%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET974+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 : n003.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 6.27s 8.74s
% Output : Refutation 6.50s
% 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 : 48 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 192 ( 20 ~; 3 |; 12 &; 150 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 0 ^; 59 !; 6 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ disjoint ) )
| ( B @ ( A @ disjoint ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ disjoint ) )
| ( B @ ( A @ disjoint ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ disjoint ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ disjoint ) )
| ( B @ ( A @ disjoint ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(49,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(35,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(18,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ set_intersection2 ) @ ( G @ in ) )
& ( D @ ( B @ set_intersection2 ) @ ( F @ in ) )
& ( A
= ( G @ ( F @ ordered_pair ) ) ) )
& ( E @ ( D @ cartesian_product2 ) @ ( C @ ( B @ cartesian_product2 ) @ set_intersection2 ) @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(42,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ set_intersection2 ) @ ( G @ in ) )
& ( D @ ( B @ set_intersection2 ) @ ( F @ in ) )
& ( A
= ( G @ ( F @ ordered_pair ) ) ) )
& ( E @ ( D @ cartesian_product2 ) @ ( C @ ( B @ cartesian_product2 ) @ set_intersection2 ) @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(37,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(29,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(26,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(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(58,plain,
$false,
inference(e,[status(thm)],[14,32,49,35,18,42,37,20,29,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET974+1 : 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
% 0.25/5.53 % Computer : n003.cluster.edu
% 0.25/5.53 % Model : x86_64 x86_64
% 0.25/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/5.53 % Memory : 8046.5625MB
% 0.25/5.53 % OS : Linux 6.8.0-71-generic
% 0.25/5.53 % CPULimit : 300
% 0.25/5.53 % WCLimit : 300
% 0.25/5.53 % DateTime : Sat Sep 26 08:30:14 UTC 2026
% 0.25/5.53 % CPUTime :
% 0.25/5.53 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
% 1.39/6.41 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.12/6.70 % [INFO] Parsing done (288ms).
% 2.12/6.72 % [INFO] Running in sequential loop mode.
% 3.08/7.35 % [INFO] eprover registered as external prover.
% 3.08/7.36 % [INFO] Scanning for conjecture ...
% 3.51/7.51 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.51/7.57 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.68/7.62 % [INFO] Problem is first-order (TPTP FOF).
% 3.68/7.63 % [INFO] Type checking passed.
% 3.68/7.64 % [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 ...
% 6.27/8.73 % External prover 'e' found a proof!
% 6.27/8.73 % [INFO] Killing All external provers ...
% 6.27/8.73 % Time passed: 2990ms (effective reasoning time: 1997ms)
% 6.27/8.73 % 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)>
% 6.27/8.74 % Axioms used in derivation (11): fc1_zfmisc_1, idempotence_k3_xboole_0, d5_tarski, commutativity_k3_xboole_0, t4_xboole_0, t104_zfmisc_1, commutativity_k2_tarski, rc1_xboole_0, symmetry_r1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 6.27/8.74 % No. of inferences in proof: 26
% 6.27/8.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2990 ms resp. 1997 ms w/o parsing
% 6.50/8.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.50/8.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------