%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO897^6 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 09:13:44 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 : SYO897^6 : TPTP v9.2.1. Released v8.1.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.33 % Computer : n015.cluster.edu % 0.18/0.33 % Model : x86_64 x86_64 % 0.18/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.33 % Memory : 8042.1875MB % 0.18/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.33 % CPULimit : 300 % 0.18/0.33 % WCLimit : 300 % 0.18/0.33 % DateTime : Wed Jun 3 01:09:19 EDT 2026 % 0.18/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.37/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort tptp.mworld 0) % 0.37/0.56 (declare-const tptp.mactual tptp.mworld) % 0.37/0.56 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.37/0.56 (declare-const tptp.p (-> tptp.mworld Bool)) % 0.37/0.56 (declare-const tptp.q (-> tptp.mworld Bool)) % 0.37/0.56 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.37/0.56 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.56 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.56 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.56 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.56 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.56 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.56 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.56 (define @t1 () (@var "V" tptp.mworld)) % 0.37/0.56 (define @t2 () (@var "W" tptp.mworld)) % 0.37/0.56 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.37/0.56 (define @t4 () (not (_ tptp.mlocal (_ (_ tptp.mimplies (_ tptp.mdia tptp.p)) (_ (_ tptp.mimplies (_ tptp.mbox tptp.q)) (_ tptp.mdia tptp.q)))))) % 0.37/0.56 (define @t5 () (@var "Phi" (-> tptp.mworld Bool))) % 0.37/0.56 (define @t6 () (lambda (@list @t5) (_ @t5 tptp.mactual))) % 0.37/0.56 (define @t7 () (@var "A" (-> tptp.mworld Bool))) % 0.37/0.56 (define @t8 () (_ @t7 @t2)) % 0.37/0.56 (define @t9 () (lambda (@list @t7 @t2) (not @t8))) % 0.37/0.56 (define @t10 () (@var "B" (-> tptp.mworld Bool))) % 0.37/0.56 (define @t11 () (_ @t10 @t2)) % 0.37/0.56 (define @t12 () (@list @t7 @t10 @t2)) % 0.37/0.56 (define @t13 () (lambda @t12 (and @t8 @t11))) % 0.37/0.56 (define @t14 () (lambda @t12 (or @t8 @t11))) % 0.37/0.56 (define @t15 () (lambda @t12 (=> @t8 @t11))) % 0.37/0.56 (define @t16 () (lambda @t12 (= @t8 @t11))) % 0.37/0.56 (define @t17 () (_ @t5 @t1)) % 0.37/0.56 (define @t18 () (@list @t1)) % 0.37/0.56 (define @t19 () (forall @t18 (=> @t3 @t17))) % 0.37/0.56 (define @t20 () (@list @t5 @t2)) % 0.37/0.56 (define @t21 () (lambda @t20 @t19)) % 0.37/0.56 (define @t22 () (and @t3 @t17)) % 0.37/0.56 (define @t23 () (exists @t18 @t22)) % 0.37/0.56 (define @t24 () (lambda @t20 @t23)) % 0.37/0.56 (define @t25 () (tptp.q @t1)) % 0.37/0.56 (define @t26 () (not @t25)) % 0.37/0.56 (define @t27 () (not (tptp.mrel tptp.mactual @t1))) % 0.37/0.56 (define @t28 () (not (tptp.p @t1))) % 0.37/0.56 (define @t29 () (forall @t18 (or @t27 @t28))) % 0.37/0.56 (define @t30 () (tptp.mrel @t2 @t1)) % 0.37/0.56 (define @t31 () (not @t30)) % 0.37/0.56 (define @t32 () (not (forall @t18 (or @t31 @t26)))) % 0.37/0.56 (define @t33 () (forall @t18 (or @t31 @t25))) % 0.37/0.56 (define @t34 () (=> @t33 @t32)) % 0.37/0.56 (define @t35 () (not (forall @t18 (or @t31 @t28)))) % 0.37/0.56 (define @t36 () (@list @t2)) % 0.37/0.56 (define @t37 () (lambda @t36 (=> @t35 @t34))) % 0.37/0.56 (define @t38 () (_ @t37 tptp.mactual)) % 0.37/0.56 (define @t39 () (lambda @t36 @t34)) % 0.37/0.56 (define @t40 () (_ @t39 @t2)) % 0.37/0.56 (define @t41 () (=> @t35 @t40)) % 0.37/0.56 (define @t42 () (lambda @t36 @t41)) % 0.37/0.56 (define @t43 () (@list @t10 @t2)) % 0.37/0.56 (define @t44 () (lambda @t36 @t32)) % 0.37/0.56 (define @t45 () (_ @t44 @t2)) % 0.37/0.56 (define @t46 () (=> @t33 @t45)) % 0.37/0.56 (define @t47 () (lambda @t36 @t46)) % 0.37/0.56 (define @t48 () (_ @t5 @t1)) % 0.37/0.56 (define @t49 () (lambda @t20 (not (forall @t18 (or @t31 (not @t48)))))) % 0.37/0.56 (define @t50 () (_ @t49 tptp.q)) % 0.37/0.56 (define @t51 () (lambda @t36 @t33)) % 0.37/0.56 (define @t52 () (_ @t51 @t2)) % 0.37/0.56 (define @t53 () (=> @t52 @t11)) % 0.37/0.56 (define @t54 () (lambda @t43 @t53)) % 0.37/0.56 (define @t55 () (_ (lambda @t20 (forall @t18 (or @t31 @t48))) tptp.q)) % 0.37/0.56 (define @t56 () (lambda @t36 @t35)) % 0.37/0.56 (define @t57 () (_ @t56 @t2)) % 0.37/0.56 (define @t58 () (=> @t57 @t11)) % 0.37/0.56 (define @t59 () (lambda @t43 @t58)) % 0.37/0.56 (define @t60 () (_ @t49 tptp.p)) % 0.37/0.56 (define @t61 () (not @t17)) % 0.37/0.56 (define @t62 () (not @t3)) % 0.37/0.56 (define @t63 () (or @t62 @t61)) % 0.37/0.56 (define @t64 () (forall @t18 (not @t22))) % 0.37/0.56 (define @t65 () (not @t64)) % 0.37/0.56 (define @t66 () (or @t62 @t17)) % 0.37/0.56 (define @t67 () (@quantifiers_skolemize @t29 0)) % 0.37/0.56 (define @t68 () (tptp.mrel tptp.mactual @t67)) % 0.37/0.56 (define @t69 () (not @t68)) % 0.37/0.56 (define @t70 () (or @t69 (not (tptp.p @t67)))) % 0.37/0.56 (define @t71 () (@list @t67)) % 0.37/0.56 (define @t72 () (tptp.q @t67)) % 0.37/0.56 (define @t73 () (or @t69 @t72)) % 0.37/0.56 (define @t74 () (not @t72)) % 0.37/0.56 (define @t75 () (or @t69 @t74)) % 0.37/0.56 (assume @p1 (forall (@list @t2 @t1) @t3)) % 0.37/0.56 (assume @p2 @t4) % 0.37/0.56 (assume @p3 true) % 0.37/0.56 (step @p4 (= tptp.mlocal @t6) :rule refl :args (@t6)) % 0.37/0.56 (step @p5 (= tptp.mnot @t9) :rule refl :args (@t9)) % 0.37/0.56 (step @p6 (= tptp.mand @t13) :rule refl :args (@t13)) % 0.37/0.56 (step @p7 (= tptp.mor @t14) :rule refl :args (@t14)) % 0.37/0.56 (step @p8 (= tptp.mimplies @t15) :rule refl :args (@t15)) % 0.37/0.56 (step @p9 (= tptp.mequiv @t16) :rule refl :args (@t16)) % 0.37/0.56 (step @p10 (= tptp.mbox @t21) :rule refl :args (@t21)) % 0.37/0.56 (step @p11 (= tptp.mdia @t24) :rule refl :args (@t24)) % 0.37/0.56 (step @p12 :rule beta-reduce :args ((= @t38 (=> (not @t29) (=> (forall @t18 (or @t27 @t25)) (not (forall @t18 (or @t27 @t26)))))))) % 0.37/0.56 (step @p13 :rule beta-reduce :args ((= (_ @t6 @t37) @t38))) % 0.37/0.56 (step @p14 :rule trans :premises (@p13 @p12)) % 0.37/0.56 (step @p15 :rule beta-reduce :args ((= @t40 @t34))) % 0.37/0.56 (step @p16 :rule refl :args (@t35)) % 0.37/0.56 (step @p17 :rule cong :premises (@p16 @p15) :args (@t41)) % 0.37/0.56 (step @p18 :rule cong :premises (@p17) :args (@t42)) % 0.37/0.56 (step @p19 :rule beta-reduce :args ((= (_ (lambda @t43 (=> @t35 @t11)) @t39) @t42))) % 0.37/0.56 (step @p20 :rule trans :premises (@p19 @p18)) % 0.37/0.56 (step @p21 :rule beta-reduce :args ((= @t45 @t32))) % 0.37/0.56 (step @p22 :rule refl :args (@t33)) % 0.37/0.56 (step @p23 :rule cong :premises (@p22 @p21) :args (@t46)) % 0.37/0.56 (step @p24 :rule cong :premises (@p23) :args (@t47)) % 0.37/0.56 (step @p25 :rule beta-reduce :args ((= (_ (lambda @t43 (=> @t33 @t11)) @t44) @t47))) % 0.37/0.56 (step @p26 :rule trans :premises (@p25 @p24)) % 0.37/0.56 (step @p27 :rule beta-reduce :args ((= @t50 @t44))) % 0.37/0.56 (step @p28 :rule refl :args (@t11)) % 0.37/0.56 (step @p29 :rule beta-reduce :args ((= @t52 @t33))) % 0.37/0.56 (step @p30 :rule cong :premises (@p29 @p28) :args (@t53)) % 0.37/0.56 (step @p31 :rule cong :premises (@p30) :args (@t54)) % 0.37/0.56 (step @p32 :rule beta-reduce :args ((= (_ @t15 @t51) @t54))) % 0.37/0.56 (step @p33 :rule trans :premises (@p32 @p31)) % 0.37/0.56 (step @p34 :rule beta-reduce :args ((= @t55 @t51))) % 0.37/0.56 (step @p35 :rule refl :args (@t15)) % 0.37/0.56 (step @p36 :rule ho_cong :premises (@p35 @p34)) % 0.37/0.56 (step @p37 :rule trans :premises (@p36 @p33)) % 0.37/0.56 (step @p38 :rule ho_cong :premises (@p37 @p27)) % 0.37/0.56 (step @p39 :rule trans :premises (@p38 @p26)) % 0.37/0.56 (step @p40 :rule beta-reduce :args ((= @t57 @t35))) % 0.37/0.56 (step @p41 :rule cong :premises (@p40 @p28) :args (@t58)) % 0.37/0.56 (step @p42 :rule cong :premises (@p41) :args (@t59)) % 0.37/0.56 (step @p43 :rule beta-reduce :args ((= (_ @t15 @t56) @t59))) % 0.37/0.56 (step @p44 :rule trans :premises (@p43 @p42)) % 0.37/0.56 (step @p45 :rule beta-reduce :args ((= @t60 @t56))) % 0.37/0.56 (step @p46 :rule ho_cong :premises (@p35 @p45)) % 0.37/0.56 (step @p47 :rule trans :premises (@p46 @p44)) % 0.37/0.56 (step @p48 :rule ho_cong :premises (@p47 @p39)) % 0.37/0.56 (step @p49 :rule trans :premises (@p48 @p20)) % 0.37/0.56 (step @p50 :rule refl :args (@t6)) % 0.37/0.56 (step @p51 :rule ho_cong :premises (@p50 @p49)) % 0.37/0.56 (step @p52 :rule trans :premises (@p51 @p14)) % 0.37/0.56 (step @p53 :rule cong :premises (@p52) :args ((not (_ @t6 (_ (_ @t15 @t60) (_ (_ @t15 @t55) @t50)))))) % 0.37/0.56 (step @p54 :rule refl :args (tptp.q)) % 0.37/0.56 (step @p55 :rule refl :args (@t48)) % 0.37/0.56 (step @p56 :rule refl :args (@t17)) % 0.37/0.56 (step @p57 :rule cong :premises (@p56 @p55) :args ((= @t17 @t48))) % 0.37/0.56 (step @p58 :rule symm :premises (@p57)) % 0.37/0.56 (step @p59 :rule eq_resolve :premises (@p56 @p58)) % 0.37/0.56 (step @p60 :rule cong :premises (@p59) :args (@t61)) % 0.37/0.56 (step @p61 :rule refl :args (@t30)) % 0.37/0.56 (step @p62 :rule refl :args (@t3)) % 0.37/0.56 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t3 @t30))) % 0.37/0.56 (step @p64 :rule symm :premises (@p63)) % 0.37/0.56 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.37/0.56 (step @p66 :rule cong :premises (@p65) :args (@t62)) % 0.37/0.56 (step @p67 :rule nary_cong :premises (@p66 @p60) :args (@t63)) % 0.37/0.56 (step @p68 :rule cong :premises (@p67) :args ((forall @t18 @t63))) % 0.37/0.56 (step @p69 :rule bool-and-de-morgan :args (@t3 @t17 true)) % 0.37/0.56 (step @p70 :rule cong :premises (@p69) :args (@t64)) % 0.37/0.56 (step @p71 :rule trans :premises (@p70 @p68)) % 0.37/0.56 (step @p72 :rule cong :premises (@p71) :args (@t65)) % 0.37/0.56 (step @p73 :rule exists-elim :args ((= @t23 @t65))) % 0.37/0.56 (step @p74 :rule trans :premises (@p73 @p72)) % 0.37/0.56 (step @p75 :rule cong :premises (@p74) :args (@t24)) % 0.37/0.56 (step @p76 :rule trans :premises (@p11 @p75)) % 0.37/0.56 (step @p77 :rule ho_cong :premises (@p76 @p54)) % 0.37/0.56 (step @p78 :rule nary_cong :premises (@p66 @p59) :args (@t66)) % 0.37/0.56 (step @p79 :rule cong :premises (@p78) :args ((forall @t18 @t66))) % 0.37/0.56 (step @p80 :rule bool-impl-elim :args (@t3 @t17)) % 0.37/0.56 (step @p81 :rule cong :premises (@p80) :args (@t19)) % 0.37/0.56 (step @p82 :rule trans :premises (@p81 @p79)) % 0.37/0.56 (step @p83 :rule cong :premises (@p82) :args (@t21)) % 0.37/0.56 (step @p84 :rule trans :premises (@p10 @p83)) % 0.37/0.56 (step @p85 :rule ho_cong :premises (@p84 @p54)) % 0.37/0.56 (step @p86 :rule ho_cong :premises (@p8 @p85)) % 0.37/0.56 (step @p87 :rule ho_cong :premises (@p86 @p77)) % 0.37/0.56 (step @p88 :rule refl :args (tptp.p)) % 0.37/0.56 (step @p89 :rule ho_cong :premises (@p76 @p88)) % 0.37/0.56 (step @p90 :rule ho_cong :premises (@p8 @p89)) % 0.37/0.56 (step @p91 :rule ho_cong :premises (@p90 @p87)) % 0.37/0.56 (step @p92 :rule ho_cong :premises (@p4 @p91)) % 0.37/0.56 (step @p93 :rule cong :premises (@p92) :args (@t4)) % 0.37/0.56 (step @p94 :rule trans :premises (@p93 @p53)) % 0.37/0.56 (step @p95 :rule eq_resolve :premises (@p2 @p94)) % 0.37/0.56 (step @p96 :rule not_implies_elim1 :premises (@p95)) % 0.37/0.56 (step @p97 :rule skolemize :premises (@p96)) % 0.37/0.56 (step @p98 :rule bool-double-not-elim :args (@t68)) % 0.37/0.56 (step @p99 :rule refl :args (@t70)) % 0.37/0.56 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or @t70 (not @t69)))) % 0.37/0.56 (step @p101 :rule cnf_or_neg :args (@t70 0)) % 0.37/0.56 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 0.37/0.56 (step @p103 :rule reordering :premises (@p102) :args ((or @t68 @t70))) % 0.37/0.56 (step @p104 :rule chain_m_resolution :premises (@p103 @p97) :args (@t68 (@list true) (@list @t70))) % 0.37/0.56 (step @p105 :rule not_implies_elim2 :premises (@p95)) % 0.37/0.56 (step @p106 :rule not_implies_elim2 :premises (@p105)) % 0.37/0.56 (step @p107 :rule not_not_elim :premises (@p106)) % 0.37/0.56 (step @p108 :rule instantiate :premises (@p107) :args (@t71)) % 0.37/0.56 (step @p109 :rule not_implies_elim1 :premises (@p105)) % 0.37/0.56 (step @p110 :rule instantiate :premises (@p109) :args (@t71)) % 0.37/0.56 (step @p111 :rule cnf_or_pos :args (@t73)) % 0.37/0.56 (step @p112 :rule reordering :premises (@p111) :args ((or @t69 @t72 (not @t73)))) % 0.37/0.56 (step @p113 :rule chain_m_resolution :premises (@p112 @p104 @p110) :args (@t72 (@list false false) (@list @t68 @t73))) % 0.37/0.56 (step @p114 :rule cnf_or_pos :args (@t75)) % 0.37/0.56 (step @p115 :rule reordering :premises (@p114) :args ((or @t69 @t74 (not @t75)))) % 0.37/0.56 (step @p116 false :rule chain_m_resolution :premises (@p115 @p113 @p108 @p104) :args (false (@list false false false) (@list @t72 @t75 @t68))) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------