%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE150+2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n024.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 08:28:24 AM UTC 2026 % Result : Theorem 0.34s 0.55s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : KLE150+2 : TPTP v9.2.1. Released v4.0.0. % 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 : n024.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 00:20:45 EDT 2026 % 0.07/0.25 % CPUTime : % 0.07/0.32 %----Proving TF0_NAR, FOF, or CNF % 0.34/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.34/0.55 % SZS status Theorem % 0.34/0.55 % SZS output start Proof % 0.34/0.55 ( % 0.34/0.55 (declare-sort $$unsorted 0) % 0.34/0.55 (declare-const tptp.strong_iteration (-> $$unsorted $$unsorted)) % 0.34/0.55 (declare-const tptp.star (-> $$unsorted $$unsorted)) % 0.34/0.55 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.34/0.55 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.55 (declare-const tptp.zero $$unsorted) % 0.34/0.55 (declare-const tptp.one $$unsorted) % 0.34/0.55 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.55 (define @t1 () (@var "A" $$unsorted)) % 0.34/0.55 (define @t2 () (@var "B" $$unsorted)) % 0.34/0.55 (define @t3 () (tptp.addition @t1 @t2)) % 0.34/0.55 (define @t4 () (@list @t1 @t2)) % 0.34/0.55 (define @t5 () (@var "C" $$unsorted)) % 0.34/0.55 (define @t6 () (tptp.addition @t2 @t5)) % 0.34/0.55 (define @t7 () (@list @t1)) % 0.34/0.55 (define @t8 () (tptp.addition @t1 @t1)) % 0.34/0.55 (define @t9 () (forall @t7 (= @t8 @t1))) % 0.34/0.55 (define @t10 () (tptp.multiplication @t1 @t2)) % 0.34/0.55 (define @t11 () (tptp.multiplication @t2 @t5)) % 0.34/0.55 (define @t12 () (@list @t1 @t2 @t5)) % 0.34/0.55 (define @t13 () (forall @t12 (= (tptp.multiplication @t1 @t11) (tptp.multiplication @t10 @t5)))) % 0.34/0.55 (define @t14 () (tptp.multiplication @t1 @t5)) % 0.34/0.55 (define @t15 () (tptp.multiplication tptp.zero @t1)) % 0.34/0.55 (define @t16 () (forall @t7 (= @t15 tptp.zero))) % 0.34/0.55 (define @t17 () (tptp.star @t1)) % 0.34/0.55 (define @t18 () (tptp.addition @t14 @t2)) % 0.34/0.55 (define @t19 () (tptp.strong_iteration @t1)) % 0.34/0.55 (define @t20 () (tptp.leq @t1 @t2)) % 0.34/0.55 (define @t21 () (= @t20 (= @t3 @t2))) % 0.34/0.55 (define @t22 () (forall @t4 @t21)) % 0.34/0.55 (define @t23 () (@var "X0" $$unsorted)) % 0.34/0.55 (define @t24 () (tptp.multiplication @t23 tptp.zero)) % 0.34/0.55 (define @t25 () (tptp.strong_iteration @t24)) % 0.34/0.55 (define @t26 () (tptp.addition tptp.one @t24)) % 0.34/0.55 (define @t27 () (tptp.leq @t26 @t25)) % 0.34/0.55 (define @t28 () (tptp.leq @t25 @t26)) % 0.34/0.55 (define @t29 () (@list @t23)) % 0.34/0.55 (define @t30 () (forall @t29 (and @t28 @t27))) % 0.34/0.55 (define @t31 () (not @t30)) % 0.34/0.55 (define @t32 () (@var "BOUND_VARIABLE_7550" $$unsorted)) % 0.34/0.55 (define @t33 () (tptp.multiplication @t32 tptp.zero)) % 0.34/0.55 (define @t34 () (forall (@list @t32) (tptp.leq (tptp.strong_iteration @t33) (tptp.addition tptp.one @t33)))) % 0.34/0.55 (define @t35 () (@quantifiers_skolemize @t34 0)) % 0.34/0.55 (define @t36 () (tptp.multiplication @t35 tptp.zero)) % 0.34/0.55 (define @t37 () (tptp.addition tptp.one @t36)) % 0.34/0.55 (define @t38 () (tptp.strong_iteration @t36)) % 0.34/0.55 (define @t39 () (@list @t36)) % 0.34/0.55 (define @t40 () (tptp.multiplication @t38 tptp.zero)) % 0.34/0.55 (define @t41 () (tptp.star @t36)) % 0.34/0.55 (define @t42 () (tptp.multiplication @t35 (tptp.multiplication tptp.zero @t38))) % 0.34/0.55 (define @t43 () (tptp.multiplication @t36 @t38)) % 0.34/0.55 (define @t44 () (= @t42 @t43)) % 0.34/0.55 (define @t45 () (@list false)) % 0.34/0.55 (define @t46 () (@list @t13)) % 0.34/0.55 (define @t47 () (= @t37 (tptp.addition @t38 @t37))) % 0.34/0.55 (define @t48 () (tptp.leq @t38 @t37)) % 0.34/0.55 (define @t49 () (= @t48 @t47)) % 0.34/0.55 (define @t50 () (@list false false)) % 0.34/0.55 (define @t51 () (not @t48)) % 0.34/0.55 (define @t52 () (not @t34)) % 0.34/0.55 (define @t53 () (@var "BOUND_VARIABLE_7558" $$unsorted)) % 0.34/0.55 (define @t54 () (tptp.multiplication @t53 tptp.zero)) % 0.34/0.55 (define @t55 () (forall (@list @t53) (tptp.leq (tptp.addition tptp.one @t54) (tptp.strong_iteration @t54)))) % 0.34/0.55 (define @t56 () (@quantifiers_skolemize @t55 0)) % 0.34/0.55 (define @t57 () (tptp.multiplication @t56 tptp.zero)) % 0.34/0.55 (define @t58 () (tptp.strong_iteration @t57)) % 0.34/0.55 (define @t59 () (tptp.addition tptp.one @t57)) % 0.34/0.55 (define @t60 () (@list @t58)) % 0.34/0.55 (define @t61 () (tptp.multiplication @t56 (tptp.multiplication tptp.zero @t58))) % 0.34/0.55 (define @t62 () (tptp.multiplication @t57 @t58)) % 0.34/0.55 (define @t63 () (= @t61 @t62)) % 0.34/0.55 (define @t64 () (= @t58 (tptp.addition @t59 @t58))) % 0.34/0.55 (define @t65 () (tptp.leq @t59 @t58)) % 0.34/0.55 (define @t66 () (= @t65 @t64)) % 0.34/0.55 (define @t67 () (not @t65)) % 0.34/0.55 (define @t68 () (not @t55)) % 0.34/0.55 (define @t69 () (forall @t29 @t27)) % 0.34/0.55 (define @t70 () (@list @t23)) % 0.34/0.55 (define @t71 () (forall @t29 @t28)) % 0.34/0.55 (define @t72 () (and @t71 @t69)) % 0.34/0.55 (assume @p1 (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 0.34/0.55 (assume @p2 (forall (@list @t5 @t2 @t1) (= (tptp.addition @t1 @t6) (tptp.addition @t3 @t5)))) % 0.34/0.55 (assume @p3 (forall @t7 (= (tptp.addition @t1 tptp.zero) @t1))) % 0.34/0.55 (assume @p4 @t9) % 0.34/0.55 (assume @p5 @t13) % 0.34/0.55 (assume @p6 (forall @t7 (= (tptp.multiplication @t1 tptp.one) @t1))) % 0.34/0.55 (assume @p7 (forall @t7 (= (tptp.multiplication tptp.one @t1) @t1))) % 0.34/0.55 (assume @p8 (forall @t12 (= (tptp.multiplication @t1 @t6) (tptp.addition @t10 @t14)))) % 0.34/0.55 (assume @p9 (forall @t12 (= (tptp.multiplication @t3 @t5) (tptp.addition @t14 @t11)))) % 0.34/0.55 (assume @p10 @t16) % 0.34/0.55 (assume @p11 (forall @t7 (= (tptp.addition tptp.one (tptp.multiplication @t1 @t17)) @t17))) % 0.34/0.55 (assume @p12 (forall @t7 (= (tptp.addition tptp.one (tptp.multiplication @t17 @t1)) @t17))) % 0.34/0.55 (assume @p13 (forall @t12 (=> (tptp.leq @t18 @t5) (tptp.leq (tptp.multiplication @t17 @t2) @t5)))) % 0.34/0.55 (assume @p14 (forall @t12 (=> (tptp.leq (tptp.addition (tptp.multiplication @t5 @t1) @t2) @t5) (tptp.leq (tptp.multiplication @t2 @t17) @t5)))) % 0.34/0.55 (assume @p15 (forall @t7 (= @t19 (tptp.addition (tptp.multiplication @t1 @t19) tptp.one)))) % 0.34/0.55 (assume @p16 (forall @t12 (=> (tptp.leq @t5 @t18) (tptp.leq @t5 (tptp.multiplication @t19 @t2))))) % 0.34/0.55 (assume @p17 (forall @t7 (= @t19 (tptp.addition @t17 (tptp.multiplication @t19 tptp.zero))))) % 0.34/0.55 (assume @p18 @t22) % 0.34/0.55 (assume @p19 @t31) % 0.34/0.55 (assume @p20 true) % 0.34/0.55 (step @p21 :rule eq-symm :args (@t3 @t2)) % 0.34/0.55 (step @p22 :rule refl :args (@t20)) % 0.34/0.55 (step @p23 :rule cong :premises (@p22 @p21) :args (@t21)) % 0.34/0.55 (step @p24 :rule cong :premises (@p23) :args (@t22)) % 0.34/0.55 (step @p25 :rule eq_resolve :premises (@p18 @p24)) % 0.34/0.55 (step @p26 :rule instantiate :premises (@p25) :args ((@list @t38 @t37))) % 0.34/0.55 (step @p27 :rule refl :args (@t37)) % 0.34/0.55 (step @p28 :rule instantiate :premises (@p17) :args (@t39)) % 0.34/0.55 (step @p29 :rule symm :premises (@p28)) % 0.34/0.55 (step @p30 :rule cong :premises (@p29 @p27) :args ((tptp.addition (tptp.addition @t41 @t40) @t37))) % 0.34/0.55 (step @p31 :rule instantiate :premises (@p1) :args ((@list @t41 @t40))) % 0.34/0.55 (step @p32 :rule symm :premises (@p31)) % 0.34/0.55 (step @p33 :rule cong :premises (@p32 @p27) :args ((tptp.addition (tptp.addition @t40 @t41) @t37))) % 0.34/0.55 (step @p34 :rule eq-symm :args (@t15 tptp.zero)) % 0.34/0.55 (step @p35 :rule cong :premises (@p34) :args (@t16)) % 0.34/0.55 (step @p36 :rule eq_resolve :premises (@p10 @p35)) % 0.34/0.55 (step @p37 :rule instantiate :premises (@p36) :args ((@list @t38))) % 0.34/0.55 (step @p38 :rule symm :premises (@p37)) % 0.34/0.55 (step @p39 :rule refl :args (@t35)) % 0.34/0.55 (step @p40 :rule cong :premises (@p39 @p38) :args (@t42)) % 0.34/0.55 (step @p41 :rule eq-symm :args (@t42 @t43)) % 0.34/0.55 (step @p42 :rule refl :args (@t13)) % 0.34/0.55 (step @p43 :rule cong :premises (@p42 @p41) :args ((=> @t13 @t44))) % 0.34/0.55 (assume-push @p129 @t13) % 0.34/0.55 (step @p45 :rule instantiate :premises (@p5) :args ((@list @t35 tptp.zero @t38))) % 0.34/0.55 (step-pop @p130 :rule scope :premises (@p45)) % 0.34/0.55 (step @p46 :rule process_scope :premises (@p130) :args (@t44)) % 0.34/0.55 (step @p48 :rule eq_resolve :premises (@p46 @p43)) % 0.34/0.55 (step @p49 :rule implies_elim :premises (@p48)) % 0.34/0.55 (step @p50 :rule chain_m_resolution :premises (@p49 @p5) :args ((= @t43 @t42) @t45 @t46)) % 0.34/0.55 (step @p51 :rule trans :premises (@p50 @p40)) % 0.34/0.55 (step @p52 :rule refl :args (tptp.one)) % 0.34/0.55 (step @p53 :rule cong :premises (@p52 @p51) :args ((tptp.addition tptp.one @t43))) % 0.34/0.55 (step @p54 :rule instantiate :premises (@p1) :args ((@list @t43 tptp.one))) % 0.34/0.55 (step @p55 :rule trans :premises (@p54 @p53)) % 0.34/0.55 (step @p56 :rule trans :premises (@p32 @p29)) % 0.34/0.55 (step @p57 :rule symm :premises (@p56)) % 0.34/0.55 (step @p58 :rule cong :premises (@p57 @p55) :args ((tptp.addition @t38 (tptp.addition @t43 tptp.one)))) % 0.34/0.55 (step @p59 :rule symm :premises (@p55)) % 0.34/0.55 (step @p60 :rule instantiate :premises (@p15) :args (@t39)) % 0.34/0.55 (step @p61 :rule symm :premises (@p60)) % 0.34/0.55 (step @p62 :rule symm :premises (@p54)) % 0.34/0.55 (step @p63 :rule symm :premises (@p53)) % 0.34/0.55 (step @p64 :rule trans :premises (@p63 @p62 @p61)) % 0.34/0.55 (step @p65 :rule cong :premises (@p64 @p59) :args ((tptp.addition @t37 @t37))) % 0.34/0.55 (step @p66 :rule eq-symm :args (@t8 @t1)) % 0.34/0.55 (step @p67 :rule cong :premises (@p66) :args (@t9)) % 0.34/0.55 (step @p68 :rule eq_resolve :premises (@p4 @p67)) % 0.34/0.55 (step @p69 :rule instantiate :premises (@p68) :args ((@list @t37))) % 0.34/0.55 (step @p70 :rule trans :premises (@p69 @p65 @p58 @p33 @p30)) % 0.34/0.55 (step @p71 :rule cnf_equiv_pos2 :args (@t49)) % 0.34/0.55 (step @p72 :rule reordering :premises (@p71) :args ((or @t48 (not @t47) (not @t49)))) % 0.34/0.55 (step @p73 :rule chain_m_resolution :premises (@p72 @p70 @p26) :args (@t48 @t50 (@list @t47 @t49))) % 0.34/0.55 (step @p74 :rule refl :args (@t51)) % 0.34/0.55 (step @p75 :rule bool-double-not-elim :args (@t34)) % 0.34/0.56 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or (not @t52) @t51))) % 0.34/0.56 (assume-push @p131 @t52) % 0.34/0.56 (step @p78 :rule skolemize :premises (@p131)) % 0.34/0.56 (step-pop @p132 :rule scope :premises (@p78)) % 0.34/0.56 (step @p79 :rule process_scope :premises (@p132) :args (@t51)) % 0.34/0.56 (step @p81 :rule implies_elim :premises (@p79)) % 0.34/0.56 (step @p82 :rule eq_resolve :premises (@p81 @p76)) % 0.34/0.56 (step @p83 :rule chain_m_resolution :premises (@p82 @p73) :args (@t34 @t45 (@list @t48))) % 0.34/0.56 (step @p84 :rule instantiate :premises (@p25) :args ((@list @t59 @t58))) % 0.34/0.56 (step @p85 :rule refl :args (@t58)) % 0.34/0.56 (step @p86 :rule instantiate :premises (@p36) :args (@t60)) % 0.34/0.56 (step @p87 :rule symm :premises (@p86)) % 0.34/0.56 (step @p88 :rule refl :args (@t56)) % 0.34/0.56 (step @p89 :rule cong :premises (@p88 @p87) :args (@t61)) % 0.34/0.56 (step @p90 :rule eq-symm :args (@t61 @t62)) % 0.34/0.56 (step @p91 :rule cong :premises (@p42 @p90) :args ((=> @t13 @t63))) % 0.34/0.56 (assume-push @p133 @t13) % 0.34/0.56 (step @p93 :rule instantiate :premises (@p5) :args ((@list @t56 tptp.zero @t58))) % 0.34/0.56 (step-pop @p134 :rule scope :premises (@p93)) % 0.34/0.56 (step @p94 :rule process_scope :premises (@p134) :args (@t63)) % 0.34/0.56 (step @p96 :rule eq_resolve :premises (@p94 @p91)) % 0.34/0.56 (step @p97 :rule implies_elim :premises (@p96)) % 0.34/0.56 (step @p98 :rule chain_m_resolution :premises (@p97 @p5) :args ((= @t62 @t61) @t45 @t46)) % 0.34/0.56 (step @p99 :rule trans :premises (@p98 @p89)) % 0.34/0.56 (step @p100 :rule cong :premises (@p52 @p99) :args ((tptp.addition tptp.one @t62))) % 0.34/0.56 (step @p101 :rule instantiate :premises (@p1) :args ((@list @t62 tptp.one))) % 0.34/0.56 (step @p102 :rule instantiate :premises (@p15) :args ((@list @t57))) % 0.34/0.56 (step @p103 :rule trans :premises (@p102 @p101 @p100)) % 0.34/0.56 (step @p104 :rule cong :premises (@p103 @p85) :args ((tptp.addition @t58 @t58))) % 0.34/0.56 (step @p105 :rule instantiate :premises (@p68) :args (@t60)) % 0.34/0.56 (step @p106 :rule trans :premises (@p105 @p104)) % 0.34/0.56 (step @p107 :rule cnf_equiv_pos2 :args (@t66)) % 0.34/0.56 (step @p108 :rule reordering :premises (@p107) :args ((or @t65 (not @t64) (not @t66)))) % 0.34/0.56 (step @p109 :rule chain_m_resolution :premises (@p108 @p106 @p84) :args (@t65 @t50 (@list @t64 @t66))) % 0.34/0.56 (step @p110 :rule refl :args (@t67)) % 0.34/0.56 (step @p111 :rule bool-double-not-elim :args (@t55)) % 0.34/0.56 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or (not @t68) @t67))) % 0.34/0.56 (assume-push @p135 @t68) % 0.34/0.56 (step @p114 :rule skolemize :premises (@p135)) % 0.34/0.56 (step-pop @p136 :rule scope :premises (@p114)) % 0.34/0.56 (step @p115 :rule process_scope :premises (@p136) :args (@t67)) % 0.34/0.56 (step @p117 :rule implies_elim :premises (@p115)) % 0.34/0.56 (step @p118 :rule eq_resolve :premises (@p117 @p112)) % 0.34/0.56 (step @p119 :rule chain_m_resolution :premises (@p118 @p109) :args (@t55 @t45 (@list @t65))) % 0.34/0.56 (step @p120 :rule alpha_equiv :args (@t69 @t70 (@list @t53))) % 0.34/0.56 (step @p121 :rule alpha_equiv :args (@t71 @t70 (@list @t32))) % 0.34/0.56 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t72)) % 0.34/0.56 (step @p123 :rule quant-miniscope-and :args ((= @t30 @t72))) % 0.34/0.56 (step @p124 :rule trans :premises (@p123 @p122)) % 0.34/0.56 (step @p125 :rule cong :premises (@p124) :args (@t31)) % 0.34/0.56 (step @p126 :rule eq_resolve :premises (@p19 @p125)) % 0.34/0.56 (step @p127 :rule not_and :premises (@p126)) % 0.34/0.56 (step @p128 false :rule chain_m_resolution :premises (@p127 @p119 @p83) :args (false @t50 (@list @t55 @t34))) % 0.34/0.56 ) % 0.34/0.56 % SZS output end Proof % 0.34/0.56 % cvc5 exiting %------------------------------------------------------------------------------