%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE063+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:28:14 AM UTC 2026 % Result : Theorem 15.69s 15.96s % Output : Proof 15.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE063+1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n021.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 05:13:20 EDT 2026 % 0.18/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 15.69/15.96 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.69/15.96 --- Run --no-e-matching --full-saturate-quant at 6... % 15.69/15.96 % SZS status Theorem % 15.69/15.96 % SZS output start Proof % 15.69/15.96 ( % 15.69/15.96 (declare-sort $$unsorted 0) % 15.69/15.96 (declare-const tptp.domain (-> $$unsorted $$unsorted)) % 15.69/15.96 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 15.69/15.96 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 15.69/15.96 (declare-const tptp.zero $$unsorted) % 15.69/15.96 (declare-const tptp.one $$unsorted) % 15.69/15.96 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 15.69/15.96 (define @t1 () (@var "A" $$unsorted)) % 15.69/15.96 (define @t2 () (@var "B" $$unsorted)) % 15.69/15.96 (define @t3 () (tptp.addition @t1 @t2)) % 15.69/15.96 (define @t4 () (@list @t1 @t2)) % 15.69/15.96 (define @t5 () (@var "C" $$unsorted)) % 15.69/15.96 (define @t6 () (tptp.addition @t2 @t5)) % 15.69/15.96 (define @t7 () (tptp.addition @t1 tptp.zero)) % 15.69/15.96 (define @t8 () (@list @t1)) % 15.69/15.96 (define @t9 () (forall @t8 (= @t7 @t1))) % 15.69/15.96 (define @t10 () (tptp.multiplication @t1 @t2)) % 15.69/15.96 (define @t11 () (tptp.multiplication @t2 @t5)) % 15.69/15.96 (define @t12 () (@list @t1 @t2 @t5)) % 15.69/15.96 (define @t13 () (tptp.multiplication @t1 tptp.one)) % 15.69/15.96 (define @t14 () (forall @t8 (= @t13 @t1))) % 15.69/15.96 (define @t15 () (tptp.multiplication tptp.one @t1)) % 15.69/15.96 (define @t16 () (forall @t8 (= @t15 @t1))) % 15.69/15.96 (define @t17 () (tptp.multiplication @t1 @t5)) % 15.69/15.96 (define @t18 () (@var "X0" $$unsorted)) % 15.69/15.96 (define @t19 () (tptp.domain @t18)) % 15.69/15.96 (define @t20 () (tptp.multiplication @t19 @t18)) % 15.69/15.96 (define @t21 () (tptp.addition @t18 @t20)) % 15.69/15.96 (define @t22 () (@list @t18)) % 15.69/15.96 (define @t23 () (forall @t22 (= @t21 @t20))) % 15.69/15.96 (define @t24 () (@var "X1" $$unsorted)) % 15.69/15.96 (define @t25 () (tptp.domain @t24)) % 15.69/15.96 (define @t26 () (@list @t18 @t24)) % 15.69/15.96 (define @t27 () (tptp.addition @t19 tptp.one)) % 15.69/15.96 (define @t28 () (forall @t22 (= @t27 tptp.one))) % 15.69/15.96 (define @t29 () (tptp.addition @t19 @t25)) % 15.69/15.96 (define @t30 () (forall @t26 (= (tptp.domain (tptp.addition @t18 @t24)) @t29))) % 15.69/15.96 (define @t31 () (tptp.multiplication @t25 @t18)) % 15.69/15.96 (define @t32 () (tptp.addition @t18 @t31)) % 15.69/15.96 (define @t33 () (=> (= @t32 @t31) (= @t29 @t25))) % 15.69/15.96 (define @t34 () (forall @t26 @t33)) % 15.69/15.96 (define @t35 () (not @t34)) % 15.69/15.96 (define @t36 () (= @t31 @t32)) % 15.69/15.96 (define @t37 () (= @t25 @t29)) % 15.69/15.96 (define @t38 () (forall @t26 (or (not @t36) @t37))) % 15.69/15.96 (define @t39 () (@quantifiers_skolemize @t38 1)) % 15.69/15.96 (define @t40 () (tptp.domain @t39)) % 15.69/15.96 (define @t41 () (@quantifiers_skolemize @t38 0)) % 15.69/15.96 (define @t42 () (tptp.domain @t41)) % 15.69/15.96 (define @t43 () (= @t40 (tptp.addition @t42 @t40))) % 15.69/15.96 (define @t44 () (tptp.multiplication @t40 @t41)) % 15.69/15.96 (define @t45 () (tptp.addition @t41 @t44)) % 15.69/15.96 (define @t46 () (= @t44 @t45)) % 15.69/15.96 (define @t47 () (not @t46)) % 15.69/15.96 (define @t48 () (or @t47 @t43)) % 15.69/15.96 (define @t49 () (@list true)) % 15.69/15.96 (define @t50 () (@list @t48)) % 15.69/15.96 (define @t51 () (@list @t41)) % 15.69/15.96 (define @t52 () (@list @t39)) % 15.69/15.96 (define @t53 () (tptp.addition tptp.one @t40)) % 15.69/15.96 (define @t54 () (@list @t40)) % 15.69/15.96 (define @t55 () (tptp.domain @t40)) % 15.69/15.96 (define @t56 () (tptp.multiplication @t55 @t40)) % 15.69/15.96 (define @t57 () (tptp.multiplication @t40 @t40)) % 15.69/15.96 (define @t58 () (tptp.domain @t57)) % 15.69/15.96 (define @t59 () (tptp.multiplication @t40 @t42)) % 15.69/15.96 (define @t60 () (tptp.addition @t58 (tptp.domain @t59))) % 15.69/15.96 (define @t61 () (tptp.domain @t42)) % 15.69/15.96 (define @t62 () (@list tptp.one)) % 15.69/15.96 (define @t63 () (tptp.domain tptp.one)) % 15.69/15.96 (define @t64 () (tptp.addition @t63 @t61)) % 15.69/15.96 (define @t65 () (tptp.addition @t57 @t59)) % 15.69/15.96 (define @t66 () (tptp.domain @t65)) % 15.69/15.96 (define @t67 () (= @t66 @t60)) % 15.69/15.96 (assume @p1 (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 15.69/15.96 (assume @p2 (forall (@list @t5 @t2 @t1) (= (tptp.addition @t1 @t6) (tptp.addition @t3 @t5)))) % 15.69/15.96 (assume @p3 @t9) % 15.69/15.96 (assume @p4 (forall @t8 (= (tptp.addition @t1 @t1) @t1))) % 15.69/15.96 (assume @p5 (forall @t12 (= (tptp.multiplication @t1 @t11) (tptp.multiplication @t10 @t5)))) % 15.69/15.96 (assume @p6 @t14) % 15.69/15.96 (assume @p7 @t16) % 15.69/15.96 (assume @p8 (forall @t12 (= (tptp.multiplication @t1 @t6) (tptp.addition @t10 @t17)))) % 15.69/15.96 (assume @p9 (forall @t12 (= (tptp.multiplication @t3 @t5) (tptp.addition @t17 @t11)))) % 15.69/15.96 (assume @p10 (forall @t8 (= (tptp.multiplication @t1 tptp.zero) tptp.zero))) % 15.69/15.96 (assume @p11 (forall @t8 (= (tptp.multiplication tptp.zero @t1) tptp.zero))) % 15.69/15.96 (assume @p12 (forall @t4 (= (tptp.leq @t1 @t2) (= @t3 @t2)))) % 15.69/15.96 (assume @p13 @t23) % 15.69/15.96 (assume @p14 (forall @t26 (= (tptp.domain (tptp.multiplication @t18 @t24)) (tptp.domain (tptp.multiplication @t18 @t25))))) % 15.69/15.96 (assume @p15 @t28) % 15.69/15.96 (assume @p16 (= (tptp.domain tptp.zero) tptp.zero)) % 15.69/15.96 (assume @p17 @t30) % 15.69/15.96 (assume @p18 @t35) % 15.69/15.96 (assume @p19 true) % 15.69/15.96 (step @p20 :rule bool-impl-elim :args (@t36 @t37)) % 15.69/15.96 (step @p21 :rule cong :premises (@p20) :args ((forall @t26 (=> @t36 @t37)))) % 15.69/15.96 (step @p22 :rule eq-symm :args (@t29 @t25)) % 15.69/15.96 (step @p23 :rule eq-symm :args (@t32 @t31)) % 15.69/15.96 (step @p24 :rule cong :premises (@p23 @p22) :args (@t33)) % 15.69/15.96 (step @p25 :rule cong :premises (@p24) :args (@t34)) % 15.69/15.96 (step @p26 :rule trans :premises (@p25 @p21)) % 15.69/15.96 (step @p27 :rule cong :premises (@p26) :args (@t35)) % 15.69/15.96 (step @p28 :rule eq_resolve :premises (@p18 @p27)) % 15.69/15.96 (step @p29 :rule skolemize :premises (@p28)) % 15.69/15.96 (step @p30 :rule cnf_or_neg :args (@t48 1)) % 15.69/15.96 (step @p31 :rule chain_m_resolution :premises (@p30 @p29) :args ((not @t43) @t49 @t50)) % 15.69/15.96 (step @p32 :rule false_intro :premises (@p31)) % 15.69/15.96 (step @p33 :rule instantiate :premises (@p1) :args ((@list @t40 @t42))) % 15.69/15.96 (step @p34 :rule eq-symm :args (@t7 @t1)) % 15.69/15.96 (step @p35 :rule cong :premises (@p34) :args (@t9)) % 15.69/15.96 (step @p36 :rule eq_resolve :premises (@p3 @p35)) % 15.69/15.96 (step @p37 :rule instantiate :premises (@p36) :args (@t51)) % 15.69/15.96 (step @p38 :rule symm :premises (@p37)) % 15.69/15.96 (step @p39 :rule instantiate :premises (@p1) :args ((@list tptp.zero @t41))) % 15.69/15.96 (step @p40 :rule trans :premises (@p39 @p38)) % 15.69/15.96 (step @p41 :rule cong :premises (@p40) :args ((tptp.domain (tptp.addition tptp.zero @t41)))) % 15.69/15.96 (step @p42 :rule symm :premises (@p39)) % 15.69/15.96 (step @p43 :rule eq-symm :args (@t15 @t1)) % 15.69/15.96 (step @p44 :rule cong :premises (@p43) :args (@t16)) % 15.69/15.96 (step @p45 :rule eq_resolve :premises (@p7 @p44)) % 15.69/15.96 (step @p46 :rule instantiate :premises (@p45) :args (@t51)) % 15.69/15.96 (step @p47 :rule symm :premises (@p46)) % 15.69/15.96 (step @p48 :rule trans :premises (@p47 @p37 @p42)) % 15.69/15.96 (step @p49 :rule cong :premises (@p48) :args ((tptp.domain (tptp.multiplication tptp.one @t41)))) % 15.69/15.96 (step @p50 :rule refl :args (@t41)) % 15.69/15.96 (step @p51 :rule eq-symm :args (@t27 tptp.one)) % 15.69/15.96 (step @p52 :rule cong :premises (@p51) :args (@t28)) % 15.69/15.96 (step @p53 :rule eq_resolve :premises (@p15 @p52)) % 15.69/15.96 (step @p54 :rule instantiate :premises (@p53) :args (@t52)) % 15.69/15.96 (step @p55 :rule symm :premises (@p54)) % 15.69/15.96 (step @p56 :rule instantiate :premises (@p1) :args ((@list @t40 tptp.one))) % 15.69/15.96 (step @p57 :rule symm :premises (@p56)) % 15.69/15.96 (step @p58 :rule trans :premises (@p57 @p55)) % 15.69/15.96 (step @p59 :rule cong :premises (@p58 @p50) :args ((tptp.multiplication @t53 @t41))) % 15.69/15.96 (step @p60 :rule instantiate :premises (@p9) :args ((@list tptp.one @t40 @t41))) % 15.69/15.96 (step @p61 :rule symm :premises (@p60)) % 15.69/15.96 (step @p62 :rule refl :args (@t44)) % 15.69/15.96 (step @p63 :rule cong :premises (@p46 @p62) :args (@t45)) % 15.69/15.96 (step @p64 :rule bool-double-not-elim :args (@t46)) % 15.69/15.96 (step @p65 :rule refl :args (@t48)) % 15.69/15.96 (step @p66 :rule nary_cong :premises (@p65 @p64) :args ((or @t48 (not @t47)))) % 15.69/15.96 (step @p67 :rule cnf_or_neg :args (@t48 0)) % 15.69/15.96 (step @p68 :rule eq_resolve :premises (@p67 @p66)) % 15.69/15.96 (step @p69 :rule reordering :premises (@p68) :args ((or @t46 @t48))) % 15.69/15.96 (step @p70 :rule chain_m_resolution :premises (@p69 @p29) :args (@t46 @t49 @t50)) % 15.69/15.96 (step @p71 :rule instantiate :premises (@p36) :args ((@list @t44))) % 15.69/15.96 (step @p72 :rule symm :premises (@p71)) % 15.69/15.96 (step @p73 :rule instantiate :premises (@p1) :args ((@list tptp.zero @t44))) % 15.69/15.96 (step @p74 :rule trans :premises (@p73 @p72 @p70 @p63 @p61 @p59)) % 15.69/15.96 (step @p75 :rule cong :premises (@p74) :args ((tptp.domain (tptp.addition tptp.zero @t44)))) % 15.69/15.96 (step @p76 :rule symm :premises (@p73)) % 15.69/15.96 (step @p77 :rule trans :premises (@p71 @p76)) % 15.69/15.96 (step @p78 :rule cong :premises (@p77) :args ((tptp.domain @t44))) % 15.69/15.96 (step @p79 :rule instantiate :premises (@p14) :args ((@list @t40 @t41))) % 15.69/15.96 (step @p80 :rule symm :premises (@p79)) % 15.69/15.96 (step @p81 :rule trans :premises (@p80 @p78 @p75 @p49 @p41)) % 15.69/15.96 (step @p82 :rule instantiate :premises (@p36) :args (@t52)) % 15.69/15.96 (step @p83 :rule symm :premises (@p82)) % 15.69/15.96 (step @p84 :rule instantiate :premises (@p1) :args ((@list tptp.zero @t39))) % 15.69/15.96 (step @p85 :rule trans :premises (@p84 @p83)) % 15.69/15.96 (step @p86 :rule cong :premises (@p85) :args ((tptp.domain (tptp.addition tptp.zero @t39)))) % 15.69/15.96 (step @p87 :rule symm :premises (@p84)) % 15.69/15.96 (step @p88 :rule instantiate :premises (@p45) :args (@t52)) % 15.69/15.96 (step @p89 :rule symm :premises (@p88)) % 15.69/15.96 (step @p90 :rule trans :premises (@p89 @p82 @p87)) % 15.69/15.96 (step @p91 :rule cong :premises (@p90) :args ((tptp.domain (tptp.multiplication tptp.one @t39)))) % 15.69/15.96 (step @p92 :rule instantiate :premises (@p14) :args ((@list tptp.one @t39))) % 15.69/15.96 (step @p93 :rule symm :premises (@p92)) % 15.69/15.96 (step @p94 :rule instantiate :premises (@p45) :args (@t54)) % 15.69/15.96 (step @p95 :rule cong :premises (@p94) :args (@t55)) % 15.69/15.96 (step @p96 :rule eq-symm :args (@t13 @t1)) % 15.69/15.96 (step @p97 :rule cong :premises (@p96) :args (@t14)) % 15.69/15.96 (step @p98 :rule eq_resolve :premises (@p6 @p97)) % 15.69/15.96 (step @p99 :rule instantiate :premises (@p98) :args (@t54)) % 15.69/15.96 (step @p100 :rule symm :premises (@p99)) % 15.69/15.96 (step @p101 :rule refl :args (@t40)) % 15.69/15.96 (step @p102 :rule cong :premises (@p101 @p58) :args ((tptp.multiplication @t40 @t53))) % 15.69/15.96 (step @p103 :rule instantiate :premises (@p8) :args ((@list @t40 tptp.one @t40))) % 15.69/15.96 (step @p104 :rule symm :premises (@p103)) % 15.69/15.96 (step @p105 :rule trans :premises (@p95 @p93 @p91 @p86)) % 15.69/15.96 (step @p106 :rule cong :premises (@p105 @p101) :args (@t56)) % 15.69/15.96 (step @p107 :rule cong :premises (@p99 @p106) :args ((tptp.addition @t40 @t56))) % 15.69/15.96 (step @p108 :rule eq-symm :args (@t21 @t20)) % 15.69/15.96 (step @p109 :rule cong :premises (@p108) :args (@t23)) % 15.69/15.96 (step @p110 :rule eq_resolve :premises (@p13 @p109)) % 15.69/15.96 (step @p111 :rule instantiate :premises (@p110) :args (@t54)) % 15.69/15.96 (step @p112 :rule symm :premises (@p106)) % 15.69/15.96 (step @p113 :rule trans :premises (@p112 @p111 @p107 @p104 @p102 @p100)) % 15.69/15.96 (step @p114 :rule cong :premises (@p113) :args (@t58)) % 15.69/15.96 (step @p115 :rule trans :premises (@p114 @p95 @p93 @p91 @p86)) % 15.69/15.96 (step @p116 :rule cong :premises (@p115 @p81) :args (@t60)) % 15.69/15.96 (step @p117 :rule trans :premises (@p116 @p33)) % 15.69/15.96 (step @p118 :rule instantiate :premises (@p53) :args (@t51)) % 15.69/15.96 (step @p119 :rule symm :premises (@p118)) % 15.69/15.96 (step @p120 :rule instantiate :premises (@p1) :args ((@list @t42 tptp.one))) % 15.69/15.96 (step @p121 :rule symm :premises (@p120)) % 15.69/15.96 (step @p122 :rule instantiate :premises (@p14) :args ((@list tptp.one @t41))) % 15.69/15.96 (step @p123 :rule symm :premises (@p122)) % 15.69/15.96 (step @p124 :rule instantiate :premises (@p45) :args ((@list @t42))) % 15.69/15.96 (step @p125 :rule cong :premises (@p124) :args (@t61)) % 15.69/15.96 (step @p126 :rule trans :premises (@p125 @p123 @p49 @p41)) % 15.69/15.96 (step @p127 :rule instantiate :premises (@p53) :args (@t62)) % 15.69/15.96 (step @p128 :rule symm :premises (@p127)) % 15.69/15.96 (step @p129 :rule instantiate :premises (@p1) :args ((@list @t63 tptp.one))) % 15.69/15.96 (step @p130 :rule symm :premises (@p129)) % 15.69/15.96 (step @p131 :rule instantiate :premises (@p98) :args ((@list @t63))) % 15.69/15.96 (step @p132 :rule symm :premises (@p131)) % 15.69/15.96 (step @p133 :rule refl :args (tptp.one)) % 15.69/15.96 (step @p134 :rule cong :premises (@p133 @p132) :args ((tptp.addition tptp.one (tptp.multiplication @t63 tptp.one)))) % 15.69/15.96 (step @p135 :rule instantiate :premises (@p110) :args (@t62)) % 15.69/15.96 (step @p136 :rule trans :premises (@p131 @p135 @p134 @p130 @p128)) % 15.69/15.96 (step @p137 :rule cong :premises (@p136 @p126) :args (@t64)) % 15.69/15.96 (step @p138 :rule trans :premises (@p137 @p121 @p119)) % 15.69/15.96 (step @p139 :rule cong :premises (@p101 @p138) :args ((tptp.multiplication @t40 @t64))) % 15.69/15.96 (step @p140 :rule instantiate :premises (@p8) :args ((@list @t40 @t63 @t61))) % 15.69/15.96 (step @p141 :rule symm :premises (@p140)) % 15.69/15.96 (step @p142 :rule symm :premises (@p126)) % 15.69/15.96 (step @p143 :rule cong :premises (@p101 @p142) :args (@t59)) % 15.69/15.96 (step @p144 :rule symm :premises (@p136)) % 15.69/15.96 (step @p145 :rule cong :premises (@p101 @p144) :args ((tptp.multiplication @t40 tptp.one))) % 15.69/15.96 (step @p146 :rule trans :premises (@p99 @p145)) % 15.69/15.96 (step @p147 :rule trans :premises (@p113 @p146)) % 15.69/15.96 (step @p148 :rule cong :premises (@p147 @p143) :args (@t65)) % 15.69/15.96 (step @p149 :rule trans :premises (@p148 @p141 @p139 @p100)) % 15.69/15.96 (step @p150 :rule cong :premises (@p149) :args (@t66)) % 15.69/15.96 (step @p151 :rule trans :premises (@p150 @p95 @p93 @p91 @p86)) % 15.69/15.96 (step @p152 :rule cong :premises (@p151 @p117) :args (@t67)) % 15.69/15.96 (step @p153 :rule trans :premises (@p152 @p32)) % 15.69/15.96 (step @p154 :rule false_elim :premises (@p153)) % 15.69/15.96 (assume-push @p161 @t30) % 15.69/15.96 (step @p156 :rule instantiate :premises (@p17) :args ((@list @t57 @t59))) % 15.69/15.96 (step-pop @p162 :rule scope :premises (@p156)) % 15.69/15.96 (step @p157 :rule process_scope :premises (@p162) :args (@t67)) % 15.69/15.96 (step @p159 :rule implies_elim :premises (@p157)) % 15.69/15.96 (step @p160 false :rule chain_m_resolution :premises (@p159 @p154 @p17) :args (false (@list true false) (@list @t67 @t30))) % 15.69/15.96 ) % 15.69/15.96 % SZS output end Proof % 15.69/15.96 % cvc5 exiting %------------------------------------------------------------------------------