%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM560+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 : n025.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 08:39:50 AM UTC 2026 % Result : Theorem 1.02s 1.23s % Output : Proof 1.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM560+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 : n025.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 11:29:46 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 1.02/1.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.02/1.23 % SZS status Theorem % 1.02/1.23 % SZS output start Proof % 1.02/1.23 ( % 1.02/1.23 (declare-sort $$unsorted 0) % 1.02/1.23 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.xy $$unsorted) % 1.02/1.23 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.slcrc0 $$unsorted) % 1.02/1.23 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.xF $$unsorted) % 1.02/1.23 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.02/1.23 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.szNzAzT0 $$unsorted) % 1.02/1.23 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.sz00 $$unsorted) % 1.02/1.23 (define @t1 () (@var "W0" $$unsorted)) % 1.02/1.23 (define @t2 () (tptp.aSet0 @t1)) % 1.02/1.23 (define @t3 () (@list @t1)) % 1.02/1.23 (define @t4 () (tptp.aElement0 @t1)) % 1.02/1.23 (define @t5 () (@var "W1" $$unsorted)) % 1.02/1.23 (define @t6 () (tptp.aElement0 @t5)) % 1.02/1.23 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 1.02/1.23 (define @t8 () (@list @t5)) % 1.02/1.23 (define @t9 () (tptp.isFinite0 @t1)) % 1.02/1.23 (define @t10 () (= @t1 tptp.slcrc0)) % 1.02/1.23 (define @t11 () (tptp.isCountable0 @t1)) % 1.02/1.23 (define @t12 () (not @t9)) % 1.02/1.23 (define @t13 () (and @t2 @t11)) % 1.02/1.23 (define @t14 () (not @t10)) % 1.02/1.23 (define @t15 () (@var "W2" $$unsorted)) % 1.02/1.23 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 1.02/1.23 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 1.02/1.23 (define @t18 () (@list @t15)) % 1.02/1.23 (define @t19 () (forall @t18 (=> @t17 @t16))) % 1.02/1.23 (define @t20 () (tptp.aSet0 @t5)) % 1.02/1.23 (define @t21 () (and @t20 @t19)) % 1.02/1.23 (define @t22 () (tptp.aSubsetOf0 @t5 @t1)) % 1.02/1.23 (define @t23 () (= @t22 @t21)) % 1.02/1.23 (define @t24 () (forall @t8 @t23)) % 1.02/1.23 (define @t25 () (=> @t2 @t24)) % 1.02/1.23 (define @t26 () (forall @t3 @t25)) % 1.02/1.23 (define @t27 () (tptp.isFinite0 @t5)) % 1.02/1.23 (define @t28 () (and @t2 @t9)) % 1.02/1.23 (define @t29 () (= @t1 @t5)) % 1.02/1.23 (define @t30 () (tptp.aSubsetOf0 @t1 @t5)) % 1.02/1.23 (define @t31 () (@list @t1 @t5)) % 1.02/1.23 (define @t32 () (tptp.aSubsetOf0 @t5 @t15)) % 1.02/1.23 (define @t33 () (tptp.aSet0 @t15)) % 1.02/1.23 (define @t34 () (@list @t1 @t5 @t15)) % 1.02/1.23 (define @t35 () (@var "W3" $$unsorted)) % 1.02/1.23 (define @t36 () (= @t35 @t5)) % 1.02/1.23 (define @t37 () (tptp.aElementOf0 @t35 @t1)) % 1.02/1.23 (define @t38 () (tptp.aElement0 @t35)) % 1.02/1.23 (define @t39 () (tptp.aElementOf0 @t35 @t15)) % 1.02/1.23 (define @t40 () (@list @t35)) % 1.02/1.23 (define @t41 () (tptp.sdtpldt0 @t1 @t5)) % 1.02/1.23 (define @t42 () (and @t2 @t6)) % 1.02/1.23 (define @t43 () (tptp.sdtmndt0 @t1 @t5)) % 1.02/1.23 (define @t44 () (tptp.sdtpldt0 @t5 @t1)) % 1.02/1.23 (define @t45 () (and @t20 (tptp.isCountable0 @t5))) % 1.02/1.23 (define @t46 () (tptp.sdtmndt0 @t5 @t1)) % 1.02/1.23 (define @t47 () (and @t20 @t27)) % 1.02/1.23 (define @t48 () (tptp.szszuzczcdt0 @t1)) % 1.02/1.23 (define @t49 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 1.02/1.23 (define @t50 () (tptp.szszuzczcdt0 @t5)) % 1.02/1.23 (define @t51 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 1.02/1.23 (define @t52 () (and @t49 @t51)) % 1.02/1.23 (define @t53 () (= @t1 tptp.sz00)) % 1.02/1.23 (define @t54 () (tptp.sdtlseqdt0 @t1 @t5)) % 1.02/1.23 (define @t55 () (tptp.sdtlseqdt0 @t5 @t15)) % 1.02/1.23 (define @t56 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 1.02/1.23 (define @t57 () (tptp.sbrdtbr0 @t1)) % 1.02/1.23 (define @t58 () (and @t2 @t51)) % 1.02/1.23 (define @t59 () (tptp.szmzizndt0 @t1)) % 1.02/1.23 (define @t60 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 1.02/1.23 (define @t61 () (tptp.szmzizndt0 @t5)) % 1.02/1.23 (define @t62 () (tptp.slbdtrb0 @t1)) % 1.02/1.23 (define @t63 () (tptp.slbdtrb0 @t5)) % 1.02/1.23 (define @t64 () (tptp.aSubsetOf0 @t35 @t1)) % 1.02/1.23 (define @t65 () (tptp.slbdtsldtrb0 @t1 @t5)) % 1.02/1.23 (define @t66 () (tptp.slbdtsldtrb0 @t5 @t1)) % 1.02/1.23 (define @t67 () (tptp.aFunction0 @t1)) % 1.02/1.23 (define @t68 () (tptp.szDzozmdt0 @t1)) % 1.02/1.23 (define @t69 () (tptp.aSet0 @t68)) % 1.02/1.23 (define @t70 () (forall @t3 (=> @t67 @t69))) % 1.02/1.23 (define @t71 () (tptp.sdtlpdtrp0 @t1 @t35)) % 1.02/1.23 (define @t72 () (tptp.aElementOf0 @t35 @t68)) % 1.02/1.23 (define @t73 () (and @t72 (= @t71 @t5))) % 1.02/1.23 (define @t74 () (= @t39 @t73)) % 1.02/1.23 (define @t75 () (forall @t40 @t74)) % 1.02/1.23 (define @t76 () (and @t33 @t75)) % 1.02/1.23 (define @t77 () (tptp.sdtlbdtrb0 @t1 @t5)) % 1.02/1.23 (define @t78 () (= @t15 @t77)) % 1.02/1.23 (define @t79 () (= @t78 @t76)) % 1.02/1.23 (define @t80 () (forall @t18 @t79)) % 1.02/1.23 (define @t81 () (and @t67 @t6)) % 1.02/1.23 (define @t82 () (=> @t81 @t80)) % 1.02/1.23 (define @t83 () (forall @t31 @t82)) % 1.02/1.23 (define @t84 () (tptp.aElement0 tptp.xy)) % 1.02/1.23 (define @t85 () (tptp.aFunction0 tptp.xF)) % 1.02/1.23 (define @t86 () (tptp.szDzozmdt0 tptp.xF)) % 1.02/1.23 (define @t87 () (tptp.sdtlbdtrb0 tptp.xF tptp.xy)) % 1.02/1.23 (define @t88 () (tptp.aSubsetOf0 @t87 @t86)) % 1.02/1.23 (define @t89 () (@var "BOUND_VARIABLE_8713" $$unsorted)) % 1.02/1.23 (define @t90 () (tptp.aElementOf0 @t35 @t89)) % 1.02/1.23 (define @t91 () (and @t72 (= @t5 @t71))) % 1.02/1.23 (define @t92 () (forall @t40 (= @t90 @t91))) % 1.02/1.23 (define @t93 () (tptp.aSet0 @t89)) % 1.02/1.23 (define @t94 () (and @t93 @t92)) % 1.02/1.23 (define @t95 () (= (= @t89 @t77) @t94)) % 1.02/1.23 (define @t96 () (not @t6)) % 1.02/1.23 (define @t97 () (not @t67)) % 1.02/1.23 (define @t98 () (or @t97 @t96 @t95)) % 1.02/1.23 (define @t99 () (@list @t1 @t5 @t89)) % 1.02/1.23 (define @t100 () (forall @t99 @t98)) % 1.02/1.23 (define @t101 () (@list @t89)) % 1.02/1.23 (define @t102 () (forall @t101 @t98)) % 1.02/1.23 (define @t103 () (forall @t101 @t95)) % 1.02/1.23 (define @t104 () (or @t97 @t96 @t103)) % 1.02/1.23 (define @t105 () (forall @t18 (= @t78 (and @t33 (forall @t40 (= @t39 @t91)))))) % 1.02/1.23 (define @t106 () (or @t97 @t96 @t105)) % 1.02/1.23 (define @t107 () (forall @t40 (= (and (tptp.aElementOf0 @t35 @t86) (= tptp.xy (tptp.sdtlpdtrp0 tptp.xF @t35))) (tptp.aElementOf0 @t35 @t87)))) % 1.02/1.23 (define @t108 () (tptp.aSet0 @t87)) % 1.02/1.23 (define @t109 () (and @t108 @t107)) % 1.02/1.23 (define @t110 () (= (= @t87 @t87) @t109)) % 1.02/1.23 (define @t111 () (not @t84)) % 1.02/1.23 (define @t112 () (not @t85)) % 1.02/1.23 (define @t113 () (or @t112 @t111 @t110)) % 1.02/1.23 (define @t114 () (forall @t99 (or @t97 @t96 (= (= @t77 @t89) (and @t93 (forall @t40 (= @t91 @t90))))))) % 1.02/1.23 (define @t115 () (or @t112 @t111 @t109)) % 1.02/1.23 (define @t116 () (@list false)) % 1.02/1.23 (define @t117 () (not @t109)) % 1.02/1.23 (define @t118 () (@list @t109)) % 1.02/1.23 (define @t119 () (@var "BOUND_VARIABLE_7929" $$unsorted)) % 1.02/1.23 (define @t120 () (= (tptp.aSubsetOf0 @t119 @t1) (and (tptp.aSet0 @t119) (forall @t18 (or (not (tptp.aElementOf0 @t15 @t119)) @t16))))) % 1.02/1.23 (define @t121 () (not @t2)) % 1.02/1.23 (define @t122 () (or @t121 @t120)) % 1.02/1.23 (define @t123 () (@list @t119)) % 1.02/1.23 (define @t124 () (forall @t123 @t122)) % 1.02/1.23 (define @t125 () (forall @t123 @t120)) % 1.02/1.23 (define @t126 () (or @t121 @t125)) % 1.02/1.23 (define @t127 () (forall @t8 (= @t22 (and @t20 (forall @t18 (or (not @t17) @t16)))))) % 1.02/1.23 (define @t128 () (tptp.aSet0 @t86)) % 1.02/1.23 (define @t129 () (or @t112 @t128)) % 1.02/1.23 (define @t130 () (@list false false)) % 1.02/1.23 (define @t131 () (forall @t18 (or (not (tptp.aElementOf0 @t15 @t87)) (tptp.aElementOf0 @t15 @t86)))) % 1.02/1.23 (define @t132 () (and @t108 @t131)) % 1.02/1.23 (define @t133 () (= @t88 @t132)) % 1.02/1.23 (define @t134 () (not @t128)) % 1.02/1.23 (define @t135 () (or @t134 @t133)) % 1.02/1.23 (define @t136 () (not @t132)) % 1.02/1.23 (define @t137 () (@list true false)) % 1.02/1.23 (define @t138 () (@quantifiers_skolemize @t131 0)) % 1.02/1.23 (define @t139 () (tptp.aElementOf0 @t138 @t87)) % 1.02/1.23 (define @t140 () (tptp.aElementOf0 @t138 @t86)) % 1.02/1.23 (define @t141 () (not @t139)) % 1.02/1.23 (define @t142 () (or @t141 @t140)) % 1.02/1.23 (define @t143 () (@list true)) % 1.02/1.23 (define @t144 () (@list @t142)) % 1.02/1.23 (define @t145 () (and @t140 (= tptp.xy (tptp.sdtlpdtrp0 tptp.xF @t138)))) % 1.02/1.23 (define @t146 () (not @t145)) % 1.02/1.23 (define @t147 () (= @t145 @t139)) % 1.02/1.23 (define @t148 () (= @t139 @t145)) % 1.02/1.23 (assume @p1 (forall @t3 (=> @t2 true))) % 1.02/1.23 (assume @p2 (forall @t3 (=> @t4 true))) % 1.02/1.23 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 1.02/1.23 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 1.02/1.23 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 1.02/1.23 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 1.02/1.23 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 1.02/1.23 (assume @p8 (forall @t3 (=> @t13 @t12))) % 1.02/1.23 (assume @p9 (forall @t3 (=> @t13 @t14))) % 1.02/1.23 (assume @p10 @t26) % 1.02/1.23 (assume @p11 (forall @t3 (=> @t28 (forall @t8 (=> @t22 @t27))))) % 1.02/1.23 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 1.02/1.23 (assume @p13 (forall @t31 (=> (and @t2 @t20) (=> (and @t30 @t22) @t29)))) % 1.02/1.23 (assume @p14 (forall @t34 (=> (and @t2 @t20 @t33) (=> (and @t30 @t32) (tptp.aSubsetOf0 @t1 @t15))))) % 1.02/1.23 (assume @p15 (forall @t31 (=> @t42 (forall @t18 (= (= @t15 @t41) (and @t33 (forall @t40 (= @t39 (and @t38 (or @t37 @t36)))))))))) % 1.02/1.23 (assume @p16 (forall @t31 (=> @t42 (forall @t18 (= (= @t15 @t43) (and @t33 (forall @t40 (= @t39 (and @t38 @t37 (not @t36)))))))))) % 1.02/1.23 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t43 @t5) @t1)))))) % 1.02/1.23 (assume @p18 (forall @t31 (=> (and @t4 @t20) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t44 @t1) @t5))))) % 1.02/1.23 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t45 (tptp.isCountable0 @t44)))))) % 1.02/1.23 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t45 (tptp.isCountable0 @t46)))))) % 1.02/1.23 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t47 (tptp.isFinite0 @t44)))))) % 1.02/1.23 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t47 (tptp.isFinite0 @t46)))))) % 1.02/1.23 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 1.02/1.23 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 1.02/1.23 (assume @p25 (forall @t3 (=> @t49 (and (tptp.aElementOf0 @t48 tptp.szNzAzT0) (not (= @t48 tptp.sz00)))))) % 1.02/1.23 (assume @p26 (forall @t31 (=> @t52 (=> (= @t48 @t50) @t29)))) % 1.02/1.23 (assume @p27 (forall @t3 (=> @t49 (or @t53 (exists @t8 (and @t51 (= @t1 @t50))))))) % 1.02/1.23 (assume @p28 (forall @t3 (=> @t49 (not (= @t1 @t48))))) % 1.02/1.23 (assume @p29 (forall @t31 (=> @t52 (=> @t54 true)))) % 1.02/1.23 (assume @p30 (forall @t3 (=> @t49 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 1.02/1.23 (assume @p31 (forall @t3 (=> @t49 (not (tptp.sdtlseqdt0 @t48 tptp.sz00))))) % 1.02/1.23 (assume @p32 (forall @t31 (=> @t52 (= @t54 (tptp.sdtlseqdt0 @t48 @t50))))) % 1.02/1.23 (assume @p33 (forall @t3 (=> @t49 (tptp.sdtlseqdt0 @t1 @t48)))) % 1.02/1.23 (assume @p34 (forall @t3 (=> @t49 (tptp.sdtlseqdt0 @t1 @t1)))) % 1.02/1.23 (assume @p35 (forall @t31 (=> @t52 (=> (and @t54 (tptp.sdtlseqdt0 @t5 @t1)) @t29)))) % 1.02/1.23 (assume @p36 (forall @t34 (=> (and @t49 @t51 @t56) (=> (and @t54 @t55) (tptp.sdtlseqdt0 @t1 @t15))))) % 1.02/1.23 (assume @p37 (forall @t31 (=> @t52 (or @t54 (tptp.sdtlseqdt0 @t50 @t1))))) % 1.02/1.23 (assume @p38 (forall @t31 (=> @t52 (=> (tptp.iLess0 @t1 @t5) true)))) % 1.02/1.23 (assume @p39 (forall @t3 (=> @t49 (tptp.iLess0 @t1 @t48)))) % 1.02/1.23 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t57)))) % 1.02/1.23 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t57 tptp.szNzAzT0) @t9)))) % 1.02/1.23 (assume @p42 (forall @t3 (=> @t2 (= (= @t57 tptp.sz00) @t10)))) % 1.02/1.23 (assume @p43 (forall @t3 (=> @t28 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t41) (tptp.szszuzczcdt0 @t57)))))))) % 1.02/1.23 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t43)) @t57)))))) % 1.02/1.23 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t22) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t57)))))) % 1.02/1.23 (assume @p46 (forall @t31 (=> @t58 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t57)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 1.02/1.23 (assume @p47 (forall @t3 (=> (and @t60 @t14) (forall @t8 (= (= @t5 @t59) (and @t7 (forall @t18 (=> @t16 @t55)))))))) % 1.02/1.23 (assume @p48 (forall @t3 (=> (and @t60 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 1.02/1.23 (assume @p49 (forall @t31 (=> (and @t60 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t59 @t5) (tptp.aElementOf0 @t61 @t1)) (= @t59 @t61))))) % 1.02/1.23 (assume @p50 (forall @t3 (=> @t49 (forall @t8 (= (= @t5 @t62) (and @t20 (forall @t18 (= @t17 (and @t56 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 1.02/1.23 (assume @p51 (forall @t3 (=> @t49 (tptp.isFinite0 @t62)))) % 1.02/1.23 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 1.02/1.23 (assume @p53 (forall @t31 (=> @t52 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t50)) (or (tptp.aElementOf0 @t1 @t63) @t29))))) % 1.02/1.23 (assume @p54 (forall @t31 (=> @t52 (= @t54 (tptp.aSubsetOf0 @t62 @t63))))) % 1.02/1.23 (assume @p55 (forall @t3 (=> (and @t60 @t9) (exists @t8 (and @t51 (tptp.aSubsetOf0 @t1 @t63)))))) % 1.02/1.23 (assume @p56 (forall @t3 (=> @t49 (= (tptp.sbrdtbr0 @t62) @t1)))) % 1.02/1.23 (assume @p57 (forall @t31 (=> @t58 (forall @t18 (= (= @t15 @t65) (and @t33 (forall @t40 (= @t39 (and @t64 (= (tptp.sbrdtbr0 @t35) @t5)))))))))) % 1.02/1.23 (assume @p58 (forall @t3 (=> @t28 (forall @t8 (=> @t51 (tptp.isFinite0 @t65)))))) % 1.02/1.23 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t51 (not (= @t65 tptp.slcrc0))))))) % 1.02/1.23 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t51 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t65)))))) % 1.02/1.23 (assume @p61 (forall @t3 (=> @t49 (forall (@list @t5 @t15) (=> (and @t20 @t33 (not @t53)) (=> (and (tptp.aSubsetOf0 @t66 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t66 tptp.slcrc0))) @t32)))))) % 1.02/1.23 (assume @p62 (forall @t31 (=> @t58 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t65) (tptp.isFinite0 @t15)) (exists @t40 (and @t64 (tptp.isFinite0 @t35) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t35 @t5))))))))) % 1.02/1.23 (assume @p63 (forall @t3 (=> @t67 true))) % 1.02/1.23 (assume @p64 @t70) % 1.02/1.23 (assume @p65 (forall @t3 (=> @t67 (forall @t8 (=> (tptp.aElementOf0 @t5 @t68) (tptp.aElement0 (tptp.sdtlpdtrp0 @t1 @t5))))))) % 1.02/1.23 (assume @p66 @t83) % 1.02/1.23 (assume @p67 (and @t85 @t84)) % 1.02/1.23 (assume @p68 (not @t88)) % 1.02/1.23 (assume @p69 true) % 1.02/1.23 (step @p70 :rule eq-symm :args (@t90 @t91)) % 1.02/1.23 (step @p71 :rule cong :premises (@p70) :args (@t92)) % 1.02/1.23 (step @p72 :rule refl :args (@t93)) % 1.02/1.23 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t94)) % 1.02/1.23 (step @p74 :rule eq-symm :args (@t89 @t77)) % 1.02/1.23 (step @p75 :rule cong :premises (@p74 @p73) :args (@t95)) % 1.02/1.23 (step @p76 :rule refl :args (@t96)) % 1.02/1.23 (step @p77 :rule refl :args (@t97)) % 1.02/1.23 (step @p78 :rule nary_cong :premises (@p77 @p76 @p75) :args (@t98)) % 1.02/1.23 (step @p79 :rule cong :premises (@p78) :args (@t100)) % 1.02/1.23 (step @p80 :rule quant-merge-prenex :args ((= (forall @t31 @t102) @t100))) % 1.02/1.23 (step @p81 :rule alpha_equiv :args (@t103 (@list @t89) (@list @t15))) % 1.02/1.23 (step @p82 :rule refl :args (@t96)) % 1.02/1.23 (step @p83 :rule refl :args (@t97)) % 1.02/1.23 (step @p84 :rule nary_cong :premises (@p83 @p82 @p81) :args (@t104)) % 1.02/1.23 (step @p85 :rule quant-miniscope-or :args ((= @t102 @t104))) % 1.02/1.23 (step @p86 :rule trans :premises (@p85 @p84)) % 1.02/1.23 (step @p87 :rule symm :premises (@p86)) % 1.02/1.23 (step @p88 :rule cong :premises (@p87) :args ((forall @t31 @t106))) % 1.02/1.23 (step @p89 :rule trans :premises (@p88 @p80)) % 1.02/1.23 (step @p90 :rule trans :premises (@p89 @p79)) % 1.02/1.23 (step @p91 :rule aci_norm :args ((= (or (or @t97 @t96) @t105) @t106))) % 1.02/1.23 (step @p92 :rule refl :args (@t105)) % 1.02/1.23 (step @p93 :rule bool-and-de-morgan :args (@t67 @t6 true)) % 1.02/1.23 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or (not @t81) @t105))) % 1.02/1.23 (step @p95 :rule trans :premises (@p94 @p91)) % 1.02/1.23 (step @p96 :rule bool-impl-elim :args (@t81 @t105)) % 1.02/1.23 (step @p97 :rule trans :premises (@p96 @p95)) % 1.02/1.23 (step @p98 :rule cong :premises (@p97) :args ((forall @t31 (=> @t81 @t105)))) % 1.02/1.23 (step @p99 :rule trans :premises (@p98 @p90)) % 1.02/1.23 (step @p100 :rule eq-symm :args (@t71 @t5)) % 1.02/1.23 (step @p101 :rule refl :args (@t72)) % 1.02/1.23 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t73)) % 1.02/1.23 (step @p103 :rule refl :args (@t39)) % 1.02/1.23 (step @p104 :rule cong :premises (@p103 @p102) :args (@t74)) % 1.02/1.23 (step @p105 :rule cong :premises (@p104) :args (@t75)) % 1.02/1.23 (step @p106 :rule refl :args (@t33)) % 1.02/1.23 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t76)) % 1.02/1.23 (step @p108 :rule refl :args (@t78)) % 1.02/1.23 (step @p109 :rule cong :premises (@p108 @p107) :args (@t79)) % 1.02/1.23 (step @p110 :rule cong :premises (@p109) :args (@t80)) % 1.02/1.23 (step @p111 :rule refl :args (@t81)) % 1.02/1.23 (step @p112 :rule cong :premises (@p111 @p110) :args (@t82)) % 1.02/1.23 (step @p113 :rule cong :premises (@p112) :args (@t83)) % 1.02/1.23 (step @p114 :rule trans :premises (@p113 @p99)) % 1.02/1.23 (step @p115 :rule eq_resolve :premises (@p66 @p114)) % 1.02/1.23 (step @p116 :rule bool-eq-true :args (@t109)) % 1.02/1.23 (step @p117 :rule eq-symm :args (true @t109)) % 1.02/1.23 (step @p118 :rule trans :premises (@p117 @p116)) % 1.02/1.23 (step @p119 :rule refl :args (@t109)) % 1.02/1.23 (step @p120 :rule eq-refl :args (@t87)) % 1.02/1.23 (step @p121 :rule cong :premises (@p120 @p119) :args (@t110)) % 1.02/1.23 (step @p122 :rule trans :premises (@p121 @p118)) % 1.02/1.23 (step @p123 :rule refl :args (@t111)) % 1.02/1.23 (step @p124 :rule refl :args (@t112)) % 1.02/1.23 (step @p125 :rule nary_cong :premises (@p124 @p123 @p122) :args (@t113)) % 1.02/1.23 (step @p126 :rule refl :args (@t114)) % 1.02/1.23 (step @p127 :rule cong :premises (@p126 @p125) :args ((=> @t114 @t113))) % 1.02/1.23 (assume-push @p212 @t114) % 1.02/1.23 (step @p129 :rule instantiate :premises (@p115) :args ((@list tptp.xF tptp.xy @t87))) % 1.02/1.23 (step-pop @p213 :rule scope :premises (@p129)) % 1.02/1.23 (step @p130 :rule process_scope :premises (@p213) :args (@t113)) % 1.02/1.23 (step @p132 :rule eq_resolve :premises (@p130 @p127)) % 1.02/1.23 (step @p133 :rule implies_elim :premises (@p132)) % 1.02/1.23 (step @p134 :rule chain_m_resolution :premises (@p133 @p115) :args (@t115 @t116 (@list @t114))) % 1.02/1.23 (step @p135 :rule and_elim :premises (@p67) :args (1)) % 1.02/1.23 (step @p136 :rule and_elim :premises (@p67) :args (0)) % 1.02/1.23 (step @p137 :rule cnf_or_pos :args (@t115)) % 1.02/1.23 (step @p138 :rule reordering :premises (@p137) :args ((or @t112 @t111 @t109 (not @t115)))) % 1.02/1.23 (step @p139 :rule chain_m_resolution :premises (@p138 @p136 @p135 @p134) :args (@t109 (@list false false false) (@list @t85 @t84 @t115))) % 1.02/1.23 (step @p140 :rule cnf_and_pos :args (@t109 0)) % 1.02/1.23 (step @p141 :rule reordering :premises (@p140) :args ((or @t108 @t117))) % 1.02/1.23 (step @p142 :rule chain_m_resolution :premises (@p141 @p139) :args (@t108 @t116 @t118)) % 1.02/1.23 (step @p143 :rule quant-merge-prenex :args ((= (forall @t3 @t124) (forall (@list @t1 @t119) @t122)))) % 1.02/1.23 (step @p144 :rule alpha_equiv :args (@t125 (@list @t119) (@list @t5))) % 1.02/1.23 (step @p145 :rule refl :args (@t121)) % 1.02/1.23 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t126)) % 1.02/1.23 (step @p147 :rule quant-miniscope-or :args ((= @t124 @t126))) % 1.02/1.23 (step @p148 :rule trans :premises (@p147 @p146)) % 1.02/1.23 (step @p149 :rule symm :premises (@p148)) % 1.02/1.23 (step @p150 :rule cong :premises (@p149) :args ((forall @t3 (or @t121 @t127)))) % 1.02/1.23 (step @p151 :rule trans :premises (@p150 @p143)) % 1.02/1.23 (step @p152 :rule bool-impl-elim :args (@t2 @t127)) % 1.02/1.23 (step @p153 :rule cong :premises (@p152) :args ((forall @t3 (=> @t2 @t127)))) % 1.02/1.23 (step @p154 :rule trans :premises (@p153 @p151)) % 1.02/1.23 (step @p155 :rule bool-impl-elim :args (@t17 @t16)) % 1.02/1.23 (step @p156 :rule cong :premises (@p155) :args (@t19)) % 1.02/1.23 (step @p157 :rule refl :args (@t20)) % 1.02/1.23 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t21)) % 1.02/1.23 (step @p159 :rule refl :args (@t22)) % 1.02/1.23 (step @p160 :rule cong :premises (@p159 @p158) :args (@t23)) % 1.02/1.23 (step @p161 :rule cong :premises (@p160) :args (@t24)) % 1.02/1.23 (step @p162 :rule refl :args (@t2)) % 1.02/1.23 (step @p163 :rule cong :premises (@p162 @p161) :args (@t25)) % 1.02/1.23 (step @p164 :rule cong :premises (@p163) :args (@t26)) % 1.02/1.23 (step @p165 :rule trans :premises (@p164 @p154)) % 1.02/1.23 (step @p166 :rule eq_resolve :premises (@p10 @p165)) % 1.02/1.23 (step @p167 :rule instantiate :premises (@p166) :args ((@list @t86 @t87))) % 1.02/1.23 (step @p168 :rule bool-impl-elim :args (@t67 @t69)) % 1.02/1.23 (step @p169 :rule cong :premises (@p168) :args (@t70)) % 1.02/1.23 (step @p170 :rule eq_resolve :premises (@p64 @p169)) % 1.02/1.23 (step @p171 :rule instantiate :premises (@p170) :args ((@list tptp.xF))) % 1.02/1.23 (step @p172 :rule cnf_or_pos :args (@t129)) % 1.02/1.23 (step @p173 :rule reordering :premises (@p172) :args ((or @t112 @t128 (not @t129)))) % 1.02/1.23 (step @p174 :rule chain_m_resolution :premises (@p173 @p136 @p171) :args (@t128 @t130 (@list @t85 @t129))) % 1.02/1.23 (step @p175 :rule cnf_or_pos :args (@t135)) % 1.02/1.23 (step @p176 :rule reordering :premises (@p175) :args ((or @t134 @t133 (not @t135)))) % 1.02/1.23 (step @p177 :rule chain_m_resolution :premises (@p176 @p174 @p167) :args (@t133 @t130 (@list @t128 @t135))) % 1.02/1.23 (step @p178 :rule cnf_equiv_pos2 :args (@t133)) % 1.02/1.23 (step @p179 :rule reordering :premises (@p178) :args ((or @t88 @t136 (not @t133)))) % 1.02/1.23 (step @p180 :rule chain_m_resolution :premises (@p179 @p68 @p177) :args (@t136 @t137 (@list @t88 @t133))) % 1.02/1.23 (step @p181 :rule cnf_and_neg :args (@t132)) % 1.02/1.23 (step @p182 :rule chain_m_resolution :premises (@p181 @p180 @p142) :args ((not @t131) @t137 (@list @t132 @t108))) % 1.02/1.23 (step @p183 :rule skolemize :premises (@p182)) % 1.02/1.23 (step @p184 :rule bool-double-not-elim :args (@t139)) % 1.02/1.23 (step @p185 :rule refl :args (@t142)) % 1.02/1.23 (step @p186 :rule nary_cong :premises (@p185 @p184) :args ((or @t142 (not @t141)))) % 1.02/1.23 (step @p187 :rule cnf_or_neg :args (@t142 0)) % 1.02/1.23 (step @p188 :rule eq_resolve :premises (@p187 @p186)) % 1.02/1.23 (step @p189 :rule reordering :premises (@p188) :args ((or @t139 @t142))) % 1.02/1.23 (step @p190 :rule chain_m_resolution :premises (@p189 @p183) :args (@t139 @t143 @t144)) % 1.02/1.23 (step @p191 :rule cnf_or_neg :args (@t142 1)) % 1.02/1.23 (step @p192 :rule chain_m_resolution :premises (@p191 @p183) :args ((not @t140) @t143 @t144)) % 1.02/1.23 (step @p193 :rule cnf_and_pos :args (@t145 0)) % 1.02/1.23 (step @p194 :rule reordering :premises (@p193) :args ((or @t140 @t146))) % 1.02/1.23 (step @p195 :rule chain_m_resolution :premises (@p194 @p192) :args (@t146 @t143 (@list @t140))) % 1.02/1.23 (step @p196 :rule cnf_and_pos :args (@t109 1)) % 1.02/1.23 (step @p197 :rule reordering :premises (@p196) :args ((or @t107 @t117))) % 1.02/1.23 (step @p198 :rule chain_m_resolution :premises (@p197 @p139) :args (@t107 @t116 @t118)) % 1.02/1.23 (step @p199 :rule eq-symm :args (@t145 @t139)) % 1.02/1.23 (step @p200 :rule refl :args (@t107)) % 1.02/1.23 (step @p201 :rule cong :premises (@p200 @p199) :args ((=> @t107 @t147))) % 1.02/1.23 (assume-push @p214 @t107) % 1.02/1.23 (step @p203 :rule instantiate :premises (@p198) :args ((@list @t138))) % 1.02/1.23 (step-pop @p215 :rule scope :premises (@p203)) % 1.02/1.23 (step @p204 :rule process_scope :premises (@p215) :args (@t147)) % 1.02/1.23 (step @p206 :rule eq_resolve :premises (@p204 @p201)) % 1.02/1.23 (step @p207 :rule implies_elim :premises (@p206)) % 1.02/1.23 (step @p208 :rule chain_m_resolution :premises (@p207 @p198) :args (@t148 @t116 (@list @t107))) % 1.02/1.23 (step @p209 :rule cnf_equiv_pos1 :args (@t148)) % 1.02/1.23 (step @p210 :rule reordering :premises (@p209) :args ((or @t141 @t145 (not @t148)))) % 1.02/1.23 (step @p211 false :rule chain_m_resolution :premises (@p210 @p208 @p195 @p190) :args (false (@list false true false) (@list @t148 @t145 @t139))) % 1.02/1.23 ) % 1.02/1.23 % SZS output end Proof % 1.02/1.23 % cvc5 exiting %------------------------------------------------------------------------------