%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU156+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:37:48 AM UTC 2026
% Result : Theorem 5.42s 3.49s
% Output : Refutation 5.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 110 ( 12 ~; 0 |; 7 &; 82 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 53 !; 4 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(34,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(36,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(29,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(31,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(26,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[14,34,43,36,20,46,29,50,31,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU156+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.25/0.51 % Computer : n002.cluster.edu
% 0.25/0.51 % Model : x86_64 x86_64
% 0.25/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.51 % Memory : 8046.5625MB
% 0.25/0.51 % OS : Linux 6.8.0-71-generic
% 0.25/0.51 % CPULimit : 300
% 0.25/0.51 % WCLimit : 300
% 0.25/0.51 % DateTime : Sat Sep 26 08:44:21 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.38/1.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.66 % [INFO] Parsing done (275ms).
% 1.85/1.68 % [INFO] Running in sequential loop mode.
% 2.85/2.28 % [INFO] eprover registered as external prover.
% 2.85/2.29 % [INFO] Scanning for conjecture ...
% 3.23/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.37/2.50 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.37/2.54 % [INFO] Problem is first-order (TPTP FOF).
% 3.37/2.55 % [INFO] Type checking passed.
% 3.37/2.55 % [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 ...
% 5.42/3.49 % External prover 'e' found a proof!
% 5.42/3.49 % [INFO] Killing All external provers ...
% 5.42/3.49 % Time passed: 2766ms (effective reasoning time: 1793ms)
% 5.42/3.49 % 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)>
% 5.42/3.49 % Axioms used in derivation (11): fc1_zfmisc_1, d5_tarski, t8_zfmisc_1, t9_zfmisc_1, commutativity_k2_tarski, t69_enumset1, reflexivity_r1_tarski, t6_zfmisc_1, rc1_xboole_0, t10_zfmisc_1, rc2_xboole_0
% 5.42/3.49 % No. of inferences in proof: 26
% 5.42/3.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2766 ms resp. 1793 ms w/o parsing
% 5.78/3.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.78/3.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------