%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO005^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 0.46s 0.64s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO005^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n021.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 23:52:35 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.46/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.64 % SZS status Theorem % 0.46/0.64 % SZS output start Proof % 0.46/0.64 ( % 0.46/0.64 (declare-sort $$unsorted 0) % 0.46/0.64 (define tptp.leibeq1 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.46/0.64 (define tptp.leibeq2 () (let ((_let_1 (@var "Y" (-> $$unsorted $$unsorted)))) (let ((_let_2 (@var "P" (-> (-> $$unsorted $$unsorted) Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.46/0.64 (define @t1 () (@var "X" $$unsorted)) % 0.46/0.64 (define @t2 () (@var "G" (-> $$unsorted $$unsorted))) % 0.46/0.64 (define @t3 () (_ @t2 @t1)) % 0.46/0.64 (define @t4 () (@var "F" (-> $$unsorted $$unsorted))) % 0.46/0.64 (define @t5 () (_ @t4 @t1)) % 0.46/0.64 (define @t6 () (@list @t1)) % 0.46/0.64 (define @t7 () (forall @t6 (_ (_ tptp.leibeq1 @t5) @t3))) % 0.46/0.64 (define @t8 () (=> (_ (_ tptp.leibeq2 @t4) @t2) @t7)) % 0.46/0.64 (define @t9 () (@list @t4 @t2)) % 0.46/0.64 (define @t10 () (forall @t9 @t8)) % 0.46/0.64 (define @t11 () (not @t10)) % 0.46/0.64 (define @t12 () (@var "V" $$unsorted)) % 0.46/0.64 (define @t13 () (@var "Q" (-> $$unsorted Bool))) % 0.46/0.64 (define @t14 () (_ @t13 @t12)) % 0.46/0.64 (define @t15 () (@var "U" $$unsorted)) % 0.46/0.64 (define @t16 () (_ @t13 @t15)) % 0.46/0.64 (define @t17 () (@list @t13)) % 0.46/0.64 (define @t18 () (forall @t17 (=> @t16 @t14))) % 0.46/0.64 (define @t19 () (@list @t15 @t12)) % 0.46/0.64 (define @t20 () (lambda @t19 @t18)) % 0.46/0.64 (define @t21 () (@var "Y" (-> $$unsorted $$unsorted))) % 0.46/0.64 (define @t22 () (@var "P" (-> (-> $$unsorted $$unsorted) Bool))) % 0.46/0.64 (define @t23 () (_ @t22 @t21)) % 0.46/0.64 (define @t24 () (@var "X" (-> $$unsorted $$unsorted))) % 0.46/0.64 (define @t25 () (_ @t22 @t24)) % 0.46/0.64 (define @t26 () (@list @t22)) % 0.46/0.64 (define @t27 () (forall @t26 (=> @t25 @t23))) % 0.46/0.64 (define @t28 () (@list @t24 @t21)) % 0.46/0.64 (define @t29 () (lambda @t28 @t27)) % 0.46/0.64 (define @t30 () (@var "BOUND_VARIABLE_7534" $$unsorted)) % 0.46/0.64 (define @t31 () (@var "BOUND_VARIABLE_7536" (-> $$unsorted Bool))) % 0.46/0.64 (define @t32 () (_ @t31 (_ @t2 @t30))) % 0.46/0.64 (define @t33 () (not (_ @t31 (_ @t4 @t30)))) % 0.46/0.64 (define @t34 () (not (_ @t22 @t4))) % 0.46/0.64 (define @t35 () (forall @t26 (or @t34 (_ @t22 @t2)))) % 0.46/0.64 (define @t36 () (not @t35)) % 0.46/0.64 (define @t37 () (or @t36 @t33 @t32)) % 0.46/0.64 (define @t38 () (or @t33 @t32)) % 0.46/0.64 (define @t39 () (or @t36 @t38)) % 0.46/0.64 (define @t40 () (@list @t4 @t2 @t30 @t31)) % 0.46/0.64 (define @t41 () (forall @t40 @t39)) % 0.46/0.64 (define @t42 () (@list @t30 @t31)) % 0.46/0.64 (define @t43 () (forall @t42 @t39)) % 0.46/0.64 (define @t44 () (forall @t42 @t38)) % 0.46/0.64 (define @t45 () (or @t36 @t44)) % 0.46/0.64 (define @t46 () (_ @t2 @t1)) % 0.46/0.64 (define @t47 () (_ @t4 @t1)) % 0.46/0.64 (define @t48 () (not (_ @t13 @t47))) % 0.46/0.64 (define @t49 () (or @t48 (_ @t13 @t46))) % 0.46/0.64 (define @t50 () (forall (@list @t1 @t13) @t49)) % 0.46/0.64 (define @t51 () (_ @t13 @t3)) % 0.46/0.64 (define @t52 () (or @t48 @t51)) % 0.46/0.64 (define @t53 () (forall @t17 @t52)) % 0.46/0.64 (define @t54 () (_ @t13 @t12)) % 0.46/0.64 (define @t55 () (@list @t12)) % 0.46/0.64 (define @t56 () (_ @t13 @t5)) % 0.46/0.64 (define @t57 () (not @t56)) % 0.46/0.64 (define @t58 () (or @t57 @t54)) % 0.46/0.64 (define @t59 () (forall @t17 @t58)) % 0.46/0.64 (define @t60 () (lambda @t55 @t59)) % 0.46/0.64 (define @t61 () (_ @t13 @t15)) % 0.46/0.64 (define @t62 () (_ (lambda @t19 (forall @t17 (or (not @t61) @t54))) @t5)) % 0.46/0.64 (define @t63 () (forall @t6 (_ @t62 @t3))) % 0.46/0.64 (define @t64 () (_ @t22 @t21)) % 0.46/0.64 (define @t65 () (lambda (@list @t21) (forall @t26 (or @t34 @t64)))) % 0.46/0.64 (define @t66 () (_ @t22 @t24)) % 0.46/0.64 (define @t67 () (_ (lambda @t28 (forall @t26 (or (not @t66) @t64))) @t4)) % 0.46/0.64 (define @t68 () (=> (_ @t67 @t2) @t63)) % 0.46/0.64 (define @t69 () (forall @t9 @t68)) % 0.46/0.64 (define @t70 () (not @t16)) % 0.46/0.64 (define @t71 () (or @t70 @t14)) % 0.46/0.64 (define @t72 () (not @t25)) % 0.46/0.64 (define @t73 () (or @t72 @t23)) % 0.46/0.64 (define @t74 () (forall @t40 @t37)) % 0.46/0.64 (define @t75 () (@quantifiers_skolemize @t74 2)) % 0.46/0.64 (define @t76 () (@quantifiers_skolemize @t74 1)) % 0.46/0.64 (define @t77 () (@quantifiers_skolemize @t74 3)) % 0.46/0.64 (define @t78 () (_ @t77 (_ @t76 @t75))) % 0.46/0.64 (define @t79 () (@quantifiers_skolemize @t74 0)) % 0.46/0.64 (define @t80 () (_ @t77 (_ @t79 @t75))) % 0.46/0.64 (define @t81 () (not @t80)) % 0.46/0.64 (define @t82 () (forall @t26 (or (not (_ @t22 @t79)) (_ @t22 @t76)))) % 0.46/0.64 (define @t83 () (not @t82)) % 0.46/0.64 (define @t84 () (or @t83 @t81 @t78)) % 0.46/0.64 (define @t85 () (@list true)) % 0.46/0.64 (define @t86 () (@list @t84)) % 0.46/0.64 (define @t87 () (= @t79 @t76)) % 0.46/0.64 (define @t88 () (@var "BOUND_VARIABLE_14980" (-> $$unsorted $$unsorted))) % 0.46/0.64 (define @t89 () (lambda (@list @t88) (= @t88 @t79))) % 0.46/0.64 (define @t90 () (_ @t89 @t76)) % 0.46/0.64 (define @t91 () (_ @t89 @t79)) % 0.46/0.64 (define @t92 () (not @t91)) % 0.46/0.64 (define @t93 () (or @t92 @t90)) % 0.46/0.64 (assume @p1 @t11) % 0.46/0.64 (assume @p2 true) % 0.46/0.64 (step @p3 (= tptp.leibeq1 @t20) :rule refl :args (@t20)) % 0.46/0.64 (step @p4 (= tptp.leibeq2 @t29) :rule refl :args (@t29)) % 0.46/0.64 (step @p5 :rule evaluate :args ((= true false))) % 0.46/0.64 (step @p6 :rule aci_norm :args ((= @t39 @t37))) % 0.46/0.64 (step @p7 :rule cong :premises (@p6) :args (@t41)) % 0.46/0.64 (step @p8 :rule quant-merge-prenex :args ((= (forall @t9 @t43) @t41))) % 0.46/0.64 (step @p9 :rule alpha_equiv :args (@t44 (@list @t30 @t31) (@list @t1 @t13))) % 0.46/0.64 (step @p10 :rule refl :args (@t36)) % 0.46/0.64 (step @p11 :rule nary_cong :premises (@p10 @p9) :args (@t45)) % 0.46/0.64 (step @p12 :rule quant-miniscope-or :args ((= @t43 @t45))) % 0.46/0.64 (step @p13 :rule trans :premises (@p12 @p11)) % 0.46/0.64 (step @p14 :rule symm :premises (@p13)) % 0.46/0.64 (step @p15 :rule cong :premises (@p14) :args ((forall @t9 (or @t36 @t50)))) % 0.46/0.64 (step @p16 :rule trans :premises (@p15 @p8)) % 0.46/0.64 (step @p17 :rule trans :premises (@p16 @p7)) % 0.46/0.64 (step @p18 :rule bool-impl-elim :args (@t35 @t50)) % 0.46/0.64 (step @p19 :rule cong :premises (@p18) :args ((forall @t9 (=> @t35 @t50)))) % 0.46/0.64 (step @p20 :rule trans :premises (@p19 @p17)) % 0.46/0.64 (step @p21 :rule quant-merge-prenex :args ((= (forall @t6 (forall @t17 @t49)) @t50))) % 0.46/0.64 (step @p22 :rule refl :args (@t46)) % 0.46/0.64 (step @p23 :rule refl :args (@t3)) % 0.46/0.64 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t3 @t46))) % 0.46/0.64 (step @p25 :rule symm :premises (@p24)) % 0.46/0.64 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.46/0.64 (step @p27 :rule cong :premises (@p26) :args (@t51)) % 0.46/0.64 (step @p28 :rule refl :args (@t48)) % 0.46/0.64 (step @p29 :rule nary_cong :premises (@p28 @p27) :args (@t52)) % 0.46/0.64 (step @p30 :rule cong :premises (@p29) :args (@t53)) % 0.46/0.64 (step @p31 :rule beta-reduce :args ((= (_ (lambda @t55 (forall @t17 (or @t48 @t54))) @t3) @t53))) % 0.46/0.64 (step @p32 :rule trans :premises (@p31 @p30)) % 0.46/0.64 (step @p33 :rule refl :args (@t3)) % 0.46/0.64 (step @p34 :rule refl :args (@t54)) % 0.46/0.64 (step @p35 :rule refl :args (@t47)) % 0.46/0.64 (step @p36 :rule refl :args (@t5)) % 0.46/0.64 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t5 @t47))) % 0.46/0.64 (step @p38 :rule symm :premises (@p37)) % 0.46/0.64 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.46/0.64 (step @p40 :rule cong :premises (@p39) :args (@t56)) % 0.46/0.64 (step @p41 :rule cong :premises (@p40) :args (@t57)) % 0.46/0.64 (step @p42 :rule nary_cong :premises (@p41 @p34) :args (@t58)) % 0.46/0.64 (step @p43 :rule cong :premises (@p42) :args (@t59)) % 0.46/0.64 (step @p44 :rule cong :premises (@p43) :args (@t60)) % 0.46/0.64 (step @p45 :rule beta-reduce :args ((= @t62 @t60))) % 0.46/0.64 (step @p46 :rule trans :premises (@p45 @p44)) % 0.46/0.64 (step @p47 :rule ho_cong :premises (@p46 @p33)) % 0.46/0.64 (step @p48 :rule trans :premises (@p47 @p32)) % 0.46/0.64 (step @p49 :rule cong :premises (@p48) :args (@t63)) % 0.46/0.64 (step @p50 :rule trans :premises (@p49 @p21)) % 0.46/0.64 (step @p51 :rule beta-reduce :args ((= (_ @t65 @t2) @t35))) % 0.46/0.64 (step @p52 :rule refl :args (@t2)) % 0.46/0.64 (step @p53 :rule beta-reduce :args ((= @t67 @t65))) % 0.46/0.64 (step @p54 :rule ho_cong :premises (@p53 @p52)) % 0.46/0.64 (step @p55 :rule trans :premises (@p54 @p51)) % 0.46/0.64 (step @p56 :rule cong :premises (@p55 @p50) :args (@t68)) % 0.46/0.64 (step @p57 :rule cong :premises (@p56) :args (@t69)) % 0.46/0.64 (step @p58 :rule trans :premises (@p57 @p20)) % 0.46/0.64 (step @p59 :rule cong :premises (@p58) :args ((not @t69))) % 0.46/0.64 (step @p60 :rule refl :args (@t5)) % 0.46/0.64 (step @p61 :rule refl :args (@t54)) % 0.46/0.64 (step @p62 :rule refl :args (@t14)) % 0.46/0.64 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t14 @t54))) % 0.46/0.64 (step @p64 :rule symm :premises (@p63)) % 0.46/0.64 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.46/0.64 (step @p66 :rule refl :args (@t61)) % 0.46/0.64 (step @p67 :rule refl :args (@t16)) % 0.46/0.64 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t16 @t61))) % 0.46/0.64 (step @p69 :rule symm :premises (@p68)) % 0.46/0.64 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.46/0.64 (step @p71 :rule cong :premises (@p70) :args (@t70)) % 0.46/0.64 (step @p72 :rule nary_cong :premises (@p71 @p65) :args (@t71)) % 0.46/0.64 (step @p73 :rule cong :premises (@p72) :args ((forall @t17 @t71))) % 0.46/0.64 (step @p74 :rule bool-impl-elim :args (@t16 @t14)) % 0.46/0.64 (step @p75 :rule cong :premises (@p74) :args (@t18)) % 0.46/0.64 (step @p76 :rule trans :premises (@p75 @p73)) % 0.46/0.64 (step @p77 :rule cong :premises (@p76) :args (@t20)) % 0.46/0.64 (step @p78 :rule trans :premises (@p3 @p77)) % 0.46/0.64 (step @p79 :rule ho_cong :premises (@p78 @p60)) % 0.46/0.64 (step @p80 :rule ho_cong :premises (@p79 @p33)) % 0.46/0.64 (step @p81 :rule cong :premises (@p80) :args (@t7)) % 0.46/0.64 (step @p82 :rule refl :args (@t4)) % 0.46/0.64 (step @p83 :rule refl :args (@t64)) % 0.46/0.64 (step @p84 :rule refl :args (@t23)) % 0.46/0.64 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t23 @t64))) % 0.46/0.64 (step @p86 :rule symm :premises (@p85)) % 0.46/0.64 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.46/0.64 (step @p88 :rule refl :args (@t66)) % 0.46/0.64 (step @p89 :rule refl :args (@t25)) % 0.46/0.64 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t25 @t66))) % 0.46/0.64 (step @p91 :rule symm :premises (@p90)) % 0.46/0.64 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 0.46/0.64 (step @p93 :rule cong :premises (@p92) :args (@t72)) % 0.46/0.64 (step @p94 :rule nary_cong :premises (@p93 @p87) :args (@t73)) % 0.46/0.64 (step @p95 :rule cong :premises (@p94) :args ((forall @t26 @t73))) % 0.46/0.64 (step @p96 :rule bool-impl-elim :args (@t25 @t23)) % 0.46/0.64 (step @p97 :rule cong :premises (@p96) :args (@t27)) % 0.46/0.64 (step @p98 :rule trans :premises (@p97 @p95)) % 0.46/0.64 (step @p99 :rule cong :premises (@p98) :args (@t29)) % 0.46/0.64 (step @p100 :rule trans :premises (@p4 @p99)) % 0.46/0.64 (step @p101 :rule ho_cong :premises (@p100 @p82)) % 0.46/0.64 (step @p102 :rule ho_cong :premises (@p101 @p52)) % 0.46/0.64 (step @p103 :rule cong :premises (@p102 @p81) :args (@t8)) % 0.46/0.64 (step @p104 :rule cong :premises (@p103) :args (@t10)) % 0.46/0.64 (step @p105 :rule cong :premises (@p104) :args (@t11)) % 0.46/0.64 (step @p106 :rule trans :premises (@p105 @p59)) % 0.46/0.64 (step @p107 :rule eq_resolve :premises (@p1 @p106)) % 0.46/0.64 (step @p108 :rule skolemize :premises (@p107)) % 0.46/0.64 (step @p109 :rule cnf_or_neg :args (@t84 2)) % 0.46/0.64 (step @p110 :rule chain_m_resolution :premises (@p109 @p108) :args ((not @t78) @t85 @t86)) % 0.46/0.64 (step @p111 :rule false_intro :premises (@p110)) % 0.46/0.64 (step @p112 :rule refl :args (@t75)) % 0.46/0.64 (step @p113 :rule bool-double-not-elim :args (@t82)) % 0.46/0.64 (step @p114 :rule refl :args (@t84)) % 0.46/0.64 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t84 (not @t83)))) % 0.46/0.64 (step @p116 :rule cnf_or_neg :args (@t84 0)) % 0.46/0.64 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.46/0.64 (step @p118 :rule reordering :premises (@p117) :args ((or @t82 @t84))) % 0.46/0.64 (step @p119 :rule chain_m_resolution :premises (@p118 @p108) :args (@t82 @t85 @t86)) % 0.46/0.64 (step @p120 :rule aci_norm :args ((= (or false @t87) @t87))) % 0.46/0.64 (step @p121 :rule eq-symm :args (@t76 @t79)) % 0.46/0.64 (step @p122 :rule beta-reduce :args ((= @t90 (= @t76 @t79)))) % 0.46/0.64 (step @p123 :rule trans :premises (@p122 @p121)) % 0.46/0.64 (step @p124 :rule evaluate :args ((not true))) % 0.46/0.64 (step @p125 :rule eq-refl :args (@t79)) % 0.46/0.64 (step @p126 :rule beta-reduce :args ((= @t91 (= @t79 @t79)))) % 0.46/0.64 (step @p127 :rule trans :premises (@p126 @p125)) % 0.46/0.64 (step @p128 :rule cong :premises (@p127) :args (@t92)) % 0.46/0.64 (step @p129 :rule trans :premises (@p128 @p124)) % 0.46/0.64 (step @p130 :rule nary_cong :premises (@p129 @p123) :args (@t93)) % 0.46/0.64 (step @p131 :rule trans :premises (@p130 @p120)) % 0.46/0.64 (step @p132 :rule refl :args (@t82)) % 0.46/0.64 (step @p133 :rule cong :premises (@p132 @p131) :args ((=> @t82 @t93))) % 0.46/0.64 (assume-push @p153 @t82) % 0.46/0.64 (step @p135 :rule instantiate :premises (@p119) :args ((@list @t89))) % 0.46/0.64 (step-pop @p154 :rule scope :premises (@p135)) % 0.46/0.64 (step @p136 :rule process_scope :premises (@p154) :args (@t93)) % 0.46/0.64 (step @p138 :rule eq_resolve :premises (@p136 @p133)) % 0.46/0.64 (step @p139 :rule implies_elim :premises (@p138)) % 0.46/0.64 (step @p140 :rule chain_m_resolution :premises (@p139 @p119) :args (@t87 (@list false) (@list @t82))) % 0.46/0.64 (step @p141 :rule ho_cong :premises (@p140 @p112)) % 0.46/0.64 (step @p142 :rule cong :premises (@p141) :args (@t80)) % 0.46/0.64 (step @p143 :rule bool-double-not-elim :args (@t80)) % 0.46/0.64 (step @p144 :rule nary_cong :premises (@p114 @p143) :args ((or @t84 (not @t81)))) % 0.46/0.64 (step @p145 :rule cnf_or_neg :args (@t84 1)) % 0.46/0.64 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 0.46/0.64 (step @p147 :rule reordering :premises (@p146) :args ((or @t80 @t84))) % 0.46/0.64 (step @p148 :rule chain_m_resolution :premises (@p147 @p108) :args (@t80 @t85 @t86)) % 0.46/0.64 (step @p149 :rule true_intro :premises (@p148)) % 0.46/0.64 (step @p150 :rule symm :premises (@p149)) % 0.46/0.64 (step @p151 :rule trans :premises (@p150 @p142 @p111)) % 0.46/0.64 (step @p152 false :rule eq_resolve :premises (@p151 @p5)) % 0.46/0.64 ) % 0.46/0.64 % SZS output end Proof % 0.46/0.64 % cvc5 exiting %------------------------------------------------------------------------------