%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO001^1 : 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 : n018.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 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO001^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n018.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 23:51:20 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.39/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (define tptp.leibeq () (let ((_let_1 (@var "Y" $$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)))))))) % 0.39/0.57 (define @t1 () (@var "Z" $$unsorted)) % 0.39/0.57 (define @t2 () (@var "X" $$unsorted)) % 0.39/0.57 (define @t3 () (_ tptp.leibeq @t2)) % 0.39/0.57 (define @t4 () (@var "Y" $$unsorted)) % 0.39/0.57 (define @t5 () (and (_ @t3 @t4) (_ (_ tptp.leibeq @t4) @t1))) % 0.39/0.57 (define @t6 () (=> @t5 (_ @t3 @t1))) % 0.39/0.57 (define @t7 () (@list @t2 @t4 @t1)) % 0.39/0.57 (define @t8 () (forall @t7 @t6)) % 0.39/0.57 (define @t9 () (not @t8)) % 0.39/0.57 (define @t10 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.57 (define @t11 () (_ @t10 @t4)) % 0.39/0.57 (define @t12 () (_ @t10 @t2)) % 0.39/0.57 (define @t13 () (@list @t10)) % 0.39/0.57 (define @t14 () (forall @t13 (=> @t12 @t11))) % 0.39/0.57 (define @t15 () (@list @t2 @t4)) % 0.39/0.57 (define @t16 () (lambda @t15 @t14)) % 0.39/0.57 (define @t17 () (@var "BOUND_VARIABLE_7491" (-> $$unsorted Bool))) % 0.39/0.57 (define @t18 () (_ @t17 @t1)) % 0.39/0.57 (define @t19 () (not (_ @t17 @t2))) % 0.39/0.57 (define @t20 () (_ @t10 @t1)) % 0.39/0.57 (define @t21 () (_ @t10 @t4)) % 0.39/0.57 (define @t22 () (not @t21)) % 0.39/0.57 (define @t23 () (forall @t13 (or @t22 @t20))) % 0.39/0.57 (define @t24 () (not @t23)) % 0.39/0.57 (define @t25 () (_ @t10 @t2)) % 0.39/0.57 (define @t26 () (not @t25)) % 0.39/0.57 (define @t27 () (forall @t13 (or @t26 @t21))) % 0.39/0.57 (define @t28 () (not @t27)) % 0.39/0.57 (define @t29 () (or @t28 @t24 @t19 @t18)) % 0.39/0.57 (define @t30 () (or @t19 @t18)) % 0.39/0.57 (define @t31 () (or @t28 @t24 @t30)) % 0.39/0.57 (define @t32 () (@list @t2 @t4 @t1 @t17)) % 0.39/0.57 (define @t33 () (forall @t32 @t31)) % 0.39/0.57 (define @t34 () (@list @t17)) % 0.39/0.57 (define @t35 () (forall @t34 @t31)) % 0.39/0.57 (define @t36 () (forall @t34 @t30)) % 0.39/0.57 (define @t37 () (or @t28 @t24 @t36)) % 0.39/0.57 (define @t38 () (forall @t13 (or @t26 @t20))) % 0.39/0.57 (define @t39 () (or @t28 @t24 @t38)) % 0.39/0.57 (define @t40 () (and @t27 @t23)) % 0.39/0.57 (define @t41 () (lambda (@list @t4) @t27)) % 0.39/0.57 (define @t42 () (lambda @t15 @t27)) % 0.39/0.57 (define @t43 () (_ @t42 @t2)) % 0.39/0.57 (define @t44 () (@var "BOUND_VARIABLE_7461" $$unsorted)) % 0.39/0.57 (define @t45 () (_ @t10 @t44)) % 0.39/0.57 (define @t46 () (lambda (@list @t44) (forall @t13 (or @t22 @t45)))) % 0.39/0.57 (define @t47 () (and (_ @t43 @t4) (_ (_ @t42 @t4) @t1))) % 0.39/0.57 (define @t48 () (=> @t47 (_ @t43 @t1))) % 0.39/0.57 (define @t49 () (forall @t7 @t48)) % 0.39/0.57 (define @t50 () (not @t12)) % 0.39/0.57 (define @t51 () (or @t50 @t11)) % 0.39/0.57 (define @t52 () (forall @t32 @t29)) % 0.39/0.57 (define @t53 () (@quantifiers_skolemize @t52 2)) % 0.39/0.57 (define @t54 () (@quantifiers_skolemize @t52 3)) % 0.39/0.57 (define @t55 () (_ @t54 @t53)) % 0.39/0.57 (define @t56 () (@quantifiers_skolemize @t52 0)) % 0.39/0.57 (define @t57 () (_ @t54 @t56)) % 0.39/0.57 (define @t58 () (not @t57)) % 0.39/0.57 (define @t59 () (@quantifiers_skolemize @t52 1)) % 0.39/0.57 (define @t60 () (_ @t10 @t59)) % 0.39/0.57 (define @t61 () (forall @t13 (or (not @t60) (_ @t10 @t53)))) % 0.39/0.57 (define @t62 () (not @t61)) % 0.39/0.57 (define @t63 () (forall @t13 (or (not (_ @t10 @t56)) @t60))) % 0.39/0.57 (define @t64 () (not @t63)) % 0.39/0.57 (define @t65 () (or @t64 @t62 @t58 @t55)) % 0.39/0.57 (define @t66 () (@list true)) % 0.39/0.57 (define @t67 () (@list @t65)) % 0.39/0.57 (define @t68 () (@list @t54)) % 0.39/0.57 (define @t69 () (_ @t54 @t59)) % 0.39/0.57 (define @t70 () (or @t58 @t69)) % 0.39/0.57 (define @t71 () (not @t69)) % 0.39/0.57 (define @t72 () (or @t71 @t55)) % 0.39/0.57 (assume @p1 @t9) % 0.39/0.57 (assume @p2 true) % 0.39/0.57 (step @p3 (= tptp.leibeq @t16) :rule refl :args (@t16)) % 0.39/0.57 (step @p4 :rule aci_norm :args ((= @t31 @t29))) % 0.39/0.57 (step @p5 :rule cong :premises (@p4) :args (@t33)) % 0.39/0.57 (step @p6 :rule quant-merge-prenex :args ((= (forall @t7 @t35) @t33))) % 0.39/0.57 (step @p7 :rule alpha_equiv :args (@t36 (@list @t17) (@list @t10))) % 0.39/0.57 (step @p8 :rule refl :args (@t24)) % 0.39/0.57 (step @p9 :rule refl :args (@t28)) % 0.39/0.57 (step @p10 :rule nary_cong :premises (@p9 @p8 @p7) :args (@t37)) % 0.39/0.57 (step @p11 :rule quant-miniscope-or :args ((= @t35 @t37))) % 0.39/0.57 (step @p12 :rule trans :premises (@p11 @p10)) % 0.39/0.57 (step @p13 :rule symm :premises (@p12)) % 0.39/0.57 (step @p14 :rule cong :premises (@p13) :args ((forall @t7 @t39))) % 0.39/0.57 (step @p15 :rule trans :premises (@p14 @p6)) % 0.39/0.57 (step @p16 :rule trans :premises (@p15 @p5)) % 0.39/0.57 (step @p17 :rule aci_norm :args ((= (or (or @t28 @t24) @t38) @t39))) % 0.39/0.57 (step @p18 :rule refl :args (@t38)) % 0.39/0.57 (step @p19 :rule bool-and-de-morgan :args (@t27 @t23 true)) % 0.39/0.57 (step @p20 :rule nary_cong :premises (@p19 @p18) :args ((or (not @t40) @t38))) % 0.39/0.57 (step @p21 :rule trans :premises (@p20 @p17)) % 0.39/0.57 (step @p22 :rule bool-impl-elim :args (@t40 @t38)) % 0.39/0.57 (step @p23 :rule trans :premises (@p22 @p21)) % 0.39/0.57 (step @p24 :rule cong :premises (@p23) :args ((forall @t7 (=> @t40 @t38)))) % 0.39/0.57 (step @p25 :rule trans :premises (@p24 @p16)) % 0.39/0.57 (step @p26 :rule beta-reduce :args ((= (_ @t41 @t1) @t38))) % 0.39/0.57 (step @p27 :rule refl :args (@t1)) % 0.39/0.57 (step @p28 :rule beta-reduce :args ((= @t43 @t41))) % 0.39/0.57 (step @p29 :rule ho_cong :premises (@p28 @p27)) % 0.39/0.57 (step @p30 :rule trans :premises (@p29 @p26)) % 0.39/0.57 (step @p31 :rule beta-reduce :args ((= (_ @t46 @t1) @t23))) % 0.39/0.57 (step @p32 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t44) (forall @t13 (or @t26 @t45))) @t4) @t46))) % 0.39/0.57 (step @p33 :rule refl :args (@t4)) % 0.39/0.57 (step @p34 :rule alpha_equiv :args (@t42 (@list @t4) (@list @t44))) % 0.39/0.57 (step @p35 :rule ho_cong :premises (@p34 @p33)) % 0.39/0.57 (step @p36 :rule trans :premises (@p35 @p32)) % 0.39/0.57 (step @p37 :rule ho_cong :premises (@p36 @p27)) % 0.39/0.57 (step @p38 :rule trans :premises (@p37 @p31)) % 0.39/0.57 (step @p39 :rule beta-reduce :args ((= (_ @t41 @t4) @t27))) % 0.39/0.57 (step @p40 :rule refl :args (@t4)) % 0.39/0.57 (step @p41 :rule ho_cong :premises (@p28 @p40)) % 0.39/0.57 (step @p42 :rule trans :premises (@p41 @p39)) % 0.39/0.57 (step @p43 :rule nary_cong :premises (@p42 @p38) :args (@t47)) % 0.39/0.57 (step @p44 :rule cong :premises (@p43 @p30) :args (@t48)) % 0.39/0.57 (step @p45 :rule cong :premises (@p44) :args (@t49)) % 0.39/0.57 (step @p46 :rule trans :premises (@p45 @p25)) % 0.39/0.57 (step @p47 :rule cong :premises (@p46) :args ((not @t49))) % 0.39/0.57 (step @p48 :rule refl :args (@t2)) % 0.39/0.57 (step @p49 :rule refl :args (@t21)) % 0.39/0.57 (step @p50 :rule refl :args (@t11)) % 0.39/0.57 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t11 @t21))) % 0.39/0.57 (step @p52 :rule symm :premises (@p51)) % 0.39/0.57 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.39/0.57 (step @p54 :rule refl :args (@t25)) % 0.39/0.57 (step @p55 :rule refl :args (@t12)) % 0.39/0.57 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t12 @t25))) % 0.39/0.57 (step @p57 :rule symm :premises (@p56)) % 0.39/0.57 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.39/0.57 (step @p59 :rule cong :premises (@p58) :args (@t50)) % 0.39/0.57 (step @p60 :rule nary_cong :premises (@p59 @p53) :args (@t51)) % 0.39/0.57 (step @p61 :rule cong :premises (@p60) :args ((forall @t13 @t51))) % 0.39/0.57 (step @p62 :rule bool-impl-elim :args (@t12 @t11)) % 0.39/0.57 (step @p63 :rule cong :premises (@p62) :args (@t14)) % 0.39/0.57 (step @p64 :rule trans :premises (@p63 @p61)) % 0.39/0.57 (step @p65 :rule cong :premises (@p64) :args (@t16)) % 0.39/0.57 (step @p66 :rule trans :premises (@p3 @p65)) % 0.39/0.57 (step @p67 :rule ho_cong :premises (@p66 @p48)) % 0.39/0.57 (step @p68 :rule ho_cong :premises (@p67 @p27)) % 0.39/0.57 (step @p69 :rule ho_cong :premises (@p66 @p40)) % 0.39/0.57 (step @p70 :rule ho_cong :premises (@p69 @p27)) % 0.39/0.57 (step @p71 :rule ho_cong :premises (@p67 @p40)) % 0.39/0.57 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t5)) % 0.39/0.57 (step @p73 :rule cong :premises (@p72 @p68) :args (@t6)) % 0.39/0.57 (step @p74 :rule cong :premises (@p73) :args (@t8)) % 0.39/0.57 (step @p75 :rule cong :premises (@p74) :args (@t9)) % 0.39/0.57 (step @p76 :rule trans :premises (@p75 @p47)) % 0.39/0.57 (step @p77 :rule eq_resolve :premises (@p1 @p76)) % 0.39/0.57 (step @p78 :rule skolemize :premises (@p77)) % 0.39/0.57 (step @p79 :rule cnf_or_neg :args (@t65 3)) % 0.39/0.57 (step @p80 :rule chain_m_resolution :premises (@p79 @p78) :args ((not @t55) @t66 @t67)) % 0.39/0.57 (step @p81 :rule bool-double-not-elim :args (@t61)) % 0.39/0.57 (step @p82 :rule refl :args (@t65)) % 0.39/0.57 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t65 (not @t62)))) % 0.39/0.57 (step @p84 :rule cnf_or_neg :args (@t65 1)) % 0.39/0.57 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 0.39/0.57 (step @p86 :rule reordering :premises (@p85) :args ((or @t61 @t65))) % 0.39/0.57 (step @p87 :rule chain_m_resolution :premises (@p86 @p78) :args (@t61 @t66 @t67)) % 0.39/0.57 (step @p88 :rule instantiate :premises (@p87) :args (@t68)) % 0.39/0.57 (step @p89 :rule bool-double-not-elim :args (@t63)) % 0.39/0.57 (step @p90 :rule nary_cong :premises (@p82 @p89) :args ((or @t65 (not @t64)))) % 0.39/0.57 (step @p91 :rule cnf_or_neg :args (@t65 0)) % 0.39/0.57 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 0.39/0.57 (step @p93 :rule reordering :premises (@p92) :args ((or @t63 @t65))) % 0.39/0.57 (step @p94 :rule chain_m_resolution :premises (@p93 @p78) :args (@t63 @t66 @t67)) % 0.39/0.57 (step @p95 :rule instantiate :premises (@p94) :args (@t68)) % 0.39/0.57 (step @p96 :rule bool-double-not-elim :args (@t57)) % 0.39/0.57 (step @p97 :rule nary_cong :premises (@p82 @p96) :args ((or @t65 (not @t58)))) % 0.39/0.57 (step @p98 :rule cnf_or_neg :args (@t65 2)) % 0.39/0.57 (step @p99 :rule eq_resolve :premises (@p98 @p97)) % 0.39/0.57 (step @p100 :rule reordering :premises (@p99) :args ((or @t57 @t65))) % 0.39/0.57 (step @p101 :rule chain_m_resolution :premises (@p100 @p78) :args (@t57 @t66 @t67)) % 0.39/0.57 (step @p102 :rule cnf_or_pos :args (@t70)) % 0.39/0.57 (step @p103 :rule reordering :premises (@p102) :args ((or @t58 @t69 (not @t70)))) % 0.39/0.57 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p95) :args (@t69 (@list false false) (@list @t57 @t70))) % 0.39/0.57 (step @p105 :rule cnf_or_pos :args (@t72)) % 0.39/0.57 (step @p106 :rule reordering :premises (@p105) :args ((or @t55 @t71 (not @t72)))) % 0.39/0.57 (step @p107 false :rule chain_m_resolution :premises (@p106 @p104 @p88 @p80) :args (false (@list false false true) (@list @t69 @t72 @t55))) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------