%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG086+2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:45:37 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG086+2 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n017.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 14:05:16 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (declare-const tptp.xz $$unsorted) % 0.36/0.59 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.sz00 $$unsorted) % 0.36/0.59 (declare-const tptp.xx $$unsorted) % 0.36/0.59 (declare-const tptp.xI $$unsorted) % 0.36/0.59 (declare-const tptp.sz10 $$unsorted) % 0.36/0.59 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.xy $$unsorted) % 0.36/0.59 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.xJ $$unsorted) % 0.36/0.59 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (define @t1 () (@var "W0" $$unsorted)) % 0.36/0.59 (define @t2 () (tptp.aElement0 @t1)) % 0.36/0.59 (define @t3 () (@list @t1)) % 0.36/0.59 (define @t4 () (tptp.smndt0 @t1)) % 0.36/0.59 (define @t5 () (@var "W1" $$unsorted)) % 0.36/0.59 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.36/0.59 (define @t7 () (tptp.aElement0 @t5)) % 0.36/0.59 (define @t8 () (and @t2 @t7)) % 0.36/0.59 (define @t9 () (@list @t1 @t5)) % 0.36/0.59 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.36/0.59 (define @t11 () (@var "W2" $$unsorted)) % 0.36/0.59 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.36/0.59 (define @t13 () (tptp.aElement0 @t11)) % 0.36/0.59 (define @t14 () (and @t2 @t7 @t13)) % 0.36/0.59 (define @t15 () (@list @t1 @t5 @t11)) % 0.36/0.59 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.36/0.59 (define @t17 () (tptp.smndt0 tptp.sz10)) % 0.36/0.59 (define @t18 () (tptp.aSet0 @t1)) % 0.36/0.59 (define @t19 () (tptp.aElementOf0 @t5 @t1)) % 0.36/0.59 (define @t20 () (@list @t5)) % 0.36/0.59 (define @t21 () (tptp.aElementOf0 @t11 @t1)) % 0.36/0.59 (define @t22 () (tptp.aElementOf0 @t11 @t5)) % 0.36/0.59 (define @t23 () (@list @t11)) % 0.36/0.59 (define @t24 () (and @t18 (tptp.aSet0 @t5))) % 0.36/0.59 (define @t25 () (@var "W3" $$unsorted)) % 0.36/0.59 (define @t26 () (@var "W5" $$unsorted)) % 0.36/0.59 (define @t27 () (@var "W4" $$unsorted)) % 0.36/0.59 (define @t28 () (tptp.aElementOf0 @t25 @t11)) % 0.36/0.59 (define @t29 () (@list @t25)) % 0.36/0.59 (define @t30 () (tptp.aSet0 @t11)) % 0.36/0.59 (define @t31 () (tptp.aElementOf0 @t5 tptp.xJ)) % 0.36/0.59 (define @t32 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.36/0.59 (define @t33 () (tptp.sdtpldt1 tptp.xI tptp.xJ)) % 0.36/0.59 (define @t34 () (= @t6 tptp.xx)) % 0.36/0.59 (define @t35 () (and @t32 @t31 @t34)) % 0.36/0.59 (define @t36 () (exists @t9 @t35)) % 0.36/0.59 (define @t37 () (and @t32 @t31 (= tptp.xx @t6))) % 0.36/0.59 (define @t38 () (exists @t9 @t37)) % 0.36/0.59 (define @t39 () (not @t38)) % 0.36/0.59 (define @t40 () (not @t34)) % 0.36/0.59 (define @t41 () (not @t31)) % 0.36/0.59 (define @t42 () (not @t32)) % 0.36/0.59 (define @t43 () (or @t42 @t41 @t40)) % 0.36/0.59 (define @t44 () (forall @t9 (not @t35))) % 0.36/0.59 (define @t45 () (not @t44)) % 0.36/0.59 (define @t46 () (forall @t9 @t43)) % 0.36/0.59 (assume @p1 (forall @t3 (=> @t2 true))) % 0.36/0.59 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.36/0.59 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.36/0.59 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.36/0.59 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.36/0.59 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.36/0.59 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.36/0.59 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.36/0.59 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.36/0.59 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.36/0.59 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.36/0.59 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.36/0.59 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.36/0.59 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 (tptp.sdtasdt0 @t1 @t11))) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 0.36/0.59 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t17 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t17)))))) % 0.36/0.59 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.36/0.59 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or (= @t1 tptp.sz00) (= @t5 tptp.sz00)))))) % 0.36/0.59 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.36/0.59 (assume @p19 (forall @t3 (=> @t18 true))) % 0.36/0.59 (assume @p20 (forall @t3 (=> @t18 (forall @t20 (=> @t19 @t7))))) % 0.36/0.59 (assume @p21 (forall @t9 (=> @t24 (=> (and (forall @t23 (=> @t21 @t22)) (forall @t23 (=> @t22 @t21))) (= @t1 @t5))))) % 0.36/0.59 (assume @p22 (forall @t9 (=> @t24 (forall @t23 (= (= @t11 (tptp.sdtpldt1 @t1 @t5)) (and @t30 (forall @t29 (= @t28 (exists (@list @t27 @t26) (and (tptp.aElementOf0 @t27 @t1) (tptp.aElementOf0 @t26 @t5) (= (tptp.sdtpldt0 @t27 @t26) @t25))))))))))) % 0.36/0.59 (assume @p23 (forall @t9 (=> @t24 (forall @t23 (= (= @t11 (tptp.sdtasasdt0 @t1 @t5)) (and @t30 (forall @t29 (= @t28 (and (tptp.aElementOf0 @t25 @t1) (tptp.aElementOf0 @t25 @t5)))))))))) % 0.36/0.59 (assume @p24 (forall @t3 (= (tptp.aIdeal0 @t1) (and @t18 (forall @t20 (=> @t19 (and (forall @t23 (=> @t21 (tptp.aElementOf0 @t12 @t1))) (forall @t23 (=> @t13 (tptp.aElementOf0 (tptp.sdtasdt0 @t11 @t5) @t1)))))))))) % 0.36/0.59 (assume @p25 (and (tptp.aSet0 tptp.xI) (forall @t3 (=> @t32 (and (forall @t20 (=> (tptp.aElementOf0 @t5 tptp.xI) (tptp.aElementOf0 @t6 tptp.xI))) (forall @t20 (=> @t7 (tptp.aElementOf0 @t16 tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xJ) (and (forall @t20 (=> @t31 (tptp.aElementOf0 @t6 tptp.xJ))) (forall @t20 (=> @t7 (tptp.aElementOf0 @t16 tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ))) % 0.36/0.59 (assume @p26 (and @t36 (tptp.aElementOf0 tptp.xx @t33) (exists @t9 (and @t32 @t31 (= @t6 tptp.xy))) (tptp.aElementOf0 tptp.xy @t33) (tptp.aElement0 tptp.xz))) % 0.36/0.59 (assume @p27 @t39) % 0.36/0.59 (assume @p28 true) % 0.36/0.59 (step @p29 :rule aci_norm :args ((= (or @t42 (or @t41 @t40)) @t43))) % 0.36/0.59 (step @p30 :rule bool-and-de-morgan :args (@t31 @t34 true)) % 0.36/0.59 (step @p31 :rule refl :args (@t42)) % 0.36/0.59 (step @p32 :rule nary_cong :premises (@p31 @p30) :args ((or @t42 (not (and @t31 @t34))))) % 0.36/0.59 (step @p33 :rule bool-and-de-morgan :args (@t32 @t31 (and @t34))) % 0.36/0.59 (step @p34 :rule trans :premises (@p33 @p32)) % 0.36/0.59 (step @p35 :rule trans :premises (@p34 @p29)) % 0.36/0.59 (step @p36 :rule cong :premises (@p35) :args (@t44)) % 0.36/0.59 (step @p37 :rule cong :premises (@p36) :args (@t45)) % 0.36/0.59 (step @p38 :rule exists-elim :args ((= @t36 @t45))) % 0.36/0.59 (step @p39 :rule trans :premises (@p38 @p37)) % 0.36/0.59 (step @p40 :rule and_elim :premises (@p26) :args (0)) % 0.36/0.59 (step @p41 :rule eq_resolve :premises (@p40 @p39)) % 0.36/0.59 (step @p42 :rule bool-double-not-elim :args (@t46)) % 0.36/0.59 (step @p43 :rule eq-symm :args (tptp.xx @t6)) % 0.36/0.59 (step @p44 :rule refl :args (@t31)) % 0.36/0.59 (step @p45 :rule refl :args (@t32)) % 0.36/0.59 (step @p46 :rule nary_cong :premises (@p45 @p44 @p43) :args (@t37)) % 0.36/0.59 (step @p47 :rule cong :premises (@p46) :args (@t38)) % 0.36/0.59 (step @p48 :rule trans :premises (@p47 @p39)) % 0.36/0.59 (step @p49 :rule cong :premises (@p48) :args (@t39)) % 0.36/0.59 (step @p50 :rule trans :premises (@p49 @p42)) % 0.36/0.59 (step @p51 :rule eq_resolve :premises (@p27 @p50)) % 0.36/0.59 (step @p52 false :rule chain_m_resolution :premises (@p51 @p41) :args (false (@list true) (@list @t46))) % 0.36/0.59 ) % 0.36/0.59 % SZS output end Proof % 0.36/0.59 % cvc5 exiting %------------------------------------------------------------------------------