%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n016.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 3.55s 2.32s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 5 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 111 ( 9 ~; 2 |; 3 &; 88 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 28 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ singleton @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ singleton @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(14,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(21,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)],[6]) ).
thf(4,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(16,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ singleton @ ( D @ cartesian_product2 ) @ ( A @ singleton @ ( C @ cartesian_product2 ) @ disjoint ) )
& ( D @ ( B @ singleton @ cartesian_product2 ) @ ( C @ ( A @ singleton @ cartesian_product2 ) @ disjoint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ singleton @ ( D @ cartesian_product2 ) @ ( A @ singleton @ ( C @ cartesian_product2 ) @ disjoint ) )
& ( D @ ( B @ singleton @ cartesian_product2 ) @ ( C @ ( A @ singleton @ cartesian_product2 ) @ disjoint ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ singleton @ ( D @ cartesian_product2 ) @ ( A @ singleton @ ( C @ cartesian_product2 ) @ disjoint ) )
& ( D @ ( B @ singleton @ cartesian_product2 ) @ ( C @ ( A @ singleton @ cartesian_product2 ) @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[25,14,21,16,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.15/0.40 % Computer : n016.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 08:33:47 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.19 % [INFO] Parsing done (187ms).
% 1.42/1.20 % [INFO] Running in sequential loop mode.
% 2.03/1.61 % [INFO] eprover registered as external prover.
% 2.03/1.62 % [INFO] Scanning for conjecture ...
% 2.21/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.21/1.76 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.21/1.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.78 % [INFO] Type checking passed.
% 2.21/1.79 % [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 ...
% 3.55/2.32 % External prover 'e' found a proof!
% 3.55/2.32 % [INFO] Killing All external provers ...
% 3.55/2.32 % Time passed: 1769ms (effective reasoning time: 1112ms)
% 3.55/2.32 % 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)>
% 3.55/2.32 % Axioms used in derivation (5): t17_zfmisc_1, symmetry_r1_xboole_0, rc2_xboole_0, t127_zfmisc_1, rc1_xboole_0
% 3.55/2.32 % No. of inferences in proof: 14
% 3.55/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1769 ms resp. 1112 ms w/o parsing
% 3.55/2.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.55/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------