%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:31:31 AM UTC 2026
% Result : Theorem 4.64s 2.00s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 70 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 212 ( 50 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 713 ( 2 ~; 0 |; 88 &; 569 @)
% ( 2 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 15 con; 0-4 aty)
% Number of variables : 160 ( 0 ^; 136 !; 24 ?; 160 :)
% Comments :
%------------------------------------------------------------------------------
thf(surjection_decl,type,
surjection: $i > $o ).
thf(g_decl,type,
g: $i ).
thf(morphism_decl,type,
morphism: $i > $i > $i > $o ).
thf(h_decl,type,
h: $i ).
thf(c_decl,type,
c: $i ).
thf(r_decl,type,
r: $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(commute_decl,type,
commute: $i > $i > $i > $i > $o ).
thf(injection_decl,type,
injection: $i > $o ).
thf(gamma_decl,type,
gamma: $i ).
thf(alpha_decl,type,
alpha: $i ).
thf(subtract_decl,type,
subtract: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(zero_decl,type,
zero: $i > $i ).
thf(exact_decl,type,
exact: $i > $i > $o ).
thf(f_decl,type,
f: $i ).
thf(d_decl,type,
d: $i ).
thf(delta_decl,type,
delta: $i ).
thf(e_decl,type,
e: $i ).
thf(beta_decl,type,
beta: $i ).
thf(gammma_decl,type,
gammma: $i ).
thf(35,axiom,
! [A: $i] :
( ( e @ ( A @ element ) )
=> ? [B: $i,C: $i] :
( ( ( C @ ( B @ ( b @ subtract ) ) @ ( g @ apply ) )
= A )
& ( b @ ( C @ element ) )
& ( b @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma12) ).
thf(153,plain,
! [A: $i] :
( ( e @ ( A @ element ) )
=> ? [B: $i,C: $i] :
( ( ( C @ ( B @ ( b @ subtract ) ) @ ( g @ apply ) )
= A )
& ( b @ ( C @ element ) )
& ( b @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
r @ ( c @ ( h @ morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_morphism) ).
thf(37,plain,
r @ ( c @ ( h @ morphism ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ morphism ) ) )
& ( A @ injection ) )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( A @ apply ) )
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ element ) )
& ( B @ ( D @ element ) ) )
=> ( D = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties) ).
thf(106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ morphism ) ) )
& ( A @ injection ) )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( A @ apply ) )
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ element ) )
& ( B @ ( D @ element ) ) )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ morphism ) ) )
& ( A @ surjection ) )
=> ! [D: $i] :
( ( C @ ( D @ element ) )
=> ? [E: $i] :
( ( ( E @ ( A @ apply ) )
= D )
& ( B @ ( E @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjection_properties) ).
thf(132,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ morphism ) ) )
& ( A @ surjection ) )
=> ! [D: $i] :
( ( C @ ( D @ element ) )
=> ? [E: $i] :
( ( ( E @ ( A @ apply ) )
= D )
& ( B @ ( E @ element ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
gamma @ injection,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_injection) ).
thf(44,plain,
gamma @ injection,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
b @ ( a @ ( alpha @ morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).
thf(49,plain,
b @ ( a @ ( alpha @ morphism ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
f @ surjection,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_surjection) ).
thf(112,plain,
f @ surjection,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
d @ ( a @ ( f @ morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_morphism) ).
thf(63,plain,
d @ ( a @ ( f @ morphism ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( ( ( F @ ( B @ apply ) )
= ( E @ zero ) )
& ( D @ ( F @ element ) ) )
<=> ? [G: $i] :
( ( ( G @ ( A @ apply ) )
= F )
& ( C @ ( G @ element ) ) ) )
& ( E @ ( D @ ( B @ morphism ) ) )
& ( D @ ( C @ ( A @ morphism ) ) ) )
=> ( B @ ( A @ exact ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_exact) ).
thf(50,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( ? [G: $i] :
( ( ( G @ ( A @ apply ) )
= F )
& ( C @ ( G @ element ) ) )
=> ( ( ( F @ ( B @ apply ) )
= ( E @ zero ) )
& ( D @ ( F @ element ) ) ) )
& ( ( ( ( F @ ( B @ apply ) )
= ( E @ zero ) )
& ( D @ ( F @ element ) ) )
=> ? [G: $i] :
( ( ( G @ ( A @ apply ) )
= F )
& ( C @ ( G @ element ) ) ) ) )
& ( E @ ( D @ ( B @ morphism ) ) )
& ( D @ ( C @ ( A @ morphism ) ) ) )
=> ( B @ ( A @ exact ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( D @ morphism ) ) )
& ( G @ ( E @ ( C @ morphism ) ) )
& ( H @ ( F @ ( B @ morphism ) ) )
& ( F @ ( E @ ( A @ morphism ) ) )
& ( D @ ( C @ ( B @ ( A @ commute ) ) ) ) )
=> ! [I: $i] :
( ( E @ ( I @ element ) )
=> ( ( I @ ( A @ apply ) @ ( B @ apply ) )
= ( I @ ( C @ apply ) @ ( D @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commute_properties) ).
thf(72,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( D @ morphism ) ) )
& ( G @ ( E @ ( C @ morphism ) ) )
& ( H @ ( F @ ( B @ morphism ) ) )
& ( F @ ( E @ ( A @ morphism ) ) )
& ( D @ ( C @ ( B @ ( A @ commute ) ) ) ) )
=> ! [I: $i] :
( ( E @ ( I @ element ) )
=> ( ( I @ ( A @ apply ) @ ( B @ apply ) )
= ( I @ ( C @ apply ) @ ( D @ apply ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
! [A: $i] :
( ( e @ ( A @ element ) )
=> ? [B: $i,C: $i,D: $i] :
( ( ( D @ ( alpha @ apply ) @ ( g @ apply ) )
= C )
& ( ( D @ ( f @ apply ) @ ( gamma @ apply ) )
= C )
& ( a @ ( D @ element ) )
& ( ( A @ ( B @ ( g @ apply ) @ ( e @ subtract ) ) )
= C )
& ( e @ ( C @ element ) )
& ( b @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma8) ).
thf(139,plain,
! [A: $i] :
( ( e @ ( A @ element ) )
=> ? [B: $i,C: $i,D: $i] :
( ( ( D @ ( alpha @ apply ) @ ( g @ apply ) )
= C )
& ( ( D @ ( f @ apply ) @ ( gamma @ apply ) )
= C )
& ( a @ ( D @ element ) )
& ( ( A @ ( B @ ( g @ apply ) @ ( e @ subtract ) ) )
= C )
& ( e @ ( C @ element ) )
& ( b @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
delta @ ( gammma @ exact ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_delta_exact) ).
thf(82,plain,
delta @ ( gammma @ exact ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ ( B @ morphism ) ) )
& ( D @ ( C @ ( A @ morphism ) ) )
& ( B @ ( A @ exact ) ) )
=> ! [F: $i] :
( ( ( ( F @ ( B @ apply ) )
= ( E @ zero ) )
& ( D @ ( F @ element ) ) )
<=> ? [G: $i] :
( ( ( G @ ( A @ apply ) )
= F )
& ( C @ ( G @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exact_properties) ).
thf(83,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ ( B @ morphism ) ) )
& ( D @ ( C @ ( A @ morphism ) ) )
& ( B @ ( A @ exact ) ) )
=> ! [F: $i] :
( ( ? [G: $i] :
( ( ( G @ ( A @ apply ) )
= F )
& ( C @ ( G @ element ) ) )
=> ( ( ( F @ ( B @ apply ) )
= ( E @ zero ) )
& ( D @ ( F @ element ) ) ) )
& ( ( ( ( F @ ( B @ apply ) )
= ( E @ zero ) )
& ( D @ ( F @ element ) ) )
=> ? [G: $i] :
( ( ( G @ ( A @ apply ) )
= F )
& ( C @ ( G @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ ( B @ ( A @ subtract ) ) )
= ( A @ zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_to_0) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ ( B @ ( A @ subtract ) ) )
= ( A @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(31,axiom,
beta @ surjection,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_surjection) ).
thf(138,plain,
beta @ surjection,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) ) )
=> ( A @ ( C @ ( B @ ( A @ subtract ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_in_domain) ).
thf(110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) ) )
=> ( A @ ( C @ ( B @ ( A @ subtract ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( C @ ( D @ element ) )
=> ? [E: $i] :
( ( ( E @ ( A @ apply ) )
= D )
& ( B @ ( E @ element ) ) ) )
& ( C @ ( B @ ( A @ morphism ) ) ) )
=> ( A @ surjection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_surjection) ).
thf(125,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( C @ ( D @ element ) )
=> ? [E: $i] :
( ( ( E @ ( A @ apply ) )
= D )
& ( B @ ( E @ element ) ) ) )
& ( C @ ( B @ ( A @ morphism ) ) ) )
=> ( A @ surjection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ morphism ) ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( E @ element ) )
& ( B @ ( D @ element ) ) )
=> ( ( E @ ( D @ ( B @ subtract ) ) @ ( A @ apply ) )
= ( E @ ( A @ apply ) @ ( D @ ( A @ apply ) @ ( C @ subtract ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_distribution) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ morphism ) ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( E @ element ) )
& ( B @ ( D @ element ) ) )
=> ( ( E @ ( D @ ( B @ subtract ) ) @ ( A @ apply ) )
= ( E @ ( A @ apply ) @ ( D @ ( A @ apply ) @ ( C @ subtract ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,axiom,
delta @ ( g @ ( h @ ( beta @ commute ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
thf(152,plain,
delta @ ( g @ ( h @ ( beta @ commute ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( E @ ( I @ element ) )
=> ( ( I @ ( A @ apply ) @ ( B @ apply ) )
= ( I @ ( C @ apply ) @ ( D @ apply ) ) ) )
& ( H @ ( G @ ( D @ morphism ) ) )
& ( G @ ( E @ ( C @ morphism ) ) )
& ( H @ ( F @ ( B @ morphism ) ) )
& ( F @ ( E @ ( A @ morphism ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ commute ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_commute) ).
thf(38,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( E @ ( I @ element ) )
=> ( ( I @ ( A @ apply ) @ ( B @ apply ) )
= ( I @ ( C @ apply ) @ ( D @ apply ) ) ) )
& ( H @ ( G @ ( D @ morphism ) ) )
& ( G @ ( E @ ( C @ morphism ) ) )
& ( H @ ( F @ ( B @ morphism ) ) )
& ( F @ ( E @ ( A @ morphism ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ commute ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
h @ surjection,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_surjection) ).
thf(137,plain,
h @ surjection,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subtract ) ) @ ( B @ ( A @ subtract ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_cancellation) ).
thf(65,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subtract ) ) @ ( B @ ( A @ subtract ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( A @ apply ) )
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ element ) )
& ( B @ ( D @ element ) ) )
=> ( D = E ) )
& ( C @ ( B @ ( A @ morphism ) ) ) )
=> ( A @ injection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( A @ apply ) )
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ element ) )
& ( B @ ( D @ element ) ) )
=> ( D = E ) )
& ( C @ ( B @ ( A @ morphism ) ) ) )
=> ( A @ injection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
gamma @ ( f @ ( g @ ( alpha @ commute ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_g_f_gamma_commute) ).
thf(124,plain,
gamma @ ( f @ ( g @ ( alpha @ commute ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(20,axiom,
c @ ( b @ ( beta @ morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_morphism) ).
thf(96,plain,
c @ ( b @ ( beta @ morphism ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
alpha @ injection,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_injection) ).
thf(45,plain,
alpha @ injection,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
r @ ( e @ ( delta @ morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',delta_morphism) ).
thf(64,plain,
r @ ( e @ ( delta @ morphism ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [A: $i] :
( ( e @ ( A @ element ) )
=> ? [B: $i,C: $i] :
( ( ( C @ ( g @ apply ) @ ( delta @ apply ) )
= B )
& ( ( C @ ( beta @ apply ) @ ( h @ apply ) )
= B )
& ( b @ ( C @ element ) )
& ( ( A @ ( delta @ apply ) )
= B )
& ( r @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma3) ).
thf(113,plain,
! [A: $i] :
( ( e @ ( A @ element ) )
=> ? [B: $i,C: $i] :
( ( ( C @ ( g @ apply ) @ ( delta @ apply ) )
= B )
& ( ( C @ ( beta @ apply ) @ ( h @ apply ) )
= B )
& ( b @ ( C @ element ) )
& ( ( A @ ( delta @ apply ) )
= B )
& ( r @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
e @ ( d @ ( gamma @ morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_morphism) ).
thf(81,plain,
e @ ( d @ ( gamma @ morphism ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ morphism ) ) )
=> ( ( ( B @ zero @ ( A @ apply ) )
= ( C @ zero ) )
& ! [D: $i] :
( ( B @ ( D @ element ) )
=> ( C @ ( D @ ( A @ apply ) @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',morphism) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ morphism ) ) )
=> ( ( ( B @ zero @ ( A @ apply ) )
= ( C @ zero ) )
& ! [D: $i] :
( ( B @ ( D @ element ) )
=> ( C @ ( D @ ( A @ apply ) @ element ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(33,axiom,
delta @ surjection,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',delta_surjection) ).
thf(151,plain,
delta @ surjection,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
g @ surjection,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_surjection) ).
thf(2,negated_conjecture,
~ ( g @ surjection ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ( g @ surjection ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
e @ ( b @ ( g @ morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
thf(131,plain,
e @ ( b @ ( g @ morphism ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,axiom,
beta @ ( alpha @ exact ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_beta_exact) ).
thf(68,plain,
beta @ ( alpha @ exact ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(193,plain,
$false,
inference(e,[status(thm)],[153,37,106,132,44,49,112,63,50,72,139,82,83,69,138,110,125,46,152,38,137,65,97,124,96,45,64,113,81,76,151,36,131,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n004.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 15:53:50 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.83 % [INFO] Parsing done (122ms).
% 0.94/0.84 % [INFO] Running in sequential loop mode.
% 1.64/1.05 % [INFO] eprover registered as external prover.
% 1.64/1.05 % [INFO] Scanning for conjecture ...
% 1.64/1.10 % [INFO] Found a conjecture (or negated_conjecture) and 33 axioms. Running axiom selection ...
% 1.93/1.15 % [INFO] Axiom selection finished. Selected 33 axioms (removed 0 axioms).
% 2.14/1.20 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.21 % [INFO] Type checking passed.
% 2.14/1.22 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.64/1.99 % External prover 'e' found a proof!
% 4.64/1.99 % [INFO] Killing All external provers ...
% 4.64/1.99 % Time passed: 1505ms (effective reasoning time: 1150ms)
% 4.64/1.99 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.64/2.00 % Axioms used in derivation (33): surjection_properties, lemma8, beta_morphism, gamma_morphism, subtract_cancellation, lemma12, alpha_g_f_gamma_commute, properties_for_surjection, morphism, commute_properties, subtract_in_domain, subtract_to_0, beta_h_g_delta_commute, delta_morphism, h_morphism, alpha_morphism, injection_properties, properties_for_exact, subtract_distribution, h_surjection, f_morphism, f_surjection, properties_for_injection, delta_surjection, properties_for_commute, gamma_injection, exact_properties, gamma_delta_exact, lemma3, alpha_injection, beta_surjection, g_morphism, alpha_beta_exact
% 4.64/2.00 % No. of inferences in proof: 70
% 4.64/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1505 ms resp. 1150 ms w/o parsing
% 4.64/2.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.64/2.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------