%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET055-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 : Thu Aug 31 14:37:11 EDT 2023

% Result   : Unsatisfiable 0.19s 0.64s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET055-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.33  % Computer : n013.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Sat Aug 26 08:54:32 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.50  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hQTib4tBuR/cvc5---1.0.5_17602.p...
% 0.19/0.52  ------- get file name : TPTP file name is SET055-7
% 0.19/0.52  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17602.smt2...
% 0.19/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.64  % SZS status Unsatisfiable for SET055-7
% 0.19/0.65  % SZS output start Proof for SET055-7
% 0.19/0.65  (
% 0.19/0.65  (let ((_let_1 (tptp.equalish tptp.x tptp.x))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted)) (tptp.subclass X X)))) (let ((_let_4 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (tptp.equalish X Y))))) (let ((_let_6 (tptp.subclass tptp.x tptp.x))) (let ((_let_7 (_let_3))) (let ((_let_8 (ASSUME :args _let_7))) (let ((_let_9 (not _let_6))) (let ((_let_10 (or _let_9 _let_9 _let_1))) (let ((_let_11 (_let_5))) (let ((_let_12 (ASSUME :args _let_11))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_8 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X X) true))))) :args _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_10))) :args ((or _let_1 _let_9 (not _let_10)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (tptp.x tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.equalish X Y) true))))) :args _let_11)) _let_12 :args (_let_10 false _let_5)) :args (_let_9 true _let_1 false _let_10)) _let_8 :args (false true _let_6 false _let_3)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equalish X Y)) (tptp.equalish Y X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.equalish X Y)) (not (tptp.equalish Y Z)) (tptp.equalish X Z))) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (or (not (tptp.equalish D E)) (tptp.equalish (tptp.apply D F) (tptp.apply E F)))) (forall ((G $$unsorted) (H $$unsorted) (I $$unsorted)) (or (not (tptp.equalish G H)) (tptp.equalish (tptp.apply I G) (tptp.apply I H)))) (forall ((J $$unsorted) (K $$unsorted)) (or (not (tptp.equalish J K)) (tptp.equalish (tptp.cantor J) (tptp.cantor K)))) (forall ((L $$unsorted) (M $$unsorted)) (or (not (tptp.equalish L M)) (tptp.equalish (tptp.complement L) (tptp.complement M)))) (forall ((N $$unsorted) (O $$unsorted) (P $$unsorted)) (or (not (tptp.equalish N O)) (tptp.equalish (tptp.compose N P) (tptp.compose O P)))) (forall ((Q $$unsorted) (R $$unsorted) (S $$unsorted)) (or (not (tptp.equalish Q R)) (tptp.equalish (tptp.compose S Q) (tptp.compose S R)))) (forall ((T $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.equalish T U)) (tptp.equalish (tptp.cross_product T V) (tptp.cross_product U V)))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.equalish W X)) (tptp.equalish (tptp.cross_product Y W) (tptp.cross_product Y X)))) (forall ((Z $$unsorted) (A1 $$unsorted)) (or (not (tptp.equalish Z A1)) (tptp.equalish (tptp.diagonalise Z) (tptp.diagonalise A1)))) (forall ((B1 $$unsorted) (C1 $$unsorted) (D1 $$unsorted)) (or (not (tptp.equalish B1 C1)) (tptp.equalish (tptp.symmetric_difference B1 D1) (tptp.symmetric_difference C1 D1)))) (forall ((E1 $$unsorted) (F1 $$unsorted) (G1 $$unsorted)) (or (not (tptp.equalish E1 F1)) (tptp.equalish (tptp.symmetric_difference G1 E1) (tptp.symmetric_difference G1 F1)))) (forall ((H1 $$unsorted) (I1 $$unsorted) (J1 $$unsorted) (K1 $$unsorted)) (or (not (tptp.equalish H1 I1)) (tptp.equalish (tptp.domain H1 J1 K1) (tptp.domain I1 J1 K1)))) (forall ((L1 $$unsorted) (M1 $$unsorted) (N1 $$unsorted) (O1 $$unsorted)) (or (not (tptp.equalish L1 M1)) (tptp.equalish (tptp.domain N1 L1 O1) (tptp.domain N1 M1 O1)))) (forall ((P1 $$unsorted) (Q1 $$unsorted) (R1 $$unsorted) (S1 $$unsorted)) (or (not (tptp.equalish P1 Q1)) (tptp.equalish (tptp.domain R1 S1 P1) (tptp.domain R1 S1 Q1)))) (forall ((T1 $$unsorted) (U1 $$unsorted)) (or (not (tptp.equalish T1 U1)) (tptp.equalish (tptp.domain_of T1) (tptp.domain_of U1)))) (forall ((V1 $$unsorted) (W1 $$unsorted)) (or (not (tptp.equalish V1 W1)) (tptp.equalish (tptp.first V1) (tptp.first W1)))) (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (tptp.equalish X1 Y1)) (tptp.equalish (tptp.flip X1) (tptp.flip Y1)))) (forall ((Z1 $$unsorted) (A2 $$unsorted) (B2 $$unsorted)) (or (not (tptp.equalish Z1 A2)) (tptp.equalish (tptp.image Z1 B2) (tptp.image A2 B2)))) (forall ((C2 $$unsorted) (D2 $$unsorted) (E2 $$unsorted)) (or (not (tptp.equalish C2 D2)) (tptp.equalish (tptp.image E2 C2) (tptp.image E2 D2)))) (forall ((F2 $$unsorted) (G2 $$unsorted) (H2 $$unsorted)) (or (not (tptp.equalish F2 G2)) (tptp.equalish (tptp.intersection F2 H2) (tptp.intersection G2 H2)))) (forall ((I2 $$unsorted) (J2 $$unsorted) (K2 $$unsorted)) (or (not (tptp.equalish I2 J2)) (tptp.equalish (tptp.intersection K2 I2) (tptp.intersection K2 J2)))) (forall ((L2 $$unsorted) (M2 $$unsorted)) (or (not (tptp.equalish L2 M2)) (tptp.equalish (tptp.inverse L2) (tptp.inverse M2)))) (forall ((N2 $$unsorted) (O2 $$unsorted) (P2 $$unsorted) (Q2 $$unsorted)) (or (not (tptp.equalish N2 O2)) (tptp.equalish (tptp.not_homomorphism1 N2 P2 Q2) (tptp.not_homomorphism1 O2 P2 Q2)))) (forall ((R2 $$unsorted) (S2 $$unsorted) (T2 $$unsorted) (U2 $$unsorted)) (or (not (tptp.equalish R2 S2)) (tptp.equalish (tptp.not_homomorphism1 T2 R2 U2) (tptp.not_homomorphism1 T2 S2 U2)))) (forall ((V2 $$unsorted) (W2 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.equalish V2 W2)) (tptp.equalish (tptp.not_homomorphism1 X2 Y2 V2) (tptp.not_homomorphism1 X2 Y2 W2)))) (forall ((Z2 $$unsorted) (A3 $$unsorted) (B3 $$unsorted) (C3 $$unsorted)) (or (not (tptp.equalish Z2 A3)) (tptp.equalish (tptp.not_homomorphism2 Z2 B3 C3) (tptp.not_homomorphism2 A3 B3 C3)))) (forall ((D3 $$unsorted) (E3 $$unsorted) (F3 $$unsorted) (G3 $$unsorted)) (or (not (tptp.equalish D3 E3)) (tptp.equalish (tptp.not_homomorphism2 F3 D3 G3) (tptp.not_homomorphism2 F3 E3 G3)))) (forall ((H3 $$unsorted) (I3 $$unsorted) (J3 $$unsorted) (K3 $$unsorted)) (or (not (tptp.equalish H3 I3)) (tptp.equalish (tptp.not_homomorphism2 J3 K3 H3) (tptp.not_homomorphism2 J3 K3 I3)))) (forall ((L3 $$unsorted) (M3 $$unsorted) (N3 $$unsorted)) (or (not (tptp.equalish L3 M3)) (tptp.equalish (tptp.not_subclass_element L3 N3) (tptp.not_subclass_element M3 N3)))) (forall ((O3 $$unsorted) (P3 $$unsorted) (Q3 $$unsorted)) (or (not (tptp.equalish O3 P3)) (tptp.equalish (tptp.not_subclass_element Q3 O3) (tptp.not_subclass_element Q3 P3)))) (forall ((R3 $$unsorted) (S3 $$unsorted) (T3 $$unsorted)) (or (not (tptp.equalish R3 S3)) (tptp.equalish (tptp.ordered_pair R3 T3) (tptp.ordered_pair S3 T3)))) (forall ((U3 $$unsorted) (V3 $$unsorted) (W3 $$unsorted)) (or (not (tptp.equalish U3 V3)) (tptp.equalish (tptp.ordered_pair W3 U3) (tptp.ordered_pair W3 V3)))) (forall ((X3 $$unsorted) (Y3 $$unsorted)) (or (not (tptp.equalish X3 Y3)) (tptp.equalish (tptp.power_class X3) (tptp.power_class Y3)))) (forall ((Z3 $$unsorted) (A4 $$unsorted) (B4 $$unsorted) (C4 $$unsorted)) (or (not (tptp.equalish Z3 A4)) (tptp.equalish (tptp.range Z3 B4 C4) (tptp.range A4 B4 C4)))) (forall ((D4 $$unsorted) (E4 $$unsorted) (F4 $$unsorted) (G4 $$unsorted)) (or (not (tptp.equalish D4 E4)) (tptp.equalish (tptp.range F4 D4 G4) (tptp.range F4 E4 G4)))) (forall ((H4 $$unsorted) (I4 $$unsorted) (J4 $$unsorted) (K4 $$unsorted)) (or (not (tptp.equalish H4 I4)) (tptp.equalish (tptp.range J4 K4 H4) (tptp.range J4 K4 I4)))) (forall ((L4 $$unsorted) (M4 $$unsorted)) (or (not (tptp.equalish L4 M4)) (tptp.equalish (tptp.range_of L4) (tptp.range_of M4)))) (forall ((N4 $$unsorted) (O4 $$unsorted)) (or (not (tptp.equalish N4 O4)) (tptp.equalish (tptp.regular N4) (tptp.regular O4)))) (forall ((P4 $$unsorted) (Q4 $$unsorted) (R4 $$unsorted) (S4 $$unsorted)) (or (not (tptp.equalish P4 Q4)) (tptp.equalish (tptp.restrict P4 R4 S4) (tptp.restrict Q4 R4 S4)))) (forall ((T4 $$unsorted) (U4 $$unsorted) (V4 $$unsorted) (W4 $$unsorted)) (or (not (tptp.equalish T4 U4)) (tptp.equalish (tptp.restrict V4 T4 W4) (tptp.restrict V4 U4 W4)))) (forall ((X4 $$unsorted) (Y4 $$unsorted) (Z4 $$unsorted) (A5 $$unsorted)) (or (not (tptp.equalish X4 Y4)) (tptp.equalish (tptp.restrict Z4 A5 X4) (tptp.restrict Z4 A5 Y4)))) (forall ((B5 $$unsorted) (C5 $$unsorted)) (or (not (tptp.equalish B5 C5)) (tptp.equalish (tptp.rotate B5) (tptp.rotate C5)))) (forall ((D5 $$unsorted) (E5 $$unsorted)) (or (not (tptp.equalish D5 E5)) (tptp.equalish (tptp.second D5) (tptp.second E5)))) (forall ((F5 $$unsorted) (G5 $$unsorted)) (or (not (tptp.equalish F5 G5)) (tptp.equalish (tptp.singleton F5) (tptp.singleton G5)))) (forall ((H5 $$unsorted) (I5 $$unsorted)) (or (not (tptp.equalish H5 I5)) (tptp.equalish (tptp.successor H5) (tptp.successor I5)))) (forall ((J5 $$unsorted) (K5 $$unsorted)) (or (not (tptp.equalish J5 K5)) (tptp.equalish (tptp.sum_class J5) (tptp.sum_class K5)))) (forall ((L5 $$unsorted) (M5 $$unsorted) (N5 $$unsorted)) (or (not (tptp.equalish L5 M5)) (tptp.equalish (tptp.union L5 N5) (tptp.union M5 N5)))) (forall ((O5 $$unsorted) (P5 $$unsorted) (Q5 $$unsorted)) (or (not (tptp.equalish O5 P5)) (tptp.equalish (tptp.union Q5 O5) (tptp.union Q5 P5)))) (forall ((R5 $$unsorted) (S5 $$unsorted) (T5 $$unsorted)) (or (not (tptp.equalish R5 S5)) (tptp.equalish (tptp.unordered_pair R5 T5) (tptp.unordered_pair S5 T5)))) (forall ((U5 $$unsorted) (V5 $$unsorted) (W5 $$unsorted)) (or (not (tptp.equalish U5 V5)) (tptp.equalish (tptp.unordered_pair W5 U5) (tptp.unordered_pair W5 V5)))) (forall ((X5 $$unsorted) (Y5 $$unsorted) (Z5 $$unsorted) (A6 $$unsorted)) (or (not (tptp.equalish X5 Y5)) (not (tptp.compatible X5 Z5 A6)) (tptp.compatible Y5 Z5 A6))) (forall ((B6 $$unsorted) (C6 $$unsorted) (D6 $$unsorted) (E6 $$unsorted)) (or (not (tptp.equalish B6 C6)) (not (tptp.compatible D6 B6 E6)) (tptp.compatible D6 C6 E6))) (forall ((F6 $$unsorted) (G6 $$unsorted) (H6 $$unsorted) (I6 $$unsorted)) (or (not (tptp.equalish F6 G6)) (not (tptp.compatible H6 I6 F6)) (tptp.compatible H6 I6 G6))) (forall ((J6 $$unsorted) (K6 $$unsorted)) (or (not (tptp.equalish J6 K6)) (not (tptp.function J6)) (tptp.function K6))) (forall ((L6 $$unsorted) (M6 $$unsorted) (N6 $$unsorted) (O6 $$unsorted)) (or (not (tptp.equalish L6 M6)) (not (tptp.homomorphism L6 N6 O6)) (tptp.homomorphism M6 N6 O6))) (forall ((P6 $$unsorted) (Q6 $$unsorted) (R6 $$unsorted) (S6 $$unsorted)) (or (not (tptp.equalish P6 Q6)) (not (tptp.homomorphism R6 P6 S6)) (tptp.homomorphism R6 Q6 S6))) (forall ((T6 $$unsorted) (U6 $$unsorted) (V6 $$unsorted) (W6 $$unsorted)) (or (not (tptp.equalish T6 U6)) (not (tptp.homomorphism V6 W6 T6)) (tptp.homomorphism V6 W6 U6))) (forall ((X6 $$unsorted) (Y6 $$unsorted)) (or (not (tptp.equalish X6 Y6)) (not (tptp.inductive X6)) (tptp.inductive Y6))) (forall ((Z6 $$unsorted) (A7 $$unsorted) (B7 $$unsorted)) (or (not (tptp.equalish Z6 A7)) (not (tptp.member Z6 B7)) (tptp.member A7 B7))) (forall ((C7 $$unsorted) (D7 $$unsorted) (E7 $$unsorted)) (or (not (tptp.equalish C7 D7)) (not (tptp.member E7 C7)) (tptp.member E7 D7))) (forall ((F7 $$unsorted) (G7 $$unsorted)) (or (not (tptp.equalish F7 G7)) (not (tptp.one_to_one F7)) (tptp.one_to_one G7))) (forall ((H7 $$unsorted) (I7 $$unsorted)) (or (not (tptp.equalish H7 I7)) (not (tptp.operation H7)) (tptp.operation I7))) (forall ((J7 $$unsorted) (K7 $$unsorted)) (or (not (tptp.equalish J7 K7)) (not (tptp.single_valued_class J7)) (tptp.single_valued_class K7))) (forall ((L7 $$unsorted) (M7 $$unsorted) (N7 $$unsorted)) (or (not (tptp.equalish L7 M7)) (not (tptp.subclass L7 N7)) (tptp.subclass M7 N7))) (forall ((O7 $$unsorted) (P7 $$unsorted) (Q7 $$unsorted)) (or (not (tptp.equalish O7 P7)) (not (tptp.subclass Q7 O7)) (tptp.subclass Q7 P7))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equalish X Y)) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equalish X Y)) (tptp.subclass Y X))) _let_5 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (tptp.equalish U X) (tptp.equalish U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (forall ((X $$unsorted)) (tptp.equalish (tptp.unordered_pair X X) (tptp.singleton X))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.equalish (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.equalish (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_4) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member _let_1 tptp.element_relation)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.equalish (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.equalish (tptp.intersection (tptp.complement (tptp.intersection X Y)) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y)))) (tptp.symmetric_difference X Y))) (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (tptp.equalish (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (tptp.equalish (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.equalish (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.equalish (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))) (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.rotate X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))) (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.flip X))))) (forall ((Y $$unsorted)) (tptp.equalish (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))) (forall ((Z $$unsorted)) (tptp.equalish (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (tptp.equalish (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (tptp.equalish (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))) (forall ((Xr $$unsorted) (X $$unsorted)) (tptp.equalish (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))) (forall ((X $$unsorted)) (tptp.equalish (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_4) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (tptp.equalish (tptp.successor X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.equalish (tptp.successor X) Y)) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 tptp.successor_relation)))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))) (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))) (tptp.inductive tptp.omega) (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))) (tptp.member tptp.omega tptp.universal_class) (forall ((X $$unsorted)) (tptp.equalish (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((X $$unsorted)) (tptp.equalish (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))) (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 (tptp.compose Yr Xr))))) (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))) (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))) (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))) (forall ((X $$unsorted)) (or (tptp.equalish X tptp.null_class) (tptp.member (tptp.regular X) X))) (forall ((X $$unsorted)) (or (tptp.equalish X tptp.null_class) (tptp.equalish (tptp.intersection X (tptp.regular X)) tptp.null_class))) (forall ((Xf $$unsorted) (Y $$unsorted)) (tptp.equalish (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (tptp.function tptp.choice) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.equalish Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))) (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) (tptp.equalish (tptp.intersection _let_4 (tptp.intersection _let_4 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (tptp.equalish (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (forall ((Xr $$unsorted)) (tptp.equalish (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))) (forall ((X $$unsorted)) (tptp.equalish (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.operation Xf)) (tptp.equalish (tptp.cross_product _let_2 _let_2) _let_1))))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.function Xf)) (not (tptp.equalish (tptp.cross_product _let_2 _let_2) _let_1)) (not (tptp.subclass (tptp.range_of Xf) _let_2)) (tptp.operation Xf))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.equalish (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (Xh1 $$unsorted)) (or (not (tptp.function Xh)) (not (tptp.equalish (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh1 Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member _let_1 (tptp.domain_of Xf1))) (tptp.equalish (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 _let_1)))))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (let ((_let_1 (tptp.not_homomorphism2 Xh Xf1 Xf2))) (let ((_let_2 (tptp.not_homomorphism1 Xh Xf1 Xf2))) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (tptp.equalish (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh _let_2) (tptp.apply Xh _let_1))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair _let_2 _let_1))))) (tptp.homomorphism Xh Xf1 Xf2))))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V tptp.universal_class))) _let_3 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y Z)) (tptp.subclass X Z))) _let_2)))))))))))))))
% 0.19/0.65  )
% 0.19/0.65  % SZS output end Proof for SET055-7
% 0.19/0.65  % cvc5---1.0.5 exiting
% 0.19/0.66  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------