%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO030^1 : 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 : n011.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 09:11:48 AM UTC 2026 % Result : Theorem 1.61s 1.89s % Output : Proof 1.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO030^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 23:51:35 EDT 2026 % 0.17/0.34 % CPUTime : % 0.25/0.50 %----Proving TH0 % 1.61/1.89 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.61/1.89 % SZS status Theorem % 1.61/1.89 % SZS output start Proof % 1.61/1.89 ( % 1.61/1.89 (define tptp.leibeq () (let ((_let_1 (@var "Y" Bool))) (let ((_let_2 (@var "P" (-> Bool Bool)))) (let ((_let_3 (@var "X" Bool))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 1.61/1.89 (define @t1 () (@var "X" Bool)) % 1.61/1.89 (define @t2 () (@var "F" (-> Bool Bool))) % 1.61/1.89 (define @t3 () (_ @t2 @t1)) % 1.61/1.89 (define @t4 () (@list @t1)) % 1.61/1.89 (define @t5 () (exists @t4 (_ (_ tptp.leibeq @t3) @t1))) % 1.61/1.89 (define @t6 () (@list @t2)) % 1.61/1.89 (define @t7 () (forall @t6 @t5)) % 1.61/1.89 (define @t8 () (not @t7)) % 1.61/1.89 (define @t9 () (not @t8)) % 1.61/1.89 (define @t10 () (@var "Y" Bool)) % 1.61/1.89 (define @t11 () (@var "P" (-> Bool Bool))) % 1.61/1.89 (define @t12 () (_ @t11 @t10)) % 1.61/1.89 (define @t13 () (_ @t11 @t1)) % 1.61/1.89 (define @t14 () (@list @t11)) % 1.61/1.89 (define @t15 () (forall @t14 (=> @t13 @t12))) % 1.61/1.89 (define @t16 () (@list @t1 @t10)) % 1.61/1.89 (define @t17 () (lambda @t16 @t15)) % 1.61/1.89 (define @t18 () (_ @t11 @t1)) % 1.61/1.89 (define @t19 () (_ @t2 @t1)) % 1.61/1.89 (define @t20 () (not (_ @t11 @t19))) % 1.61/1.89 (define @t21 () (forall @t14 (or @t20 @t18))) % 1.61/1.89 (define @t22 () (not (forall @t4 (not @t21)))) % 1.61/1.89 (define @t23 () (_ @t11 @t10)) % 1.61/1.89 (define @t24 () (@list @t10)) % 1.61/1.89 (define @t25 () (_ @t11 @t3)) % 1.61/1.89 (define @t26 () (not @t25)) % 1.61/1.89 (define @t27 () (or @t26 @t23)) % 1.61/1.89 (define @t28 () (forall @t14 @t27)) % 1.61/1.89 (define @t29 () (lambda @t24 @t28)) % 1.61/1.89 (define @t30 () (_ (lambda @t16 (forall @t14 (or (not @t18) @t23))) @t3)) % 1.61/1.89 (define @t31 () (exists @t4 (_ @t30 @t1))) % 1.61/1.89 (define @t32 () (forall @t6 @t31)) % 1.61/1.89 (define @t33 () (not @t13)) % 1.61/1.89 (define @t34 () (or @t33 @t12)) % 1.61/1.89 (define @t35 () (= @t1 true)) % 1.61/1.89 (define @t36 () (not @t35)) % 1.61/1.89 (define @t37 () (@var "BOUND_VARIABLE_42711" Bool)) % 1.61/1.89 (define @t38 () (lambda (@list @t37) (ite (= @t37 true) false true))) % 1.61/1.89 (define @t39 () (_ @t38 @t1)) % 1.61/1.89 (define @t40 () (_ @t11 @t39)) % 1.61/1.89 (define @t41 () (not @t40)) % 1.61/1.89 (define @t42 () (or @t41 @t18)) % 1.61/1.89 (define @t43 () (forall @t14 @t42)) % 1.61/1.89 (define @t44 () (not @t43)) % 1.61/1.89 (define @t45 () (forall @t4 @t44)) % 1.61/1.89 (define @t46 () (not @t45)) % 1.61/1.89 (define @t47 () (forall @t6 @t22)) % 1.61/1.89 (define @t48 () (@list @t38)) % 1.61/1.89 (define @t49 () (forall @t4 (not (forall @t14 (or (not (_ @t11 (not @t1))) @t18))))) % 1.61/1.89 (define @t50 () (not @t49)) % 1.61/1.89 (define @t51 () (@list false)) % 1.61/1.89 (define @t52 () (@quantifiers_skolemize @t49 0)) % 1.61/1.89 (define @t53 () (not @t52)) % 1.61/1.89 (define @t54 () (forall @t14 (or (not (_ @t11 @t53)) (_ @t11 @t52)))) % 1.61/1.89 (define @t55 () (not @t54)) % 1.61/1.89 (define @t56 () (not @t55)) % 1.61/1.89 (define @t57 () (@var "BOUND_VARIABLE_339419" Bool)) % 1.61/1.89 (define @t58 () (lambda (@list @t57) @t57)) % 1.61/1.89 (define @t59 () (_ @t58 @t52)) % 1.61/1.89 (define @t60 () (_ @t58 @t53)) % 1.61/1.89 (define @t61 () (not @t60)) % 1.61/1.89 (define @t62 () (or @t61 @t59)) % 1.61/1.89 (define @t63 () (= @t52 true)) % 1.61/1.89 (define @t64 () (not @t63)) % 1.61/1.89 (define @t65 () (_ @t38 @t52)) % 1.61/1.89 (define @t66 () (= @t53 true)) % 1.61/1.89 (define @t67 () (not @t66)) % 1.61/1.89 (define @t68 () (_ @t38 @t53)) % 1.61/1.89 (define @t69 () (not @t68)) % 1.61/1.89 (define @t70 () (or @t69 @t65)) % 1.61/1.89 (assume @p1 @t9) % 1.61/1.89 (assume @p2 true) % 1.61/1.89 (step @p3 (= tptp.leibeq @t17) :rule refl :args (@t17)) % 1.61/1.89 (step @p4 :rule exists-elim :args ((= (exists @t4 @t21) @t22))) % 1.61/1.89 (step @p5 :rule beta-reduce :args ((= (_ (lambda @t24 (forall @t14 (or @t20 @t23))) @t1) @t21))) % 1.61/1.89 (step @p6 :rule refl :args (@t1)) % 1.61/1.89 (step @p7 :rule refl :args (@t23)) % 1.61/1.89 (step @p8 :rule refl :args (@t19)) % 1.61/1.89 (step @p9 :rule refl :args (@t3)) % 1.61/1.89 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t3 @t19))) % 1.61/1.89 (step @p11 :rule symm :premises (@p10)) % 1.61/1.89 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 1.61/1.89 (step @p13 :rule cong :premises (@p12) :args (@t25)) % 1.61/1.89 (step @p14 :rule cong :premises (@p13) :args (@t26)) % 1.61/1.89 (step @p15 :rule nary_cong :premises (@p14 @p7) :args (@t27)) % 1.61/1.89 (step @p16 :rule cong :premises (@p15) :args (@t28)) % 1.61/1.89 (step @p17 :rule cong :premises (@p16) :args (@t29)) % 1.61/1.89 (step @p18 :rule beta-reduce :args ((= @t30 @t29))) % 1.61/1.89 (step @p19 :rule trans :premises (@p18 @p17)) % 1.61/1.89 (step @p20 :rule ho_cong :premises (@p19 @p6)) % 1.61/1.89 (step @p21 :rule trans :premises (@p20 @p5)) % 1.61/1.89 (step @p22 :rule cong :premises (@p21) :args (@t31)) % 1.61/1.89 (step @p23 :rule trans :premises (@p22 @p4)) % 1.61/1.89 (step @p24 :rule cong :premises (@p23) :args (@t32)) % 1.61/1.89 (step @p25 :rule bool-double-not-elim :args (@t32)) % 1.61/1.89 (step @p26 :rule trans :premises (@p25 @p24)) % 1.61/1.89 (step @p27 :rule refl :args (@t3)) % 1.61/1.89 (step @p28 :rule refl :args (@t23)) % 1.61/1.89 (step @p29 :rule refl :args (@t12)) % 1.61/1.89 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t12 @t23))) % 1.61/1.89 (step @p31 :rule symm :premises (@p30)) % 1.61/1.89 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 1.61/1.89 (step @p33 :rule refl :args (@t18)) % 1.61/1.89 (step @p34 :rule refl :args (@t13)) % 1.61/1.89 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t13 @t18))) % 1.61/1.89 (step @p36 :rule symm :premises (@p35)) % 1.61/1.89 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 1.61/1.89 (step @p38 :rule cong :premises (@p37) :args (@t33)) % 1.61/1.89 (step @p39 :rule nary_cong :premises (@p38 @p32) :args (@t34)) % 1.61/1.89 (step @p40 :rule cong :premises (@p39) :args ((forall @t14 @t34))) % 1.61/1.89 (step @p41 :rule bool-impl-elim :args (@t13 @t12)) % 1.61/1.89 (step @p42 :rule cong :premises (@p41) :args (@t15)) % 1.61/1.89 (step @p43 :rule trans :premises (@p42 @p40)) % 1.61/1.89 (step @p44 :rule cong :premises (@p43) :args (@t17)) % 1.61/1.89 (step @p45 :rule trans :premises (@p3 @p44)) % 1.61/1.89 (step @p46 :rule ho_cong :premises (@p45 @p27)) % 1.61/1.89 (step @p47 :rule ho_cong :premises (@p46 @p6)) % 1.61/1.89 (step @p48 :rule cong :premises (@p47) :args (@t5)) % 1.61/1.89 (step @p49 :rule cong :premises (@p48) :args (@t7)) % 1.61/1.89 (step @p50 :rule cong :premises (@p49) :args (@t8)) % 1.61/1.89 (step @p51 :rule cong :premises (@p50) :args (@t9)) % 1.61/1.89 (step @p52 :rule trans :premises (@p51 @p26)) % 1.61/1.89 (step @p53 :rule eq_resolve :premises (@p1 @p52)) % 1.61/1.89 (step @p54 :rule refl :args (@t18)) % 1.61/1.89 (step @p55 :rule bool-eq-true :args (@t1)) % 1.61/1.89 (step @p56 :rule cong :premises (@p55) :args (@t36)) % 1.61/1.89 (step @p57 :rule aci_norm :args ((= (and @t36 true) @t36))) % 1.61/1.89 (step @p58 :rule ite-then-false :args (@t35 true)) % 1.61/1.89 (step @p59 :rule trans :premises (@p58 @p57)) % 1.61/1.89 (step @p60 :rule trans :premises (@p59 @p56)) % 1.61/1.89 (step @p61 :rule beta-reduce :args ((= @t39 (ite @t35 false true)))) % 1.61/1.89 (step @p62 :rule trans :premises (@p61 @p60)) % 1.61/1.89 (step @p63 :rule cong :premises (@p62) :args (@t40)) % 1.61/1.89 (step @p64 :rule cong :premises (@p63) :args (@t41)) % 1.61/1.89 (step @p65 :rule nary_cong :premises (@p64 @p54) :args (@t42)) % 1.61/1.89 (step @p66 :rule cong :premises (@p65) :args (@t43)) % 1.61/1.89 (step @p67 :rule cong :premises (@p66) :args (@t44)) % 1.61/1.89 (step @p68 :rule cong :premises (@p67) :args (@t45)) % 1.61/1.89 (step @p69 :rule cong :premises (@p68) :args (@t46)) % 1.61/1.89 (step @p70 :rule refl :args (@t47)) % 1.61/1.89 (step @p71 :rule cong :premises (@p70 @p69) :args ((=> @t47 @t46))) % 1.61/1.89 (assume-push @p140 @t47) % 1.61/1.89 (step @p73 :rule instantiate :premises (@p53) :args (@t48)) % 1.61/1.89 (step-pop @p141 :rule scope :premises (@p73)) % 1.61/1.89 (step @p74 :rule process_scope :premises (@p141) :args (@t46)) % 1.61/1.89 (step @p76 :rule eq_resolve :premises (@p74 @p71)) % 1.61/1.89 (step @p77 :rule implies_elim :premises (@p76)) % 1.61/1.89 (step @p78 :rule chain_m_resolution :premises (@p77 @p53) :args (@t50 @t51 (@list @t47))) % 1.61/1.89 (step @p79 :rule refl :args (@t54)) % 1.61/1.89 (step @p80 :rule bool-double-not-elim :args (@t49)) % 1.61/1.89 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or (not @t50) @t54))) % 1.61/1.89 (step @p82 :rule bool-double-not-elim :args (@t54)) % 1.61/1.89 (step @p83 :rule refl :args (@t50)) % 1.61/1.89 (step @p84 :rule cong :premises (@p83 @p82) :args ((=> @t50 @t56))) % 1.61/1.89 (assume-push @p142 @t50) % 1.61/1.89 (step @p86 :rule skolemize :premises (@p78)) % 1.61/1.89 (step-pop @p143 :rule scope :premises (@p86)) % 1.61/1.89 (step @p87 :rule process_scope :premises (@p143) :args (@t56)) % 1.61/1.89 (step @p89 :rule eq_resolve :premises (@p87 @p84)) % 1.61/1.89 (step @p90 :rule implies_elim :premises (@p89)) % 1.61/1.89 (step @p91 :rule eq_resolve :premises (@p90 @p81)) % 1.61/1.89 (step @p92 :rule chain_m_resolution :premises (@p91 @p78) :args (@t54 (@list true) (@list @t49))) % 1.61/1.89 (step @p93 :rule aci_norm :args ((= (or @t52 @t52) @t52))) % 1.61/1.89 (step @p94 :rule beta-reduce :args ((= @t59 @t52))) % 1.61/1.89 (step @p95 :rule bool-double-not-elim :args (@t52)) % 1.61/1.89 (step @p96 :rule beta-reduce :args ((= @t60 @t53))) % 1.61/1.89 (step @p97 :rule cong :premises (@p96) :args (@t61)) % 1.61/1.89 (step @p98 :rule trans :premises (@p97 @p95)) % 1.61/1.89 (step @p99 :rule nary_cong :premises (@p98 @p94) :args (@t62)) % 1.61/1.89 (step @p100 :rule trans :premises (@p99 @p93)) % 1.61/1.89 (step @p101 :rule cong :premises (@p79 @p100) :args ((=> @t54 @t62))) % 1.61/1.89 (assume-push @p144 @t54) % 1.61/1.89 (step @p103 :rule instantiate :premises (@p92) :args ((@list @t58))) % 1.61/1.89 (step-pop @p145 :rule scope :premises (@p103)) % 1.61/1.89 (step @p104 :rule process_scope :premises (@p145) :args (@t62)) % 1.61/1.89 (step @p106 :rule eq_resolve :premises (@p104 @p101)) % 1.61/1.89 (step @p107 :rule implies_elim :premises (@p106)) % 1.61/1.89 (step @p108 :rule reordering :premises (@p107) :args ((or @t52 @t55))) % 1.61/1.89 (step @p109 :rule chain_m_resolution :premises (@p108 @p92) :args (@t52 @t51 (@list @t54))) % 1.61/1.89 (step @p110 :rule aci_norm :args ((= (or @t53 @t53) @t53))) % 1.61/1.89 (step @p111 :rule bool-eq-true :args (@t52)) % 1.61/1.89 (step @p112 :rule cong :premises (@p111) :args (@t64)) % 1.61/1.89 (step @p113 :rule aci_norm :args ((= (and @t64 true) @t64))) % 1.61/1.89 (step @p114 :rule ite-then-false :args (@t63 true)) % 1.61/1.89 (step @p115 :rule trans :premises (@p114 @p113)) % 1.61/1.89 (step @p116 :rule trans :premises (@p115 @p112)) % 1.61/1.89 (step @p117 :rule beta-reduce :args ((= @t65 (ite @t63 false true)))) % 1.61/1.89 (step @p118 :rule trans :premises (@p117 @p116)) % 1.61/1.89 (step @p119 :rule bool-eq-true :args (@t53)) % 1.61/1.89 (step @p120 :rule cong :premises (@p119) :args (@t67)) % 1.61/1.89 (step @p121 :rule trans :premises (@p120 @p95)) % 1.61/1.89 (step @p122 :rule aci_norm :args ((= (and @t67 true) @t67))) % 1.61/1.89 (step @p123 :rule ite-then-false :args (@t66 true)) % 1.61/1.89 (step @p124 :rule trans :premises (@p123 @p122)) % 1.61/1.89 (step @p125 :rule trans :premises (@p124 @p121)) % 1.61/1.89 (step @p126 :rule beta-reduce :args ((= @t68 (ite @t66 false true)))) % 1.61/1.89 (step @p127 :rule trans :premises (@p126 @p125)) % 1.61/1.89 (step @p128 :rule cong :premises (@p127) :args (@t69)) % 1.61/1.89 (step @p129 :rule nary_cong :premises (@p128 @p118) :args (@t70)) % 1.61/1.89 (step @p130 :rule trans :premises (@p129 @p110)) % 1.61/1.89 (step @p131 :rule cong :premises (@p79 @p130) :args ((=> @t54 @t70))) % 1.61/1.89 (assume-push @p146 @t54) % 1.61/1.89 (step @p133 :rule instantiate :premises (@p92) :args (@t48)) % 1.61/1.89 (step-pop @p147 :rule scope :premises (@p133)) % 1.61/1.89 (step @p134 :rule process_scope :premises (@p147) :args (@t70)) % 1.61/1.89 (step @p136 :rule eq_resolve :premises (@p134 @p131)) % 1.61/1.89 (step @p137 :rule implies_elim :premises (@p136)) % 1.61/1.89 (step @p138 :rule reordering :premises (@p137) :args ((or @t53 @t55))) % 1.61/1.89 (step @p139 false :rule chain_m_resolution :premises (@p138 @p109 @p92) :args (false (@list false false) (@list @t52 @t54))) % 1.61/1.89 ) % 1.61/1.89 % SZS output end Proof % 1.61/1.89 % cvc5 exiting %------------------------------------------------------------------------------