%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU277+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 08:38:18 AM UTC 2026
% Result : Theorem 7.50s 8.80s
% Output : Refutation 7.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 151 ( 20 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 390 ( 10 ~; 0 |; 87 &; 265 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 90 ( 0 ^; 44 !; 46 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( F
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( F = E )
& ( A @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( F
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( F = E )
& ( A @ ( A @ cartesian_product2 ) @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( F = E )
& ( A @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(116,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(65,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(53,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(81,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(35,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(112,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i,G: $i] :
( ( B @ ( G @ ( C @ apply ) @ ( F @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( G @ ( F @ ordered_pair ) ) ) )
& ( A @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i,G: $i] :
( ( B @ ( G @ ( C @ apply ) @ ( F @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( G @ ( F @ ordered_pair ) ) ) )
& ( A @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i,G: $i] :
( ( B @ ( G @ ( C @ apply ) @ ( F @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( G @ ( F @ ordered_pair ) ) ) )
& ( A @ ( A @ cartesian_product2 ) @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i,G: $i] :
( ( B @ ( G @ ( C @ apply ) @ ( F @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( G @ ( F @ ordered_pair ) ) ) )
& ( A @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(47,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(83,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(33,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(72,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(43,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(40,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(55,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(129,plain,
$false,
inference(e,[status(thm)],[88,116,60,65,53,81,35,112,19,47,83,70,33,72,43,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU277+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.13 % 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
% 0.23/5.51 % Computer : n007.cluster.edu
% 0.23/5.51 % Model : x86_64 x86_64
% 0.23/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/5.51 % Memory : 8046.5625MB
% 0.23/5.51 % OS : Linux 6.8.0-71-generic
% 0.23/5.51 % CPULimit : 300
% 0.23/5.51 % WCLimit : 300
% 0.23/5.51 % DateTime : Sat Sep 26 09:01:43 UTC 2026
% 0.23/5.52 % CPUTime :
% 0.23/5.52 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
% 1.16/6.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/6.35 % [INFO] Parsing done (283ms).
% 1.63/6.37 % [INFO] Running in sequential loop mode.
% 2.78/7.00 % [INFO] eprover registered as external prover.
% 2.78/7.01 % [INFO] Scanning for conjecture ...
% 3.25/7.19 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 3.58/7.30 % [INFO] Axiom selection finished. Selected 16 axioms (removed 3 axioms).
% 3.58/7.35 % [INFO] Problem is first-order (TPTP FOF).
% 3.58/7.37 % [INFO] Type checking passed.
% 3.58/7.37 % [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 ...
% 6.94/8.80 % External prover 'e' found a proof!
% 7.50/8.80 % [INFO] Killing All external provers ...
% 7.50/8.80 % Time passed: 3100ms (effective reasoning time: 2419ms)
% 7.50/8.80 % 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)>
% 7.50/8.80 % Axioms used in derivation (16): fc1_zfmisc_1, rc3_funct_1, rc1_funct_1, s1_tarski__e6_21__wellord2__1, cc2_ordinal1, cc1_ordinal1, cc1_funct_1, rc3_ordinal1, rc2_ordinal1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, rc2_funct_1, cc3_ordinal1, cc2_funct_1, rc1_ordinal1
% 7.50/8.80 % No. of inferences in proof: 36
% 7.50/8.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3100 ms resp. 2419 ms w/o parsing
% 7.76/8.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.76/8.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------