%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET976+1 : 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 : n010.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 08:31:27 AM UTC 2026
% Result : Theorem 3.80s 2.47s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 16 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 156 ( 8 ~; 0 |; 12 &; 119 @)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 43 !; 4 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(60,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(53,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(50,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ singleton @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( B = D )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ singleton @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( B = D )
& ( C @ ( A @ in ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( C @ ( A @ in ) ) )
=> ( D @ singleton @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ singleton @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( B = D )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,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(47,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)],[6]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(62,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(65,plain,
$false,
inference(e,[status(thm)],[60,21,53,50,11,26,23,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET976+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n010.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 08:29:31 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.19 % [INFO] Parsing done (191ms).
% 1.41/1.20 % [INFO] Running in sequential loop mode.
% 2.01/1.61 % [INFO] eprover registered as external prover.
% 2.01/1.62 % [INFO] Scanning for conjecture ...
% 2.21/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.21/1.77 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.21/1.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.79 % [INFO] Type checking passed.
% 2.21/1.80 % [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 ...
% 3.80/2.47 % External prover 'e' found a proof!
% 3.80/2.47 % [INFO] Killing All external provers ...
% 3.80/2.47 % Time passed: 1919ms (effective reasoning time: 1258ms)
% 3.80/2.47 % 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)>
% 3.80/2.47 % Axioms used in derivation (8): d5_tarski, commutativity_k2_tarski, l55_zfmisc_1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, fc1_zfmisc_1, d1_tarski
% 3.80/2.47 % No. of inferences in proof: 20
% 3.80/2.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1919 ms resp. 1258 ms w/o parsing
% 4.07/2.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.07/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------