%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM754^1 : 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 : 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 08:40:34 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 : NUM754^1 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n015.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 12:12:49 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.48 %----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.frac 0) % 0.37/0.56 (declare-const tptp.pf (-> tptp.frac tptp.frac tptp.frac)) % 0.37/0.56 (declare-const tptp.moref (-> tptp.frac tptp.frac Bool)) % 0.37/0.56 (declare-const tptp.z tptp.frac) % 0.37/0.56 (declare-const tptp.u tptp.frac) % 0.37/0.56 (declare-const tptp.eq (-> tptp.frac tptp.frac Bool)) % 0.37/0.56 (declare-const tptp.x tptp.frac) % 0.37/0.56 (declare-const tptp.y tptp.frac) % 0.37/0.56 (define @t1 () (_ (_ tptp.eq tptp.x) tptp.y)) % 0.37/0.56 (define @t2 () (_ (_ tptp.moref tptp.z) tptp.u)) % 0.37/0.56 (define @t3 () (@var "Xu" tptp.frac)) % 0.37/0.56 (define @t4 () (@var "Xz" tptp.frac)) % 0.37/0.56 (define @t5 () (_ (_ tptp.moref @t4) @t3)) % 0.37/0.56 (define @t6 () (@var "Xy" tptp.frac)) % 0.37/0.56 (define @t7 () (_ (_ tptp.eq @t6) @t3)) % 0.37/0.56 (define @t8 () (=> @t7 @t5)) % 0.37/0.56 (define @t9 () (@var "Xx" tptp.frac)) % 0.37/0.56 (define @t10 () (_ tptp.eq @t9)) % 0.37/0.56 (define @t11 () (_ @t10 @t4)) % 0.37/0.56 (define @t12 () (=> @t11 @t8)) % 0.37/0.56 (define @t13 () (_ (_ tptp.moref @t9) @t6)) % 0.37/0.56 (define @t14 () (@list @t9 @t6 @t4 @t3)) % 0.37/0.56 (define @t15 () (forall @t14 (=> @t13 @t12))) % 0.37/0.56 (define @t16 () (_ tptp.pf @t6)) % 0.37/0.56 (define @t17 () (_ @t16 @t3)) % 0.37/0.56 (define @t18 () (_ tptp.pf @t9)) % 0.37/0.56 (define @t19 () (_ @t18 @t4)) % 0.37/0.56 (define @t20 () (_ (_ tptp.moref @t19) @t17)) % 0.37/0.56 (define @t21 () (=> @t5 @t20)) % 0.37/0.56 (define @t22 () (_ @t10 @t6)) % 0.37/0.56 (define @t23 () (forall @t14 (=> @t22 @t21))) % 0.37/0.56 (define @t24 () (_ @t16 @t9)) % 0.37/0.56 (define @t25 () (_ @t18 @t6)) % 0.37/0.56 (define @t26 () (_ (_ tptp.eq @t25) @t24)) % 0.37/0.56 (define @t27 () (forall (@list @t9 @t6) @t26)) % 0.37/0.56 (define @t28 () (_ (_ tptp.pf tptp.u) tptp.y)) % 0.37/0.56 (define @t29 () (_ (_ tptp.pf tptp.z) tptp.x)) % 0.37/0.56 (define @t30 () (_ (_ tptp.moref @t29) @t28)) % 0.37/0.56 (define @t31 () (not @t30)) % 0.37/0.56 (define @t32 () (tptp.pf @t6 @t3)) % 0.37/0.56 (define @t33 () (tptp.pf @t9 @t4)) % 0.37/0.56 (define @t34 () (tptp.moref @t33 @t32)) % 0.37/0.56 (define @t35 () (tptp.moref @t4 @t3)) % 0.37/0.56 (define @t36 () (not @t5)) % 0.37/0.56 (define @t37 () (tptp.eq @t9 @t6)) % 0.37/0.56 (define @t38 () (not @t22)) % 0.37/0.56 (define @t39 () (or @t38 @t36 @t20)) % 0.37/0.56 (define @t40 () (tptp.eq @t6 @t3)) % 0.37/0.56 (define @t41 () (not @t7)) % 0.37/0.56 (define @t42 () (tptp.eq @t9 @t4)) % 0.37/0.56 (define @t43 () (not @t11)) % 0.37/0.56 (define @t44 () (tptp.moref @t9 @t6)) % 0.37/0.56 (define @t45 () (not @t13)) % 0.37/0.56 (define @t46 () (or @t45 @t43 @t41 @t5)) % 0.37/0.56 (define @t47 () (or @t43 @t41 @t5)) % 0.37/0.56 (define @t48 () (tptp.pf tptp.u tptp.y)) % 0.37/0.56 (define @t49 () (tptp.pf tptp.z tptp.x)) % 0.37/0.56 (define @t50 () (tptp.pf tptp.y tptp.u)) % 0.37/0.56 (define @t51 () (tptp.pf tptp.x tptp.z)) % 0.37/0.56 (define @t52 () (tptp.pf @t6 @t9)) % 0.37/0.56 (define @t53 () (tptp.pf @t9 @t6)) % 0.37/0.56 (define @t54 () (tptp.eq @t53 @t52)) % 0.37/0.56 (define @t55 () (tptp.moref @t49 @t48)) % 0.37/0.56 (define @t56 () (tptp.eq @t50 @t48)) % 0.37/0.56 (define @t57 () (not @t56)) % 0.37/0.56 (define @t58 () (tptp.eq @t51 @t49)) % 0.37/0.56 (define @t59 () (not @t58)) % 0.37/0.56 (define @t60 () (tptp.moref @t51 @t50)) % 0.37/0.56 (define @t61 () (not @t60)) % 0.37/0.56 (define @t62 () (or @t61 @t59 @t57 @t55)) % 0.37/0.56 (define @t63 () (tptp.moref tptp.z tptp.u)) % 0.37/0.56 (define @t64 () (tptp.eq tptp.x tptp.y)) % 0.37/0.56 (define @t65 () (not @t63)) % 0.37/0.56 (define @t66 () (not @t64)) % 0.37/0.56 (define @t67 () (or @t66 @t65 @t60)) % 0.37/0.56 (define @t68 () (not @t67)) % 0.37/0.56 (define @t69 () (forall @t14 (or (not @t37) (not @t35) @t34))) % 0.37/0.56 (assume @p1 @t1) % 0.37/0.56 (assume @p2 @t2) % 0.37/0.56 (assume @p3 @t15) % 0.37/0.56 (assume @p4 @t23) % 0.37/0.56 (assume @p5 @t27) % 0.37/0.56 (assume @p6 @t31) % 0.37/0.56 (assume @p7 true) % 0.37/0.56 (step @p8 :rule refl :args ((tptp.moref @t19 @t17))) % 0.37/0.56 (step @p9 :rule refl :args (@t32)) % 0.37/0.56 (step @p10 :rule refl :args (@t33)) % 0.37/0.56 (step @p11 :rule cong :premises (@p10 @p9) :args (@t34)) % 0.37/0.56 (step @p12 :rule trans :premises (@p11 @p8)) % 0.37/0.56 (step @p13 :rule refl :args (tptp.moref)) % 0.37/0.56 (step @p14 :rule ho_cong :premises (@p13 @p10)) % 0.37/0.56 (step @p15 :rule ho_cong :premises (@p14 @p9)) % 0.37/0.56 (step @p16 :rule cong :premises (@p15 @p12) :args ((= (_ (_ tptp.moref @t33) @t32) @t34))) % 0.37/0.56 (step @p17 :rule symm :premises (@p16)) % 0.37/0.56 (step @p18 :rule refl :args (@t20)) % 0.37/0.56 (step @p19 :rule eq_resolve :premises (@p18 @p17)) % 0.37/0.56 (step @p20 :rule refl :args (@t17)) % 0.37/0.56 (step @p21 :rule cong :premises (@p20 @p9) :args ((= @t17 @t32))) % 0.37/0.56 (step @p22 :rule symm :premises (@p21)) % 0.37/0.56 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 0.37/0.56 (step @p24 :rule refl :args (@t19)) % 0.37/0.56 (step @p25 :rule cong :premises (@p24 @p10) :args ((= @t19 @t33))) % 0.37/0.56 (step @p26 :rule symm :premises (@p25)) % 0.37/0.56 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.37/0.56 (step @p28 :rule ho_cong :premises (@p13 @p27)) % 0.37/0.56 (step @p29 :rule ho_cong :premises (@p28 @p23)) % 0.37/0.56 (step @p30 :rule trans :premises (@p29 @p19)) % 0.37/0.56 (step @p31 :rule refl :args (@t35)) % 0.37/0.56 (step @p32 :rule refl :args (@t5)) % 0.37/0.56 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t5 @t35))) % 0.37/0.56 (step @p34 :rule symm :premises (@p33)) % 0.37/0.56 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.37/0.56 (step @p36 :rule cong :premises (@p35) :args (@t36)) % 0.37/0.56 (step @p37 :rule refl :args (@t37)) % 0.37/0.56 (step @p38 :rule refl :args (@t22)) % 0.37/0.56 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t22 @t37))) % 0.37/0.56 (step @p40 :rule symm :premises (@p39)) % 0.37/0.56 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.37/0.56 (step @p42 :rule cong :premises (@p41) :args (@t38)) % 0.37/0.56 (step @p43 :rule nary_cong :premises (@p42 @p36 @p30) :args (@t39)) % 0.37/0.56 (step @p44 :rule cong :premises (@p43) :args ((forall @t14 @t39))) % 0.37/0.56 (step @p45 :rule aci_norm :args ((= (or @t38 (or @t36 @t20)) @t39))) % 0.37/0.56 (step @p46 :rule bool-impl-elim :args (@t5 @t20)) % 0.37/0.56 (step @p47 :rule refl :args (@t38)) % 0.37/0.56 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or @t38 @t21))) % 0.37/0.56 (step @p49 :rule trans :premises (@p48 @p45)) % 0.37/0.56 (step @p50 :rule bool-impl-elim :args (@t22 @t21)) % 0.37/0.56 (step @p51 :rule trans :premises (@p50 @p49)) % 0.37/0.56 (step @p52 :rule cong :premises (@p51) :args (@t23)) % 0.37/0.56 (step @p53 :rule trans :premises (@p52 @p44)) % 0.37/0.56 (step @p54 :rule eq_resolve :premises (@p4 @p53)) % 0.37/0.56 (step @p55 :rule refl :args (@t40)) % 0.37/0.56 (step @p56 :rule refl :args (@t7)) % 0.37/0.56 (step @p57 :rule cong :premises (@p56 @p55) :args ((= @t7 @t40))) % 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 (@t41)) % 0.37/0.56 (step @p61 :rule refl :args (@t42)) % 0.37/0.56 (step @p62 :rule refl :args (@t11)) % 0.37/0.56 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t11 @t42))) % 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 (@t43)) % 0.37/0.56 (step @p67 :rule refl :args (@t44)) % 0.37/0.56 (step @p68 :rule refl :args (@t13)) % 0.37/0.56 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t13 @t44))) % 0.37/0.56 (step @p70 :rule symm :premises (@p69)) % 0.37/0.56 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.37/0.56 (step @p72 :rule cong :premises (@p71) :args (@t45)) % 0.37/0.56 (step @p73 :rule nary_cong :premises (@p72 @p66 @p60 @p35) :args (@t46)) % 0.37/0.56 (step @p74 :rule cong :premises (@p73) :args ((forall @t14 @t46))) % 0.37/0.56 (step @p75 :rule aci_norm :args ((= (or @t45 @t47) @t46))) % 0.37/0.56 (step @p76 :rule aci_norm :args ((= (or @t43 (or @t41 @t5)) @t47))) % 0.37/0.56 (step @p77 :rule bool-impl-elim :args (@t7 @t5)) % 0.37/0.56 (step @p78 :rule refl :args (@t43)) % 0.37/0.56 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((or @t43 @t8))) % 0.37/0.56 (step @p80 :rule trans :premises (@p79 @p76)) % 0.37/0.56 (step @p81 :rule bool-impl-elim :args (@t11 @t8)) % 0.37/0.56 (step @p82 :rule trans :premises (@p81 @p80)) % 0.37/0.56 (step @p83 :rule refl :args (@t45)) % 0.37/0.56 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or @t45 @t12))) % 0.37/0.56 (step @p85 :rule trans :premises (@p84 @p75)) % 0.37/0.56 (step @p86 :rule bool-impl-elim :args (@t13 @t12)) % 0.37/0.56 (step @p87 :rule trans :premises (@p86 @p85)) % 0.37/0.56 (step @p88 :rule cong :premises (@p87) :args (@t15)) % 0.37/0.56 (step @p89 :rule trans :premises (@p88 @p74)) % 0.37/0.56 (step @p90 :rule eq_resolve :premises (@p3 @p89)) % 0.37/0.56 (step @p91 :rule instantiate :premises (@p90) :args ((@list @t51 @t50 @t49 @t48))) % 0.37/0.56 (step @p92 :rule refl :args ((tptp.eq @t25 @t24))) % 0.37/0.56 (step @p93 :rule refl :args (@t52)) % 0.37/0.56 (step @p94 :rule refl :args (@t53)) % 0.37/0.56 (step @p95 :rule cong :premises (@p94 @p93) :args (@t54)) % 0.37/0.56 (step @p96 :rule trans :premises (@p95 @p92)) % 0.37/0.56 (step @p97 :rule refl :args (tptp.eq)) % 0.37/0.56 (step @p98 :rule ho_cong :premises (@p97 @p94)) % 0.37/0.56 (step @p99 :rule ho_cong :premises (@p98 @p93)) % 0.37/0.56 (step @p100 :rule cong :premises (@p99 @p96) :args ((= (_ (_ tptp.eq @t53) @t52) @t54))) % 0.37/0.56 (step @p101 :rule symm :premises (@p100)) % 0.37/0.56 (step @p102 :rule refl :args (@t26)) % 0.37/0.56 (step @p103 :rule eq_resolve :premises (@p102 @p101)) % 0.37/0.56 (step @p104 :rule refl :args (@t24)) % 0.37/0.56 (step @p105 :rule cong :premises (@p104 @p93) :args ((= @t24 @t52))) % 0.37/0.56 (step @p106 :rule symm :premises (@p105)) % 0.37/0.56 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.37/0.57 (step @p108 :rule refl :args (@t25)) % 0.37/0.57 (step @p109 :rule cong :premises (@p108 @p94) :args ((= @t25 @t53))) % 0.37/0.57 (step @p110 :rule symm :premises (@p109)) % 0.37/0.57 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.37/0.57 (step @p112 :rule ho_cong :premises (@p97 @p111)) % 0.37/0.57 (step @p113 :rule ho_cong :premises (@p112 @p107)) % 0.37/0.57 (step @p114 :rule trans :premises (@p113 @p103)) % 0.37/0.57 (step @p115 :rule cong :premises (@p114) :args (@t27)) % 0.37/0.57 (step @p116 :rule eq_resolve :premises (@p5 @p115)) % 0.37/0.57 (step @p117 :rule instantiate :premises (@p116) :args ((@list tptp.y tptp.u))) % 0.37/0.57 (step @p118 :rule instantiate :premises (@p116) :args ((@list tptp.x tptp.z))) % 0.37/0.57 (step @p119 :rule refl :args ((tptp.moref @t29 @t28))) % 0.37/0.57 (step @p120 :rule refl :args (@t48)) % 0.37/0.57 (step @p121 :rule refl :args (@t49)) % 0.37/0.57 (step @p122 :rule cong :premises (@p121 @p120) :args (@t55)) % 0.37/0.57 (step @p123 :rule trans :premises (@p122 @p119)) % 0.37/0.57 (step @p124 :rule ho_cong :premises (@p13 @p121)) % 0.37/0.57 (step @p125 :rule ho_cong :premises (@p124 @p120)) % 0.37/0.57 (step @p126 :rule cong :premises (@p125 @p123) :args ((= (_ (_ tptp.moref @t49) @t48) @t55))) % 0.37/0.57 (step @p127 :rule symm :premises (@p126)) % 0.37/0.57 (step @p128 :rule refl :args (@t30)) % 0.37/0.57 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.37/0.57 (step @p130 :rule refl :args (@t28)) % 0.37/0.57 (step @p131 :rule cong :premises (@p130 @p120) :args ((= @t28 @t48))) % 0.37/0.57 (step @p132 :rule symm :premises (@p131)) % 0.37/0.57 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.37/0.57 (step @p134 :rule refl :args (@t29)) % 0.37/0.57 (step @p135 :rule cong :premises (@p134 @p121) :args ((= @t29 @t49))) % 0.37/0.57 (step @p136 :rule symm :premises (@p135)) % 0.37/0.57 (step @p137 :rule eq_resolve :premises (@p134 @p136)) % 0.37/0.57 (step @p138 :rule refl :args (tptp.moref)) % 0.37/0.57 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.37/0.57 (step @p140 :rule ho_cong :premises (@p139 @p133)) % 0.37/0.57 (step @p141 :rule trans :premises (@p140 @p129)) % 0.37/0.57 (step @p142 :rule cong :premises (@p141) :args (@t31)) % 0.37/0.57 (step @p143 :rule eq_resolve :premises (@p6 @p142)) % 0.37/0.57 (step @p144 :rule cnf_or_pos :args (@t62)) % 0.37/0.57 (step @p145 :rule reordering :premises (@p144) :args ((or @t55 @t59 @t57 @t61 (not @t62)))) % 0.37/0.57 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p118 @p117 @p91) :args (@t61 (@list true false false false) (@list @t55 @t58 @t56 @t62))) % 0.37/0.57 (step @p147 :rule refl :args (@t63)) % 0.37/0.57 (step @p148 :rule refl :args (@t2)) % 0.37/0.57 (step @p149 :rule cong :premises (@p148 @p147) :args ((= @t2 @t63))) % 0.37/0.57 (step @p150 :rule symm :premises (@p149)) % 0.37/0.57 (step @p151 :rule eq_resolve :premises (@p148 @p150)) % 0.37/0.57 (step @p152 :rule eq_resolve :premises (@p2 @p151)) % 0.37/0.57 (step @p153 :rule refl :args (@t64)) % 0.37/0.57 (step @p154 :rule refl :args (@t1)) % 0.37/0.57 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t1 @t64))) % 0.37/0.57 (step @p156 :rule symm :premises (@p155)) % 0.37/0.57 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 0.37/0.57 (step @p158 :rule eq_resolve :premises (@p1 @p157)) % 0.37/0.57 (step @p159 :rule cnf_or_pos :args (@t67)) % 0.37/0.57 (step @p160 :rule reordering :premises (@p159) :args ((or @t66 @t65 @t60 @t68))) % 0.37/0.57 (step @p161 :rule chain_m_resolution :premises (@p160 @p158 @p152 @p146) :args (@t68 (@list false false true) (@list @t64 @t63 @t60))) % 0.37/0.57 (assume-push @p168 @t69) % 0.37/0.57 (step @p163 :rule instantiate :premises (@p54) :args ((@list tptp.x tptp.y tptp.z tptp.u))) % 0.37/0.57 (step-pop @p169 :rule scope :premises (@p163)) % 0.37/0.57 (step @p164 :rule process_scope :premises (@p169) :args (@t67)) % 0.37/0.57 (step @p166 :rule implies_elim :premises (@p164)) % 0.37/0.57 (step @p167 false :rule chain_m_resolution :premises (@p166 @p161 @p54) :args (false (@list true false) (@list @t67 @t69))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------