%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG101+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 : n024.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 08:45:41 AM UTC 2026 % Result : Theorem 0.16s 0.39s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : RNG101+2 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 09:07:00 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.39 % SZS status Theorem % 0.16/0.39 % SZS output start Proof % 0.16/0.39 ( % 0.16/0.39 (declare-sort $$unsorted 0) % 0.16/0.39 (declare-const tptp.xx $$unsorted) % 0.16/0.39 (declare-const tptp.xy $$unsorted) % 0.16/0.39 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.16/0.39 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.16/0.39 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.sz00 $$unsorted) % 0.16/0.39 (declare-const tptp.sz10 $$unsorted) % 0.16/0.39 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.16/0.39 (declare-const tptp.xc $$unsorted) % 0.16/0.39 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.39 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.39 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.39 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.39 (declare-const tptp.xz $$unsorted) % 0.16/0.39 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.39 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.16/0.39 (define @t1 () (@var "W0" $$unsorted)) % 0.16/0.39 (define @t2 () (tptp.aElement0 @t1)) % 0.16/0.39 (define @t3 () (@list @t1)) % 0.16/0.39 (define @t4 () (tptp.smndt0 @t1)) % 0.16/0.39 (define @t5 () (@var "W1" $$unsorted)) % 0.16/0.39 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.16/0.39 (define @t7 () (tptp.aElement0 @t5)) % 0.16/0.39 (define @t8 () (and @t2 @t7)) % 0.16/0.39 (define @t9 () (@list @t1 @t5)) % 0.16/0.39 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.16/0.39 (define @t11 () (@var "W2" $$unsorted)) % 0.16/0.39 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.16/0.39 (define @t13 () (tptp.aElement0 @t11)) % 0.16/0.39 (define @t14 () (and @t2 @t7 @t13)) % 0.16/0.39 (define @t15 () (@list @t1 @t5 @t11)) % 0.16/0.39 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.16/0.39 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.16/0.39 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.16/0.39 (define @t19 () (= @t5 tptp.sz00)) % 0.16/0.39 (define @t20 () (= @t1 tptp.sz00)) % 0.16/0.39 (define @t21 () (tptp.aSet0 @t1)) % 0.16/0.39 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.16/0.39 (define @t23 () (@list @t5)) % 0.16/0.39 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 0.16/0.39 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 0.16/0.39 (define @t26 () (@list @t11)) % 0.16/0.39 (define @t27 () (tptp.aSet0 @t5)) % 0.16/0.39 (define @t28 () (and @t21 @t27)) % 0.16/0.39 (define @t29 () (@var "W3" $$unsorted)) % 0.16/0.39 (define @t30 () (@var "W5" $$unsorted)) % 0.16/0.39 (define @t31 () (@var "W4" $$unsorted)) % 0.16/0.39 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 0.16/0.39 (define @t33 () (@list @t29)) % 0.16/0.39 (define @t34 () (tptp.aSet0 @t11)) % 0.16/0.39 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 0.16/0.39 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 0.16/0.39 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 0.16/0.39 (define @t38 () (tptp.aIdeal0 @t1)) % 0.16/0.39 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 0.16/0.39 (define @t40 () (tptp.aElement0 @t29)) % 0.16/0.39 (define @t41 () (@list @t11 @t29)) % 0.16/0.39 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 0.16/0.39 (define @t43 () (tptp.slsdtgt0 tptp.xc)) % 0.16/0.39 (define @t44 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.16/0.39 (define @t45 () (and @t2 (= @t44 tptp.xx))) % 0.16/0.39 (define @t46 () (exists @t3 @t45)) % 0.16/0.39 (define @t47 () (not @t46)) % 0.16/0.39 (define @t48 () (= tptp.xx @t44)) % 0.16/0.39 (define @t49 () (and @t2 @t48)) % 0.16/0.39 (define @t50 () (forall @t3 (not @t49))) % 0.16/0.39 (define @t51 () (not @t50)) % 0.16/0.39 (define @t52 () (forall @t3 (or (not @t2) (not @t48)))) % 0.16/0.39 (assume @p1 (forall @t3 (=> @t2 true))) % 0.16/0.39 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.16/0.39 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.16/0.39 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.16/0.39 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.16/0.39 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.16/0.39 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.16/0.39 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.16/0.39 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.16/0.39 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.16/0.39 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.16/0.39 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.16/0.39 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.16/0.39 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t17)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 0.16/0.39 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.16/0.39 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.16/0.39 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.16/0.39 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.16/0.39 (assume @p19 (forall @t3 (=> @t21 true))) % 0.16/0.39 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 0.16/0.39 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 0.16/0.39 (assume @p22 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t35) (and @t34 (forall @t33 (= @t32 (exists (@list @t31 @t30) (and (tptp.aElementOf0 @t31 @t1) (tptp.aElementOf0 @t30 @t5) (= (tptp.sdtpldt0 @t31 @t30) @t29))))))))))) % 0.16/0.39 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 0.16/0.39 (assume @p24 (forall @t3 (= @t38 (and @t21 (forall @t23 (=> @t22 (and (forall @t26 (=> @t24 (tptp.aElementOf0 @t12 @t1))) (forall @t26 (=> @t13 (tptp.aElementOf0 @t37 @t1)))))))))) % 0.16/0.39 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 0.16/0.39 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 0.16/0.39 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.16/0.39 (assume @p28 (forall @t9 (=> @t39 (=> (forall @t26 (=> @t13 (tptp.aElementOf0 @t11 @t35))) (forall @t41 (=> (and @t13 @t40) (exists (@list @t31) (and (tptp.aElement0 @t31) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t29 @t5))))))))) % 0.16/0.39 (assume @p29 (forall @t3 (=> @t42 true))) % 0.16/0.39 (assume @p30 (forall @t3 (=> (and @t2 (not @t20)) (tptp.aNaturalNumber0 (tptp.sbrdtbr0 @t1))))) % 0.16/0.39 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.16/0.39 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t19)) (exists @t41 (and @t13 @t40 (= @t1 (tptp.sdtpldt0 @t37 @t29)) (=> (not (= @t29 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t29) (tptp.sbrdtbr0 @t5)))))))) % 0.16/0.39 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 0.16/0.39 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.16/0.39 (assume @p35 (forall @t9 (=> @t8 (forall @t26 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t33 (=> (and (tptp.aDivisorOf0 @t29 @t1) (tptp.aDivisorOf0 @t29 @t5)) (tptp.doDivides0 @t29 @t11))))))))) % 0.16/0.39 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.16/0.39 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 (tptp.slsdtgt0 @t1)) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 0.16/0.39 (assume @p38 (tptp.aElement0 tptp.xc)) % 0.16/0.39 (assume @p39 (and @t46 (tptp.aElementOf0 tptp.xx @t43) (exists @t3 (and @t2 (= @t44 tptp.xy))) (tptp.aElementOf0 tptp.xy @t43) (tptp.aElement0 tptp.xz))) % 0.16/0.39 (assume @p40 @t47) % 0.16/0.39 (assume @p41 true) % 0.16/0.39 (step @p42 :rule bool-and-de-morgan :args (@t2 @t48 true)) % 0.16/0.39 (step @p43 :rule cong :premises (@p42) :args (@t50)) % 0.16/0.39 (step @p44 :rule cong :premises (@p43) :args (@t51)) % 0.16/0.39 (step @p45 :rule exists-elim :args ((= (exists @t3 @t49) @t51))) % 0.16/0.39 (step @p46 :rule trans :premises (@p45 @p44)) % 0.16/0.39 (step @p47 :rule eq-symm :args (@t44 tptp.xx)) % 0.16/0.39 (step @p48 :rule refl :args (@t2)) % 0.16/0.39 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t45)) % 0.16/0.39 (step @p50 :rule cong :premises (@p49) :args (@t46)) % 0.16/0.39 (step @p51 :rule trans :premises (@p50 @p46)) % 0.16/0.39 (step @p52 :rule and_elim :premises (@p39) :args (0)) % 0.16/0.39 (step @p53 :rule eq_resolve :premises (@p52 @p51)) % 0.16/0.39 (step @p54 :rule bool-double-not-elim :args (@t52)) % 0.16/0.39 (step @p55 :rule cong :premises (@p51) :args (@t47)) % 0.16/0.39 (step @p56 :rule trans :premises (@p55 @p54)) % 0.16/0.39 (step @p57 :rule eq_resolve :premises (@p40 @p56)) % 0.16/0.39 (step @p58 false :rule chain_m_resolution :premises (@p57 @p53) :args (false (@list true) (@list @t52))) % 0.16/0.39 ) % 0.16/0.39 % SZS output end Proof % 0.16/0.39 % cvc5 exiting %------------------------------------------------------------------------------