%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM656^1 : 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 : n009.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 08:40:13 AM UTC 2026 % Result : Theorem 0.34s 0.56s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM656^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.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 11:44:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.34/0.49 %----Proving TH0 % 0.34/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.34/0.56 % SZS status Theorem % 0.34/0.56 % SZS output start Proof % 0.34/0.56 ( % 0.34/0.56 (declare-sort tptp.nat 0) % 0.34/0.56 (declare-const tptp.more (-> tptp.nat tptp.nat Bool)) % 0.34/0.56 (declare-const tptp.less (-> tptp.nat tptp.nat Bool)) % 0.34/0.56 (declare-const tptp.x tptp.nat) % 0.34/0.56 (declare-const tptp.y tptp.nat) % 0.34/0.56 (define @t1 () (_ (_ tptp.more tptp.x) tptp.y)) % 0.34/0.56 (define @t2 () (@var "Xa" Bool)) % 0.34/0.56 (define @t3 () (@var "Xy" tptp.nat)) % 0.34/0.56 (define @t4 () (@var "Xx" tptp.nat)) % 0.34/0.56 (define @t5 () (= @t4 @t3)) % 0.34/0.56 (define @t6 () (not @t5)) % 0.34/0.56 (define @t7 () (_ (_ tptp.less @t4) @t3)) % 0.34/0.56 (define @t8 () (=> @t7 @t6)) % 0.34/0.56 (define @t9 () (not @t8)) % 0.34/0.56 (define @t10 () (not @t7)) % 0.34/0.56 (define @t11 () (_ (_ tptp.more @t4) @t3)) % 0.34/0.56 (define @t12 () (=> @t11 @t10)) % 0.34/0.56 (define @t13 () (=> @t12 @t9)) % 0.34/0.56 (define @t14 () (not @t13)) % 0.34/0.56 (define @t15 () (not @t11)) % 0.34/0.56 (define @t16 () (=> @t5 @t15)) % 0.34/0.56 (define @t17 () (=> @t16 (not @t14))) % 0.34/0.56 (define @t18 () (not @t17)) % 0.34/0.56 (define @t19 () (@list @t4 @t3)) % 0.34/0.56 (define @t20 () (forall @t19 @t18)) % 0.34/0.56 (define @t21 () (= tptp.x tptp.y)) % 0.34/0.56 (define @t22 () (_ (_ tptp.less tptp.x) tptp.y)) % 0.34/0.56 (define @t23 () (not @t22)) % 0.34/0.56 (define @t24 () (=> @t23 @t21)) % 0.34/0.56 (define @t25 () (@var "BOUND_VARIABLE_7489" tptp.nat)) % 0.34/0.56 (define @t26 () (not (tptp.less @t25 @t25))) % 0.34/0.56 (define @t27 () (not (= @t25 @t25))) % 0.34/0.56 (define @t28 () (or @t26 @t27)) % 0.34/0.56 (define @t29 () (@list @t25)) % 0.34/0.56 (define @t30 () (@var "BOUND_VARIABLE_7487" tptp.nat)) % 0.34/0.56 (define @t31 () (not (= @t30 @t25))) % 0.34/0.56 (define @t32 () (tptp.less @t30 @t25)) % 0.34/0.56 (define @t33 () (not @t32)) % 0.34/0.56 (define @t34 () (or @t31 @t33 @t31)) % 0.34/0.56 (define @t35 () (@list @t30)) % 0.34/0.56 (define @t36 () (or @t33 @t31)) % 0.34/0.56 (define @t37 () (forall @t35 @t36)) % 0.34/0.56 (define @t38 () (forall @t29 @t37)) % 0.34/0.56 (define @t39 () (forall (@list @t25 @t30) @t36)) % 0.34/0.56 (define @t40 () (@list @t30 @t25)) % 0.34/0.56 (define @t41 () (_ (_ tptp.less @t30) @t25)) % 0.34/0.56 (define @t42 () (not @t41)) % 0.34/0.56 (define @t43 () (or @t42 @t31)) % 0.34/0.56 (define @t44 () (forall @t40 @t43)) % 0.34/0.56 (define @t45 () (@var "BOUND_VARIABLE_7476" tptp.nat)) % 0.34/0.56 (define @t46 () (@var "BOUND_VARIABLE_7474" tptp.nat)) % 0.34/0.56 (define @t47 () (tptp.less @t46 @t45)) % 0.34/0.56 (define @t48 () (_ (_ tptp.less @t46) @t45)) % 0.34/0.56 (define @t49 () (not @t48)) % 0.34/0.56 (define @t50 () (tptp.more @t46 @t45)) % 0.34/0.56 (define @t51 () (_ (_ tptp.more @t46) @t45)) % 0.34/0.56 (define @t52 () (not @t51)) % 0.34/0.56 (define @t53 () (or @t52 @t49)) % 0.34/0.56 (define @t54 () (forall (@list @t46 @t45) @t53)) % 0.34/0.56 (define @t55 () (@var "BOUND_VARIABLE_7464" tptp.nat)) % 0.34/0.56 (define @t56 () (not (tptp.more @t55 @t55))) % 0.34/0.56 (define @t57 () (not (= @t55 @t55))) % 0.34/0.56 (define @t58 () (or @t57 @t56)) % 0.34/0.56 (define @t59 () (@list @t55)) % 0.34/0.56 (define @t60 () (@var "BOUND_VARIABLE_7462" tptp.nat)) % 0.34/0.56 (define @t61 () (tptp.more @t60 @t55)) % 0.34/0.56 (define @t62 () (not @t61)) % 0.34/0.56 (define @t63 () (not (= @t60 @t55))) % 0.34/0.56 (define @t64 () (or @t63 @t63 @t62)) % 0.34/0.56 (define @t65 () (@list @t60)) % 0.34/0.56 (define @t66 () (or @t63 @t62)) % 0.34/0.56 (define @t67 () (forall @t65 @t66)) % 0.34/0.56 (define @t68 () (forall @t59 @t67)) % 0.34/0.56 (define @t69 () (forall (@list @t55 @t60) @t66)) % 0.34/0.56 (define @t70 () (@list @t60 @t55)) % 0.34/0.56 (define @t71 () (_ (_ tptp.more @t60) @t55)) % 0.34/0.56 (define @t72 () (not @t71)) % 0.34/0.56 (define @t73 () (or @t63 @t72)) % 0.34/0.56 (define @t74 () (forall @t70 @t73)) % 0.34/0.56 (define @t75 () (or @t10 @t6)) % 0.34/0.56 (define @t76 () (forall @t19 @t75)) % 0.34/0.56 (define @t77 () (@list @t4 @t3)) % 0.34/0.56 (define @t78 () (or @t15 @t10)) % 0.34/0.56 (define @t79 () (forall @t19 @t78)) % 0.34/0.56 (define @t80 () (or @t6 @t15)) % 0.34/0.56 (define @t81 () (forall @t19 @t80)) % 0.34/0.56 (define @t82 () (and @t81 @t79 @t76)) % 0.34/0.56 (define @t83 () (and @t80 @t78 @t75)) % 0.34/0.56 (define @t84 () (tptp.more tptp.x tptp.y)) % 0.34/0.56 (define @t85 () (tptp.less tptp.x tptp.y)) % 0.34/0.56 (define @t86 () (not @t85)) % 0.34/0.56 (define @t87 () (not @t84)) % 0.34/0.56 (define @t88 () (or @t87 @t86)) % 0.34/0.56 (define @t89 () (@list false false)) % 0.34/0.56 (define @t90 () (tptp.more tptp.x tptp.x)) % 0.34/0.56 (define @t91 () (forall @t59 @t56)) % 0.34/0.56 (assume @p1 @t1) % 0.34/0.56 (assume @p2 (forall (@list @t2) (=> (not (not @t2)) @t2))) % 0.34/0.56 (assume @p3 @t20) % 0.34/0.56 (assume @p4 (not (not @t24))) % 0.34/0.56 (assume @p5 true) % 0.34/0.56 (step @p6 :rule aci_norm :args ((= (or @t26 false) @t26))) % 0.34/0.56 (step @p7 :rule evaluate :args ((not true))) % 0.34/0.56 (step @p8 :rule eq-refl :args (@t25)) % 0.34/0.56 (step @p9 :rule cong :premises (@p8) :args (@t27)) % 0.34/0.56 (step @p10 :rule trans :premises (@p9 @p7)) % 0.34/0.56 (step @p11 :rule refl :args (@t26)) % 0.34/0.56 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t28)) % 0.34/0.56 (step @p13 :rule trans :premises (@p12 @p6)) % 0.34/0.56 (step @p14 :rule cong :premises (@p13) :args ((forall @t29 @t28))) % 0.34/0.56 (step @p15 :rule quant-var-elim-eq :args ((= (forall @t35 @t34) @t28))) % 0.34/0.56 (step @p16 :rule aci_norm :args ((= @t36 @t34))) % 0.34/0.56 (step @p17 :rule cong :premises (@p16) :args (@t37)) % 0.34/0.56 (step @p18 :rule trans :premises (@p17 @p15)) % 0.34/0.56 (step @p19 :rule cong :premises (@p18) :args (@t38)) % 0.34/0.56 (step @p20 :rule quant-merge-prenex :args ((= @t38 @t39))) % 0.34/0.56 (step @p21 :rule symm :premises (@p20)) % 0.34/0.56 (step @p22 :rule quant_var_reordering :args ((= (forall @t40 @t36) @t39))) % 0.34/0.56 (step @p23 :rule trans :premises (@p22 @p21 @p19)) % 0.34/0.56 (step @p24 :rule trans :premises (@p23 @p14)) % 0.34/0.56 (step @p25 :rule refl :args (@t31)) % 0.34/0.56 (step @p26 :rule refl :args (@t32)) % 0.34/0.56 (step @p27 :rule refl :args (@t41)) % 0.34/0.56 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t41 @t32))) % 0.34/0.56 (step @p29 :rule symm :premises (@p28)) % 0.34/0.56 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.34/0.56 (step @p31 :rule cong :premises (@p30) :args (@t42)) % 0.34/0.56 (step @p32 :rule nary_cong :premises (@p31 @p25) :args (@t43)) % 0.34/0.56 (step @p33 :rule cong :premises (@p32) :args (@t44)) % 0.34/0.56 (step @p34 :rule trans :premises (@p33 @p24)) % 0.34/0.56 (step @p35 :rule refl :args (@t47)) % 0.34/0.56 (step @p36 :rule refl :args (@t48)) % 0.34/0.56 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t48 @t47))) % 0.34/0.56 (step @p38 :rule symm :premises (@p37)) % 0.34/0.56 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.34/0.56 (step @p40 :rule cong :premises (@p39) :args (@t49)) % 0.34/0.56 (step @p41 :rule refl :args (@t50)) % 0.34/0.56 (step @p42 :rule refl :args (@t51)) % 0.34/0.56 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t51 @t50))) % 0.34/0.56 (step @p44 :rule symm :premises (@p43)) % 0.34/0.56 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.34/0.56 (step @p46 :rule cong :premises (@p45) :args (@t52)) % 0.34/0.56 (step @p47 :rule nary_cong :premises (@p46 @p40) :args (@t53)) % 0.34/0.56 (step @p48 :rule cong :premises (@p47) :args (@t54)) % 0.34/0.56 (step @p49 :rule aci_norm :args ((= (or false @t56) @t56))) % 0.34/0.56 (step @p50 :rule refl :args (@t56)) % 0.34/0.56 (step @p51 :rule eq-refl :args (@t55)) % 0.34/0.56 (step @p52 :rule cong :premises (@p51) :args (@t57)) % 0.34/0.56 (step @p53 :rule trans :premises (@p52 @p7)) % 0.34/0.56 (step @p54 :rule nary_cong :premises (@p53 @p50) :args (@t58)) % 0.34/0.56 (step @p55 :rule trans :premises (@p54 @p49)) % 0.34/0.56 (step @p56 :rule cong :premises (@p55) :args ((forall @t59 @t58))) % 0.34/0.56 (step @p57 :rule quant-var-elim-eq :args ((= (forall @t65 @t64) @t58))) % 0.34/0.56 (step @p58 :rule aci_norm :args ((= @t66 @t64))) % 0.34/0.56 (step @p59 :rule cong :premises (@p58) :args (@t67)) % 0.34/0.56 (step @p60 :rule trans :premises (@p59 @p57)) % 0.34/0.56 (step @p61 :rule cong :premises (@p60) :args (@t68)) % 0.34/0.56 (step @p62 :rule quant-merge-prenex :args ((= @t68 @t69))) % 0.34/0.56 (step @p63 :rule symm :premises (@p62)) % 0.34/0.56 (step @p64 :rule quant_var_reordering :args ((= (forall @t70 @t66) @t69))) % 0.34/0.56 (step @p65 :rule trans :premises (@p64 @p63 @p61)) % 0.34/0.56 (step @p66 :rule trans :premises (@p65 @p56)) % 0.34/0.56 (step @p67 :rule refl :args (@t61)) % 0.34/0.56 (step @p68 :rule refl :args (@t71)) % 0.34/0.56 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t71 @t61))) % 0.34/0.56 (step @p70 :rule symm :premises (@p69)) % 0.34/0.56 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.34/0.56 (step @p72 :rule cong :premises (@p71) :args (@t72)) % 0.34/0.56 (step @p73 :rule refl :args (@t63)) % 0.34/0.56 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t73)) % 0.34/0.56 (step @p75 :rule cong :premises (@p74) :args (@t74)) % 0.34/0.56 (step @p76 :rule trans :premises (@p75 @p66)) % 0.34/0.56 (step @p77 :rule nary_cong :premises (@p76 @p48 @p34) :args ((and @t74 @t54 @t44))) % 0.34/0.56 (step @p78 :rule alpha_equiv :args (@t76 @t77 (@list @t30 @t25))) % 0.34/0.56 (step @p79 :rule alpha_equiv :args (@t79 @t77 (@list @t46 @t45))) % 0.34/0.56 (step @p80 :rule alpha_equiv :args (@t81 @t77 (@list @t60 @t55))) % 0.34/0.56 (step @p81 :rule nary_cong :premises (@p80 @p79 @p78) :args (@t82)) % 0.34/0.56 (step @p82 :rule quant-miniscope-and :args ((= (forall @t19 @t83) @t82))) % 0.34/0.56 (step @p83 :rule trans :premises (@p82 @p81)) % 0.34/0.56 (step @p84 :rule trans :premises (@p83 @p77)) % 0.34/0.56 (step @p85 :rule aci_norm :args ((= (and @t80 (and @t78 @t75)) @t83))) % 0.34/0.56 (step @p86 :rule bool-impl-elim :args (@t7 @t6)) % 0.34/0.56 (step @p87 :rule bool-impl-elim :args (@t11 @t10)) % 0.34/0.56 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((and @t12 @t8))) % 0.34/0.57 (step @p89 :rule bool-double-not-elim :args (@t8)) % 0.34/0.57 (step @p90 :rule refl :args (@t12)) % 0.34/0.57 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((and @t12 (not @t9)))) % 0.34/0.57 (step @p92 :rule bool-implies-de-morgan :args (@t12 @t9)) % 0.34/0.57 (step @p93 :rule trans :premises (@p92 @p91)) % 0.34/0.57 (step @p94 :rule trans :premises (@p93 @p88)) % 0.34/0.57 (step @p95 :rule bool-impl-elim :args (@t5 @t15)) % 0.34/0.57 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((and @t16 @t14))) % 0.34/0.57 (step @p97 :rule trans :premises (@p96 @p85)) % 0.34/0.57 (step @p98 :rule bool-implies-de-morgan :args (@t16 @t13)) % 0.34/0.57 (step @p99 :rule trans :premises (@p98 @p97)) % 0.34/0.57 (step @p100 :rule cong :premises (@p99) :args ((forall @t19 (not (=> @t16 @t13))))) % 0.34/0.57 (step @p101 :rule trans :premises (@p100 @p84)) % 0.34/0.57 (step @p102 :rule bool-double-not-elim :args (@t13)) % 0.34/0.57 (step @p103 :rule refl :args (@t16)) % 0.34/0.57 (step @p104 :rule cong :premises (@p103 @p102) :args (@t17)) % 0.34/0.57 (step @p105 :rule cong :premises (@p104) :args (@t18)) % 0.34/0.57 (step @p106 :rule cong :premises (@p105) :args (@t20)) % 0.34/0.57 (step @p107 :rule trans :premises (@p106 @p101)) % 0.34/0.57 (step @p108 :rule eq_resolve :premises (@p3 @p107)) % 0.34/0.57 (step @p109 :rule and_elim :premises (@p108) :args (0)) % 0.34/0.57 (step @p110 :rule refl :args (@t84)) % 0.34/0.57 (step @p111 :rule refl :args (@t1)) % 0.34/0.57 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t1 @t84))) % 0.34/0.57 (step @p113 :rule symm :premises (@p112)) % 0.34/0.57 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.34/0.57 (step @p115 :rule eq_resolve :premises (@p1 @p114)) % 0.34/0.57 (step @p116 :rule true_intro :premises (@p115)) % 0.34/0.57 (step @p117 :rule and_elim :premises (@p108) :args (1)) % 0.34/0.57 (step @p118 :rule instantiate :premises (@p117) :args ((@list tptp.x tptp.y))) % 0.34/0.57 (step @p119 :rule cnf_or_pos :args (@t88)) % 0.34/0.57 (step @p120 :rule reordering :premises (@p119) :args ((or @t86 @t87 (not @t88)))) % 0.34/0.57 (step @p121 :rule chain_m_resolution :premises (@p120 @p115 @p118) :args (@t86 @t89 (@list @t84 @t88))) % 0.34/0.57 (step @p122 :rule refl :args (@t21)) % 0.34/0.57 (step @p123 :rule bool-double-not-elim :args (@t85)) % 0.34/0.57 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or (not @t86) @t21))) % 0.34/0.57 (step @p125 :rule refl :args (@t85)) % 0.34/0.57 (step @p126 :rule refl :args (@t22)) % 0.34/0.57 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t22 @t85))) % 0.34/0.57 (step @p128 :rule symm :premises (@p127)) % 0.34/0.57 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.34/0.57 (step @p130 :rule cong :premises (@p129) :args (@t23)) % 0.34/0.57 (step @p131 :rule cong :premises (@p130 @p122) :args (@t24)) % 0.34/0.57 (step @p132 :rule bool-double-not-elim :args (@t24)) % 0.34/0.57 (step @p133 :rule trans :premises (@p132 @p131)) % 0.34/0.57 (step @p134 :rule eq_resolve :premises (@p4 @p133)) % 0.34/0.57 (step @p135 :rule implies_elim :premises (@p134)) % 0.34/0.57 (step @p136 :rule eq_resolve :premises (@p135 @p124)) % 0.34/0.57 (step @p137 :rule reordering :premises (@p136) :args ((or @t21 @t85))) % 0.34/0.57 (step @p138 :rule chain_m_resolution :premises (@p137 @p121) :args (@t21 (@list true) (@list @t85))) % 0.34/0.57 (step @p139 :rule refl :args (tptp.x)) % 0.34/0.57 (step @p140 :rule cong :premises (@p139 @p138) :args (@t90)) % 0.34/0.57 (step @p141 :rule trans :premises (@p140 @p116)) % 0.34/0.57 (step @p142 :rule true_elim :premises (@p141)) % 0.34/0.57 (assume-push @p149 @t91) % 0.34/0.57 (step @p144 :rule instantiate :premises (@p109) :args ((@list tptp.x))) % 0.34/0.57 (step-pop @p150 :rule scope :premises (@p144)) % 0.34/0.57 (step @p145 :rule process_scope :premises (@p150) :args ((not @t90))) % 0.34/0.57 (step @p147 :rule implies_elim :premises (@p145)) % 0.34/0.57 (step @p148 false :rule chain_m_resolution :premises (@p147 @p142 @p109) :args (false @t89 (@list @t90 @t91))) % 0.34/0.57 ) % 0.34/0.57 % SZS output end Proof % 0.34/0.57 % cvc5 exiting %------------------------------------------------------------------------------