%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM552+3 : 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 : n013.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 08:39:49 AM UTC 2026 % Result : Theorem 0.36s 0.67s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM552+3 : 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 : n013.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 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 11:29:00 EDT 2026 % 0.17/0.35 % CPUTime : % 0.26/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.67 % SZS status Theorem % 0.36/0.67 % SZS output start Proof % 0.36/0.67 ( % 0.36/0.67 (declare-sort $$unsorted 0) % 0.36/0.67 (declare-const tptp.xQ $$unsorted) % 0.36/0.67 (declare-const tptp.xx $$unsorted) % 0.36/0.67 (declare-const tptp.xT $$unsorted) % 0.36/0.67 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.xS $$unsorted) % 0.36/0.67 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.xy $$unsorted) % 0.36/0.67 (declare-const tptp.slcrc0 $$unsorted) % 0.36/0.67 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.xk $$unsorted) % 0.36/0.67 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.szNzAzT0 $$unsorted) % 0.36/0.67 (declare-const tptp.sz00 $$unsorted) % 0.36/0.67 (define @t1 () (@var "W0" $$unsorted)) % 0.36/0.67 (define @t2 () (tptp.aSet0 @t1)) % 0.36/0.67 (define @t3 () (@list @t1)) % 0.36/0.67 (define @t4 () (tptp.aElement0 @t1)) % 0.36/0.67 (define @t5 () (@var "W1" $$unsorted)) % 0.36/0.67 (define @t6 () (tptp.aElement0 @t5)) % 0.36/0.67 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.36/0.67 (define @t8 () (@list @t5)) % 0.36/0.67 (define @t9 () (tptp.isFinite0 @t1)) % 0.36/0.67 (define @t10 () (= @t1 tptp.slcrc0)) % 0.36/0.67 (define @t11 () (tptp.isCountable0 @t1)) % 0.36/0.67 (define @t12 () (not @t9)) % 0.36/0.67 (define @t13 () (and @t2 @t11)) % 0.36/0.67 (define @t14 () (not @t10)) % 0.36/0.67 (define @t15 () (@var "W2" $$unsorted)) % 0.36/0.67 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.36/0.67 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.36/0.67 (define @t18 () (@list @t15)) % 0.36/0.67 (define @t19 () (tptp.aSet0 @t5)) % 0.36/0.67 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.36/0.67 (define @t21 () (tptp.isFinite0 @t5)) % 0.36/0.67 (define @t22 () (and @t2 @t9)) % 0.36/0.67 (define @t23 () (= @t1 @t5)) % 0.36/0.67 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.36/0.67 (define @t25 () (@list @t1 @t5)) % 0.36/0.67 (define @t26 () (tptp.aSet0 @t15)) % 0.36/0.67 (define @t27 () (@list @t1 @t5 @t15)) % 0.36/0.67 (define @t28 () (@var "W3" $$unsorted)) % 0.36/0.67 (define @t29 () (= @t28 @t5)) % 0.36/0.67 (define @t30 () (tptp.aElementOf0 @t28 @t1)) % 0.36/0.67 (define @t31 () (tptp.aElement0 @t28)) % 0.36/0.67 (define @t32 () (tptp.aElementOf0 @t28 @t15)) % 0.36/0.67 (define @t33 () (@list @t28)) % 0.36/0.67 (define @t34 () (tptp.sdtpldt0 @t1 @t5)) % 0.36/0.67 (define @t35 () (and @t2 @t6)) % 0.36/0.67 (define @t36 () (tptp.sdtmndt0 @t1 @t5)) % 0.36/0.67 (define @t37 () (tptp.sdtpldt0 @t5 @t1)) % 0.36/0.67 (define @t38 () (and @t19 (tptp.isCountable0 @t5))) % 0.36/0.67 (define @t39 () (tptp.sdtmndt0 @t5 @t1)) % 0.36/0.67 (define @t40 () (and @t19 @t21)) % 0.36/0.67 (define @t41 () (tptp.szszuzczcdt0 @t1)) % 0.36/0.67 (define @t42 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.36/0.67 (define @t43 () (tptp.szszuzczcdt0 @t5)) % 0.36/0.67 (define @t44 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.36/0.67 (define @t45 () (and @t42 @t44)) % 0.36/0.67 (define @t46 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.36/0.67 (define @t47 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.36/0.67 (define @t48 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.36/0.67 (define @t49 () (tptp.sbrdtbr0 @t1)) % 0.36/0.67 (define @t50 () (not @t7)) % 0.36/0.67 (define @t51 () (and @t2 @t44)) % 0.36/0.67 (define @t52 () (tptp.szmzizndt0 @t1)) % 0.36/0.67 (define @t53 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.36/0.67 (define @t54 () (tptp.szmzizndt0 @t5)) % 0.36/0.67 (define @t55 () (tptp.slbdtrb0 @t1)) % 0.36/0.67 (define @t56 () (tptp.slbdtrb0 @t5)) % 0.36/0.67 (define @t57 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.36/0.67 (define @t58 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 0.36/0.67 (define @t59 () (tptp.aElementOf0 @t1 @t58)) % 0.36/0.67 (define @t60 () (= @t49 tptp.xk)) % 0.36/0.67 (define @t61 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.36/0.67 (define @t62 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xS)))) % 0.36/0.67 (define @t63 () (forall @t3 (and (=> @t59 (and @t2 @t62 @t61 @t60)) (=> (and (or (and @t2 @t62) @t61) @t60) @t59)))) % 0.36/0.67 (define @t64 () (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) % 0.36/0.67 (define @t65 () (tptp.aElementOf0 @t1 @t64)) % 0.36/0.67 (define @t66 () (forall @t3 (=> @t59 @t65))) % 0.36/0.67 (define @t67 () (tptp.aSubsetOf0 @t1 tptp.xT)) % 0.36/0.67 (define @t68 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.36/0.67 (define @t69 () (forall @t8 (=> @t7 @t68))) % 0.36/0.67 (define @t70 () (and @t2 @t69)) % 0.36/0.67 (define @t71 () (or @t70 @t67)) % 0.36/0.67 (define @t72 () (and @t71 @t60)) % 0.36/0.67 (define @t73 () (=> @t72 @t65)) % 0.36/0.67 (define @t74 () (and @t2 @t69 @t67 @t60)) % 0.36/0.67 (define @t75 () (=> @t65 @t74)) % 0.36/0.67 (define @t76 () (and @t75 @t73)) % 0.36/0.67 (define @t77 () (forall @t3 @t76)) % 0.36/0.67 (define @t78 () (tptp.aElementOf0 tptp.xQ @t58)) % 0.36/0.67 (define @t79 () (tptp.sbrdtbr0 tptp.xQ)) % 0.36/0.67 (define @t80 () (= @t79 tptp.xk)) % 0.36/0.67 (define @t81 () (tptp.aSet0 tptp.xQ)) % 0.36/0.67 (define @t82 () (tptp.aElementOf0 tptp.xx tptp.xT)) % 0.36/0.67 (define @t83 () (tptp.aElementOf0 tptp.xx tptp.xQ)) % 0.36/0.67 (define @t84 () (@var "BOUND_VARIABLE_8728" $$unsorted)) % 0.36/0.67 (define @t85 () (tptp.aElementOf0 @t84 @t64)) % 0.36/0.67 (define @t86 () (tptp.sbrdtbr0 @t84)) % 0.36/0.67 (define @t87 () (not (= @t86 tptp.xk))) % 0.36/0.67 (define @t88 () (and (or (not (tptp.aSet0 @t84)) (not (forall @t8 (or (not (tptp.aElementOf0 @t5 @t84)) @t68)))) (not (tptp.aSubsetOf0 @t84 tptp.xT)))) % 0.36/0.67 (define @t89 () (or @t88 @t87 @t85)) % 0.36/0.67 (define @t90 () (forall (@list @t84) @t89)) % 0.36/0.67 (define @t91 () (@var "BOUND_VARIABLE_8712" $$unsorted)) % 0.36/0.67 (define @t92 () (tptp.sbrdtbr0 @t91)) % 0.36/0.67 (define @t93 () (= tptp.xk @t92)) % 0.36/0.67 (define @t94 () (tptp.aSubsetOf0 @t91 tptp.xT)) % 0.36/0.67 (define @t95 () (@var "BOUND_VARIABLE_8753" $$unsorted)) % 0.36/0.67 (define @t96 () (or (not (tptp.aElementOf0 @t95 @t91)) (tptp.aElementOf0 @t95 tptp.xT))) % 0.36/0.67 (define @t97 () (tptp.aSet0 @t91)) % 0.36/0.67 (define @t98 () (and @t97 @t96 @t94 @t93)) % 0.36/0.67 (define @t99 () (not (tptp.aElementOf0 @t91 @t64))) % 0.36/0.67 (define @t100 () (or @t99 @t98)) % 0.36/0.67 (define @t101 () (@list @t95)) % 0.36/0.67 (define @t102 () (forall @t101 @t100)) % 0.36/0.67 (define @t103 () (@list @t91)) % 0.36/0.67 (define @t104 () (forall @t101 @t93)) % 0.36/0.67 (define @t105 () (forall @t101 @t94)) % 0.36/0.67 (define @t106 () (forall @t101 @t96)) % 0.36/0.67 (define @t107 () (forall @t101 @t97)) % 0.36/0.67 (define @t108 () (and @t107 @t106 @t105 @t104)) % 0.36/0.67 (define @t109 () (forall @t101 @t98)) % 0.36/0.67 (define @t110 () (or @t99 @t109)) % 0.36/0.67 (define @t111 () (forall @t8 (or (not (tptp.aElementOf0 @t5 @t91)) @t68))) % 0.36/0.67 (define @t112 () (and @t97 @t111 @t94 (= @t92 tptp.xk))) % 0.36/0.67 (define @t113 () (or @t99 @t112)) % 0.36/0.67 (define @t114 () (forall @t103 @t113)) % 0.36/0.67 (define @t115 () (not @t60)) % 0.36/0.67 (define @t116 () (not @t67)) % 0.36/0.67 (define @t117 () (forall @t8 (or @t50 @t68))) % 0.36/0.67 (define @t118 () (and (or (not @t2) (not @t117)) @t116)) % 0.36/0.67 (define @t119 () (or @t118 @t115 @t65)) % 0.36/0.67 (define @t120 () (forall @t3 @t119)) % 0.36/0.67 (define @t121 () (@list @t1)) % 0.36/0.67 (define @t122 () (and @t2 @t117 @t67 @t60)) % 0.36/0.67 (define @t123 () (or (not @t65) @t122)) % 0.36/0.67 (define @t124 () (forall @t3 @t123)) % 0.36/0.67 (define @t125 () (and @t124 @t120)) % 0.36/0.67 (define @t126 () (and @t2 @t117)) % 0.36/0.67 (define @t127 () (or @t126 @t67)) % 0.36/0.67 (define @t128 () (and @t127 @t60)) % 0.36/0.67 (define @t129 () (and (=> @t65 @t122) (=> @t128 @t65))) % 0.36/0.67 (define @t130 () (not @t83)) % 0.36/0.67 (define @t131 () (or @t130 @t82)) % 0.36/0.67 (define @t132 () (not @t131)) % 0.36/0.67 (define @t133 () (and @t81 @t131 (tptp.aSubsetOf0 tptp.xQ tptp.xT) (= tptp.xk @t79))) % 0.36/0.67 (define @t134 () (not @t133)) % 0.36/0.67 (define @t135 () (tptp.aElementOf0 tptp.xQ @t64)) % 0.36/0.67 (define @t136 () (not @t78)) % 0.36/0.67 (define @t137 () (or @t136 @t135)) % 0.36/0.67 (define @t138 () (not @t135)) % 0.36/0.67 (define @t139 () (or @t138 @t133)) % 0.36/0.67 (assume @p1 (forall @t3 (=> @t2 true))) % 0.36/0.67 (assume @p2 (forall @t3 (=> @t4 true))) % 0.36/0.67 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.36/0.67 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.36/0.67 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.36/0.67 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.36/0.67 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.36/0.67 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.36/0.67 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.36/0.67 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.36/0.67 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.36/0.67 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.36/0.67 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.36/0.67 (assume @p14 (forall @t27 (=> (and @t2 @t19 @t26) (=> (and @t24 (tptp.aSubsetOf0 @t5 @t15)) (tptp.aSubsetOf0 @t1 @t15))))) % 0.36/0.67 (assume @p15 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t34) (and @t26 (forall @t33 (= @t32 (and @t31 (or @t30 @t29)))))))))) % 0.36/0.67 (assume @p16 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t36) (and @t26 (forall @t33 (= @t32 (and @t31 @t30 (not @t29)))))))))) % 0.36/0.67 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t36 @t5) @t1)))))) % 0.36/0.67 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t37 @t1) @t5))))) % 0.36/0.67 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t37)))))) % 0.36/0.67 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t39)))))) % 0.36/0.67 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t37)))))) % 0.36/0.67 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t39)))))) % 0.36/0.67 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.36/0.67 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.36/0.67 (assume @p25 (forall @t3 (=> @t42 (and (tptp.aElementOf0 @t41 tptp.szNzAzT0) (not (= @t41 tptp.sz00)))))) % 0.36/0.67 (assume @p26 (forall @t25 (=> @t45 (=> (= @t41 @t43) @t23)))) % 0.36/0.67 (assume @p27 (forall @t3 (=> @t42 (or (= @t1 tptp.sz00) (exists @t8 (and @t44 (= @t1 @t43))))))) % 0.36/0.67 (assume @p28 (forall @t3 (=> @t42 (not (= @t1 @t41))))) % 0.36/0.67 (assume @p29 (forall @t25 (=> @t45 (=> @t46 true)))) % 0.36/0.67 (assume @p30 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.36/0.67 (assume @p31 (forall @t3 (=> @t42 (not (tptp.sdtlseqdt0 @t41 tptp.sz00))))) % 0.36/0.67 (assume @p32 (forall @t25 (=> @t45 (= @t46 (tptp.sdtlseqdt0 @t41 @t43))))) % 0.36/0.67 (assume @p33 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t41)))) % 0.36/0.67 (assume @p34 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.36/0.67 (assume @p35 (forall @t25 (=> @t45 (=> (and @t46 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 0.36/0.67 (assume @p36 (forall @t27 (=> (and @t42 @t44 @t48) (=> (and @t46 @t47) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.36/0.67 (assume @p37 (forall @t25 (=> @t45 (or @t46 (tptp.sdtlseqdt0 @t43 @t1))))) % 0.36/0.67 (assume @p38 (forall @t25 (=> @t45 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.36/0.67 (assume @p39 (forall @t3 (=> @t42 (tptp.iLess0 @t1 @t41)))) % 0.36/0.67 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t49)))) % 0.36/0.67 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t49 tptp.szNzAzT0) @t9)))) % 0.36/0.67 (assume @p42 (forall @t3 (=> @t2 (= (= @t49 tptp.sz00) @t10)))) % 0.36/0.67 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> @t50 (= (tptp.sbrdtbr0 @t34) (tptp.szszuzczcdt0 @t49)))))))) % 0.36/0.67 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t36)) @t49)))))) % 0.36/0.67 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t49)))))) % 0.36/0.67 (assume @p46 (forall @t25 (=> @t51 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t49)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.36/0.67 (assume @p47 (forall @t3 (=> (and @t53 @t14) (forall @t8 (= (= @t5 @t52) (and @t7 (forall @t18 (=> @t16 @t47)))))))) % 0.36/0.67 (assume @p48 (forall @t3 (=> (and @t53 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.36/0.67 (assume @p49 (forall @t25 (=> (and @t53 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t52 @t5) (tptp.aElementOf0 @t54 @t1)) (= @t52 @t54))))) % 0.36/0.67 (assume @p50 (forall @t3 (=> @t42 (forall @t8 (= (= @t5 @t55) (and @t19 (forall @t18 (= @t17 (and @t48 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.36/0.67 (assume @p51 (forall @t3 (=> @t42 (tptp.isFinite0 @t55)))) % 0.36/0.67 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.36/0.67 (assume @p53 (forall @t25 (=> @t45 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t43)) (or (tptp.aElementOf0 @t1 @t56) @t23))))) % 0.36/0.67 (assume @p54 (forall @t25 (=> @t45 (= @t46 (tptp.aSubsetOf0 @t55 @t56))))) % 0.36/0.67 (assume @p55 (forall @t3 (=> (and @t53 @t9) (exists @t8 (and @t44 (tptp.aSubsetOf0 @t1 @t56)))))) % 0.36/0.67 (assume @p56 (forall @t3 (=> @t42 (= (tptp.sbrdtbr0 @t55) @t1)))) % 0.36/0.67 (assume @p57 (forall @t25 (=> @t51 (forall @t18 (= (= @t15 @t57) (and @t26 (forall @t33 (= @t32 (and (tptp.aSubsetOf0 @t28 @t1) (= (tptp.sbrdtbr0 @t28) @t5)))))))))) % 0.36/0.67 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t44 (tptp.isFinite0 @t57)))))) % 0.36/0.67 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t44 (not (= @t57 tptp.slcrc0))))))) % 0.36/0.67 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t44 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t57)))))) % 0.36/0.67 (assume @p61 (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 0.36/0.67 (assume @p62 (and (tptp.aSet0 tptp.xS) (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00)))) % 0.36/0.67 (assume @p63 (and (tptp.aSet0 @t58) @t63 (tptp.aSet0 @t64) @t77 @t66 (tptp.aSubsetOf0 @t58 @t64) (not (=> @t63 (or (not (exists @t3 @t59)) (= @t58 tptp.slcrc0)))))) % 0.36/0.67 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 0.36/0.67 (assume @p65 (and @t81 (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xQ) (tptp.aElementOf0 @t1 tptp.xS))) (tptp.aSubsetOf0 tptp.xQ tptp.xS) @t80 @t78)) % 0.36/0.67 (assume @p66 (and @t81 (tptp.isFinite0 tptp.xQ) @t80)) % 0.36/0.67 (assume @p67 (and (tptp.aElement0 tptp.xy) (tptp.aElementOf0 tptp.xy tptp.xQ))) % 0.36/0.67 (assume @p68 (not (=> @t83 @t82))) % 0.36/0.67 (assume @p69 true) % 0.36/0.67 (step @p70 :rule refl :args (@t85)) % 0.36/0.67 (step @p71 :rule eq-symm :args (@t86 tptp.xk)) % 0.36/0.67 (step @p72 :rule cong :premises (@p71) :args (@t87)) % 0.36/0.67 (step @p73 :rule refl :args (@t88)) % 0.36/0.67 (step @p74 :rule nary_cong :premises (@p73 @p72 @p70) :args (@t89)) % 0.36/0.67 (step @p75 :rule cong :premises (@p74) :args (@t90)) % 0.36/0.67 (step @p76 :rule quant-merge-prenex :args ((= (forall @t103 @t102) (forall (@list @t91 @t95) @t100)))) % 0.36/0.67 (step @p77 :rule quant-unused-vars :args ((= @t104 @t93))) % 0.36/0.67 (step @p78 :rule quant-unused-vars :args ((= @t105 @t94))) % 0.36/0.67 (step @p79 :rule alpha_equiv :args (@t106 (@list @t95) (@list @t5))) % 0.36/0.67 (step @p80 :rule quant-unused-vars :args ((= @t107 @t97))) % 0.36/0.67 (step @p81 :rule nary_cong :premises (@p80 @p79 @p78 @p77) :args (@t108)) % 0.36/0.67 (step @p82 :rule quant-miniscope-and :args ((= @t109 @t108))) % 0.36/0.67 (step @p83 :rule trans :premises (@p82 @p81)) % 0.36/0.67 (step @p84 :rule refl :args (@t99)) % 0.36/0.67 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t110)) % 0.36/0.67 (step @p86 :rule quant-miniscope-or :args ((= @t102 @t110))) % 0.36/0.67 (step @p87 :rule trans :premises (@p86 @p85)) % 0.36/0.67 (step @p88 :rule symm :premises (@p87)) % 0.36/0.67 (step @p89 :rule cong :premises (@p88) :args ((forall @t103 (or @t99 (and @t97 @t111 @t94 @t93))))) % 0.36/0.67 (step @p90 :rule trans :premises (@p89 @p76)) % 0.36/0.67 (step @p91 :rule eq-symm :args (@t92 tptp.xk)) % 0.36/0.67 (step @p92 :rule refl :args (@t94)) % 0.36/0.67 (step @p93 :rule refl :args (@t111)) % 0.36/0.67 (step @p94 :rule refl :args (@t97)) % 0.36/0.67 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92 @p91) :args (@t112)) % 0.36/0.67 (step @p96 :rule refl :args (@t99)) % 0.36/0.67 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t113)) % 0.36/0.67 (step @p98 :rule cong :premises (@p97) :args (@t114)) % 0.36/0.67 (step @p99 :rule trans :premises (@p98 @p90)) % 0.36/0.67 (step @p100 :rule nary_cong :premises (@p99 @p75) :args ((and @t114 @t90))) % 0.36/0.67 (step @p101 :rule alpha_equiv :args (@t120 @t121 (@list @t84))) % 0.36/0.67 (step @p102 :rule alpha_equiv :args (@t124 @t121 (@list @t91))) % 0.36/0.67 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t125)) % 0.36/0.67 (step @p104 :rule quant-miniscope-and :args ((= (forall @t3 (and @t123 @t119)) @t125))) % 0.36/0.67 (step @p105 :rule trans :premises (@p104 @p103)) % 0.36/0.67 (step @p106 :rule trans :premises (@p105 @p100)) % 0.36/0.67 (step @p107 :rule aci_norm :args ((= (or (or @t118 @t115) @t65) @t119))) % 0.36/0.67 (step @p108 :rule refl :args (@t65)) % 0.36/0.67 (step @p109 :rule refl :args (@t115)) % 0.36/0.67 (step @p110 :rule refl :args (@t116)) % 0.36/0.67 (step @p111 :rule bool-and-de-morgan :args (@t2 @t117 true)) % 0.36/0.67 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((and (not @t126) @t116))) % 0.36/0.67 (step @p113 :rule bool-or-de-morgan :args (@t126 @t67 false)) % 0.36/0.67 (step @p114 :rule trans :premises (@p113 @p112)) % 0.36/0.67 (step @p115 :rule nary_cong :premises (@p114 @p109) :args ((or (not @t127) @t115))) % 0.36/0.67 (step @p116 :rule bool-and-de-morgan :args (@t127 @t60 true)) % 0.36/0.67 (step @p117 :rule trans :premises (@p116 @p115)) % 0.36/0.67 (step @p118 :rule nary_cong :premises (@p117 @p108) :args ((or (not @t128) @t65))) % 0.36/0.67 (step @p119 :rule trans :premises (@p118 @p107)) % 0.36/0.67 (step @p120 :rule bool-impl-elim :args (@t128 @t65)) % 0.36/0.67 (step @p121 :rule trans :premises (@p120 @p119)) % 0.36/0.67 (step @p122 :rule bool-impl-elim :args (@t65 @t122)) % 0.36/0.67 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t129)) % 0.36/0.67 (step @p124 :rule cong :premises (@p123) :args ((forall @t3 @t129))) % 0.36/0.67 (step @p125 :rule trans :premises (@p124 @p106)) % 0.36/0.67 (step @p126 :rule refl :args (@t65)) % 0.36/0.67 (step @p127 :rule refl :args (@t60)) % 0.36/0.67 (step @p128 :rule refl :args (@t67)) % 0.36/0.67 (step @p129 :rule bool-impl-elim :args (@t7 @t68)) % 0.36/0.67 (step @p130 :rule cong :premises (@p129) :args (@t69)) % 0.36/0.67 (step @p131 :rule refl :args (@t2)) % 0.36/0.67 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t70)) % 0.36/0.67 (step @p133 :rule nary_cong :premises (@p132 @p128) :args (@t71)) % 0.36/0.67 (step @p134 :rule nary_cong :premises (@p133 @p127) :args (@t72)) % 0.36/0.67 (step @p135 :rule cong :premises (@p134 @p126) :args (@t73)) % 0.36/0.67 (step @p136 :rule nary_cong :premises (@p131 @p130 @p128 @p127) :args (@t74)) % 0.36/0.67 (step @p137 :rule cong :premises (@p126 @p136) :args (@t75)) % 0.36/0.67 (step @p138 :rule nary_cong :premises (@p137 @p135) :args (@t76)) % 0.36/0.67 (step @p139 :rule cong :premises (@p138) :args (@t77)) % 0.36/0.67 (step @p140 :rule trans :premises (@p139 @p125)) % 0.36/0.67 (step @p141 :rule and_elim :premises (@p63) :args (3)) % 0.36/0.67 (step @p142 :rule eq_resolve :premises (@p141 @p140)) % 0.36/0.67 (step @p143 :rule and_elim :premises (@p142) :args (0)) % 0.36/0.67 (step @p144 :rule instantiate :premises (@p143) :args ((@list tptp.xQ tptp.xx))) % 0.36/0.67 (step @p145 :rule not_implies_elim1 :premises (@p68)) % 0.36/0.67 (step @p146 :rule not_implies_elim2 :premises (@p68)) % 0.36/0.67 (step @p147 :rule cnf_or_pos :args (@t131)) % 0.36/0.67 (step @p148 :rule reordering :premises (@p147) :args ((or @t82 @t130 @t132))) % 0.36/0.67 (step @p149 :rule chain_m_resolution :premises (@p148 @p146 @p145) :args (@t132 (@list true false) (@list @t82 @t83))) % 0.36/0.67 (step @p150 :rule cnf_and_pos :args (@t133 1)) % 0.36/0.67 (step @p151 :rule reordering :premises (@p150) :args ((or @t131 @t134))) % 0.36/0.67 (step @p152 :rule chain_m_resolution :premises (@p151 @p149) :args (@t134 (@list true) (@list @t131))) % 0.36/0.67 (step @p153 :rule bool-impl-elim :args (@t59 @t65)) % 0.36/0.67 (step @p154 :rule cong :premises (@p153) :args (@t66)) % 0.36/0.67 (step @p155 :rule and_elim :premises (@p63) :args (4)) % 0.36/0.67 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.36/0.67 (step @p157 :rule instantiate :premises (@p156) :args ((@list tptp.xQ))) % 0.36/0.67 (step @p158 :rule and_elim :premises (@p65) :args (4)) % 0.36/0.67 (step @p159 :rule cnf_or_pos :args (@t137)) % 0.36/0.67 (step @p160 :rule reordering :premises (@p159) :args ((or @t136 @t135 (not @t137)))) % 0.36/0.67 (step @p161 :rule chain_m_resolution :premises (@p160 @p158 @p157) :args (@t135 (@list false false) (@list @t78 @t137))) % 0.36/0.67 (step @p162 :rule cnf_or_pos :args (@t139)) % 0.36/0.67 (step @p163 :rule reordering :premises (@p162) :args ((or @t138 @t133 (not @t139)))) % 0.36/0.67 (step @p164 false :rule chain_m_resolution :premises (@p163 @p161 @p152 @p144) :args (false (@list false true false) (@list @t135 @t133 @t139))) % 0.36/0.67 ) % 0.36/0.67 % SZS output end Proof % 0.36/0.67 % cvc5 exiting %------------------------------------------------------------------------------