop @p323 :rule scope :premises (@p206)) % 0.71/0.92 (step @p207 :rule process_scope :premises (@p323) :args (@t152)) % 0.71/0.92 (step @p209 :rule eq_resolve :premises (@p207 @p204)) % 0.71/0.92 (step @p210 :rule implies_elim :premises (@p209)) % 0.71/0.92 (step @p211 :rule chain_m_resolution :premises (@p210 @p195) :args (@t151 @t122 (@list @t153))) % 0.71/0.92 (step @p212 :rule cnf_and_pos :args (@t151 0)) % 0.71/0.92 (step @p213 :rule reordering :premises (@p212) :args ((or @t150 (not @t151)))) % 0.71/0.92 (step @p214 :rule chain_m_resolution :premises (@p213 @p211) :args (@t150 @t122 (@list @t151))) % 0.71/0.92 (step @p215 :rule true_intro :premises (@p214)) % 0.71/0.92 (step @p216 :rule cong :premises (@p52) :args (@t154)) % 0.71/0.92 (step @p217 :rule trans :premises (@p216 @p215)) % 0.71/0.92 (step @p218 :rule true_elim :premises (@p217)) % 0.71/0.92 (step @p219 :rule cnf_or_pos :args (@t160)) % 0.71/0.92 (step @p220 :rule reordering :premises (@p219) :args ((or @t159 @t158 (not @t160)))) % 0.71/0.92 (step @p221 :rule chain_m_resolution :premises (@p220 @p218 @p187) :args (@t158 @t119 (@list @t154 @t160))) % 0.71/0.92 (step @p222 :rule instantiate :premises (@p67) :args ((@list tptp.sz00))) % 0.71/0.92 (step @p223 :rule cnf_or_pos :args (@t163)) % 0.71/0.92 (step @p224 :rule reordering :premises (@p223) :args ((or @t162 @t161 (not @t163)))) % 0.71/0.92 (step @p225 :rule chain_m_resolution :premises (@p224 @p24 @p222) :args (@t161 @t119 (@list @t53 @t163))) % 0.71/0.92 (step @p226 :rule cnf_equiv_pos2 :args (@t158)) % 0.71/0.92 (step @p227 :rule reordering :premises (@p226) :args ((or @t157 @t164 (not @t158)))) % 0.71/0.92 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p221) :args (@t164 @t165 (@list @t157 @t158))) % 0.71/0.92 (step @p229 :rule cnf_and_pos :args (@t115 0)) % 0.71/0.92 (step @p230 :rule reordering :premises (@p229) :args ((or @t114 @t121))) % 0.71/0.92 (step @p231 :rule chain_m_resolution :premises (@p230 @p112) :args (@t114 @t122 @t123)) % 0.71/0.92 (step @p232 :rule cnf_and_neg :args (@t156)) % 0.71/0.92 (step @p233 :rule reordering :premises (@p232) :args ((or (not @t114) @t156 @t166))) % 0.71/0.92 (step @p234 :rule chain_m_resolution :premises (@p233 @p231 @p228) :args (@t166 (@list false true) (@list @t114 @t156))) % 0.71/0.92 (step @p235 :rule skolemize :premises (@p234)) % 0.71/0.92 (step @p236 :rule cnf_or_neg :args (@t171 1)) % 0.71/0.92 (step @p237 :rule chain_m_resolution :premises (@p236 @p235) :args (@t172 @t173 @t174)) % 0.71/0.92 (step @p238 :rule bool-double-not-elim :args (@t169)) % 0.71/0.92 (step @p239 :rule refl :args (@t171)) % 0.71/0.92 (step @p240 :rule nary_cong :premises (@p239 @p238) :args ((or @t171 (not @t170)))) % 0.71/0.92 (step @p241 :rule cnf_or_neg :args (@t171 0)) % 0.71/0.92 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.71/0.92 (step @p243 :rule reordering :premises (@p242) :args ((or @t169 @t171))) % 0.71/0.92 (step @p244 :rule chain_m_resolution :premises (@p243 @p235) :args (@t169 @t173 @t174)) % 0.71/0.92 (step @p245 :rule symm :premises (@p52)) % 0.71/0.92 (step @p246 :rule bool-double-not-elim :args (@t168)) % 0.71/0.92 (step @p247 :rule refl :args (@t170)) % 0.71/0.92 (step @p248 :rule refl :args (@t175)) % 0.71/0.92 (step @p249 :rule refl :args (@t177)) % 0.71/0.92 (step @p250 :rule nary_cong :premises (@p249 @p248 @p247 @p246) :args ((or @t177 @t175 @t170 (not @t172)))) % 0.71/0.92 (assume-push @p324 @t172) % 0.71/0.92 (assume-push @p325 @t176) % 0.71/0.92 (assume-push @p326 @t147) % 0.71/0.92 (assume-push @p327 @t169) % 0.71/0.92 (step @p255 :rule evaluate :args ((= true false))) % 0.71/0.92 (step @p256 :rule false_intro :premises (@p237)) % 0.71/0.92 (step @p257 :rule symm :premises (@p326)) % 0.71/0.92 (step @p258 :rule trans :premises (@p257 @p245)) % 0.71/0.92 (step @p259 :rule refl :args (@t167)) % 0.71/0.92 (step @p260 :rule cong :premises (@p259 @p258) :args (@t169)) % 0.71/0.92 (step @p261 :rule true_intro :premises (@p244)) % 0.71/0.92 (step @p262 :rule symm :premises (@p261)) % 0.71/0.92 (step @p263 :rule trans :premises (@p262 @p260 @p256)) % 0.71/0.92 (step @p264 false :rule eq_resolve :premises (@p263 @p255)) % 0.71/0.92 (step-pop @p328 :rule scope :premises (@p264)) % 0.71/0.92 (step-pop @p329 :rule scope :premises (@p328)) % 0.71/0.92 (step-pop @p330 :rule scope :premises (@p329)) % 0.71/0.92 (step-pop @p331 :rule scope :premises (@p330)) % 0.71/0.92 (step @p265 :rule process_scope :premises (@p331) :args (false)) % 0.71/0.92 (assume-push @p332 @t176) % 0.71/0.92 (assume-push @p333 @t147) % 0.71/0.92 (assume-push @p334 @t169) % 0.71/0.92 (assume-push @p335 @t172) % 0.71/0.92 (step @p274 :rule and_intro :premises (@p237 @p245 @p333 @p244)) % 0.71/0.92 (step-pop @p336 :rule scope :premises (@p274)) % 0.71/0.92 (step-pop @p337 :rule scope :premises (@p336)) % 0.71/0.92 (step-pop @p338 :rule scope :premises (@p337)) % 0.71/0.92 (step-pop @p339 :rule scope :premises (@p338)) % 0.71/0.92 (step @p275 :rule process_scope :premises (@p339) :args (@t178)) % 0.71/0.92 (step @p280 :rule implies_elim :premises (@p275)) % 0.71/0.92 (step @p281 :rule resolution :premises (@p280 @p265) :args (true @t178)) % 0.71/0.92 (step @p282 :rule not_and :premises (@p281)) % 0.71/0.92 (step @p283 :rule eq_resolve :premises (@p282 @p250)) % 0.71/0.92 (step @p284 :rule reordering :premises (@p283) :args ((or @t175 @t177 @t170 @t168))) % 0.71/0.92 (step @p285 :rule chain_m_resolution :premises (@p284 @p245 @p244 @p237) :args (@t175 (@list false false true) (@list @t176 @t169 @t168))) % 0.71/0.92 (step @p286 :rule cnf_or_pos :args (@t148)) % 0.71/0.92 (step @p287 :rule reordering :premises (@p286) :args ((or @t147 @t120 @t144 @t142 (not @t148)))) % 0.71/0.92 (step @p288 :rule chain_m_resolution :premises (@p287 @p285 @p109 @p186 @p185) :args (@t142 (@list true false false false) (@list @t147 @t86 @t85 @t148))) % 0.71/0.92 (step @p289 :rule cnf_and_pos :args (@t142 0)) % 0.71/0.92 (step @p290 :rule reordering :premises (@p289) :args ((or @t141 (not @t142)))) % 0.71/0.92 (step @p291 :rule chain_m_resolution :premises (@p290 @p288) :args (@t141 @t122 (@list @t142))) % 0.71/0.92 (step @p292 :rule cnf_or_pos :args (@t181)) % 0.71/0.92 (step @p293 :rule reordering :premises (@p292) :args ((or @t179 @t180 (not @t181)))) % 0.71/0.92 (step @p294 :rule chain_m_resolution :premises (@p293 @p291 @p116) :args (@t179 @t119 (@list @t141 @t181))) % 0.71/0.92 (step @p295 :rule cnf_or_pos :args (@t185)) % 0.71/0.92 (step @p296 :rule reordering :premises (@p295) :args ((or @t184 @t183 (not @t185)))) % 0.71/0.92 (step @p297 :rule chain_m_resolution :premises (@p296 @p294 @p79) :args (@t183 @t119 (@list @t179 @t185))) % 0.71/0.92 (step @p298 :rule cnf_and_pos :args (@t183 0)) % 0.71/0.92 (step @p299 :rule reordering :premises (@p298) :args ((or @t182 (not @t183)))) % 0.71/0.92 (step @p300 :rule chain_m_resolution :premises (@p299 @p297) :args (@t182 @t122 (@list @t183))) % 0.71/0.92 (step @p301 :rule refl :args (@t89)) % 0.71/0.92 (step @p302 :rule bool-double-not-elim :args (@t147)) % 0.71/0.92 (step @p303 :rule nary_cong :premises (@p302 @p301) :args ((or (not @t175) @t89))) % 0.71/0.92 (step @p304 :rule cong :premises (@p173) :args (@t91)) % 0.71/0.92 (step @p305 :rule cong :premises (@p304 @p301) :args (@t92)) % 0.71/0.92 (step @p306 :rule eq_resolve :premises (@p56 @p305)) % 0.71/0.92 (step @p307 :rule implies_elim :premises (@p306)) % 0.71/0.92 (step @p308 :rule eq_resolve :premises (@p307 @p303)) % 0.71/0.92 (step @p309 :rule reordering :premises (@p308) :args ((or @t89 @t147))) % 0.71/0.92 (step @p310 :rule chain_m_resolution :premises (@p309 @p285) :args (@t89 @t173 (@list @t147))) % 0.71/0.92 (step @p311 :rule cnf_or_pos :args (@t188)) % 0.71/0.92 (step @p312 :rule reordering :premises (@p311) :args ((or @t186 @t187 @t189))) % 0.71/0.92 (step @p313 :rule chain_m_resolution :premises (@p312 @p310 @p300) :args (@t189 @t119 (@list @t89 @t182))) % 0.71/0.92 (assume-push @p340 @t97) % 0.71/0.92 (step @p315 :rule instantiate :premises (@p67) :args ((@list @t88))) % 0.71/0.92 (step-pop @p341 :rule scope :premises (@p315)) % 0.71/0.92 (step @p316 :rule process_scope :premises (@p341) :args (@t188)) % 0.71/0.92 (step @p318 :rule implies_elim :premises (@p316)) % 0.71/0.92 (step @p319 false :rule chain_m_resolution :premises (@p318 @p313 @p67) :args (false @t165 (@list @t188 @t97))) % 0.71/0.92 ) % 0.71/0.92 % SZS output end Proof % 0.71/0.92 % cvc5 exiting %------------------------------------------------------------------------------