%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM549+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 : n002.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 08:39:48 AM UTC 2026 % Result : Theorem 0.51s 0.71s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM549+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 % 0.16/0.34 % Computer : n002.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 11:29:03 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.51/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.51/0.71 % SZS status Theorem % 0.51/0.71 % SZS output start Proof % 0.51/0.71 ( % 0.51/0.71 (declare-sort $$unsorted 0) % 0.51/0.71 (declare-const tptp.xQ $$unsorted) % 0.51/0.71 (declare-const tptp.xx $$unsorted) % 0.51/0.71 (declare-const tptp.xT $$unsorted) % 0.51/0.71 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.xS $$unsorted) % 0.51/0.71 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.slcrc0 $$unsorted) % 0.51/0.71 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.xk $$unsorted) % 0.51/0.71 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.szNzAzT0 $$unsorted) % 0.51/0.71 (declare-const tptp.sz00 $$unsorted) % 0.51/0.71 (define @t1 () (@var "W0" $$unsorted)) % 0.51/0.71 (define @t2 () (tptp.aSet0 @t1)) % 0.51/0.71 (define @t3 () (@list @t1)) % 0.51/0.71 (define @t4 () (tptp.aElement0 @t1)) % 0.51/0.71 (define @t5 () (@var "W1" $$unsorted)) % 0.51/0.71 (define @t6 () (tptp.aElement0 @t5)) % 0.51/0.71 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.51/0.71 (define @t8 () (@list @t5)) % 0.51/0.71 (define @t9 () (forall @t8 (=> @t7 @t6))) % 0.51/0.71 (define @t10 () (=> @t2 @t9)) % 0.51/0.71 (define @t11 () (forall @t3 @t10)) % 0.51/0.71 (define @t12 () (tptp.isFinite0 @t1)) % 0.51/0.71 (define @t13 () (exists @t8 @t7)) % 0.51/0.71 (define @t14 () (not @t13)) % 0.51/0.71 (define @t15 () (and @t2 @t14)) % 0.51/0.71 (define @t16 () (= @t1 tptp.slcrc0)) % 0.51/0.71 (define @t17 () (= @t16 @t15)) % 0.51/0.71 (define @t18 () (forall @t3 @t17)) % 0.51/0.71 (define @t19 () (tptp.isCountable0 @t1)) % 0.51/0.71 (define @t20 () (not @t12)) % 0.51/0.71 (define @t21 () (and @t2 @t19)) % 0.51/0.71 (define @t22 () (not @t16)) % 0.51/0.71 (define @t23 () (@var "W2" $$unsorted)) % 0.51/0.71 (define @t24 () (tptp.aElementOf0 @t23 @t1)) % 0.51/0.71 (define @t25 () (tptp.aElementOf0 @t23 @t5)) % 0.51/0.71 (define @t26 () (@list @t23)) % 0.51/0.71 (define @t27 () (tptp.aSet0 @t5)) % 0.51/0.71 (define @t28 () (tptp.aSubsetOf0 @t5 @t1)) % 0.51/0.71 (define @t29 () (tptp.isFinite0 @t5)) % 0.51/0.71 (define @t30 () (and @t2 @t12)) % 0.51/0.71 (define @t31 () (= @t1 @t5)) % 0.51/0.71 (define @t32 () (tptp.aSubsetOf0 @t1 @t5)) % 0.51/0.71 (define @t33 () (@list @t1 @t5)) % 0.51/0.71 (define @t34 () (tptp.aSet0 @t23)) % 0.51/0.71 (define @t35 () (@list @t1 @t5 @t23)) % 0.51/0.71 (define @t36 () (@var "W3" $$unsorted)) % 0.51/0.71 (define @t37 () (= @t36 @t5)) % 0.51/0.71 (define @t38 () (tptp.aElementOf0 @t36 @t1)) % 0.51/0.71 (define @t39 () (tptp.aElement0 @t36)) % 0.51/0.71 (define @t40 () (tptp.aElementOf0 @t36 @t23)) % 0.51/0.71 (define @t41 () (@list @t36)) % 0.51/0.71 (define @t42 () (tptp.sdtpldt0 @t1 @t5)) % 0.51/0.71 (define @t43 () (and @t2 @t6)) % 0.51/0.71 (define @t44 () (tptp.sdtmndt0 @t1 @t5)) % 0.51/0.71 (define @t45 () (tptp.sdtpldt0 @t5 @t1)) % 0.51/0.71 (define @t46 () (and @t27 (tptp.isCountable0 @t5))) % 0.51/0.71 (define @t47 () (tptp.sdtmndt0 @t5 @t1)) % 0.51/0.71 (define @t48 () (and @t27 @t29)) % 0.51/0.71 (define @t49 () (tptp.szszuzczcdt0 @t1)) % 0.51/0.71 (define @t50 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.51/0.71 (define @t51 () (tptp.szszuzczcdt0 @t5)) % 0.51/0.71 (define @t52 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.51/0.71 (define @t53 () (and @t50 @t52)) % 0.51/0.71 (define @t54 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.51/0.71 (define @t55 () (tptp.sdtlseqdt0 @t5 @t23)) % 0.51/0.71 (define @t56 () (tptp.aElementOf0 @t23 tptp.szNzAzT0)) % 0.51/0.71 (define @t57 () (tptp.sbrdtbr0 @t1)) % 0.51/0.71 (define @t58 () (= @t57 tptp.sz00)) % 0.51/0.71 (define @t59 () (=> @t2 (= @t58 @t16))) % 0.51/0.71 (define @t60 () (forall @t3 @t59)) % 0.51/0.71 (define @t61 () (not @t7)) % 0.51/0.71 (define @t62 () (and @t2 @t52)) % 0.51/0.71 (define @t63 () (tptp.szmzizndt0 @t1)) % 0.51/0.71 (define @t64 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.51/0.71 (define @t65 () (tptp.szmzizndt0 @t5)) % 0.51/0.71 (define @t66 () (tptp.slbdtrb0 @t1)) % 0.51/0.71 (define @t67 () (tptp.slbdtrb0 @t5)) % 0.51/0.71 (define @t68 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.51/0.71 (define @t69 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 0.51/0.71 (define @t70 () (tptp.aElementOf0 @t1 @t69)) % 0.51/0.71 (define @t71 () (= @t57 tptp.xk)) % 0.51/0.71 (define @t72 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.51/0.71 (define @t73 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xS)))) % 0.51/0.71 (define @t74 () (forall @t3 (and (=> @t70 (and @t2 @t73 @t72 @t71)) (=> (and (or (and @t2 @t73) @t72) @t71) @t70)))) % 0.51/0.71 (define @t75 () (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) % 0.51/0.71 (define @t76 () (tptp.aElementOf0 @t1 @t75)) % 0.51/0.71 (define @t77 () (tptp.aSubsetOf0 @t1 tptp.xT)) % 0.51/0.71 (define @t78 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xT)))) % 0.51/0.71 (define @t79 () (tptp.sbrdtbr0 tptp.xQ)) % 0.51/0.71 (define @t80 () (= @t79 tptp.xk)) % 0.51/0.71 (define @t81 () (tptp.aElementOf0 @t1 tptp.xQ)) % 0.51/0.71 (define @t82 () (tptp.aSet0 tptp.xQ)) % 0.51/0.71 (define @t83 () (and @t4 @t81)) % 0.51/0.71 (define @t84 () (exists @t3 @t83)) % 0.51/0.71 (define @t85 () (not @t84)) % 0.51/0.71 (define @t86 () (forall @t8 @t61)) % 0.51/0.71 (define @t87 () (= tptp.slcrc0 tptp.xQ)) % 0.51/0.71 (define @t88 () (forall @t8 (not (tptp.aElementOf0 @t5 tptp.xQ)))) % 0.51/0.71 (define @t89 () (and @t82 @t88)) % 0.51/0.71 (define @t90 () (= tptp.xQ tptp.slcrc0)) % 0.51/0.71 (define @t91 () (= @t90 @t89)) % 0.51/0.71 (define @t92 () (forall @t3 (= @t16 (and @t2 @t86)))) % 0.51/0.71 (define @t93 () (@list tptp.xQ)) % 0.51/0.71 (define @t94 () (= @t89 @t87)) % 0.51/0.71 (define @t95 () (@list false)) % 0.51/0.71 (define @t96 () (= @t16 (= tptp.sz00 @t57))) % 0.51/0.71 (define @t97 () (= tptp.sz00 @t79)) % 0.51/0.71 (define @t98 () (= @t90 @t97)) % 0.51/0.71 (define @t99 () (not @t82)) % 0.51/0.71 (define @t100 () (or @t99 @t98)) % 0.51/0.71 (define @t101 () (not @t2)) % 0.51/0.71 (define @t102 () (forall @t3 (or @t101 @t96))) % 0.51/0.71 (define @t103 () (= @t87 @t97)) % 0.51/0.71 (define @t104 () (or @t99 @t103)) % 0.51/0.71 (define @t105 () (not @t87)) % 0.51/0.71 (define @t106 () (@list true false)) % 0.51/0.71 (define @t107 () (not @t89)) % 0.51/0.71 (define @t108 () (not @t88)) % 0.51/0.71 (define @t109 () (@quantifiers_skolemize @t88 0)) % 0.51/0.71 (define @t110 () (tptp.aElementOf0 @t109 tptp.xQ)) % 0.51/0.71 (define @t111 () (not @t110)) % 0.51/0.71 (define @t112 () (not @t111)) % 0.51/0.71 (define @t113 () (forall @t3 (not @t83))) % 0.51/0.71 (define @t114 () (not @t113)) % 0.51/0.71 (define @t115 () (@var "BOUND_VARIABLE_7888" $$unsorted)) % 0.51/0.71 (define @t116 () (tptp.aElement0 @t115)) % 0.51/0.71 (define @t117 () (not (tptp.aElementOf0 @t115 @t1))) % 0.51/0.71 (define @t118 () (or @t117 @t116)) % 0.51/0.71 (define @t119 () (or @t101 @t118)) % 0.51/0.71 (define @t120 () (forall (@list @t1 @t115) @t119)) % 0.51/0.71 (define @t121 () (@list @t115)) % 0.51/0.71 (define @t122 () (forall @t121 @t119)) % 0.51/0.71 (define @t123 () (forall @t121 @t118)) % 0.51/0.71 (define @t124 () (or @t101 @t123)) % 0.51/0.71 (define @t125 () (forall @t8 (or @t61 @t6))) % 0.51/0.71 (define @t126 () (tptp.aElement0 @t109)) % 0.51/0.71 (define @t127 () (or @t99 @t111 @t126)) % 0.51/0.71 (define @t128 () (@list false false false)) % 0.51/0.71 (define @t129 () (not @t126)) % 0.51/0.71 (define @t130 () (or @t129 @t111)) % 0.51/0.71 (assume @p1 (forall @t3 (=> @t2 true))) % 0.51/0.71 (assume @p2 (forall @t3 (=> @t4 true))) % 0.51/0.71 (assume @p3 @t11) % 0.51/0.71 (assume @p4 (forall @t3 (=> @t2 (=> @t12 true)))) % 0.51/0.71 (assume @p5 @t18) % 0.51/0.71 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.51/0.71 (assume @p7 (forall @t3 (=> @t2 (=> @t19 true)))) % 0.51/0.71 (assume @p8 (forall @t3 (=> @t21 @t20))) % 0.51/0.71 (assume @p9 (forall @t3 (=> @t21 @t22))) % 0.51/0.71 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t28 (and @t27 (forall @t26 (=> @t25 @t24)))))))) % 0.51/0.71 (assume @p11 (forall @t3 (=> @t30 (forall @t8 (=> @t28 @t29))))) % 0.51/0.71 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.51/0.71 (assume @p13 (forall @t33 (=> (and @t2 @t27) (=> (and @t32 @t28) @t31)))) % 0.51/0.71 (assume @p14 (forall @t35 (=> (and @t2 @t27 @t34) (=> (and @t32 (tptp.aSubsetOf0 @t5 @t23)) (tptp.aSubsetOf0 @t1 @t23))))) % 0.51/0.71 (assume @p15 (forall @t33 (=> @t43 (forall @t26 (= (= @t23 @t42) (and @t34 (forall @t41 (= @t40 (and @t39 (or @t38 @t37)))))))))) % 0.51/0.71 (assume @p16 (forall @t33 (=> @t43 (forall @t26 (= (= @t23 @t44) (and @t34 (forall @t41 (= @t40 (and @t39 @t38 (not @t37)))))))))) % 0.51/0.71 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t44 @t5) @t1)))))) % 0.51/0.71 (assume @p18 (forall @t33 (=> (and @t4 @t27) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t45 @t1) @t5))))) % 0.51/0.71 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isCountable0 @t45)))))) % 0.51/0.71 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isCountable0 @t47)))))) % 0.51/0.71 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t48 (tptp.isFinite0 @t45)))))) % 0.51/0.71 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t48 (tptp.isFinite0 @t47)))))) % 0.51/0.71 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.51/0.71 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.51/0.71 (assume @p25 (forall @t3 (=> @t50 (and (tptp.aElementOf0 @t49 tptp.szNzAzT0) (not (= @t49 tptp.sz00)))))) % 0.51/0.71 (assume @p26 (forall @t33 (=> @t53 (=> (= @t49 @t51) @t31)))) % 0.51/0.71 (assume @p27 (forall @t3 (=> @t50 (or (= @t1 tptp.sz00) (exists @t8 (and @t52 (= @t1 @t51))))))) % 0.51/0.71 (assume @p28 (forall @t3 (=> @t50 (not (= @t1 @t49))))) % 0.51/0.71 (assume @p29 (forall @t33 (=> @t53 (=> @t54 true)))) % 0.51/0.71 (assume @p30 (forall @t3 (=> @t50 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.51/0.71 (assume @p31 (forall @t3 (=> @t50 (not (tptp.sdtlseqdt0 @t49 tptp.sz00))))) % 0.51/0.71 (assume @p32 (forall @t33 (=> @t53 (= @t54 (tptp.sdtlseqdt0 @t49 @t51))))) % 0.51/0.71 (assume @p33 (forall @t3 (=> @t50 (tptp.sdtlseqdt0 @t1 @t49)))) % 0.51/0.71 (assume @p34 (forall @t3 (=> @t50 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.51/0.71 (assume @p35 (forall @t33 (=> @t53 (=> (and @t54 (tptp.sdtlseqdt0 @t5 @t1)) @t31)))) % 0.51/0.71 (assume @p36 (forall @t35 (=> (and @t50 @t52 @t56) (=> (and @t54 @t55) (tptp.sdtlseqdt0 @t1 @t23))))) % 0.51/0.71 (assume @p37 (forall @t33 (=> @t53 (or @t54 (tptp.sdtlseqdt0 @t51 @t1))))) % 0.51/0.71 (assume @p38 (forall @t33 (=> @t53 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.51/0.71 (assume @p39 (forall @t3 (=> @t50 (tptp.iLess0 @t1 @t49)))) % 0.51/0.71 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t57)))) % 0.51/0.71 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t57 tptp.szNzAzT0) @t12)))) % 0.51/0.71 (assume @p42 @t60) % 0.51/0.71 (assume @p43 (forall @t3 (=> @t30 (forall @t8 (=> @t6 (=> @t61 (= (tptp.sbrdtbr0 @t42) (tptp.szszuzczcdt0 @t57)))))))) % 0.51/0.71 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t12 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t44)) @t57)))))) % 0.51/0.71 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t12 @t28) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t57)))))) % 0.51/0.71 (assume @p46 (forall @t33 (=> @t62 (=> (and @t12 (tptp.sdtlseqdt0 @t5 @t57)) (exists @t26 (and (tptp.aSubsetOf0 @t23 @t1) (= (tptp.sbrdtbr0 @t23) @t5))))))) % 0.51/0.71 (assume @p47 (forall @t3 (=> (and @t64 @t22) (forall @t8 (= (= @t5 @t63) (and @t7 (forall @t26 (=> @t24 @t55)))))))) % 0.51/0.71 (assume @p48 (forall @t3 (=> (and @t64 @t12 @t22) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t26 (=> @t24 (tptp.sdtlseqdt0 @t23 @t5))))))))) % 0.51/0.71 (assume @p49 (forall @t33 (=> (and @t64 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t22 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t63 @t5) (tptp.aElementOf0 @t65 @t1)) (= @t63 @t65))))) % 0.51/0.71 (assume @p50 (forall @t3 (=> @t50 (forall @t8 (= (= @t5 @t66) (and @t27 (forall @t26 (= @t25 (and @t56 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t23) @t1)))))))))) % 0.51/0.71 (assume @p51 (forall @t3 (=> @t50 (tptp.isFinite0 @t66)))) % 0.51/0.71 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.51/0.71 (assume @p53 (forall @t33 (=> @t53 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t51)) (or (tptp.aElementOf0 @t1 @t67) @t31))))) % 0.51/0.71 (assume @p54 (forall @t33 (=> @t53 (= @t54 (tptp.aSubsetOf0 @t66 @t67))))) % 0.51/0.71 (assume @p55 (forall @t3 (=> (and @t64 @t12) (exists @t8 (and @t52 (tptp.aSubsetOf0 @t1 @t67)))))) % 0.51/0.71 (assume @p56 (forall @t3 (=> @t50 (= (tptp.sbrdtbr0 @t66) @t1)))) % 0.51/0.71 (assume @p57 (forall @t33 (=> @t62 (forall @t26 (= (= @t23 @t68) (and @t34 (forall @t41 (= @t40 (and (tptp.aSubsetOf0 @t36 @t1) (= (tptp.sbrdtbr0 @t36) @t5)))))))))) % 0.51/0.71 (assume @p58 (forall @t3 (=> @t30 (forall @t8 (=> @t52 (tptp.isFinite0 @t68)))))) % 0.51/0.71 (assume @p59 (forall @t3 (=> (and @t2 @t20) (forall @t8 (=> @t52 (not (= @t68 tptp.slcrc0))))))) % 0.51/0.71 (assume @p60 (forall @t3 (=> @t21 (forall @t8 (=> (and @t52 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t68)))))) % 0.51/0.71 (assume @p61 (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 0.51/0.71 (assume @p62 (and (tptp.aSet0 tptp.xS) (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00)))) % 0.51/0.71 (assume @p63 (and (tptp.aSet0 @t69) @t74 (tptp.aSet0 @t75) (forall @t3 (and (=> @t76 (and @t2 @t78 @t77 @t71)) (=> (and (or (and @t2 @t78) @t77) @t71) @t76))) (forall @t3 (=> @t70 @t76)) (tptp.aSubsetOf0 @t69 @t75) (not (=> @t74 (or (not (exists @t3 @t70)) (= @t69 tptp.slcrc0)))))) % 0.51/0.71 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 0.51/0.71 (assume @p65 (and @t82 (forall @t3 (=> @t81 (tptp.aElementOf0 @t1 tptp.xS))) (tptp.aSubsetOf0 tptp.xQ tptp.xS) @t80 (tptp.aElementOf0 tptp.xQ @t69))) % 0.51/0.71 (assume @p66 (and @t82 (tptp.isFinite0 tptp.xQ) @t80)) % 0.51/0.71 (assume @p67 @t85) % 0.51/0.71 (assume @p68 true) % 0.51/0.71 (step @p69 :rule bool-double-not-elim :args (@t86)) % 0.51/0.71 (step @p70 :rule exists-elim :args ((= @t13 (not @t86)))) % 0.51/0.71 (step @p71 :rule cong :premises (@p70) :args (@t14)) % 0.51/0.71 (step @p72 :rule trans :premises (@p71 @p69)) % 0.51/0.71 (step @p73 :rule refl :args (@t2)) % 0.51/0.71 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t15)) % 0.51/0.71 (step @p75 :rule refl :args (@t16)) % 0.51/0.71 (step @p76 :rule cong :premises (@p75 @p74) :args (@t17)) % 0.51/0.71 (step @p77 :rule cong :premises (@p76) :args (@t18)) % 0.51/0.71 (step @p78 :rule eq_resolve :premises (@p5 @p77)) % 0.51/0.71 (step @p79 :rule eq-symm :args (@t87 @t89)) % 0.51/0.71 (step @p80 :rule refl :args (@t89)) % 0.51/0.71 (step @p81 :rule eq-symm :args (tptp.xQ tptp.slcrc0)) % 0.51/0.71 (step @p82 :rule cong :premises (@p81 @p80) :args (@t91)) % 0.51/0.71 (step @p83 :rule trans :premises (@p82 @p79)) % 0.51/0.71 (step @p84 :rule refl :args (@t92)) % 0.51/0.71 (step @p85 :rule cong :premises (@p84 @p83) :args ((=> @t92 @t91))) % 0.51/0.71 (assume-push @p189 @t92) % 0.51/0.71 (step @p87 :rule instantiate :premises (@p78) :args (@t93)) % 0.51/0.71 (step-pop @p190 :rule scope :premises (@p87)) % 0.51/0.71 (step @p88 :rule process_scope :premises (@p190) :args (@t91)) % 0.51/0.71 (step @p90 :rule eq_resolve :premises (@p88 @p85)) % 0.51/0.71 (step @p91 :rule implies_elim :premises (@p90)) % 0.51/0.71 (step @p92 :rule chain_m_resolution :premises (@p91 @p78) :args (@t94 @t95 (@list @t92))) % 0.51/0.71 (step @p93 :rule bool-impl-elim :args (@t2 @t96)) % 0.51/0.71 (step @p94 :rule cong :premises (@p93) :args ((forall @t3 (=> @t2 @t96)))) % 0.51/0.71 (step @p95 :rule eq-symm :args (@t57 tptp.sz00)) % 0.51/0.71 (step @p96 :rule cong :premises (@p75 @p95) :args ((= @t16 @t58))) % 0.51/0.71 (step @p97 :rule eq-symm :args (@t58 @t16)) % 0.51/0.71 (step @p98 :rule trans :premises (@p97 @p96)) % 0.51/0.71 (step @p99 :rule cong :premises (@p73 @p98) :args (@t59)) % 0.51/0.71 (step @p100 :rule cong :premises (@p99) :args (@t60)) % 0.51/0.71 (step @p101 :rule trans :premises (@p100 @p94)) % 0.51/0.71 (step @p102 :rule eq_resolve :premises (@p42 @p101)) % 0.51/0.71 (step @p103 :rule refl :args (@t97)) % 0.51/0.71 (step @p104 :rule cong :premises (@p81 @p103) :args (@t98)) % 0.51/0.71 (step @p105 :rule refl :args (@t99)) % 0.51/0.71 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t100)) % 0.51/0.71 (step @p107 :rule refl :args (@t102)) % 0.51/0.71 (step @p108 :rule cong :premises (@p107 @p106) :args ((=> @t102 @t100))) % 0.51/0.71 (assume-push @p191 @t102) % 0.51/0.71 (step @p110 :rule instantiate :premises (@p102) :args (@t93)) % 0.51/0.71 (step-pop @p192 :rule scope :premises (@p110)) % 0.51/0.71 (step @p111 :rule process_scope :premises (@p192) :args (@t100)) % 0.51/0.71 (step @p113 :rule eq_resolve :premises (@p111 @p108)) % 0.51/0.71 (step @p114 :rule implies_elim :premises (@p113)) % 0.51/0.71 (step @p115 :rule chain_m_resolution :premises (@p114 @p102) :args (@t104 @t95 (@list @t102))) % 0.51/0.71 (step @p116 :rule and_elim :premises (@p65) :args (0)) % 0.51/0.71 (step @p117 :rule cnf_or_pos :args (@t104)) % 0.51/0.71 (step @p118 :rule reordering :premises (@p117) :args ((or @t99 @t103 (not @t104)))) % 0.51/0.71 (step @p119 :rule chain_m_resolution :premises (@p118 @p116 @p115) :args (@t103 (@list false false) (@list @t82 @t104))) % 0.51/0.71 (step @p120 :rule and_elim :premises (@p62) :args (2)) % 0.51/0.71 (step @p121 :rule symm :premises (@p120)) % 0.51/0.71 (step @p122 :rule false_intro :premises (@p121)) % 0.51/0.71 (step @p123 :rule and_elim :premises (@p65) :args (3)) % 0.51/0.71 (step @p124 :rule refl :args (tptp.sz00)) % 0.51/0.71 (step @p125 :rule cong :premises (@p124 @p123) :args (@t97)) % 0.51/0.71 (step @p126 :rule trans :premises (@p125 @p122)) % 0.51/0.71 (step @p127 :rule false_elim :premises (@p126)) % 0.51/0.71 (step @p128 :rule cnf_equiv_pos1 :args (@t103)) % 0.51/0.71 (step @p129 :rule reordering :premises (@p128) :args ((or @t97 @t105 (not @t103)))) % 0.51/0.71 (step @p130 :rule chain_m_resolution :premises (@p129 @p127 @p119) :args (@t105 @t106 (@list @t97 @t103))) % 0.51/0.71 (step @p131 :rule cnf_equiv_pos1 :args (@t94)) % 0.51/0.71 (step @p132 :rule reordering :premises (@p131) :args ((or @t87 @t107 (not @t94)))) % 0.51/0.71 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p92) :args (@t107 @t106 (@list @t87 @t94))) % 0.51/0.71 (step @p134 :rule cnf_and_neg :args (@t89)) % 0.51/0.71 (step @p135 :rule reordering :premises (@p134) :args ((or @t99 @t89 @t108))) % 0.51/0.71 (step @p136 :rule chain_m_resolution :premises (@p135 @p116 @p133) :args (@t108 (@list false true) (@list @t82 @t89))) % 0.51/0.71 (step @p137 :rule refl :args (@t110)) % 0.51/0.71 (step @p138 :rule bool-double-not-elim :args (@t88)) % 0.51/0.71 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or (not @t108) @t110))) % 0.51/0.71 (step @p140 :rule bool-double-not-elim :args (@t110)) % 0.51/0.71 (step @p141 :rule refl :args (@t108)) % 0.51/0.71 (step @p142 :rule cong :premises (@p141 @p140) :args ((=> @t108 @t112))) % 0.51/0.71 (assume-push @p193 @t108) % 0.51/0.71 (step @p144 :rule skolemize :premises (@p136)) % 0.51/0.71 (step-pop @p194 :rule scope :premises (@p144)) % 0.51/0.71 (step @p145 :rule process_scope :premises (@p194) :args (@t112)) % 0.51/0.71 (step @p147 :rule eq_resolve :premises (@p145 @p142)) % 0.51/0.71 (step @p148 :rule implies_elim :premises (@p147)) % 0.51/0.71 (step @p149 :rule eq_resolve :premises (@p148 @p139)) % 0.51/0.71 (step @p150 :rule chain_m_resolution :premises (@p149 @p136) :args (@t110 (@list true) (@list @t88))) % 0.51/0.71 (step @p151 :rule bool-double-not-elim :args ((forall @t3 (or (not @t4) (not @t81))))) % 0.51/0.71 (step @p152 :rule bool-and-de-morgan :args (@t4 @t81 true)) % 0.51/0.71 (step @p153 :rule cong :premises (@p152) :args (@t113)) % 0.51/0.71 (step @p154 :rule cong :premises (@p153) :args (@t114)) % 0.51/0.71 (step @p155 :rule exists-elim :args ((= @t84 @t114))) % 0.51/0.71 (step @p156 :rule trans :premises (@p155 @p154)) % 0.51/0.71 (step @p157 :rule cong :premises (@p156) :args (@t85)) % 0.51/0.71 (step @p158 :rule trans :premises (@p157 @p151)) % 0.51/0.71 (step @p159 :rule eq_resolve :premises (@p67 @p158)) % 0.51/0.71 (step @p160 :rule instantiate :premises (@p159) :args ((@list @t109))) % 0.51/0.71 (step @p161 :rule aci_norm :args ((= @t119 (or @t101 @t117 @t116)))) % 0.51/0.71 (step @p162 :rule cong :premises (@p161) :args (@t120)) % 0.51/0.71 (step @p163 :rule quant-merge-prenex :args ((= (forall @t3 @t122) @t120))) % 0.51/0.71 (step @p164 :rule alpha_equiv :args (@t123 (@list @t115) (@list @t5))) % 0.51/0.71 (step @p165 :rule refl :args (@t101)) % 0.51/0.71 (step @p166 :rule nary_cong :premises (@p165 @p164) :args (@t124)) % 0.51/0.71 (step @p167 :rule quant-miniscope-or :args ((= @t122 @t124))) % 0.51/0.71 (step @p168 :rule trans :premises (@p167 @p166)) % 0.51/0.71 (step @p169 :rule symm :premises (@p168)) % 0.51/0.71 (step @p170 :rule cong :premises (@p169) :args ((forall @t3 (or @t101 @t125)))) % 0.51/0.71 (step @p171 :rule trans :premises (@p170 @p163)) % 0.51/0.71 (step @p172 :rule trans :premises (@p171 @p162)) % 0.51/0.71 (step @p173 :rule bool-impl-elim :args (@t2 @t125)) % 0.51/0.71 (step @p174 :rule cong :premises (@p173) :args ((forall @t3 (=> @t2 @t125)))) % 0.51/0.71 (step @p175 :rule trans :premises (@p174 @p172)) % 0.51/0.71 (step @p176 :rule bool-impl-elim :args (@t7 @t6)) % 0.51/0.71 (step @p177 :rule cong :premises (@p176) :args (@t9)) % 0.51/0.71 (step @p178 :rule cong :premises (@p73 @p177) :args (@t10)) % 0.51/0.71 (step @p179 :rule cong :premises (@p178) :args (@t11)) % 0.51/0.71 (step @p180 :rule trans :premises (@p179 @p175)) % 0.51/0.71 (step @p181 :rule eq_resolve :premises (@p3 @p180)) % 0.51/0.71 (step @p182 :rule instantiate :premises (@p181) :args ((@list tptp.xQ @t109))) % 0.51/0.71 (step @p183 :rule cnf_or_pos :args (@t127)) % 0.51/0.71 (step @p184 :rule reordering :premises (@p183) :args ((or @t99 @t111 @t126 (not @t127)))) % 0.51/0.71 (step @p185 :rule chain_m_resolution :premises (@p184 @p116 @p150 @p182) :args (@t126 @t128 (@list @t82 @t110 @t127))) % 0.51/0.71 (step @p186 :rule cnf_or_pos :args (@t130)) % 0.51/0.71 (step @p187 :rule reordering :premises (@p186) :args ((or @t111 @t129 (not @t130)))) % 0.51/0.71 (step @p188 false :rule chain_m_resolution :premises (@p187 @p185 @p160 @p150) :args (false @t128 (@list @t126 @t130 @t110))) % 0.51/0.71 ) % 0.51/0.71 % SZS output end Proof % 0.51/0.72 % cvc5 exiting %------------------------------------------------------------------------------