%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET968+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:49:04 AM UTC 2026 % Result : Theorem 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET968+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n029.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % 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 16:20:02 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.39/0.57 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (define @t1 () (@var "A" $$unsorted)) % 0.39/0.57 (define @t2 () (@var "B" $$unsorted)) % 0.39/0.57 (define @t3 () (tptp.set_union2 @t2 @t1)) % 0.39/0.57 (define @t4 () (tptp.set_union2 @t1 @t2)) % 0.39/0.57 (define @t5 () (@list @t1 @t2)) % 0.39/0.57 (define @t6 () (tptp.empty @t1)) % 0.39/0.57 (define @t7 () (not @t6)) % 0.39/0.57 (define @t8 () (@list @t1)) % 0.39/0.57 (define @t9 () (@var "C" $$unsorted)) % 0.39/0.57 (define @t10 () (= (tptp.cartesian_product2 @t9 @t4) (tptp.set_union2 (tptp.cartesian_product2 @t9 @t1) (tptp.cartesian_product2 @t9 @t2)))) % 0.39/0.57 (define @t11 () (tptp.cartesian_product2 @t2 @t9)) % 0.39/0.57 (define @t12 () (tptp.cartesian_product2 @t1 @t9)) % 0.39/0.57 (define @t13 () (= (tptp.cartesian_product2 @t4 @t9) (tptp.set_union2 @t12 @t11))) % 0.39/0.57 (define @t14 () (@list @t1 @t2 @t9)) % 0.39/0.57 (define @t15 () (forall @t14 (and @t13 @t10))) % 0.39/0.57 (define @t16 () (@var "D" $$unsorted)) % 0.39/0.57 (define @t17 () (forall (@list @t1 @t2 @t9 @t16) (= (tptp.cartesian_product2 @t4 (tptp.set_union2 @t9 @t16)) (tptp.set_union2 (tptp.set_union2 (tptp.set_union2 @t12 (tptp.cartesian_product2 @t1 @t16)) @t11) (tptp.cartesian_product2 @t2 @t16))))) % 0.39/0.57 (define @t18 () (forall @t14 @t10)) % 0.39/0.57 (define @t19 () (@list @t1 @t2 @t9)) % 0.39/0.57 (define @t20 () (@var "BOUND_VARIABLE_7503" $$unsorted)) % 0.39/0.57 (define @t21 () (@var "BOUND_VARIABLE_7501" $$unsorted)) % 0.39/0.57 (define @t22 () (@var "BOUND_VARIABLE_7499" $$unsorted)) % 0.39/0.57 (define @t23 () (forall @t14 @t13)) % 0.39/0.57 (define @t24 () (and @t23 @t18)) % 0.39/0.57 (define @t25 () (@quantifiers_skolemize @t17 3)) % 0.39/0.57 (define @t26 () (@quantifiers_skolemize @t17 2)) % 0.39/0.57 (define @t27 () (tptp.set_union2 @t26 @t25)) % 0.39/0.57 (define @t28 () (@quantifiers_skolemize @t17 1)) % 0.39/0.57 (define @t29 () (@quantifiers_skolemize @t17 0)) % 0.39/0.57 (define @t30 () (tptp.cartesian_product2 @t29 @t27)) % 0.39/0.57 (define @t31 () (tptp.set_union2 (tptp.cartesian_product2 @t29 @t26) (tptp.cartesian_product2 @t29 @t25))) % 0.39/0.57 (define @t32 () (forall (@list @t22 @t21 @t20) (= (tptp.cartesian_product2 @t20 (tptp.set_union2 @t22 @t21)) (tptp.set_union2 (tptp.cartesian_product2 @t20 @t22) (tptp.cartesian_product2 @t20 @t21))))) % 0.39/0.57 (define @t33 () (= @t30 @t31)) % 0.39/0.57 (define @t34 () (@list @t26 @t25 @t29)) % 0.39/0.57 (define @t35 () (= @t31 @t30)) % 0.39/0.57 (define @t36 () (tptp.cartesian_product2 @t28 @t25)) % 0.39/0.57 (define @t37 () (tptp.cartesian_product2 @t28 @t26)) % 0.39/0.57 (define @t38 () (tptp.cartesian_product2 @t28 @t27)) % 0.39/0.57 (define @t39 () (tptp.set_union2 @t30 @t38)) % 0.39/0.57 (define @t40 () (tptp.cartesian_product2 (tptp.set_union2 @t29 @t28) @t27)) % 0.39/0.57 (define @t41 () (= @t40 @t39)) % 0.39/0.57 (define @t42 () (tptp.set_union2 @t37 @t36)) % 0.39/0.57 (define @t43 () (tptp.set_union2 (tptp.set_union2 @t31 @t37) @t36)) % 0.39/0.57 (define @t44 () (= @t43 (tptp.set_union2 @t31 @t42))) % 0.39/0.57 (define @t45 () (= @t38 @t42)) % 0.39/0.57 (define @t46 () (= @t40 @t43)) % 0.39/0.57 (define @t47 () (and @t41 @t35 @t44 @t45)) % 0.39/0.57 (assume @p1 (forall @t5 (= @t4 @t3))) % 0.39/0.57 (assume @p2 (forall @t5 (=> @t7 (not (tptp.empty @t4))))) % 0.39/0.57 (assume @p3 (forall @t5 (=> @t7 (not (tptp.empty @t3))))) % 0.39/0.57 (assume @p4 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.39/0.57 (assume @p5 (exists @t8 @t6)) % 0.39/0.57 (assume @p6 (exists @t8 @t7)) % 0.39/0.57 (assume @p7 @t15) % 0.39/0.57 (assume @p8 (not @t17)) % 0.39/0.57 (assume @p9 (forall @t14 (= (tptp.set_union2 @t4 @t9) (tptp.set_union2 @t1 (tptp.set_union2 @t2 @t9))))) % 0.39/0.57 (assume @p10 true) % 0.39/0.57 (step @p11 :rule skolemize :premises (@p8)) % 0.39/0.57 (step @p12 :rule alpha_equiv :args (@t18 @t19 (@list @t22 @t21 @t20))) % 0.39/0.57 (step @p13 :rule alpha_equiv :args (@t23 @t19 (@list (@var "BOUND_VARIABLE_7485" $$unsorted) (@var "BOUND_VARIABLE_7487" $$unsorted) (@var "BOUND_VARIABLE_7489" $$unsorted)))) % 0.39/0.57 (step @p14 :rule nary_cong :premises (@p13 @p12) :args (@t24)) % 0.39/0.57 (step @p15 :rule quant-miniscope-and :args ((= @t15 @t24))) % 0.39/0.57 (step @p16 :rule trans :premises (@p15 @p14)) % 0.39/0.57 (step @p17 :rule eq_resolve :premises (@p7 @p16)) % 0.39/0.57 (step @p18 :rule and_elim :premises (@p17) :args (0)) % 0.39/0.57 (step @p19 :rule instantiate :premises (@p18) :args ((@list @t29 @t28 @t27))) % 0.39/0.57 (step @p20 :rule and_elim :premises (@p17) :args (1)) % 0.39/0.57 (step @p21 :rule eq-symm :args (@t30 @t31)) % 0.39/0.57 (step @p22 :rule refl :args (@t32)) % 0.39/0.57 (step @p23 :rule cong :premises (@p22 @p21) :args ((=> @t32 @t33))) % 0.39/0.57 (assume-push @p53 @t32) % 0.39/0.57 (step @p25 :rule instantiate :premises (@p20) :args (@t34)) % 0.39/0.57 (step-pop @p54 :rule scope :premises (@p25)) % 0.39/0.57 (step @p26 :rule process_scope :premises (@p54) :args (@t33)) % 0.39/0.57 (step @p28 :rule eq_resolve :premises (@p26 @p23)) % 0.39/0.57 (step @p29 :rule implies_elim :premises (@p28)) % 0.39/0.57 (step @p30 :rule chain_m_resolution :premises (@p29 @p20) :args (@t35 (@list false) (@list @t32))) % 0.39/0.57 (step @p31 :rule instantiate :premises (@p9) :args ((@list @t31 @t37 @t36))) % 0.39/0.57 (step @p32 :rule instantiate :premises (@p20) :args ((@list @t26 @t25 @t28))) % 0.39/0.57 (assume-push @p55 @t41) % 0.39/0.57 (assume-push @p56 @t35) % 0.39/0.57 (assume-push @p57 @t44) % 0.39/0.57 (assume-push @p58 @t45) % 0.39/0.57 (step @p37 :rule symm :premises (@p31)) % 0.39/0.57 (step @p38 :rule refl :args (@t31)) % 0.39/0.57 (step @p39 :rule cong :premises (@p38 @p32) :args ((tptp.set_union2 @t31 @t38))) % 0.39/0.57 (step @p40 :rule refl :args (@t38)) % 0.39/0.57 (step @p25 :rule instantiate :premises (@p20) :args (@t34)) % 0.39/0.57 (step @p41 :rule cong :premises (@p25 @p40) :args (@t39)) % 0.39/0.57 (step @p42 :rule trans :premises (@p19 @p41 @p39 @p37)) % 0.39/0.57 (step-pop @p59 :rule scope :premises (@p42)) % 0.39/0.57 (step-pop @p60 :rule scope :premises (@p59)) % 0.39/0.57 (step-pop @p61 :rule scope :premises (@p60)) % 0.39/0.57 (step-pop @p62 :rule scope :premises (@p61)) % 0.39/0.57 (step @p43 :rule process_scope :premises (@p62) :args (@t46)) % 0.39/0.57 (step @p48 :rule implies_elim :premises (@p43)) % 0.39/0.57 (step @p49 :rule cnf_and_neg :args (@t47)) % 0.39/0.57 (step @p50 :rule resolution :premises (@p49 @p48) :args (true @t47)) % 0.39/0.57 (step @p51 :rule reordering :premises (@p50) :args ((or @t46 (not @t41) (not @t35) (not @t44) (not @t45)))) % 0.39/0.57 (step @p52 false :rule chain_m_resolution :premises (@p51 @p32 @p31 @p30 @p19 @p11) :args (false (@list false false false false true) (@list @t45 @t44 @t35 @t41 @t46))) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------