%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP019+2 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n010.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 08:24:42 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP019+2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n010.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 03:59:11 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.c_2Ebool_2E_21 (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.c_2Emin_2E_3D (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.c_2Ecomplex_2Ecomplex__inv $$unsorted) % 0.37/0.58 (declare-const tptp.ty_2Erealax_2Ereal $$unsorted) % 0.37/0.58 (declare-const tptp.c_2Enum_2E0 $$unsorted) % 0.37/0.58 (declare-const tptp.ty_2Epair_2Eprod (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 0.37/0.58 (declare-const tptp.ne (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.ty_2Enum_2Enum $$unsorted) % 0.37/0.58 (declare-const tptp.ind $$unsorted) % 0.37/0.58 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 0.37/0.58 (declare-const tptp.mem (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.i (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.c_2Ecomplex_2Ecomplex__of__num $$unsorted) % 0.37/0.58 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 0.37/0.58 (declare-const tptp.bool $$unsorted) % 0.37/0.58 (declare-const tptp.arr (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.p (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.k (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 0.37/0.58 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 0.37/0.58 (define @t1 () (@var "B" $$unsorted)) % 0.37/0.58 (define @t2 () (@var "A" $$unsorted)) % 0.37/0.58 (define @t3 () (tptp.arr @t2 @t1)) % 0.37/0.58 (define @t4 () (tptp.ne @t2)) % 0.37/0.58 (define @t5 () (@list @t2)) % 0.37/0.58 (define @t6 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t7 () (@var "F" $$unsorted)) % 0.37/0.58 (define @t8 () (tptp.ap @t7 @t6)) % 0.37/0.58 (define @t9 () (tptp.mem @t6 @t2)) % 0.37/0.58 (define @t10 () (@list @t6)) % 0.37/0.58 (define @t11 () (tptp.mem @t7 @t3)) % 0.37/0.58 (define @t12 () (@list @t2 @t1 @t7)) % 0.37/0.58 (define @t13 () (@var "R" $$unsorted)) % 0.37/0.58 (define @t14 () (@var "Q" $$unsorted)) % 0.37/0.58 (define @t15 () (tptp.p @t13)) % 0.37/0.58 (define @t16 () (tptp.p @t14)) % 0.37/0.58 (define @t17 () (tptp.mem @t13 tptp.bool)) % 0.37/0.58 (define @t18 () (@list @t13)) % 0.37/0.58 (define @t19 () (tptp.mem @t14 tptp.bool)) % 0.37/0.58 (define @t20 () (@list @t14)) % 0.37/0.58 (define @t21 () (@var "G" $$unsorted)) % 0.37/0.58 (define @t22 () (@var "Y" $$unsorted)) % 0.37/0.58 (define @t23 () (tptp.arr tptp.bool tptp.bool)) % 0.37/0.58 (define @t24 () (tptp.arr tptp.bool @t23)) % 0.37/0.58 (define @t25 () (@var "A1" $$unsorted)) % 0.37/0.58 (define @t26 () (@var "A0" $$unsorted)) % 0.37/0.58 (define @t27 () (tptp.ty_2Epair_2Eprod tptp.ty_2Erealax_2Ereal tptp.ty_2Erealax_2Ereal)) % 0.37/0.58 (define @t28 () (@var "A_27a" $$unsorted)) % 0.37/0.58 (define @t29 () (tptp.arr @t28 tptp.bool)) % 0.37/0.58 (define @t30 () (tptp.ne @t28)) % 0.37/0.58 (define @t31 () (@list @t28)) % 0.37/0.58 (define @t32 () (@var "V0t" $$unsorted)) % 0.37/0.58 (define @t33 () (tptp.p @t32)) % 0.37/0.58 (define @t34 () (@var "V1x" $$unsorted)) % 0.37/0.58 (define @t35 () (tptp.mem @t32 tptp.bool)) % 0.37/0.58 (define @t36 () (@list @t32)) % 0.37/0.58 (define @t37 () (tptp.ap tptp.c_2Ecomplex_2Ecomplex__of__num tptp.c_2Enum_2E0)) % 0.37/0.58 (define @t38 () (@var "V0z" $$unsorted)) % 0.37/0.58 (define @t39 () (= @t38 @t37)) % 0.37/0.58 (define @t40 () (tptp.ap tptp.c_2Ecomplex_2Ecomplex__inv @t38)) % 0.37/0.58 (define @t41 () (= @t40 @t37)) % 0.37/0.58 (define @t42 () (= @t41 @t39)) % 0.37/0.58 (define @t43 () (tptp.mem @t38 @t27)) % 0.37/0.58 (define @t44 () (=> @t43 @t42)) % 0.37/0.58 (define @t45 () (@list @t38)) % 0.37/0.58 (define @t46 () (forall @t45 @t44)) % 0.37/0.58 (define @t47 () (not @t41)) % 0.37/0.58 (define @t48 () (not @t39)) % 0.37/0.58 (define @t49 () (=> @t48 @t47)) % 0.37/0.58 (define @t50 () (=> @t43 @t49)) % 0.37/0.58 (define @t51 () (forall @t45 @t50)) % 0.37/0.58 (define @t52 () (not @t51)) % 0.37/0.58 (define @t53 () (= @t37 @t40)) % 0.37/0.58 (define @t54 () (not @t53)) % 0.37/0.58 (define @t55 () (not @t43)) % 0.37/0.58 (define @t56 () (or @t55 @t39 @t54)) % 0.37/0.58 (define @t57 () (=> @t48 @t54)) % 0.37/0.58 (define @t58 () (forall @t45 @t56)) % 0.37/0.58 (define @t59 () (@quantifiers_skolemize @t58 0)) % 0.37/0.58 (define @t60 () (= @t37 (tptp.ap tptp.c_2Ecomplex_2Ecomplex__inv @t59))) % 0.37/0.58 (define @t61 () (not @t60)) % 0.37/0.58 (define @t62 () (= @t37 @t59)) % 0.37/0.58 (define @t63 () (tptp.mem @t59 @t27)) % 0.37/0.58 (define @t64 () (not @t63)) % 0.37/0.58 (define @t65 () (or @t64 @t62 @t61)) % 0.37/0.58 (define @t66 () (not @t65)) % 0.37/0.58 (define @t67 () (not @t58)) % 0.37/0.58 (define @t68 () (= @t59 @t37)) % 0.37/0.58 (define @t69 () (or @t64 @t68 @t61)) % 0.37/0.58 (define @t70 () (not @t69)) % 0.37/0.58 (define @t71 () (@list true)) % 0.37/0.58 (define @t72 () (@list @t65)) % 0.37/0.58 (define @t73 () (= @t60 @t62)) % 0.37/0.58 (define @t74 () (not @t73)) % 0.37/0.58 (define @t75 () (= @t39 @t53)) % 0.37/0.58 (define @t76 () (= @t68 @t60)) % 0.37/0.58 (define @t77 () (or @t64 @t76)) % 0.37/0.58 (define @t78 () (forall @t45 (or @t55 @t75))) % 0.37/0.58 (define @t79 () (or @t64 @t73)) % 0.37/0.58 (assume @p1 (tptp.ne tptp.bool)) % 0.37/0.58 (assume @p2 (tptp.ne tptp.ind)) % 0.37/0.58 (assume @p3 (forall @t5 (=> @t4 (forall (@list @t1) (=> (tptp.ne @t1) (tptp.ne @t3)))))) % 0.37/0.58 (assume @p4 (forall @t12 (=> @t11 (forall @t10 (=> @t9 (tptp.mem @t8 @t1)))))) % 0.37/0.58 (assume @p5 (forall @t20 (=> @t19 (forall @t18 (=> @t17 (=> (= @t16 @t15) (= @t14 @t13))))))) % 0.37/0.58 (assume @p6 (forall @t12 (=> @t11 (forall (@list @t21) (=> (tptp.mem @t21 @t3) (=> (forall @t10 (=> @t9 (= @t8 (tptp.ap @t21 @t6)))) (= @t7 @t21))))))) % 0.37/0.58 (assume @p7 (forall (@list @t2 @t22 @t6) (=> @t9 (= (tptp.ap (tptp.k @t2 @t22) @t6) @t22)))) % 0.37/0.58 (assume @p8 (forall (@list @t2 @t6) (=> @t9 (= (tptp.ap (tptp.i @t2) @t6) @t6)))) % 0.37/0.58 (assume @p9 (tptp.mem tptp.c_2Ebool_2E_7E @t23)) % 0.37/0.58 (assume @p10 (forall @t20 (=> @t19 (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E @t14)) (not @t16))))) % 0.37/0.58 (assume @p11 (tptp.mem tptp.c_2Ebool_2EF tptp.bool)) % 0.37/0.58 (assume @p12 (not (tptp.p tptp.c_2Ebool_2EF))) % 0.37/0.58 (assume @p13 (tptp.mem tptp.c_2Ebool_2ET tptp.bool)) % 0.37/0.58 (assume @p14 (tptp.p tptp.c_2Ebool_2ET)) % 0.37/0.58 (assume @p15 (tptp.mem tptp.c_2Emin_2E_3D_3D_3E @t24)) % 0.37/0.58 (assume @p16 (forall @t20 (=> @t19 (forall @t18 (=> @t17 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t14) @t13)) (=> @t16 @t15))))))) % 0.37/0.58 (assume @p17 (tptp.mem tptp.c_2Ebool_2E_2F_5C @t24)) % 0.37/0.58 (assume @p18 (forall @t20 (=> @t19 (forall @t18 (=> @t17 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t14) @t13)) (and @t16 @t15))))))) % 0.37/0.58 (assume @p19 (tptp.ne tptp.ty_2Enum_2Enum)) % 0.37/0.58 (assume @p20 (tptp.mem tptp.c_2Enum_2E0 tptp.ty_2Enum_2Enum)) % 0.37/0.58 (assume @p21 (tptp.ne tptp.ty_2Erealax_2Ereal)) % 0.37/0.58 (assume @p22 (forall (@list @t26) (=> (tptp.ne @t26) (forall (@list @t25) (=> (tptp.ne @t25) (tptp.ne (tptp.ty_2Epair_2Eprod @t26 @t25))))))) % 0.37/0.58 (assume @p23 (tptp.mem tptp.c_2Ecomplex_2Ecomplex__of__num (tptp.arr tptp.ty_2Enum_2Enum @t27))) % 0.37/0.58 (assume @p24 (tptp.mem tptp.c_2Ecomplex_2Ecomplex__inv (tptp.arr @t27 @t27))) % 0.37/0.58 (assume @p25 (forall @t31 (=> @t30 (tptp.mem (tptp.c_2Emin_2E_3D @t28) (tptp.arr @t28 @t29))))) % 0.37/0.58 (assume @p26 (forall @t5 (=> @t4 (forall @t10 (=> @t9 (forall (@list @t22) (=> (tptp.mem @t22 @t2) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D @t2) @t6) @t22)) (= @t6 @t22))))))))) % 0.37/0.58 (assume @p27 (forall @t31 (=> @t30 (tptp.mem (tptp.c_2Ebool_2E_21 @t28) (tptp.arr @t29 tptp.bool))))) % 0.37/0.58 (assume @p28 (forall @t5 (=> @t4 (forall @t20 (=> (tptp.mem @t14 (tptp.arr @t2 tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 @t2) @t14)) (forall @t10 (=> @t9 (tptp.p (tptp.ap @t14 @t6)))))))))) % 0.37/0.58 (assume @p29 true) % 0.37/0.58 (assume @p30 (forall @t31 (=> @t30 (forall @t36 (=> @t35 (= (forall (@list @t34) (=> (tptp.mem @t34 @t28) @t33)) @t33)))))) % 0.37/0.58 (assume @p31 (forall @t36 (=> @t35 (and (= (=> true @t33) @t33) (= (=> @t33 true) true) (= (=> false @t33) true) (= (=> @t33 @t33) true) (= (=> @t33 false) (not @t33)))))) % 0.37/0.58 (assume @p32 @t46) % 0.37/0.58 (assume @p33 @t52) % 0.37/0.58 (step @p34 :rule aci_norm :args ((= (or @t55 (or @t39 @t54)) @t56))) % 0.37/0.58 (step @p35 :rule refl :args (@t54)) % 0.37/0.58 (step @p36 :rule bool-double-not-elim :args (@t39)) % 0.37/0.58 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or (not @t48) @t54))) % 0.37/0.58 (step @p38 :rule bool-impl-elim :args (@t48 @t54)) % 0.37/0.58 (step @p39 :rule trans :premises (@p38 @p37)) % 0.37/0.58 (step @p40 :rule refl :args (@t55)) % 0.37/0.58 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or @t55 @t57))) % 0.37/0.58 (step @p42 :rule trans :premises (@p41 @p34)) % 0.37/0.58 (step @p43 :rule bool-impl-elim :args (@t43 @t57)) % 0.37/0.58 (step @p44 :rule trans :premises (@p43 @p42)) % 0.37/0.58 (step @p45 :rule cong :premises (@p44) :args ((forall @t45 (=> @t43 @t57)))) % 0.37/0.58 (step @p46 :rule eq-symm :args (@t40 @t37)) % 0.37/0.58 (step @p47 :rule cong :premises (@p46) :args (@t47)) % 0.37/0.58 (step @p48 :rule refl :args (@t48)) % 0.37/0.58 (step @p49 :rule cong :premises (@p48 @p47) :args (@t49)) % 0.37/0.58 (step @p50 :rule refl :args (@t43)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50 @p49) :args (@t50)) % 0.37/0.58 (step @p52 :rule cong :premises (@p51) :args (@t51)) % 0.37/0.58 (step @p53 :rule trans :premises (@p52 @p45)) % 0.37/0.58 (step @p54 :rule cong :premises (@p53) :args (@t52)) % 0.37/0.58 (step @p55 :rule eq_resolve :premises (@p33 @p54)) % 0.37/0.58 (step @p56 :rule refl :args (@t66)) % 0.37/0.58 (step @p57 :rule bool-double-not-elim :args (@t58)) % 0.37/0.58 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t67) @t66))) % 0.37/0.58 (step @p59 :rule refl :args (@t61)) % 0.37/0.58 (step @p60 :rule eq-symm :args (@t59 @t37)) % 0.37/0.58 (step @p61 :rule refl :args (@t64)) % 0.37/0.58 (step @p62 :rule nary_cong :premises (@p61 @p60 @p59) :args (@t69)) % 0.37/0.58 (step @p63 :rule cong :premises (@p62) :args (@t70)) % 0.37/0.58 (step @p64 :rule refl :args (@t67)) % 0.37/0.58 (step @p65 :rule cong :premises (@p64 @p63) :args ((=> @t67 @t70))) % 0.37/0.58 (assume-push @p119 @t67) % 0.37/0.58 (step @p67 :rule skolemize :premises (@p55)) % 0.37/0.58 (step-pop @p120 :rule scope :premises (@p67)) % 0.37/0.58 (step @p68 :rule process_scope :premises (@p120) :args (@t70)) % 0.37/0.58 (step @p70 :rule eq_resolve :premises (@p68 @p65)) % 0.37/0.58 (step @p71 :rule implies_elim :premises (@p70)) % 0.37/0.58 (step @p72 :rule eq_resolve :premises (@p71 @p58)) % 0.37/0.58 (step @p73 :rule chain_m_resolution :premises (@p72 @p55) :args (@t66 @t71 (@list @t58))) % 0.37/0.58 (step @p74 :rule bool-double-not-elim :args (@t63)) % 0.37/0.58 (step @p75 :rule refl :args (@t65)) % 0.37/0.58 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or @t65 (not @t64)))) % 0.37/0.58 (step @p77 :rule cnf_or_neg :args (@t65 0)) % 0.37/0.58 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 0.37/0.58 (step @p79 :rule reordering :premises (@p78) :args ((or @t63 @t65))) % 0.37/0.58 (step @p80 :rule chain_m_resolution :premises (@p79 @p73) :args (@t63 @t71 @t72)) % 0.37/0.58 (step @p81 :rule cnf_or_neg :args (@t65 1)) % 0.37/0.58 (step @p82 :rule chain_m_resolution :premises (@p81 @p73) :args ((not @t62) @t71 @t72)) % 0.37/0.58 (step @p83 :rule bool-double-not-elim :args (@t60)) % 0.37/0.58 (step @p84 :rule nary_cong :premises (@p75 @p83) :args ((or @t65 (not @t61)))) % 0.37/0.58 (step @p85 :rule cnf_or_neg :args (@t65 2)) % 0.37/0.58 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.37/0.58 (step @p87 :rule reordering :premises (@p86) :args ((or @t60 @t65))) % 0.37/0.58 (step @p88 :rule chain_m_resolution :premises (@p87 @p73) :args (@t60 @t71 @t72)) % 0.37/0.58 (step @p89 :rule cnf_equiv_pos1 :args (@t73)) % 0.37/0.58 (step @p90 :rule reordering :premises (@p89) :args ((or @t61 @t62 @t74))) % 0.37/0.58 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p82) :args (@t74 (@list false true) (@list @t60 @t62))) % 0.37/0.58 (step @p92 :rule bool-impl-elim :args (@t43 @t75)) % 0.37/0.58 (step @p93 :rule cong :premises (@p92) :args ((forall @t45 (=> @t43 @t75)))) % 0.37/0.58 (step @p94 :rule eq-symm :args (@t53 @t39)) % 0.37/0.58 (step @p95 :rule refl :args (@t39)) % 0.37/0.58 (step @p96 :rule cong :premises (@p46 @p95) :args (@t42)) % 0.37/0.58 (step @p97 :rule trans :premises (@p96 @p94)) % 0.37/0.58 (step @p98 :rule cong :premises (@p50 @p97) :args (@t44)) % 0.37/0.58 (step @p99 :rule cong :premises (@p98) :args (@t46)) % 0.37/0.58 (step @p100 :rule trans :premises (@p99 @p93)) % 0.37/0.58 (step @p101 :rule eq_resolve :premises (@p32 @p100)) % 0.37/0.58 (step @p102 :rule eq-symm :args (@t62 @t60)) % 0.37/0.58 (step @p103 :rule refl :args (@t60)) % 0.37/0.58 (step @p104 :rule cong :premises (@p60 @p103) :args (@t76)) % 0.37/0.58 (step @p105 :rule trans :premises (@p104 @p102)) % 0.37/0.58 (step @p106 :rule nary_cong :premises (@p61 @p105) :args (@t77)) % 0.37/0.58 (step @p107 :rule refl :args (@t78)) % 0.37/0.58 (step @p108 :rule cong :premises (@p107 @p106) :args ((=> @t78 @t77))) % 0.37/0.58 (assume-push @p121 @t78) % 0.37/0.58 (step @p110 :rule instantiate :premises (@p101) :args ((@list @t59))) % 0.37/0.58 (step-pop @p122 :rule scope :premises (@p110)) % 0.37/0.58 (step @p111 :rule process_scope :premises (@p122) :args (@t77)) % 0.37/0.58 (step @p113 :rule eq_resolve :premises (@p111 @p108)) % 0.37/0.58 (step @p114 :rule implies_elim :premises (@p113)) % 0.37/0.58 (step @p115 :rule chain_m_resolution :premises (@p114 @p101) :args (@t79 (@list false) (@list @t78))) % 0.37/0.58 (step @p116 :rule cnf_or_pos :args (@t79)) % 0.37/0.58 (step @p117 :rule reordering :premises (@p116) :args ((or @t64 @t73 (not @t79)))) % 0.37/0.58 (step @p118 false :rule chain_m_resolution :premises (@p117 @p115 @p91 @p80) :args (false (@list false true false) (@list @t79 @t73 @t63))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------