%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO002^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 09:11:45 AM UTC 2026 % Result : Theorem 0.62s 0.80s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO002^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n019.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 23:51:19 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 0.62/0.80 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.62/0.80 % SZS status Theorem % 0.62/0.80 % SZS output start Proof % 0.62/0.80 ( % 0.62/0.80 (declare-sort $$unsorted 0) % 0.62/0.80 (define tptp.leibeq () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.62/0.80 (define @t1 () (@var "Y" $$unsorted)) % 0.62/0.80 (define @t2 () (@var "F" (-> $$unsorted $$unsorted))) % 0.62/0.80 (define @t3 () (_ @t2 @t1)) % 0.62/0.80 (define @t4 () (@var "X" $$unsorted)) % 0.62/0.80 (define @t5 () (_ @t2 @t4)) % 0.62/0.80 (define @t6 () (=> (_ (_ tptp.leibeq @t4) @t1) (_ (_ tptp.leibeq @t5) @t3))) % 0.62/0.80 (define @t7 () (@list @t4 @t1 @t2)) % 0.62/0.80 (define @t8 () (forall @t7 @t6)) % 0.62/0.80 (define @t9 () (not @t8)) % 0.62/0.80 (define @t10 () (@var "P" (-> $$unsorted Bool))) % 0.62/0.80 (define @t11 () (_ @t10 @t1)) % 0.62/0.80 (define @t12 () (_ @t10 @t4)) % 0.62/0.80 (define @t13 () (@list @t10)) % 0.62/0.80 (define @t14 () (forall @t13 (=> @t12 @t11))) % 0.62/0.80 (define @t15 () (@list @t4 @t1)) % 0.62/0.80 (define @t16 () (lambda @t15 @t14)) % 0.62/0.80 (define @t17 () (_ @t2 @t1)) % 0.62/0.80 (define @t18 () (@var "BOUND_VARIABLE_7484" (-> $$unsorted Bool))) % 0.62/0.80 (define @t19 () (_ @t18 @t17)) % 0.62/0.80 (define @t20 () (_ @t2 @t4)) % 0.62/0.80 (define @t21 () (not (_ @t18 @t20))) % 0.62/0.80 (define @t22 () (_ @t10 @t1)) % 0.62/0.80 (define @t23 () (_ @t10 @t4)) % 0.62/0.80 (define @t24 () (forall @t13 (or (not @t23) @t22))) % 0.62/0.80 (define @t25 () (not @t24)) % 0.62/0.80 (define @t26 () (or @t25 @t21 @t19)) % 0.62/0.80 (define @t27 () (or @t21 @t19)) % 0.62/0.80 (define @t28 () (or @t25 @t27)) % 0.62/0.80 (define @t29 () (@list @t4 @t1 @t2 @t18)) % 0.62/0.80 (define @t30 () (forall @t29 @t28)) % 0.62/0.80 (define @t31 () (@list @t18)) % 0.62/0.80 (define @t32 () (forall @t31 @t28)) % 0.62/0.80 (define @t33 () (forall @t31 @t27)) % 0.62/0.80 (define @t34 () (or @t25 @t33)) % 0.62/0.80 (define @t35 () (not (_ @t10 @t20))) % 0.62/0.80 (define @t36 () (forall @t13 (or @t35 (_ @t10 @t17)))) % 0.62/0.80 (define @t37 () (_ @t10 @t3)) % 0.62/0.80 (define @t38 () (or @t35 @t37)) % 0.62/0.80 (define @t39 () (forall @t13 @t38)) % 0.62/0.80 (define @t40 () (@list @t1)) % 0.62/0.80 (define @t41 () (_ @t10 @t5)) % 0.62/0.80 (define @t42 () (not @t41)) % 0.62/0.80 (define @t43 () (or @t42 @t22)) % 0.62/0.80 (define @t44 () (forall @t13 @t43)) % 0.62/0.80 (define @t45 () (lambda @t40 @t44)) % 0.62/0.80 (define @t46 () (lambda @t15 @t24)) % 0.62/0.80 (define @t47 () (_ @t46 @t5)) % 0.62/0.80 (define @t48 () (lambda @t40 @t24)) % 0.62/0.80 (define @t49 () (_ @t46 @t4)) % 0.62/0.80 (define @t50 () (=> (_ @t49 @t1) (_ @t47 @t3))) % 0.62/0.80 (define @t51 () (forall @t7 @t50)) % 0.62/0.80 (define @t52 () (not @t12)) % 0.62/0.80 (define @t53 () (or @t52 @t11)) % 0.62/0.80 (define @t54 () (forall @t29 @t26)) % 0.62/0.80 (define @t55 () (@quantifiers_skolemize @t54 1)) % 0.62/0.80 (define @t56 () (@quantifiers_skolemize @t54 2)) % 0.62/0.80 (define @t57 () (@quantifiers_skolemize @t54 3)) % 0.62/0.80 (define @t58 () (_ @t57 (_ @t56 @t55))) % 0.62/0.80 (define @t59 () (@quantifiers_skolemize @t54 0)) % 0.62/0.80 (define @t60 () (_ @t56 @t59)) % 0.62/0.80 (define @t61 () (_ @t57 @t60)) % 0.62/0.80 (define @t62 () (not @t61)) % 0.62/0.80 (define @t63 () (forall @t13 (or (not (_ @t10 @t59)) (_ @t10 @t55)))) % 0.62/0.80 (define @t64 () (not @t63)) % 0.62/0.80 (define @t65 () (or @t64 @t62 @t58)) % 0.62/0.80 (define @t66 () (@list true)) % 0.62/0.80 (define @t67 () (@list @t65)) % 0.62/0.80 (define @t68 () (= @t59 @t55)) % 0.62/0.80 (define @t69 () (@var "BOUND_VARIABLE_14655" $$unsorted)) % 0.62/0.80 (define @t70 () (lambda (@list @t69) (= @t69 @t59))) % 0.62/0.80 (define @t71 () (_ @t70 @t55)) % 0.62/0.80 (define @t72 () (_ @t70 @t59)) % 0.62/0.80 (define @t73 () (not @t72)) % 0.62/0.80 (define @t74 () (or @t73 @t71)) % 0.62/0.80 (assume @p1 @t9) % 0.62/0.80 (assume @p2 true) % 0.62/0.80 (step @p3 (= tptp.leibeq @t16) :rule refl :args (@t16)) % 0.62/0.80 (step @p4 :rule evaluate :args ((= true false))) % 0.62/0.80 (step @p5 :rule aci_norm :args ((= @t28 @t26))) % 0.62/0.80 (step @p6 :rule cong :premises (@p5) :args (@t30)) % 0.62/0.80 (step @p7 :rule quant-merge-prenex :args ((= (forall @t7 @t32) @t30))) % 0.62/0.80 (step @p8 :rule alpha_equiv :args (@t33 (@list @t18) (@list @t10))) % 0.62/0.80 (step @p9 :rule refl :args (@t25)) % 0.62/0.80 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t34)) % 0.62/0.80 (step @p11 :rule quant-miniscope-or :args ((= @t32 @t34))) % 0.62/0.80 (step @p12 :rule trans :premises (@p11 @p10)) % 0.62/0.80 (step @p13 :rule symm :premises (@p12)) % 0.62/0.80 (step @p14 :rule cong :premises (@p13) :args ((forall @t7 (or @t25 @t36)))) % 0.62/0.80 (step @p15 :rule trans :premises (@p14 @p7)) % 0.62/0.80 (step @p16 :rule trans :premises (@p15 @p6)) % 0.62/0.80 (step @p17 :rule bool-impl-elim :args (@t24 @t36)) % 0.62/0.80 (step @p18 :rule cong :premises (@p17) :args ((forall @t7 (=> @t24 @t36)))) % 0.62/0.80 (step @p19 :rule trans :premises (@p18 @p16)) % 0.62/0.80 (step @p20 :rule refl :args (@t17)) % 0.62/0.80 (step @p21 :rule refl :args (@t3)) % 0.62/0.80 (step @p22 :rule cong :premises (@p21 @p20) :args ((= @t3 @t17))) % 0.62/0.80 (step @p23 :rule symm :premises (@p22)) % 0.62/0.80 (step @p24 :rule eq_resolve :premises (@p21 @p23)) % 0.62/0.80 (step @p25 :rule cong :premises (@p24) :args (@t37)) % 0.62/0.80 (step @p26 :rule refl :args (@t35)) % 0.62/0.80 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t38)) % 0.62/0.80 (step @p28 :rule cong :premises (@p27) :args (@t39)) % 0.62/0.80 (step @p29 :rule beta-reduce :args ((= (_ (lambda @t40 (forall @t13 (or @t35 @t22))) @t3) @t39))) % 0.62/0.80 (step @p30 :rule trans :premises (@p29 @p28)) % 0.62/0.80 (step @p31 :rule refl :args (@t3)) % 0.62/0.80 (step @p32 :rule refl :args (@t22)) % 0.62/0.80 (step @p33 :rule refl :args (@t20)) % 0.62/0.80 (step @p34 :rule refl :args (@t5)) % 0.62/0.80 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t5 @t20))) % 0.62/0.80 (step @p36 :rule symm :premises (@p35)) % 0.62/0.80 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.62/0.80 (step @p38 :rule cong :premises (@p37) :args (@t41)) % 0.62/0.80 (step @p39 :rule cong :premises (@p38) :args (@t42)) % 0.62/0.80 (step @p40 :rule nary_cong :premises (@p39 @p32) :args (@t43)) % 0.62/0.80 (step @p41 :rule cong :premises (@p40) :args (@t44)) % 0.62/0.80 (step @p42 :rule cong :premises (@p41) :args (@t45)) % 0.62/0.80 (step @p43 :rule beta-reduce :args ((= @t47 @t45))) % 0.62/0.80 (step @p44 :rule trans :premises (@p43 @p42)) % 0.62/0.80 (step @p45 :rule ho_cong :premises (@p44 @p31)) % 0.62/0.80 (step @p46 :rule trans :premises (@p45 @p30)) % 0.62/0.80 (step @p47 :rule beta-reduce :args ((= (_ @t48 @t1) @t24))) % 0.62/0.80 (step @p48 :rule refl :args (@t1)) % 0.62/0.80 (step @p49 :rule beta-reduce :args ((= @t49 @t48))) % 0.62/0.80 (step @p50 :rule ho_cong :premises (@p49 @p48)) % 0.62/0.80 (step @p51 :rule trans :premises (@p50 @p47)) % 0.62/0.80 (step @p52 :rule cong :premises (@p51 @p46) :args (@t50)) % 0.62/0.80 (step @p53 :rule cong :premises (@p52) :args (@t51)) % 0.62/0.80 (step @p54 :rule trans :premises (@p53 @p19)) % 0.62/0.80 (step @p55 :rule cong :premises (@p54) :args ((not @t51))) % 0.62/0.80 (step @p56 :rule refl :args (@t5)) % 0.62/0.80 (step @p57 :rule refl :args (@t22)) % 0.62/0.80 (step @p58 :rule refl :args (@t11)) % 0.62/0.80 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t11 @t22))) % 0.62/0.80 (step @p60 :rule symm :premises (@p59)) % 0.62/0.80 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.62/0.80 (step @p62 :rule refl :args (@t23)) % 0.62/0.80 (step @p63 :rule refl :args (@t12)) % 0.62/0.80 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t12 @t23))) % 0.62/0.80 (step @p65 :rule symm :premises (@p64)) % 0.62/0.80 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.62/0.80 (step @p67 :rule cong :premises (@p66) :args (@t52)) % 0.62/0.80 (step @p68 :rule nary_cong :premises (@p67 @p61) :args (@t53)) % 0.62/0.80 (step @p69 :rule cong :premises (@p68) :args ((forall @t13 @t53))) % 0.62/0.80 (step @p70 :rule bool-impl-elim :args (@t12 @t11)) % 0.62/0.80 (step @p71 :rule cong :premises (@p70) :args (@t14)) % 0.62/0.80 (step @p72 :rule trans :premises (@p71 @p69)) % 0.62/0.80 (step @p73 :rule cong :premises (@p72) :args (@t16)) % 0.62/0.80 (step @p74 :rule trans :premises (@p3 @p73)) % 0.62/0.80 (step @p75 :rule ho_cong :premises (@p74 @p56)) % 0.62/0.80 (step @p76 :rule ho_cong :premises (@p75 @p31)) % 0.62/0.80 (step @p77 :rule refl :args (@t4)) % 0.62/0.80 (step @p78 :rule ho_cong :premises (@p74 @p77)) % 0.62/0.80 (step @p79 :rule ho_cong :premises (@p78 @p48)) % 0.62/0.80 (step @p80 :rule cong :premises (@p79 @p76) :args (@t6)) % 0.62/0.80 (step @p81 :rule cong :premises (@p80) :args (@t8)) % 0.62/0.80 (step @p82 :rule cong :premises (@p81) :args (@t9)) % 0.62/0.80 (step @p83 :rule trans :premises (@p82 @p55)) % 0.62/0.80 (step @p84 :rule eq_resolve :premises (@p1 @p83)) % 0.62/0.80 (step @p85 :rule skolemize :premises (@p84)) % 0.62/0.80 (step @p86 :rule cnf_or_neg :args (@t65 2)) % 0.62/0.80 (step @p87 :rule chain_m_resolution :premises (@p86 @p85) :args ((not @t58) @t66 @t67)) % 0.62/0.80 (step @p88 :rule false_intro :premises (@p87)) % 0.62/0.80 (step @p89 :rule refl :args (@t58)) % 0.62/0.80 (step @p90 :rule symm :premises (@p89)) % 0.62/0.80 (step @p91 :rule bool-double-not-elim :args (@t63)) % 0.62/0.80 (step @p92 :rule refl :args (@t65)) % 0.62/0.80 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t65 (not @t64)))) % 0.62/0.80 (step @p94 :rule cnf_or_neg :args (@t65 0)) % 0.62/0.80 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.62/0.80 (step @p96 :rule reordering :premises (@p95) :args ((or @t63 @t65))) % 0.62/0.80 (step @p97 :rule chain_m_resolution :premises (@p96 @p85) :args (@t63 @t66 @t67)) % 0.62/0.80 (step @p98 :rule aci_norm :args ((= (or false @t68) @t68))) % 0.62/0.80 (step @p99 :rule eq-symm :args (@t55 @t59)) % 0.62/0.81 (step @p100 :rule beta-reduce :args ((= @t71 (= @t55 @t59)))) % 0.62/0.81 (step @p101 :rule trans :premises (@p100 @p99)) % 0.62/0.81 (step @p102 :rule evaluate :args ((not true))) % 0.62/0.81 (step @p103 :rule eq-refl :args (@t59)) % 0.62/0.81 (step @p104 :rule beta-reduce :args ((= @t72 (= @t59 @t59)))) % 0.62/0.81 (step @p105 :rule trans :premises (@p104 @p103)) % 0.62/0.81 (step @p106 :rule cong :premises (@p105) :args (@t73)) % 0.62/0.81 (step @p107 :rule trans :premises (@p106 @p102)) % 0.62/0.81 (step @p108 :rule nary_cong :premises (@p107 @p101) :args (@t74)) % 0.62/0.81 (step @p109 :rule trans :premises (@p108 @p98)) % 0.62/0.81 (step @p110 :rule refl :args (@t63)) % 0.62/0.81 (step @p111 :rule cong :premises (@p110 @p109) :args ((=> @t63 @t74))) % 0.62/0.81 (assume-push @p133 @t63) % 0.62/0.81 (step @p113 :rule instantiate :premises (@p97) :args ((@list @t70))) % 0.62/0.81 (step-pop @p134 :rule scope :premises (@p113)) % 0.62/0.81 (step @p114 :rule process_scope :premises (@p134) :args (@t74)) % 0.62/0.81 (step @p116 :rule eq_resolve :premises (@p114 @p111)) % 0.62/0.81 (step @p117 :rule implies_elim :premises (@p116)) % 0.62/0.81 (step @p118 :rule chain_m_resolution :premises (@p117 @p97) :args (@t68 (@list false) (@list @t63))) % 0.62/0.81 (step @p119 :rule cong :premises (@p118) :args (@t60)) % 0.62/0.81 (step @p120 :rule refl :args (@t57)) % 0.62/0.81 (step @p121 :rule ho_cong :premises (@p120 @p119)) % 0.62/0.81 (step @p122 :rule refl :args (@t61)) % 0.62/0.81 (step @p123 :rule bool-double-not-elim :args (@t61)) % 0.62/0.81 (step @p124 :rule nary_cong :premises (@p92 @p123) :args ((or @t65 (not @t62)))) % 0.62/0.81 (step @p125 :rule cnf_or_neg :args (@t65 1)) % 0.62/0.81 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.62/0.81 (step @p127 :rule reordering :premises (@p126) :args ((or @t61 @t65))) % 0.62/0.81 (step @p128 :rule chain_m_resolution :premises (@p127 @p85) :args (@t61 @t66 @t67)) % 0.62/0.81 (step @p129 :rule true_intro :premises (@p128)) % 0.62/0.81 (step @p130 :rule symm :premises (@p129)) % 0.62/0.81 (step @p131 :rule trans :premises (@p130 @p122 @p121 @p90 @p88)) % 0.62/0.81 (step @p132 false :rule eq_resolve :premises (@p131 @p4)) % 0.62/0.81 ) % 0.62/0.81 % SZS output end Proof % 0.62/0.81 % cvc5 exiting %------------------------------------------------------------------------------