%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM751^1 : 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 : n012.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 08:40:33 AM UTC 2026 % Result : Theorem 0.16s 0.37s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM751^1 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 12:11:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.33 %----Proving TH0 % 0.16/0.37 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.16/0.37 % SZS status Theorem % 0.16/0.37 % SZS output start Proof % 0.16/0.37 ( % 0.16/0.37 (declare-sort tptp.frac 0) % 0.16/0.37 (declare-const tptp.z tptp.frac) % 0.16/0.37 (declare-const tptp.pf (-> tptp.frac tptp.frac tptp.frac)) % 0.16/0.37 (declare-const tptp.eq (-> tptp.frac tptp.frac Bool)) % 0.16/0.37 (declare-const tptp.moref (-> tptp.frac tptp.frac Bool)) % 0.16/0.37 (declare-const tptp.x tptp.frac) % 0.16/0.37 (declare-const tptp.y tptp.frac) % 0.16/0.37 (define @t1 () (_ (_ tptp.moref tptp.x) tptp.y)) % 0.16/0.37 (define @t2 () (@var "Xu" tptp.frac)) % 0.16/0.37 (define @t3 () (@var "Xz" tptp.frac)) % 0.16/0.37 (define @t4 () (_ (_ tptp.moref @t3) @t2)) % 0.16/0.37 (define @t5 () (@var "Xy" tptp.frac)) % 0.16/0.37 (define @t6 () (_ (_ tptp.eq @t5) @t2)) % 0.16/0.37 (define @t7 () (=> @t6 @t4)) % 0.16/0.37 (define @t8 () (@var "Xx" tptp.frac)) % 0.16/0.37 (define @t9 () (_ (_ tptp.eq @t8) @t3)) % 0.16/0.37 (define @t10 () (=> @t9 @t7)) % 0.16/0.37 (define @t11 () (_ (_ tptp.moref @t8) @t5)) % 0.16/0.37 (define @t12 () (@list @t8 @t5 @t3 @t2)) % 0.16/0.37 (define @t13 () (forall @t12 (=> @t11 @t10))) % 0.16/0.37 (define @t14 () (_ tptp.pf @t5)) % 0.16/0.37 (define @t15 () (_ @t14 @t3)) % 0.16/0.37 (define @t16 () (_ tptp.pf @t8)) % 0.16/0.37 (define @t17 () (_ @t16 @t3)) % 0.16/0.37 (define @t18 () (_ (_ tptp.moref @t17) @t15)) % 0.16/0.37 (define @t19 () (@list @t8 @t5 @t3)) % 0.16/0.37 (define @t20 () (forall @t19 (=> @t11 @t18))) % 0.16/0.37 (define @t21 () (_ @t14 @t8)) % 0.16/0.37 (define @t22 () (_ @t16 @t5)) % 0.16/0.37 (define @t23 () (_ (_ tptp.eq @t22) @t21)) % 0.16/0.37 (define @t24 () (forall (@list @t8 @t5) @t23)) % 0.16/0.37 (define @t25 () (_ tptp.pf tptp.z)) % 0.16/0.37 (define @t26 () (_ @t25 tptp.y)) % 0.16/0.37 (define @t27 () (_ @t25 tptp.x)) % 0.16/0.37 (define @t28 () (_ (_ tptp.moref @t27) @t26)) % 0.16/0.37 (define @t29 () (not @t28)) % 0.16/0.37 (define @t30 () (tptp.moref @t3 @t2)) % 0.16/0.37 (define @t31 () (tptp.eq @t5 @t2)) % 0.16/0.37 (define @t32 () (not @t6)) % 0.16/0.37 (define @t33 () (tptp.eq @t8 @t3)) % 0.16/0.37 (define @t34 () (not @t9)) % 0.16/0.37 (define @t35 () (tptp.moref @t8 @t5)) % 0.16/0.37 (define @t36 () (not @t11)) % 0.16/0.37 (define @t37 () (or @t36 @t34 @t32 @t4)) % 0.16/0.37 (define @t38 () (or @t34 @t32 @t4)) % 0.16/0.37 (define @t39 () (tptp.pf @t5 @t3)) % 0.16/0.37 (define @t40 () (tptp.pf @t8 @t3)) % 0.16/0.37 (define @t41 () (tptp.moref @t40 @t39)) % 0.16/0.37 (define @t42 () (or @t36 @t18)) % 0.16/0.37 (define @t43 () (tptp.moref tptp.x tptp.y)) % 0.16/0.37 (define @t44 () (tptp.pf tptp.y tptp.z)) % 0.16/0.37 (define @t45 () (tptp.pf tptp.x tptp.z)) % 0.16/0.37 (define @t46 () (tptp.moref @t45 @t44)) % 0.16/0.37 (define @t47 () (not @t43)) % 0.16/0.37 (define @t48 () (or @t47 @t46)) % 0.16/0.37 (define @t49 () (tptp.pf @t5 @t8)) % 0.16/0.37 (define @t50 () (tptp.pf @t8 @t5)) % 0.16/0.37 (define @t51 () (tptp.eq @t50 @t49)) % 0.16/0.37 (define @t52 () (tptp.pf tptp.z tptp.y)) % 0.16/0.37 (define @t53 () (tptp.pf tptp.z tptp.x)) % 0.16/0.37 (define @t54 () (tptp.moref @t53 @t52)) % 0.16/0.37 (define @t55 () (tptp.eq @t44 @t52)) % 0.16/0.37 (define @t56 () (not @t55)) % 0.16/0.37 (define @t57 () (tptp.eq @t45 @t53)) % 0.16/0.37 (define @t58 () (not @t57)) % 0.16/0.37 (define @t59 () (not @t46)) % 0.16/0.37 (define @t60 () (or @t59 @t58 @t56 @t54)) % 0.16/0.37 (define @t61 () (not @t60)) % 0.16/0.37 (define @t62 () (forall @t12 (or (not @t35) (not @t33) (not @t31) @t30))) % 0.16/0.37 (assume @p1 @t1) % 0.16/0.37 (assume @p2 @t13) % 0.16/0.37 (assume @p3 @t20) % 0.16/0.37 (assume @p4 @t24) % 0.16/0.37 (assume @p5 @t29) % 0.16/0.37 (assume @p6 true) % 0.16/0.37 (step @p7 :rule refl :args (@t30)) % 0.16/0.37 (step @p8 :rule refl :args (@t4)) % 0.16/0.37 (step @p9 :rule cong :premises (@p8 @p7) :args ((= @t4 @t30))) % 0.16/0.37 (step @p10 :rule symm :premises (@p9)) % 0.16/0.37 (step @p11 :rule eq_resolve :premises (@p8 @p10)) % 0.16/0.37 (step @p12 :rule refl :args (@t31)) % 0.16/0.37 (step @p13 :rule refl :args (@t6)) % 0.16/0.37 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t6 @t31))) % 0.16/0.37 (step @p15 :rule symm :premises (@p14)) % 0.16/0.37 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 0.16/0.37 (step @p17 :rule cong :premises (@p16) :args (@t32)) % 0.16/0.37 (step @p18 :rule refl :args (@t33)) % 0.16/0.37 (step @p19 :rule refl :args (@t9)) % 0.16/0.37 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t9 @t33))) % 0.16/0.37 (step @p21 :rule symm :premises (@p20)) % 0.16/0.37 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.16/0.37 (step @p23 :rule cong :premises (@p22) :args (@t34)) % 0.16/0.37 (step @p24 :rule refl :args (@t35)) % 0.16/0.37 (step @p25 :rule refl :args (@t11)) % 0.16/0.37 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t11 @t35))) % 0.16/0.37 (step @p27 :rule symm :premises (@p26)) % 0.16/0.37 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.16/0.37 (step @p29 :rule cong :premises (@p28) :args (@t36)) % 0.16/0.37 (step @p30 :rule nary_cong :premises (@p29 @p23 @p17 @p11) :args (@t37)) % 0.16/0.37 (step @p31 :rule cong :premises (@p30) :args ((forall @t12 @t37))) % 0.16/0.37 (step @p32 :rule aci_norm :args ((= (or @t36 @t38) @t37))) % 0.16/0.37 (step @p33 :rule aci_norm :args ((= (or @t34 (or @t32 @t4)) @t38))) % 0.16/0.37 (step @p34 :rule bool-impl-elim :args (@t6 @t4)) % 0.16/0.37 (step @p35 :rule refl :args (@t34)) % 0.16/0.37 (step @p36 :rule nary_cong :premises (@p35 @p34) :args ((or @t34 @t7))) % 0.16/0.37 (step @p37 :rule trans :premises (@p36 @p33)) % 0.16/0.37 (step @p38 :rule bool-impl-elim :args (@t9 @t7)) % 0.16/0.37 (step @p39 :rule trans :premises (@p38 @p37)) % 0.16/0.37 (step @p40 :rule refl :args (@t36)) % 0.16/0.37 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or @t36 @t10))) % 0.16/0.37 (step @p42 :rule trans :premises (@p41 @p32)) % 0.16/0.37 (step @p43 :rule bool-impl-elim :args (@t11 @t10)) % 0.16/0.37 (step @p44 :rule trans :premises (@p43 @p42)) % 0.16/0.37 (step @p45 :rule cong :premises (@p44) :args (@t13)) % 0.16/0.37 (step @p46 :rule trans :premises (@p45 @p31)) % 0.16/0.37 (step @p47 :rule eq_resolve :premises (@p2 @p46)) % 0.16/0.37 (step @p48 :rule refl :args ((tptp.moref @t17 @t15))) % 0.16/0.37 (step @p49 :rule refl :args (@t39)) % 0.16/0.37 (step @p50 :rule refl :args (@t40)) % 0.16/0.37 (step @p51 :rule cong :premises (@p50 @p49) :args (@t41)) % 0.16/0.37 (step @p52 :rule trans :premises (@p51 @p48)) % 0.16/0.37 (step @p53 :rule refl :args (tptp.moref)) % 0.16/0.37 (step @p54 :rule ho_cong :premises (@p53 @p50)) % 0.16/0.37 (step @p55 :rule ho_cong :premises (@p54 @p49)) % 0.16/0.37 (step @p56 :rule cong :premises (@p55 @p52) :args ((= (_ (_ tptp.moref @t40) @t39) @t41))) % 0.16/0.37 (step @p57 :rule symm :premises (@p56)) % 0.16/0.37 (step @p58 :rule refl :args (@t18)) % 0.16/0.37 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.16/0.37 (step @p60 :rule refl :args (@t15)) % 0.16/0.37 (step @p61 :rule cong :premises (@p60 @p49) :args ((= @t15 @t39))) % 0.16/0.37 (step @p62 :rule symm :premises (@p61)) % 0.16/0.37 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.16/0.37 (step @p64 :rule refl :args (@t17)) % 0.16/0.37 (step @p65 :rule cong :premises (@p64 @p50) :args ((= @t17 @t40))) % 0.16/0.37 (step @p66 :rule symm :premises (@p65)) % 0.16/0.37 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.16/0.37 (step @p68 :rule ho_cong :premises (@p53 @p67)) % 0.16/0.37 (step @p69 :rule ho_cong :premises (@p68 @p63)) % 0.16/0.37 (step @p70 :rule trans :premises (@p69 @p59)) % 0.16/0.37 (step @p71 :rule nary_cong :premises (@p29 @p70) :args (@t42)) % 0.16/0.37 (step @p72 :rule cong :premises (@p71) :args ((forall @t19 @t42))) % 0.16/0.37 (step @p73 :rule bool-impl-elim :args (@t11 @t18)) % 0.16/0.37 (step @p74 :rule cong :premises (@p73) :args (@t20)) % 0.16/0.37 (step @p75 :rule trans :premises (@p74 @p72)) % 0.16/0.37 (step @p76 :rule eq_resolve :premises (@p3 @p75)) % 0.16/0.37 (step @p77 :rule instantiate :premises (@p76) :args ((@list tptp.x tptp.y tptp.z))) % 0.16/0.37 (step @p78 :rule refl :args (@t43)) % 0.16/0.37 (step @p79 :rule refl :args (@t1)) % 0.16/0.37 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t1 @t43))) % 0.16/0.37 (step @p81 :rule symm :premises (@p80)) % 0.16/0.37 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.16/0.37 (step @p83 :rule eq_resolve :premises (@p1 @p82)) % 0.16/0.37 (step @p84 :rule cnf_or_pos :args (@t48)) % 0.16/0.37 (step @p85 :rule reordering :premises (@p84) :args ((or @t47 @t46 (not @t48)))) % 0.16/0.37 (step @p86 :rule chain_m_resolution :premises (@p85 @p83 @p77) :args (@t46 (@list false false) (@list @t43 @t48))) % 0.16/0.37 (step @p87 :rule refl :args ((tptp.eq @t22 @t21))) % 0.16/0.37 (step @p88 :rule refl :args (@t49)) % 0.16/0.37 (step @p89 :rule refl :args (@t50)) % 0.16/0.37 (step @p90 :rule cong :premises (@p89 @p88) :args (@t51)) % 0.16/0.37 (step @p91 :rule trans :premises (@p90 @p87)) % 0.16/0.37 (step @p92 :rule refl :args (tptp.eq)) % 0.16/0.37 (step @p93 :rule ho_cong :premises (@p92 @p89)) % 0.16/0.37 (step @p94 :rule ho_cong :premises (@p93 @p88)) % 0.16/0.37 (step @p95 :rule cong :premises (@p94 @p91) :args ((= (_ (_ tptp.eq @t50) @t49) @t51))) % 0.16/0.37 (step @p96 :rule symm :premises (@p95)) % 0.16/0.37 (step @p97 :rule refl :args (@t23)) % 0.16/0.37 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 0.16/0.37 (step @p99 :rule refl :args (@t21)) % 0.16/0.37 (step @p100 :rule cong :premises (@p99 @p88) :args ((= @t21 @t49))) % 0.16/0.37 (step @p101 :rule symm :premises (@p100)) % 0.16/0.37 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 0.16/0.37 (step @p103 :rule refl :args (@t22)) % 0.16/0.37 (step @p104 :rule cong :premises (@p103 @p89) :args ((= @t22 @t50))) % 0.16/0.37 (step @p105 :rule symm :premises (@p104)) % 0.16/0.37 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 0.16/0.37 (step @p107 :rule ho_cong :premises (@p92 @p106)) % 0.16/0.37 (step @p108 :rule ho_cong :premises (@p107 @p102)) % 0.16/0.37 (step @p109 :rule trans :premises (@p108 @p98)) % 0.16/0.37 (step @p110 :rule cong :premises (@p109) :args (@t24)) % 0.16/0.37 (step @p111 :rule eq_resolve :premises (@p4 @p110)) % 0.16/0.37 (step @p112 :rule instantiate :premises (@p111) :args ((@list tptp.y tptp.z))) % 0.16/0.37 (step @p113 :rule instantiate :premises (@p111) :args ((@list tptp.x tptp.z))) % 0.16/0.37 (step @p114 :rule refl :args ((tptp.moref @t27 @t26))) % 0.16/0.37 (step @p115 :rule refl :args (@t52)) % 0.16/0.37 (step @p116 :rule refl :args (@t53)) % 0.16/0.37 (step @p117 :rule cong :premises (@p116 @p115) :args (@t54)) % 0.16/0.37 (step @p118 :rule trans :premises (@p117 @p114)) % 0.16/0.37 (step @p119 :rule ho_cong :premises (@p53 @p116)) % 0.16/0.37 (step @p120 :rule ho_cong :premises (@p119 @p115)) % 0.16/0.37 (step @p121 :rule cong :premises (@p120 @p118) :args ((= (_ (_ tptp.moref @t53) @t52) @t54))) % 0.16/0.37 (step @p122 :rule symm :premises (@p121)) % 0.16/0.37 (step @p123 :rule refl :args (@t28)) % 0.16/0.37 (step @p124 :rule eq_resolve :premises (@p123 @p122)) % 0.16/0.37 (step @p125 :rule refl :args (@t26)) % 0.16/0.37 (step @p126 :rule cong :premises (@p125 @p115) :args ((= @t26 @t52))) % 0.16/0.37 (step @p127 :rule symm :premises (@p126)) % 0.16/0.37 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 0.16/0.37 (step @p129 :rule refl :args (@t27)) % 0.16/0.37 (step @p130 :rule cong :premises (@p129 @p116) :args ((= @t27 @t53))) % 0.16/0.37 (step @p131 :rule symm :premises (@p130)) % 0.16/0.37 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 0.16/0.37 (step @p133 :rule refl :args (tptp.moref)) % 0.16/0.37 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.16/0.37 (step @p135 :rule ho_cong :premises (@p134 @p128)) % 0.16/0.37 (step @p136 :rule trans :premises (@p135 @p124)) % 0.16/0.37 (step @p137 :rule cong :premises (@p136) :args (@t29)) % 0.16/0.37 (step @p138 :rule eq_resolve :premises (@p5 @p137)) % 0.16/0.37 (step @p139 :rule cnf_or_pos :args (@t60)) % 0.16/0.37 (step @p140 :rule reordering :premises (@p139) :args ((or @t54 @t58 @t56 @t59 @t61))) % 0.16/0.37 (step @p141 :rule chain_m_resolution :premises (@p140 @p138 @p113 @p112 @p86) :args (@t61 (@list true false false false) (@list @t54 @t57 @t55 @t46))) % 0.16/0.37 (assume-push @p148 @t62) % 0.16/0.37 (step @p143 :rule instantiate :premises (@p47) :args ((@list @t45 @t44 @t53 @t52))) % 0.16/0.37 (step-pop @p149 :rule scope :premises (@p143)) % 0.16/0.37 (step @p144 :rule process_scope :premises (@p149) :args (@t60)) % 0.16/0.37 (step @p146 :rule implies_elim :premises (@p144)) % 0.16/0.37 (step @p147 false :rule chain_m_resolution :premises (@p146 @p141 @p47) :args (false (@list true false) (@list @t60 @t62))) % 0.16/0.37 ) % 0.16/0.37 % SZS output end Proof % 0.16/0.37 % cvc5 exiting %------------------------------------------------------------------------------