%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:07:24 AM UTC 2026 % Result : Theorem 2.42s 2.69s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0. % 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 : n028.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 23:11:20 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 2.42/2.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.42/2.69 % SZS status Theorem % 2.42/2.69 % SZS output start Proof % 2.42/2.69 ( % 2.42/2.69 (declare-sort $$unsorted 0) % 2.42/2.69 (declare-const tptp.proj1Var (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.index (-> $$unsorted $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.proj1Lam (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.lam (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.proj3App (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.proj1App (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.nothing $$unsorted) % 2.42/2.69 (declare-const tptp.proj1Just (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.head (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.suc (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.tail (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.c $$unsorted) % 2.42/2.69 (declare-const tptp.nil $$unsorted) % 2.42/2.69 (declare-const tptp.proj1Arr (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.var (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.b $$unsorted) % 2.42/2.69 (declare-const tptp.nf (-> $$unsorted Bool)) % 2.42/2.69 (declare-const tptp.zero $$unsorted) % 2.42/2.69 (declare-const tptp.proj2Arr (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.just (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.a $$unsorted) % 2.42/2.69 (declare-const tptp.tc (-> $$unsorted $$unsorted $$unsorted Bool)) % 2.42/2.69 (declare-const tptp.proj2App (-> $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.arr (-> $$unsorted $$unsorted $$unsorted)) % 2.42/2.69 (declare-const tptp.proj1Suc (-> $$unsorted $$unsorted)) % 2.42/2.69 (define @t1 () (@var "X" $$unsorted)) % 2.42/2.69 (define @t2 () (@var "X2" $$unsorted)) % 2.42/2.69 (define @t3 () (tptp.cons @t1 @t2)) % 2.42/2.69 (define @t4 () (@list @t1 @t2)) % 2.42/2.69 (define @t5 () (tptp.arr @t1 @t2)) % 2.42/2.69 (define @t6 () (tptp.suc @t1)) % 2.42/2.69 (define @t7 () (@list @t1)) % 2.42/2.69 (define @t8 () (tptp.just @t1)) % 2.42/2.69 (define @t9 () (@var "X3" $$unsorted)) % 2.42/2.69 (define @t10 () (tptp.app @t1 @t2 @t9)) % 2.42/2.69 (define @t11 () (@list @t1 @t2 @t9)) % 2.42/2.69 (define @t12 () (tptp.lam @t1)) % 2.42/2.69 (define @t13 () (@var "X4" $$unsorted)) % 2.42/2.69 (define @t14 () (@list @t1 @t2 @t9 @t13)) % 2.42/2.69 (define @t15 () (tptp.var @t13)) % 2.42/2.69 (define @t16 () (@var "Z" $$unsorted)) % 2.42/2.69 (define @t17 () (@var "Y" $$unsorted)) % 2.42/2.69 (define @t18 () (@var "E" $$unsorted)) % 2.42/2.69 (define @t19 () (tptp.nf @t18)) % 2.42/2.69 (define @t20 () (tptp.lam @t18)) % 2.42/2.69 (define @t21 () (@list @t18)) % 2.42/2.69 (define @t22 () (forall @t21 (= (tptp.nf @t20) @t19))) % 2.42/2.69 (define @t23 () (@var "Xs" $$unsorted)) % 2.42/2.69 (define @t24 () (tptp.cons @t16 @t23)) % 2.42/2.69 (define @t25 () (@var "N" $$unsorted)) % 2.42/2.69 (define @t26 () (@var "Tx" $$unsorted)) % 2.42/2.69 (define @t27 () (@var "F" $$unsorted)) % 2.42/2.69 (define @t28 () (@var "T1" $$unsorted)) % 2.42/2.69 (define @t29 () (@var "Tx2" $$unsorted)) % 2.42/2.69 (define @t30 () (tptp.tc @t1 (tptp.var @t9) @t16)) % 2.42/2.69 (define @t31 () (tptp.index @t1 @t9)) % 2.42/2.69 (define @t32 () (@var "Tx3" $$unsorted)) % 2.42/2.69 (define @t33 () (= @t30 (= @t32 @t16))) % 2.42/2.69 (define @t34 () (= @t31 (tptp.just @t32))) % 2.42/2.69 (define @t35 () (=> @t34 @t33)) % 2.42/2.69 (define @t36 () (@list @t1 @t16 @t9 @t32)) % 2.42/2.69 (define @t37 () (forall @t36 @t35)) % 2.42/2.69 (define @t38 () (tptp.arr tptp.b tptp.b)) % 2.42/2.69 (define @t39 () (tptp.arr tptp.a @t38)) % 2.42/2.69 (define @t40 () (tptp.tc tptp.nil @t18 @t39)) % 2.42/2.69 (define @t41 () (and @t19 @t40)) % 2.42/2.69 (define @t42 () (exists @t21 @t41)) % 2.42/2.69 (define @t43 () (not @t42)) % 2.42/2.69 (define @t44 () (= @t30 (= @t16 @t32))) % 2.42/2.69 (define @t45 () (tptp.var tptp.zero)) % 2.42/2.69 (define @t46 () (tptp.cons tptp.a tptp.nil)) % 2.42/2.69 (define @t47 () (tptp.lam @t45)) % 2.42/2.69 (define @t48 () (forall @t21 (not @t41))) % 2.42/2.69 (define @t49 () (not @t48)) % 2.42/2.69 (define @t50 () (tptp.lam @t47)) % 2.42/2.69 (define @t51 () (tptp.nf @t50)) % 2.42/2.69 (define @t52 () (tptp.nf @t47)) % 2.42/2.69 (define @t53 () (= @t51 @t52)) % 2.42/2.69 (define @t54 () (= @t52 @t51)) % 2.42/2.69 (define @t55 () (@list false)) % 2.42/2.69 (define @t56 () (@list @t22)) % 2.42/2.69 (define @t57 () (tptp.nf @t45)) % 2.42/2.69 (define @t58 () (= @t52 @t57)) % 2.42/2.69 (define @t59 () (= @t57 @t52)) % 2.42/2.69 (define @t60 () (@list false false)) % 2.42/2.69 (define @t61 () (tptp.tc tptp.nil @t50 @t39)) % 2.42/2.69 (define @t62 () (not @t61)) % 2.42/2.69 (define @t63 () (not @t51)) % 2.42/2.69 (define @t64 () (or @t63 @t62)) % 2.42/2.69 (define @t65 () (tptp.tc @t46 @t47 @t38)) % 2.42/2.69 (define @t66 () (= @t61 @t65)) % 2.42/2.69 (define @t67 () (not @t65)) % 2.42/2.69 (define @t68 () (@list true false)) % 2.42/2.69 (define @t69 () (tptp.cons tptp.b @t46)) % 2.42/2.69 (define @t70 () (tptp.tc @t69 @t45 tptp.b)) % 2.42/2.69 (define @t71 () (= @t65 @t70)) % 2.42/2.69 (define @t72 () (not @t70)) % 2.42/2.69 (define @t73 () (= (tptp.index @t69 tptp.zero) (tptp.just tptp.b))) % 2.42/2.69 (define @t74 () (not @t73)) % 2.42/2.69 (define @t75 () (or @t74 @t70)) % 2.42/2.69 (define @t76 () (not @t75)) % 2.42/2.69 (define @t77 () (= tptp.b tptp.b)) % 2.42/2.69 (define @t78 () (or @t74 (= @t70 @t77))) % 2.42/2.69 (define @t79 () (forall @t36 (or (not @t34) @t44))) % 2.42/2.69 (assume @p1 (forall @t4 (= (tptp.head @t3) @t1))) % 2.42/2.69 (assume @p2 (forall @t4 (= (tptp.tail @t3) @t2))) % 2.42/2.69 (assume @p3 (forall @t4 (not (= tptp.nil @t3)))) % 2.42/2.69 (assume @p4 (forall @t4 (= (tptp.proj1Arr @t5) @t1))) % 2.42/2.69 (assume @p5 (forall @t4 (= (tptp.proj2Arr @t5) @t2))) % 2.42/2.69 (assume @p6 (forall @t4 (not (= @t5 tptp.a)))) % 2.42/2.69 (assume @p7 (forall @t4 (not (= @t5 tptp.b)))) % 2.42/2.69 (assume @p8 (forall @t4 (not (= @t5 tptp.c)))) % 2.42/2.69 (assume @p9 (not (= tptp.a tptp.b))) % 2.42/2.69 (assume @p10 (not (= tptp.a tptp.c))) % 2.42/2.69 (assume @p11 (not (= tptp.b tptp.c))) % 2.42/2.69 (assume @p12 (forall @t7 (= (tptp.proj1Suc @t6) @t1))) % 2.42/2.69 (assume @p13 (forall @t7 (not (= tptp.zero @t6)))) % 2.42/2.69 (assume @p14 (forall @t7 (= (tptp.proj1Just @t8) @t1))) % 2.42/2.69 (assume @p15 (forall @t7 (not (= tptp.nothing @t8)))) % 2.42/2.69 (assume @p16 (forall @t11 (= (tptp.proj1App @t10) @t1))) % 2.42/2.69 (assume @p17 (forall @t11 (= (tptp.proj2App @t10) @t2))) % 2.42/2.69 (assume @p18 (forall @t11 (= (tptp.proj3App @t10) @t9))) % 2.42/2.69 (assume @p19 (forall @t7 (= (tptp.proj1Lam @t12) @t1))) % 2.42/2.69 (assume @p20 (forall @t7 (= (tptp.proj1Var (tptp.var @t1)) @t1))) % 2.42/2.69 (assume @p21 (forall @t14 (not (= @t10 (tptp.lam @t13))))) % 2.42/2.69 (assume @p22 (forall @t14 (not (= @t10 @t15)))) % 2.42/2.69 (assume @p23 (forall @t4 (not (= @t12 (tptp.var @t2))))) % 2.42/2.69 (assume @p24 (forall (@list @t17 @t16 @t2) (=> (not (= @t17 (tptp.lam (tptp.proj1Lam @t17)))) (= (tptp.nf (tptp.app @t17 @t16 @t2)) (and (tptp.nf @t17) (tptp.nf @t16)))))) % 2.42/2.69 (assume @p25 (forall (@list @t16 @t2 @t9) (not (tptp.nf (tptp.app (tptp.lam @t9) @t16 @t2))))) % 2.42/2.69 (assume @p26 @t22) % 2.42/2.69 (assume @p27 (forall (@list @t13) (tptp.nf @t15))) % 2.42/2.69 (assume @p28 (forall (@list @t17) (= (tptp.index tptp.nil @t17) tptp.nothing))) % 2.42/2.69 (assume @p29 (forall (@list @t16 @t23) (= (tptp.index @t24 tptp.zero) (tptp.just @t16)))) % 2.42/2.69 (assume @p30 (forall (@list @t16 @t23 @t25) (= (tptp.index @t24 (tptp.suc @t25)) (tptp.index @t23 @t25)))) % 2.42/2.69 (assume @p31 (forall (@list @t1 @t16 @t27 @t2 @t26) (= (tptp.tc @t1 (tptp.app @t27 @t2 @t26) @t16) (and (tptp.tc @t1 @t27 (tptp.arr @t26 @t16)) (tptp.tc @t1 @t2 @t26))))) % 2.42/2.69 (assume @p32 (forall (@list @t1 @t16 @t18) (=> (not (= @t16 (tptp.arr (tptp.proj1Arr @t16) (tptp.proj2Arr @t16)))) (not (tptp.tc @t1 @t20 @t16))))) % 2.42/2.69 (assume @p33 (forall (@list @t1 @t18 @t29 @t28) (= (tptp.tc @t1 @t20 (tptp.arr @t29 @t28)) (tptp.tc (tptp.cons @t29 @t1) @t18 @t28)))) % 2.42/2.69 (assume @p34 (forall (@list @t1 @t16 @t9) (=> (= @t31 tptp.nothing) (not @t30)))) % 2.42/2.69 (assume @p35 @t37) % 2.42/2.69 (assume @p36 @t43) % 2.42/2.69 (assume @p37 true) % 2.42/2.69 (step @p38 :rule bool-impl-elim :args (@t34 @t44)) % 2.42/2.69 (step @p39 :rule cong :premises (@p38) :args ((forall @t36 (=> @t34 @t44)))) % 2.42/2.69 (step @p40 :rule eq-symm :args (@t32 @t16)) % 2.42/2.69 (step @p41 :rule refl :args (@t30)) % 2.42/2.69 (step @p42 :rule cong :premises (@p41 @p40) :args (@t33)) % 2.42/2.69 (step @p43 :rule refl :args (@t34)) % 2.42/2.69 (step @p44 :rule cong :premises (@p43 @p42) :args (@t35)) % 2.42/2.69 (step @p45 :rule cong :premises (@p44) :args (@t37)) % 2.42/2.69 (step @p46 :rule trans :premises (@p45 @p39)) % 2.42/2.69 (step @p47 :rule eq_resolve :premises (@p35 @p46)) % 2.42/2.69 (step @p48 :rule instantiate :premises (@p33) :args ((@list @t46 @t45 tptp.b tptp.b))) % 2.42/2.69 (step @p49 :rule instantiate :premises (@p33) :args ((@list tptp.nil @t47 tptp.a @t38))) % 2.42/2.69 (step @p50 :rule bool-double-not-elim :args ((forall @t21 (or (not @t19) (not @t40))))) % 2.42/2.69 (step @p51 :rule bool-and-de-morgan :args (@t19 @t40 true)) % 2.42/2.69 (step @p52 :rule cong :premises (@p51) :args (@t48)) % 2.42/2.69 (step @p53 :rule cong :premises (@p52) :args (@t49)) % 2.42/2.69 (step @p54 :rule exists-elim :args ((= @t42 @t49))) % 2.42/2.69 (step @p55 :rule trans :premises (@p54 @p53)) % 2.42/2.69 (step @p56 :rule cong :premises (@p55) :args (@t43)) % 2.42/2.69 (step @p57 :rule trans :premises (@p56 @p50)) % 2.42/2.69 (step @p58 :rule eq_resolve :premises (@p36 @p57)) % 2.42/2.69 (step @p59 :rule instantiate :premises (@p58) :args ((@list @t50))) % 2.42/2.69 (step @p60 :rule eq-symm :args (@t51 @t52)) % 2.42/2.70 (step @p61 :rule refl :args (@t22)) % 2.42/2.70 (step @p62 :rule cong :premises (@p61 @p60) :args ((=> @t22 @t53))) % 2.42/2.70 (assume-push @p119 @t22) % 2.42/2.70 (step @p64 :rule instantiate :premises (@p26) :args ((@list @t47))) % 2.42/2.70 (step-pop @p120 :rule scope :premises (@p64)) % 2.42/2.70 (step @p65 :rule process_scope :premises (@p120) :args (@t53)) % 2.42/2.70 (step @p67 :rule eq_resolve :premises (@p65 @p62)) % 2.42/2.70 (step @p68 :rule implies_elim :premises (@p67)) % 2.42/2.70 (step @p69 :rule chain_m_resolution :premises (@p68 @p26) :args (@t54 @t55 @t56)) % 2.42/2.70 (step @p70 :rule eq-symm :args (@t52 @t57)) % 2.42/2.70 (step @p71 :rule cong :premises (@p61 @p70) :args ((=> @t22 @t58))) % 2.42/2.70 (assume-push @p121 @t22) % 2.42/2.70 (step @p73 :rule instantiate :premises (@p26) :args ((@list @t45))) % 2.42/2.70 (step-pop @p122 :rule scope :premises (@p73)) % 2.42/2.70 (step @p74 :rule process_scope :premises (@p122) :args (@t58)) % 2.42/2.70 (step @p76 :rule eq_resolve :premises (@p74 @p71)) % 2.42/2.70 (step @p77 :rule implies_elim :premises (@p76)) % 2.42/2.70 (step @p78 :rule chain_m_resolution :premises (@p77 @p26) :args (@t59 @t55 @t56)) % 2.42/2.70 (step @p79 :rule instantiate :premises (@p27) :args ((@list tptp.zero))) % 2.42/2.70 (step @p80 :rule cnf_equiv_pos1 :args (@t59)) % 2.42/2.70 (step @p81 :rule reordering :premises (@p80) :args ((or (not @t57) @t52 (not @t59)))) % 2.42/2.70 (step @p82 :rule chain_m_resolution :premises (@p81 @p79 @p78) :args (@t52 @t60 (@list @t57 @t59))) % 2.42/2.70 (step @p83 :rule cnf_equiv_pos1 :args (@t54)) % 2.42/2.70 (step @p84 :rule reordering :premises (@p83) :args ((or (not @t52) @t51 (not @t54)))) % 2.42/2.70 (step @p85 :rule chain_m_resolution :premises (@p84 @p82 @p69) :args (@t51 @t60 (@list @t52 @t54))) % 2.42/2.70 (step @p86 :rule cnf_or_pos :args (@t64)) % 2.42/2.70 (step @p87 :rule reordering :premises (@p86) :args ((or @t63 @t62 (not @t64)))) % 2.42/2.70 (step @p88 :rule chain_m_resolution :premises (@p87 @p85 @p59) :args (@t62 @t60 (@list @t51 @t64))) % 2.42/2.70 (step @p89 :rule cnf_equiv_pos2 :args (@t66)) % 2.42/2.70 (step @p90 :rule reordering :premises (@p89) :args ((or @t61 @t67 (not @t66)))) % 2.42/2.70 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p49) :args (@t67 @t68 (@list @t61 @t66))) % 2.42/2.70 (step @p92 :rule cnf_equiv_pos2 :args (@t71)) % 2.42/2.70 (step @p93 :rule reordering :premises (@p92) :args ((or @t65 @t72 (not @t71)))) % 2.42/2.70 (step @p94 :rule chain_m_resolution :premises (@p93 @p91 @p48) :args (@t72 @t68 (@list @t65 @t71))) % 2.42/2.70 (step @p95 :rule instantiate :premises (@p29) :args ((@list tptp.b @t46))) % 2.42/2.70 (step @p96 :rule cnf_or_pos :args (@t75)) % 2.42/2.70 (step @p97 :rule reordering :premises (@p96) :args ((or @t74 @t70 @t76))) % 2.42/2.70 (step @p98 :rule chain_m_resolution :premises (@p97 @p95 @p94) :args (@t76 (@list false true) (@list @t73 @t70))) % 2.42/2.70 (step @p99 :rule bool-eq-true :args (@t70)) % 2.42/2.70 (step @p100 :rule eq-symm :args (true @t70)) % 2.42/2.70 (step @p101 :rule trans :premises (@p100 @p99)) % 2.42/2.70 (step @p102 :rule refl :args (@t70)) % 2.42/2.70 (step @p103 :rule eq-refl :args (tptp.b)) % 2.42/2.70 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t77 @t70))) % 2.42/2.70 (step @p105 :rule trans :premises (@p104 @p101)) % 2.42/2.70 (step @p106 :rule eq-symm :args (@t70 @t77)) % 2.42/2.70 (step @p107 :rule trans :premises (@p106 @p105)) % 2.42/2.70 (step @p108 :rule refl :args (@t74)) % 2.42/2.70 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t78)) % 2.42/2.70 (step @p110 :rule refl :args (@t79)) % 0.36/2.70 (step @p111 :rule cong :premises (@p110 @p109) :args ((=> @t79 @t78))) % 0.36/2.70 (assume-push @p123 @t79) % 0.36/2.70 (step @p113 :rule instantiate :premises (@p47) :args ((@list @t69 tptp.b tptp.zero tptp.b))) % 0.36/2.70 (step-pop @p124 :rule scope :premises (@p113)) % 0.36/2.70 (step @p114 :rule process_scope :premises (@p124) :args (@t78)) % 0.36/2.70 (step @p116 :rule eq_resolve :premises (@p114 @p111)) % 0.36/2.70 (step @p117 :rule implies_elim :premises (@p116)) % 0.36/2.70 (step @p118 false :rule chain_m_resolution :premises (@p117 @p98 @p47) :args (false @t68 (@list @t75 @t79))) % 0.36/2.70 ) % 0.36/2.70 % SZS output end Proof % 0.36/2.70 % cvc5 exiting %------------------------------------------------------------------------------