%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN321+1 : TPTP v9.2.1. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 09:08:32 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN321+1 : TPTP v9.2.1. Released v2.0.0. % 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 : n006.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 23:23:04 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort $$unsorted 0) % 0.37/0.56 (declare-const tptp.big_f (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.big_g (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (define @t1 () (@var "Z" $$unsorted)) % 0.37/0.56 (define @t2 () (@var "X" $$unsorted)) % 0.37/0.56 (define @t3 () (@list @t1)) % 0.37/0.56 (define @t4 () (forall @t3 (tptp.big_g @t2 @t1))) % 0.37/0.56 (define @t5 () (@var "Y" $$unsorted)) % 0.37/0.56 (define @t6 () (tptp.big_f @t2 @t5)) % 0.37/0.56 (define @t7 () (tptp.big_f @t1 @t5)) % 0.37/0.56 (define @t8 () (tptp.big_g @t1 @t1)) % 0.37/0.56 (define @t9 () (forall @t3 (=> @t8 @t7))) % 0.37/0.56 (define @t10 () (=> @t9 (= @t6 @t4))) % 0.37/0.56 (define @t11 () (tptp.big_f @t2 @t1)) % 0.37/0.56 (define @t12 () (exists @t3 @t11)) % 0.37/0.56 (define @t13 () (=> @t12 @t4)) % 0.37/0.56 (define @t14 () (=> @t13 @t10)) % 0.37/0.56 (define @t15 () (@list @t2 @t5)) % 0.37/0.56 (define @t16 () (exists @t15 @t14)) % 0.37/0.56 (define @t17 () (not @t16)) % 0.37/0.56 (define @t18 () (@var "BOUND_VARIABLE_7476" $$unsorted)) % 0.37/0.56 (define @t19 () (@var "BOUND_VARIABLE_7478" $$unsorted)) % 0.37/0.56 (define @t20 () (forall (@list @t18 @t19) (= (tptp.big_f @t18 @t19) (not (forall @t3 (tptp.big_g @t18 @t1)))))) % 0.37/0.56 (define @t21 () (@var "BOUND_VARIABLE_7469" $$unsorted)) % 0.37/0.56 (define @t22 () (not @t8)) % 0.37/0.56 (define @t23 () (or @t22 (tptp.big_f @t1 @t21))) % 0.37/0.56 (define @t24 () (forall (@list @t21 @t1) @t23)) % 0.37/0.56 (define @t25 () (@var "BOUND_VARIABLE_7494" $$unsorted)) % 0.37/0.56 (define @t26 () (@var "BOUND_VARIABLE_7455" $$unsorted)) % 0.37/0.56 (define @t27 () (tptp.big_g @t26 @t25)) % 0.37/0.56 (define @t28 () (@var "BOUND_VARIABLE_7490" $$unsorted)) % 0.37/0.56 (define @t29 () (not (tptp.big_f @t26 @t28))) % 0.37/0.56 (define @t30 () (or @t29 @t27)) % 0.37/0.56 (define @t31 () (forall (@list @t26 @t28 @t25) @t30)) % 0.37/0.56 (define @t32 () (@var "BOUND_VARIABLE_7467" $$unsorted)) % 0.37/0.56 (define @t33 () (forall (@list @t32 @t21 @t1) @t23)) % 0.37/0.56 (define @t34 () (forall (@list @t32 @t21) (forall @t3 @t23))) % 0.37/0.56 (define @t35 () (forall (@list @t28 @t25) @t30)) % 0.37/0.56 (define @t36 () (@list @t26)) % 0.37/0.56 (define @t37 () (forall (@list @t25) @t27)) % 0.37/0.56 (define @t38 () (@list @t1)) % 0.37/0.56 (define @t39 () (forall (@list @t28) @t29)) % 0.37/0.56 (define @t40 () (or @t39 @t37)) % 0.37/0.56 (define @t41 () (or (forall @t3 (not (tptp.big_f @t26 @t1))) (forall @t3 (tptp.big_g @t26 @t1)))) % 0.37/0.56 (define @t42 () (forall @t36 @t41)) % 0.37/0.56 (define @t43 () (@var "BOUND_VARIABLE_7457" $$unsorted)) % 0.37/0.56 (define @t44 () (forall (@list @t26 @t43) @t41)) % 0.37/0.56 (define @t45 () (not @t4)) % 0.37/0.56 (define @t46 () (= @t6 @t45)) % 0.37/0.56 (define @t47 () (forall @t15 @t46)) % 0.37/0.56 (define @t48 () (@list @t2 @t5)) % 0.37/0.56 (define @t49 () (forall @t3 (or @t22 @t7))) % 0.37/0.56 (define @t50 () (forall @t15 @t49)) % 0.37/0.56 (define @t51 () (forall @t3 (not @t11))) % 0.37/0.56 (define @t52 () (or @t51 @t4)) % 0.37/0.56 (define @t53 () (forall @t15 @t52)) % 0.37/0.56 (define @t54 () (and @t53 @t50 @t47)) % 0.37/0.56 (define @t55 () (= @t45 @t6)) % 0.37/0.56 (define @t56 () (and @t52 @t49 @t55)) % 0.37/0.56 (define @t57 () (= @t4 @t6)) % 0.37/0.56 (define @t58 () (not @t51)) % 0.37/0.56 (define @t59 () (=> @t49 @t57)) % 0.37/0.56 (define @t60 () (=> @t58 @t4)) % 0.37/0.56 (define @t61 () (=> @t60 @t59)) % 0.37/0.56 (define @t62 () (forall @t15 (not @t61))) % 0.37/0.56 (define @t63 () (not @t62)) % 0.37/0.56 (define @t64 () (@const 0 $$unsorted)) % 0.37/0.56 (define @t65 () (@list @t64 @t64)) % 0.37/0.56 (define @t66 () (tptp.big_f @t64 @t64)) % 0.37/0.56 (define @t67 () (tptp.big_g @t64 @t64)) % 0.37/0.56 (define @t68 () (not @t67)) % 0.37/0.56 (define @t69 () (or @t68 @t66)) % 0.37/0.56 (define @t70 () (forall @t3 (tptp.big_g @t64 @t1))) % 0.37/0.56 (define @t71 () (not @t70)) % 0.37/0.56 (define @t72 () (= @t66 @t71)) % 0.37/0.56 (define @t73 () (not @t72)) % 0.37/0.56 (define @t74 () (not @t71)) % 0.37/0.56 (define @t75 () (not @t66)) % 0.37/0.56 (define @t76 () (@quantifiers_skolemize @t70 0)) % 0.37/0.56 (define @t77 () (tptp.big_g @t64 @t76)) % 0.37/0.56 (define @t78 () (not @t77)) % 0.37/0.56 (define @t79 () (or @t75 @t77)) % 0.37/0.56 (define @t80 () (not @t79)) % 0.37/0.56 (assume @p1 @t17) % 0.37/0.56 (assume @p2 true) % 0.37/0.56 (step @p3 :rule bool-double-not-elim :args ((and @t31 @t24 @t20))) % 0.37/0.56 (step @p4 :rule refl :args (@t20)) % 0.37/0.56 (step @p5 :rule quant-unused-vars :args ((= @t33 @t24))) % 0.37/0.56 (step @p6 :rule quant-merge-prenex :args ((= @t34 @t33))) % 0.37/0.56 (step @p7 :rule trans :premises (@p6 @p5)) % 0.37/0.56 (step @p8 :rule quant-merge-prenex :args ((= (forall @t36 @t35) @t31))) % 0.37/0.56 (step @p9 :rule alpha_equiv :args (@t37 (@list @t25) @t38)) % 0.37/0.56 (step @p10 :rule alpha_equiv :args (@t39 (@list @t28) @t38)) % 0.37/0.56 (step @p11 :rule nary_cong :premises (@p10 @p9) :args (@t40)) % 0.37/0.56 (step @p12 :rule quant-miniscope-or :args ((= @t35 @t40))) % 0.37/0.56 (step @p13 :rule trans :premises (@p12 @p11)) % 0.37/0.56 (step @p14 :rule symm :premises (@p13)) % 0.37/0.56 (step @p15 :rule cong :premises (@p14) :args (@t42)) % 0.37/0.56 (step @p16 :rule trans :premises (@p15 @p8)) % 0.37/0.56 (step @p17 :rule quant-unused-vars :args ((= @t44 @t42))) % 0.37/0.56 (step @p18 :rule trans :premises (@p17 @p16)) % 0.37/0.56 (step @p19 :rule nary_cong :premises (@p18 @p7 @p4) :args ((and @t44 @t34 @t20))) % 0.37/0.56 (step @p20 :rule alpha_equiv :args (@t47 @t48 (@list @t18 @t19))) % 0.37/0.56 (step @p21 :rule alpha_equiv :args (@t50 @t48 (@list @t32 @t21))) % 0.37/0.56 (step @p22 :rule alpha_equiv :args (@t53 @t48 (@list @t26 @t43))) % 0.37/0.56 (step @p23 :rule nary_cong :premises (@p22 @p21 @p20) :args (@t54)) % 0.37/0.56 (step @p24 :rule quant-miniscope-and :args ((= (forall @t15 (and @t52 @t49 @t46)) @t54))) % 0.37/0.56 (step @p25 :rule trans :premises (@p24 @p23)) % 0.37/0.56 (step @p26 :rule trans :premises (@p25 @p19)) % 0.37/0.56 (step @p27 :rule eq-symm :args (@t45 @t6)) % 0.37/0.56 (step @p28 :rule refl :args (@t49)) % 0.37/0.56 (step @p29 :rule refl :args (@t52)) % 0.37/0.56 (step @p30 :rule nary_cong :premises (@p29 @p28 @p27) :args (@t56)) % 0.37/0.56 (step @p31 :rule cong :premises (@p30) :args ((forall @t15 @t56))) % 0.37/0.56 (step @p32 :rule trans :premises (@p31 @p26)) % 0.37/0.56 (step @p33 :rule aci_norm :args ((= (and @t52 (and @t49 @t55)) @t56))) % 0.37/0.56 (step @p34 :rule bool-not-eq-elim1 :args (@t4 @t6)) % 0.37/0.56 (step @p35 :rule refl :args (@t49)) % 0.37/0.56 (step @p36 :rule nary_cong :premises (@p35 @p34) :args ((and @t49 (not @t57)))) % 0.37/0.56 (step @p37 :rule bool-implies-de-morgan :args (@t49 @t57)) % 0.37/0.56 (step @p38 :rule trans :premises (@p37 @p36)) % 0.37/0.56 (step @p39 :rule refl :args (@t4)) % 0.37/0.56 (step @p40 :rule bool-double-not-elim :args (@t51)) % 0.37/0.56 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t58) @t4))) % 0.37/0.56 (step @p42 :rule bool-impl-elim :args (@t58 @t4)) % 0.37/0.56 (step @p43 :rule trans :premises (@p42 @p41)) % 0.37/0.56 (step @p44 :rule nary_cong :premises (@p43 @p38) :args ((and @t60 (not @t59)))) % 0.37/0.56 (step @p45 :rule trans :premises (@p44 @p33)) % 0.37/0.56 (step @p46 :rule bool-implies-de-morgan :args (@t60 @t59)) % 0.37/0.56 (step @p47 :rule trans :premises (@p46 @p45)) % 0.37/0.56 (step @p48 :rule cong :premises (@p47) :args (@t62)) % 0.37/0.56 (step @p49 :rule trans :premises (@p48 @p32)) % 0.37/0.56 (step @p50 :rule cong :premises (@p49) :args (@t63)) % 0.37/0.56 (step @p51 :rule exists-elim :args ((= (exists @t15 @t61) @t63))) % 0.37/0.56 (step @p52 :rule trans :premises (@p51 @p50)) % 0.37/0.56 (step @p53 :rule eq-symm :args (@t6 @t4)) % 0.37/0.56 (step @p54 :rule bool-impl-elim :args (@t8 @t7)) % 0.37/0.56 (step @p55 :rule cong :premises (@p54) :args (@t9)) % 0.37/0.56 (step @p56 :rule cong :premises (@p55 @p53) :args (@t10)) % 0.37/0.56 (step @p57 :rule refl :args (@t4)) % 0.37/0.56 (step @p58 :rule exists-elim :args ((= @t12 @t58))) % 0.37/0.56 (step @p59 :rule cong :premises (@p58 @p57) :args (@t13)) % 0.37/0.56 (step @p60 :rule cong :premises (@p59 @p56) :args (@t14)) % 0.37/0.56 (step @p61 :rule cong :premises (@p60) :args (@t16)) % 0.37/0.56 (step @p62 :rule trans :premises (@p61 @p52)) % 0.37/0.56 (step @p63 :rule cong :premises (@p62) :args (@t17)) % 0.37/0.56 (step @p64 :rule trans :premises (@p63 @p3)) % 0.37/0.56 (step @p65 :rule eq_resolve :premises (@p1 @p64)) % 0.37/0.56 (step @p66 :rule and_elim :premises (@p65) :args (0)) % 0.37/0.56 (step @p67 :rule and_elim :premises (@p65) :args (2)) % 0.37/0.56 (step @p68 :rule instantiate :premises (@p67) :args (@t65)) % 0.37/0.56 (step @p69 :rule and_elim :premises (@p65) :args (1)) % 0.37/0.56 (step @p70 :rule instantiate :premises (@p69) :args (@t65)) % 0.37/0.56 (step @p71 :rule cnf_or_pos :args (@t69)) % 0.37/0.56 (step @p72 :rule reordering :premises (@p71) :args ((or @t66 @t68 (not @t69)))) % 0.37/0.56 (step @p73 :rule bool-double-not-elim :args (@t70)) % 0.37/0.56 (step @p74 :rule refl :args (@t66)) % 0.37/0.56 (step @p75 :rule refl :args (@t73)) % 0.37/0.56 (step @p76 :rule nary_cong :premises (@p75 @p74 @p73) :args ((or @t73 @t66 @t74))) % 0.37/0.56 (step @p77 :rule cnf_equiv_pos2 :args (@t72)) % 0.37/0.56 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 0.37/0.56 (step @p79 :rule reordering :premises (@p78) :args ((or @t66 @t70 @t73))) % 0.37/0.56 (assume-push @p108 @t70) % 0.37/0.56 (step @p81 :rule instantiate :premises (@p108) :args ((@list @t64))) % 0.37/0.56 (step-pop @p109 :rule scope :premises (@p81)) % 0.37/0.56 (step @p82 :rule process_scope :premises (@p109) :args (@t67)) % 0.37/0.56 (step @p84 :rule implies_elim :premises (@p82)) % 0.37/0.56 (step @p85 :rule reordering :premises (@p84) :args ((or @t67 @t71))) % 0.37/0.56 (step @p86 :rule chain_m_resolution :premises (@p85 @p79 @p68 @p72 @p70) :args (@t66 (@list false false true false) (@list @t70 @t72 @t67 @t69))) % 0.37/0.56 (step @p87 :rule cnf_equiv_pos1 :args (@t72)) % 0.37/0.56 (step @p88 :rule reordering :premises (@p87) :args ((or @t75 @t71 @t73))) % 0.37/0.56 (step @p89 :rule chain_m_resolution :premises (@p88 @p86 @p68) :args (@t71 (@list false false) (@list @t66 @t72))) % 0.37/0.56 (step @p90 :rule refl :args (@t78)) % 0.37/0.56 (step @p91 :rule nary_cong :premises (@p73 @p90) :args ((or @t74 @t78))) % 0.37/0.56 (assume-push @p110 @t71) % 0.37/0.56 (step @p93 :rule skolemize :premises (@p110)) % 0.37/0.56 (step-pop @p111 :rule scope :premises (@p93)) % 0.37/0.56 (step @p94 :rule process_scope :premises (@p111) :args (@t78)) % 0.37/0.56 (step @p96 :rule implies_elim :premises (@p94)) % 0.37/0.56 (step @p97 :rule eq_resolve :premises (@p96 @p91)) % 0.37/0.56 (step @p98 :rule chain_m_resolution :premises (@p97 @p89) :args (@t78 (@list true) (@list @t70))) % 0.37/0.56 (step @p99 :rule cnf_or_pos :args (@t79)) % 0.37/0.56 (step @p100 :rule reordering :premises (@p99) :args ((or @t75 @t77 @t80))) % 0.37/0.56 (step @p101 :rule chain_m_resolution :premises (@p100 @p86 @p98) :args (@t80 (@list false true) (@list @t66 @t77))) % 0.37/0.56 (assume-push @p112 @t31) % 0.37/0.56 (step @p103 :rule instantiate :premises (@p66) :args ((@list @t64 @t64 @t76))) % 0.37/0.56 (step-pop @p113 :rule scope :premises (@p103)) % 0.37/0.56 (step @p104 :rule process_scope :premises (@p113) :args (@t79)) % 0.37/0.56 (step @p106 :rule implies_elim :premises (@p104)) % 0.37/0.56 (step @p107 false :rule chain_m_resolution :premises (@p106 @p101 @p66) :args (false (@list true false) (@list @t79 @t31))) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------