%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM540+2 : 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 : n027.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 08:39:46 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM540+2 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n027.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 11:28:36 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.slcrc0 $$unsorted) % 0.38/0.57 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.szNzAzT0 $$unsorted) % 0.38/0.57 (declare-const tptp.sz00 $$unsorted) % 0.38/0.57 (define @t1 () (@var "W0" $$unsorted)) % 0.38/0.57 (define @t2 () (tptp.aSet0 @t1)) % 0.38/0.57 (define @t3 () (@list @t1)) % 0.38/0.57 (define @t4 () (tptp.aElement0 @t1)) % 0.38/0.57 (define @t5 () (@var "W1" $$unsorted)) % 0.38/0.57 (define @t6 () (tptp.aElement0 @t5)) % 0.38/0.57 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.38/0.57 (define @t8 () (@list @t5)) % 0.38/0.57 (define @t9 () (tptp.isFinite0 @t1)) % 0.38/0.57 (define @t10 () (= @t1 tptp.slcrc0)) % 0.38/0.57 (define @t11 () (tptp.isCountable0 @t1)) % 0.38/0.57 (define @t12 () (and @t2 @t11)) % 0.38/0.57 (define @t13 () (not @t10)) % 0.38/0.57 (define @t14 () (@var "W2" $$unsorted)) % 0.38/0.57 (define @t15 () (tptp.aElementOf0 @t14 @t1)) % 0.38/0.57 (define @t16 () (tptp.aElementOf0 @t14 @t5)) % 0.38/0.57 (define @t17 () (@list @t14)) % 0.38/0.57 (define @t18 () (tptp.aSet0 @t5)) % 0.38/0.57 (define @t19 () (tptp.aSubsetOf0 @t5 @t1)) % 0.38/0.57 (define @t20 () (tptp.isFinite0 @t5)) % 0.38/0.57 (define @t21 () (and @t2 @t9)) % 0.38/0.57 (define @t22 () (= @t1 @t5)) % 0.38/0.57 (define @t23 () (tptp.aSubsetOf0 @t1 @t5)) % 0.38/0.57 (define @t24 () (@list @t1 @t5)) % 0.38/0.57 (define @t25 () (tptp.aSet0 @t14)) % 0.38/0.57 (define @t26 () (@list @t1 @t5 @t14)) % 0.38/0.57 (define @t27 () (@var "W3" $$unsorted)) % 0.38/0.57 (define @t28 () (= @t27 @t5)) % 0.38/0.57 (define @t29 () (tptp.aElementOf0 @t27 @t1)) % 0.38/0.57 (define @t30 () (tptp.aElement0 @t27)) % 0.38/0.57 (define @t31 () (tptp.aElementOf0 @t27 @t14)) % 0.38/0.57 (define @t32 () (@list @t27)) % 0.38/0.57 (define @t33 () (tptp.sdtpldt0 @t1 @t5)) % 0.38/0.57 (define @t34 () (and @t2 @t6)) % 0.38/0.57 (define @t35 () (tptp.sdtmndt0 @t1 @t5)) % 0.38/0.57 (define @t36 () (tptp.sdtpldt0 @t5 @t1)) % 0.38/0.57 (define @t37 () (and @t18 (tptp.isCountable0 @t5))) % 0.38/0.57 (define @t38 () (tptp.sdtmndt0 @t5 @t1)) % 0.38/0.57 (define @t39 () (and @t18 @t20)) % 0.38/0.57 (define @t40 () (tptp.szszuzczcdt0 @t1)) % 0.38/0.57 (define @t41 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.38/0.57 (define @t42 () (tptp.szszuzczcdt0 @t5)) % 0.38/0.57 (define @t43 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.38/0.57 (define @t44 () (and @t41 @t43)) % 0.38/0.57 (define @t45 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.38/0.57 (define @t46 () (tptp.sdtlseqdt0 @t5 @t14)) % 0.38/0.57 (define @t47 () (tptp.aElementOf0 @t14 tptp.szNzAzT0)) % 0.38/0.57 (define @t48 () (tptp.sbrdtbr0 @t1)) % 0.38/0.57 (define @t49 () (tptp.szmzizndt0 @t1)) % 0.38/0.57 (define @t50 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.38/0.57 (define @t51 () (tptp.szmzizndt0 @t5)) % 0.38/0.57 (define @t52 () (tptp.slbdtrb0 @t1)) % 0.38/0.57 (define @t53 () (tptp.slbdtrb0 tptp.sz00)) % 0.38/0.57 (define @t54 () (tptp.aElementOf0 @t1 @t53)) % 0.38/0.57 (define @t55 () (exists @t3 @t54)) % 0.38/0.57 (define @t56 () (not @t55)) % 0.38/0.57 (define @t57 () (or @t56 (= @t53 tptp.slcrc0))) % 0.38/0.57 (define @t58 () (forall @t3 (not @t54))) % 0.38/0.57 (define @t59 () (and (tptp.aSet0 @t53) @t58)) % 0.38/0.57 (define @t60 () (=> @t59 @t57)) % 0.38/0.57 (define @t61 () (not @t60)) % 0.38/0.57 (assume @p1 (forall @t3 (=> @t2 true))) % 0.38/0.57 (assume @p2 (forall @t3 (=> @t4 true))) % 0.38/0.57 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.38/0.57 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.38/0.57 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.38/0.57 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.38/0.57 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.38/0.57 (assume @p8 (forall @t3 (=> @t12 (not @t9)))) % 0.38/0.57 (assume @p9 (forall @t3 (=> @t12 @t13))) % 0.38/0.57 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t19 (and @t18 (forall @t17 (=> @t16 @t15)))))))) % 0.38/0.57 (assume @p11 (forall @t3 (=> @t21 (forall @t8 (=> @t19 @t20))))) % 0.38/0.57 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.38/0.57 (assume @p13 (forall @t24 (=> (and @t2 @t18) (=> (and @t23 @t19) @t22)))) % 0.38/0.57 (assume @p14 (forall @t26 (=> (and @t2 @t18 @t25) (=> (and @t23 (tptp.aSubsetOf0 @t5 @t14)) (tptp.aSubsetOf0 @t1 @t14))))) % 0.38/0.57 (assume @p15 (forall @t24 (=> @t34 (forall @t17 (= (= @t14 @t33) (and @t25 (forall @t32 (= @t31 (and @t30 (or @t29 @t28)))))))))) % 0.38/0.57 (assume @p16 (forall @t24 (=> @t34 (forall @t17 (= (= @t14 @t35) (and @t25 (forall @t32 (= @t31 (and @t30 @t29 (not @t28)))))))))) % 0.38/0.57 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t35 @t5) @t1)))))) % 0.38/0.57 (assume @p18 (forall @t24 (=> (and @t4 @t18) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t36 @t1) @t5))))) % 0.38/0.57 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t37 (tptp.isCountable0 @t36)))))) % 0.38/0.57 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t37 (tptp.isCountable0 @t38)))))) % 0.38/0.57 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t39 (tptp.isFinite0 @t36)))))) % 0.38/0.57 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t39 (tptp.isFinite0 @t38)))))) % 0.38/0.57 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.38/0.57 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.38/0.57 (assume @p25 (forall @t3 (=> @t41 (and (tptp.aElementOf0 @t40 tptp.szNzAzT0) (not (= @t40 tptp.sz00)))))) % 0.38/0.57 (assume @p26 (forall @t24 (=> @t44 (=> (= @t40 @t42) @t22)))) % 0.38/0.57 (assume @p27 (forall @t3 (=> @t41 (or (= @t1 tptp.sz00) (exists @t8 (and @t43 (= @t1 @t42))))))) % 0.38/0.57 (assume @p28 (forall @t3 (=> @t41 (not (= @t1 @t40))))) % 0.38/0.57 (assume @p29 (forall @t24 (=> @t44 (=> @t45 true)))) % 0.38/0.57 (assume @p30 (forall @t3 (=> @t41 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.38/0.57 (assume @p31 (forall @t3 (=> @t41 (not (tptp.sdtlseqdt0 @t40 tptp.sz00))))) % 0.38/0.57 (assume @p32 (forall @t24 (=> @t44 (= @t45 (tptp.sdtlseqdt0 @t40 @t42))))) % 0.38/0.57 (assume @p33 (forall @t3 (=> @t41 (tptp.sdtlseqdt0 @t1 @t40)))) % 0.38/0.57 (assume @p34 (forall @t3 (=> @t41 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.38/0.57 (assume @p35 (forall @t24 (=> @t44 (=> (and @t45 (tptp.sdtlseqdt0 @t5 @t1)) @t22)))) % 0.38/0.57 (assume @p36 (forall @t26 (=> (and @t41 @t43 @t47) (=> (and @t45 @t46) (tptp.sdtlseqdt0 @t1 @t14))))) % 0.38/0.57 (assume @p37 (forall @t24 (=> @t44 (or @t45 (tptp.sdtlseqdt0 @t42 @t1))))) % 0.38/0.57 (assume @p38 (forall @t24 (=> @t44 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.38/0.57 (assume @p39 (forall @t3 (=> @t41 (tptp.iLess0 @t1 @t40)))) % 0.38/0.57 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t48)))) % 0.38/0.57 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t48 tptp.szNzAzT0) @t9)))) % 0.38/0.57 (assume @p42 (forall @t3 (=> @t2 (= (= @t48 tptp.sz00) @t10)))) % 0.38/0.57 (assume @p43 (forall @t3 (=> @t21 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t33) (tptp.szszuzczcdt0 @t48)))))))) % 0.38/0.57 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t35)) @t48)))))) % 0.38/0.57 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t19) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t48)))))) % 0.38/0.57 (assume @p46 (forall @t24 (=> (and @t2 @t43) (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t48)) (exists @t17 (and (tptp.aSubsetOf0 @t14 @t1) (= (tptp.sbrdtbr0 @t14) @t5))))))) % 0.38/0.57 (assume @p47 (forall @t3 (=> (and @t50 @t13) (forall @t8 (= (= @t5 @t49) (and @t7 (forall @t17 (=> @t15 @t46)))))))) % 0.38/0.57 (assume @p48 (forall @t3 (=> (and @t50 @t9 @t13) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t17 (=> @t15 (tptp.sdtlseqdt0 @t14 @t5))))))))) % 0.38/0.57 (assume @p49 (forall @t24 (=> (and @t50 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t13 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t49 @t5) (tptp.aElementOf0 @t51 @t1)) (= @t49 @t51))))) % 0.38/0.57 (assume @p50 (forall @t3 (=> @t41 (forall @t8 (= (= @t5 @t52) (and @t18 (forall @t17 (= @t16 (and @t47 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t14) @t1)))))))))) % 0.38/0.57 (assume @p51 (forall @t3 (=> @t41 (tptp.isFinite0 @t52)))) % 0.38/0.57 (assume @p52 @t61) % 0.38/0.57 (assume @p53 true) % 0.38/0.57 (step @p54 :rule eq-symm :args (@t53 tptp.slcrc0)) % 0.38/0.57 (step @p55 :rule bool-double-not-elim :args (@t58)) % 0.38/0.57 (step @p56 :rule exists-elim :args ((= @t55 (not @t58)))) % 0.38/0.57 (step @p57 :rule cong :premises (@p56) :args (@t56)) % 0.38/0.57 (step @p58 :rule trans :premises (@p57 @p55)) % 0.38/0.57 (step @p59 :rule nary_cong :premises (@p58 @p54) :args (@t57)) % 0.38/0.57 (step @p60 :rule refl :args (@t59)) % 0.38/0.57 (step @p61 :rule cong :premises (@p60 @p59) :args (@t60)) % 0.38/0.57 (step @p62 :rule cong :premises (@p61) :args (@t61)) % 0.38/0.57 (step @p63 :rule eq_resolve :premises (@p52 @p62)) % 0.38/0.57 (step @p64 :rule not_implies_elim1 :premises (@p63)) % 0.38/0.57 (step @p65 :rule and_elim :premises (@p64) :args (1)) % 0.38/0.57 (step @p66 :rule not_implies_elim2 :premises (@p63)) % 0.38/0.57 (step @p67 :rule not_or_elim :premises (@p66) :args (0)) % 0.38/0.57 (step @p68 false :rule chain_m_resolution :premises (@p67 @p65) :args (false (@list false) (@list @t58))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------