%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE005+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 : 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 08:28:02 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 : KLE005+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n015.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 05:09:49 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.48 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 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 $$unsorted 0) % 0.39/0.57 (declare-const tptp.c (-> $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.test (-> $$unsorted Bool)) % 0.39/0.57 (declare-const tptp.complement (-> $$unsorted $$unsorted Bool)) % 0.39/0.57 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.39/0.57 (declare-const tptp.zero $$unsorted) % 0.39/0.57 (declare-const tptp.one $$unsorted) % 0.39/0.57 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (define @t1 () (@var "A" $$unsorted)) % 0.39/0.57 (define @t2 () (@var "B" $$unsorted)) % 0.39/0.57 (define @t3 () (tptp.addition @t1 @t2)) % 0.39/0.57 (define @t4 () (@list @t1 @t2)) % 0.39/0.57 (define @t5 () (@var "C" $$unsorted)) % 0.39/0.57 (define @t6 () (tptp.addition @t2 @t5)) % 0.39/0.57 (define @t7 () (@list @t1)) % 0.39/0.57 (define @t8 () (tptp.multiplication @t1 @t2)) % 0.39/0.57 (define @t9 () (tptp.multiplication @t2 @t5)) % 0.39/0.57 (define @t10 () (@list @t1 @t2 @t5)) % 0.39/0.57 (define @t11 () (tptp.multiplication @t1 tptp.one)) % 0.39/0.57 (define @t12 () (forall @t7 (= @t11 @t1))) % 0.39/0.57 (define @t13 () (tptp.multiplication @t1 @t5)) % 0.39/0.57 (define @t14 () (@var "X0" $$unsorted)) % 0.39/0.57 (define @t15 () (@var "X1" $$unsorted)) % 0.39/0.57 (define @t16 () (tptp.complement @t15 @t14)) % 0.39/0.57 (define @t17 () (@list @t15)) % 0.39/0.57 (define @t18 () (exists @t17 @t16)) % 0.39/0.57 (define @t19 () (tptp.test @t14)) % 0.39/0.57 (define @t20 () (= @t19 @t18)) % 0.39/0.57 (define @t21 () (@list @t14)) % 0.39/0.57 (define @t22 () (forall @t21 @t20)) % 0.39/0.57 (define @t23 () (tptp.addition @t14 @t15)) % 0.39/0.57 (define @t24 () (tptp.multiplication @t15 @t14)) % 0.39/0.57 (define @t25 () (tptp.multiplication @t14 @t15)) % 0.39/0.57 (define @t26 () (and (= @t25 tptp.zero) (= @t24 tptp.zero) (= @t23 tptp.one))) % 0.39/0.57 (define @t27 () (= @t16 @t26)) % 0.39/0.57 (define @t28 () (@list @t14 @t15)) % 0.39/0.57 (define @t29 () (forall @t28 @t27)) % 0.39/0.57 (define @t30 () (tptp.complement @t14 @t15)) % 0.39/0.57 (define @t31 () (tptp.c @t14)) % 0.39/0.57 (define @t32 () (= (= @t31 @t15) @t30)) % 0.39/0.57 (define @t33 () (=> @t19 @t32)) % 0.39/0.57 (define @t34 () (forall @t28 @t33)) % 0.39/0.57 (define @t35 () (not @t19)) % 0.39/0.57 (define @t36 () (=> @t35 (= @t31 tptp.zero))) % 0.39/0.57 (define @t37 () (forall @t21 @t36)) % 0.39/0.57 (define @t38 () (tptp.c tptp.one)) % 0.39/0.57 (define @t39 () (forall @t17 (not (tptp.complement @t15 tptp.one)))) % 0.39/0.57 (define @t40 () (@quantifiers_skolemize @t39 0)) % 0.39/0.57 (define @t41 () (@list tptp.one @t40)) % 0.39/0.57 (define @t42 () (@list tptp.one)) % 0.39/0.57 (define @t43 () (= tptp.zero @t31)) % 0.39/0.57 (define @t44 () (= tptp.zero @t38)) % 0.39/0.57 (define @t45 () (tptp.test tptp.one)) % 0.39/0.57 (define @t46 () (or @t45 @t44)) % 0.39/0.57 (define @t47 () (not @t39)) % 0.39/0.57 (define @t48 () (= @t45 @t47)) % 0.39/0.57 (define @t49 () (not @t45)) % 0.39/0.57 (define @t50 () (@list false false)) % 0.39/0.57 (define @t51 () (tptp.complement @t40 tptp.one)) % 0.39/0.57 (define @t52 () (not @t51)) % 0.39/0.57 (define @t53 () (not @t52)) % 0.39/0.57 (define @t54 () (= tptp.one (tptp.addition tptp.one @t40))) % 0.39/0.57 (define @t55 () (= tptp.zero (tptp.multiplication @t40 tptp.one))) % 0.39/0.57 (define @t56 () (= tptp.zero (tptp.multiplication tptp.one @t40))) % 0.39/0.57 (define @t57 () (and @t56 @t55 @t54)) % 0.39/0.57 (define @t58 () (= @t51 @t57)) % 0.39/0.57 (define @t59 () (not @t57)) % 0.39/0.57 (define @t60 () (@list false)) % 0.39/0.57 (define @t61 () (@list @t57)) % 0.39/0.57 (define @t62 () (= @t15 @t31)) % 0.39/0.57 (define @t63 () (= @t30 @t62)) % 0.39/0.57 (define @t64 () (tptp.complement tptp.one @t40)) % 0.39/0.57 (define @t65 () (= @t64 (= @t40 @t38))) % 0.39/0.57 (define @t66 () (or @t49 @t65)) % 0.39/0.57 (define @t67 () (forall @t28 (or @t35 @t63))) % 0.39/0.57 (define @t68 () (= @t38 @t40)) % 0.39/0.57 (define @t69 () (= @t64 @t68)) % 0.39/0.57 (define @t70 () (or @t49 @t69)) % 0.39/0.57 (define @t71 () (= tptp.one (tptp.addition @t40 tptp.one))) % 0.39/0.57 (define @t72 () (and @t55 @t56 @t71)) % 0.39/0.57 (define @t73 () (= @t64 @t72)) % 0.39/0.57 (assume @p1 (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 0.39/0.57 (assume @p2 (forall (@list @t5 @t2 @t1) (= (tptp.addition @t1 @t6) (tptp.addition @t3 @t5)))) % 0.39/0.57 (assume @p3 (forall @t7 (= (tptp.addition @t1 tptp.zero) @t1))) % 0.39/0.57 (assume @p4 (forall @t7 (= (tptp.addition @t1 @t1) @t1))) % 0.39/0.57 (assume @p5 (forall @t10 (= (tptp.multiplication @t1 @t9) (tptp.multiplication @t8 @t5)))) % 0.39/0.57 (assume @p6 @t12) % 0.39/0.57 (assume @p7 (forall @t7 (= (tptp.multiplication tptp.one @t1) @t1))) % 0.39/0.57 (assume @p8 (forall @t10 (= (tptp.multiplication @t1 @t6) (tptp.addition @t8 @t13)))) % 0.39/0.57 (assume @p9 (forall @t10 (= (tptp.multiplication @t3 @t5) (tptp.addition @t13 @t9)))) % 0.39/0.57 (assume @p10 (forall @t7 (= (tptp.multiplication @t1 tptp.zero) tptp.zero))) % 0.39/0.57 (assume @p11 (forall @t7 (= (tptp.multiplication tptp.zero @t1) tptp.zero))) % 0.39/0.57 (assume @p12 (forall @t4 (= (tptp.leq @t1 @t2) (= @t3 @t2)))) % 0.39/0.57 (assume @p13 @t22) % 0.39/0.57 (assume @p14 @t29) % 0.39/0.57 (assume @p15 @t34) % 0.39/0.57 (assume @p16 @t37) % 0.39/0.57 (assume @p17 (not (= @t38 tptp.zero))) % 0.39/0.57 (assume @p18 true) % 0.39/0.57 (step @p19 :rule evaluate :args ((= false true))) % 0.39/0.57 (step @p20 :rule eq-symm :args (@t23 tptp.one)) % 0.39/0.57 (step @p21 :rule eq-symm :args (@t24 tptp.zero)) % 0.39/0.57 (step @p22 :rule eq-symm :args (@t25 tptp.zero)) % 0.39/0.57 (step @p23 :rule nary_cong :premises (@p22 @p21 @p20) :args (@t26)) % 0.39/0.57 (step @p24 :rule refl :args (@t16)) % 0.39/0.57 (step @p25 :rule cong :premises (@p24 @p23) :args (@t27)) % 0.39/0.57 (step @p26 :rule cong :premises (@p25) :args (@t29)) % 0.39/0.57 (step @p27 :rule eq_resolve :premises (@p14 @p26)) % 0.39/0.57 (step @p28 :rule instantiate :premises (@p27) :args (@t41)) % 0.39/0.57 (step @p29 :rule exists-elim :args ((= @t18 (not (forall @t17 (not @t16)))))) % 0.39/0.57 (step @p30 :rule refl :args (@t19)) % 0.39/0.57 (step @p31 :rule cong :premises (@p30 @p29) :args (@t20)) % 0.39/0.57 (step @p32 :rule cong :premises (@p31) :args (@t22)) % 0.39/0.57 (step @p33 :rule eq_resolve :premises (@p13 @p32)) % 0.39/0.57 (step @p34 :rule instantiate :premises (@p33) :args (@t42)) % 0.39/0.57 (step @p35 :rule refl :args (@t43)) % 0.39/0.57 (step @p36 :rule bool-double-not-elim :args (@t19)) % 0.39/0.57 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or (not @t35) @t43))) % 0.39/0.57 (step @p38 :rule bool-impl-elim :args (@t35 @t43)) % 0.39/0.57 (step @p39 :rule trans :premises (@p38 @p37)) % 0.39/0.57 (step @p40 :rule cong :premises (@p39) :args ((forall @t21 (=> @t35 @t43)))) % 0.39/0.57 (step @p41 :rule eq-symm :args (@t31 tptp.zero)) % 0.39/0.57 (step @p42 :rule refl :args (@t35)) % 0.39/0.57 (step @p43 :rule cong :premises (@p42 @p41) :args (@t36)) % 0.39/0.57 (step @p44 :rule cong :premises (@p43) :args (@t37)) % 0.39/0.57 (step @p45 :rule trans :premises (@p44 @p40)) % 0.39/0.57 (step @p46 :rule eq_resolve :premises (@p16 @p45)) % 0.39/0.57 (step @p47 :rule instantiate :premises (@p46) :args (@t42)) % 0.39/0.57 (step @p48 :rule symm :premises (@p17)) % 0.39/0.57 (step @p49 :rule cnf_or_pos :args (@t46)) % 0.39/0.57 (step @p50 :rule reordering :premises (@p49) :args ((or @t44 @t45 (not @t46)))) % 0.39/0.57 (step @p51 :rule chain_m_resolution :premises (@p50 @p48 @p47) :args (@t45 (@list true false) (@list @t44 @t46))) % 0.39/0.57 (step @p52 :rule cnf_equiv_pos1 :args (@t48)) % 0.39/0.57 (step @p53 :rule reordering :premises (@p52) :args ((or @t49 @t47 (not @t48)))) % 0.39/0.57 (step @p54 :rule chain_m_resolution :premises (@p53 @p51 @p34) :args (@t47 @t50 (@list @t45 @t48))) % 0.39/0.57 (step @p55 :rule refl :args (@t51)) % 0.39/0.57 (step @p56 :rule bool-double-not-elim :args (@t39)) % 0.39/0.57 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or (not @t47) @t51))) % 0.39/0.57 (step @p58 :rule bool-double-not-elim :args (@t51)) % 0.39/0.57 (step @p59 :rule refl :args (@t47)) % 0.39/0.57 (step @p60 :rule cong :premises (@p59 @p58) :args ((=> @t47 @t53))) % 0.39/0.57 (assume-push @p134 @t47) % 0.39/0.57 (step @p62 :rule skolemize :premises (@p54)) % 0.39/0.57 (step-pop @p135 :rule scope :premises (@p62)) % 0.39/0.57 (step @p63 :rule process_scope :premises (@p135) :args (@t53)) % 0.39/0.57 (step @p65 :rule eq_resolve :premises (@p63 @p60)) % 0.39/0.57 (step @p66 :rule implies_elim :premises (@p65)) % 0.39/0.57 (step @p67 :rule eq_resolve :premises (@p66 @p57)) % 0.39/0.57 (step @p68 :rule chain_m_resolution :premises (@p67 @p54) :args (@t51 (@list true) (@list @t39))) % 0.39/0.57 (step @p69 :rule cnf_equiv_pos1 :args (@t58)) % 0.39/0.57 (step @p70 :rule reordering :premises (@p69) :args ((or @t52 @t57 (not @t58)))) % 0.39/0.57 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p28) :args (@t57 @t50 (@list @t51 @t58))) % 0.39/0.57 (step @p72 :rule cnf_and_pos :args (@t57 0)) % 0.39/0.57 (step @p73 :rule reordering :premises (@p72) :args ((or @t56 @t59))) % 0.39/0.57 (step @p74 :rule chain_m_resolution :premises (@p73 @p71) :args (@t56 @t60 @t61)) % 0.39/0.57 (step @p75 :rule cnf_and_pos :args (@t57 1)) % 0.39/0.57 (step @p76 :rule reordering :premises (@p75) :args ((or @t55 @t59))) % 0.39/0.57 (step @p77 :rule chain_m_resolution :premises (@p76 @p71) :args (@t55 @t60 @t61)) % 0.39/0.57 (step @p78 :rule symm :premises (@p77)) % 0.39/0.57 (step @p79 :rule eq-symm :args (@t11 @t1)) % 0.39/0.57 (step @p80 :rule cong :premises (@p79) :args (@t12)) % 0.39/0.57 (step @p81 :rule eq_resolve :premises (@p6 @p80)) % 0.39/0.57 (step @p82 :rule instantiate :premises (@p81) :args ((@list @t40))) % 0.39/0.57 (step @p83 :rule bool-impl-elim :args (@t19 @t63)) % 0.39/0.57 (step @p84 :rule cong :premises (@p83) :args ((forall @t28 (=> @t19 @t63)))) % 0.39/0.57 (step @p85 :rule eq-symm :args (@t62 @t30)) % 0.39/0.57 (step @p86 :rule refl :args (@t30)) % 0.39/0.57 (step @p87 :rule eq-symm :args (@t31 @t15)) % 0.39/0.57 (step @p88 :rule cong :premises (@p87 @p86) :args (@t32)) % 0.39/0.57 (step @p89 :rule trans :premises (@p88 @p85)) % 0.39/0.57 (step @p90 :rule cong :premises (@p30 @p89) :args (@t33)) % 0.39/0.57 (step @p91 :rule cong :premises (@p90) :args (@t34)) % 0.39/0.57 (step @p92 :rule trans :premises (@p91 @p84)) % 0.39/0.57 (step @p93 :rule eq_resolve :premises (@p15 @p92)) % 0.39/0.57 (step @p94 :rule eq-symm :args (@t40 @t38)) % 0.39/0.57 (step @p95 :rule refl :args (@t64)) % 0.39/0.57 (step @p96 :rule cong :premises (@p95 @p94) :args (@t65)) % 0.39/0.57 (step @p97 :rule refl :args (@t49)) % 0.39/0.57 (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t66)) % 0.39/0.57 (step @p99 :rule refl :args (@t67)) % 0.39/0.57 (step @p100 :rule cong :premises (@p99 @p98) :args ((=> @t67 @t66))) % 0.39/0.57 (assume-push @p136 @t67) % 0.39/0.57 (step @p102 :rule instantiate :premises (@p93) :args (@t41)) % 0.39/0.57 (step-pop @p137 :rule scope :premises (@p102)) % 0.39/0.57 (step @p103 :rule process_scope :premises (@p137) :args (@t66)) % 0.39/0.57 (step @p105 :rule eq_resolve :premises (@p103 @p100)) % 0.39/0.57 (step @p106 :rule implies_elim :premises (@p105)) % 0.39/0.57 (step @p107 :rule chain_m_resolution :premises (@p106 @p93) :args (@t70 @t60 (@list @t67))) % 0.39/0.57 (step @p108 :rule cnf_or_pos :args (@t70)) % 0.39/0.57 (step @p109 :rule reordering :premises (@p108) :args ((or @t49 @t69 (not @t70)))) % 0.39/0.57 (step @p110 :rule chain_m_resolution :premises (@p109 @p51 @p107) :args (@t69 @t50 (@list @t45 @t70))) % 0.39/0.57 (step @p111 :rule instantiate :premises (@p27) :args ((@list @t40 tptp.one))) % 0.39/0.57 (step @p112 :rule instantiate :premises (@p1) :args (@t41)) % 0.39/0.57 (step @p113 :rule cnf_and_pos :args (@t57 2)) % 0.39/0.57 (step @p114 :rule reordering :premises (@p113) :args ((or @t54 @t59))) % 0.39/0.57 (step @p115 :rule chain_m_resolution :premises (@p114 @p71) :args (@t54 @t60 @t61)) % 0.39/0.57 (step @p116 :rule trans :premises (@p115 @p112)) % 0.39/0.57 (step @p117 :rule cnf_and_neg :args (@t72)) % 0.39/0.57 (step @p118 :rule reordering :premises (@p117) :args ((or (not @t56) (not @t55) @t72 (not @t71)))) % 0.39/0.57 (step @p119 :rule chain_m_resolution :premises (@p118 @p74 @p77 @p116) :args (@t72 (@list false false false) (@list @t56 @t55 @t71))) % 0.39/0.57 (step @p120 :rule cnf_equiv_pos2 :args (@t73)) % 0.39/0.57 (step @p121 :rule reordering :premises (@p120) :args ((or @t64 (not @t72) (not @t73)))) % 0.39/0.57 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p111) :args (@t64 @t50 (@list @t72 @t73))) % 0.39/0.57 (step @p123 :rule cnf_equiv_pos1 :args (@t69)) % 0.39/0.57 (step @p124 :rule reordering :premises (@p123) :args ((or (not @t64) @t68 (not @t69)))) % 0.39/0.57 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p110) :args (@t68 @t50 (@list @t64 @t69))) % 0.39/0.57 (step @p126 :rule trans :premises (@p125 @p82 @p78 @p74)) % 0.39/0.57 (step @p127 :rule symm :premises (@p126)) % 0.39/0.57 (step @p128 :rule trans :premises (@p74 @p127)) % 0.39/0.57 (step @p129 :rule true_intro :premises (@p128)) % 0.39/0.57 (step @p130 :rule false_intro :premises (@p48)) % 0.39/0.57 (step @p131 :rule symm :premises (@p130)) % 0.39/0.57 (step @p132 :rule trans :premises (@p131 @p129)) % 0.39/0.57 (step @p133 false :rule eq_resolve :premises (@p132 @p19)) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------