%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET902+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 08:31:17 AM UTC 2026
% Result : Theorem 5.55s 3.33s
% Output : Refutation 5.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 33 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 136 ( 26 ~; 3 |; 19 &; 81 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 37 !; 4 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(singleton_decl,type,
singleton: $i > $i ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $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] :
~ ( ~ ( ( C = empty_set )
& ( B
= ( A @ singleton ) ) )
& ~ ( ( C
= ( A @ singleton ) )
& ( B = empty_set ) )
& ~ ( ( C
= ( A @ singleton ) )
& ( B
= ( A @ singleton ) ) )
& ( ( A @ singleton )
= ( C @ ( B @ set_union2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = empty_set )
& ( B
= ( A @ singleton ) ) )
& ~ ( ( C
= ( A @ singleton ) )
& ( B = empty_set ) )
& ~ ( ( C
= ( A @ singleton ) )
& ( B
= ( A @ singleton ) ) )
& ( ( A @ singleton )
= ( C @ ( B @ set_union2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = empty_set )
& ( B
= ( A @ singleton ) ) )
& ~ ( ( C
= ( A @ singleton ) )
& ( B = empty_set ) )
& ~ ( ( C
= ( A @ singleton ) )
& ( B
= ( A @ singleton ) ) )
& ( ( A @ singleton )
= ( C @ ( B @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(29,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(60,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(53,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(32,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(35,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(55,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(58,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(28,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(38,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[14,29,60,53,32,35,55,58,42,25,28,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET902+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
% 0.23/0.47 % Computer : n003.cluster.edu
% 0.23/0.47 % Model : x86_64 x86_64
% 0.23/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.47 % Memory : 8046.5625MB
% 0.23/0.47 % OS : Linux 6.8.0-71-generic
% 0.23/0.47 % CPULimit : 300
% 0.23/0.47 % WCLimit : 300
% 0.23/0.47 % DateTime : Sat Sep 26 08:26:39 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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
% 1.45/1.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.80/1.58 % [INFO] Parsing done (267ms).
% 2.03/1.60 % [INFO] Running in sequential loop mode.
% 2.92/2.16 % [INFO] eprover registered as external prover.
% 2.92/2.17 % [INFO] Scanning for conjecture ...
% 3.21/2.32 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.21/2.37 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.38/2.40 % [INFO] Problem is first-order (TPTP FOF).
% 3.38/2.41 % [INFO] Type checking passed.
% 3.38/2.41 % [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 ...
% 5.55/3.32 % External prover 'e' found a proof!
% 5.55/3.32 % [INFO] Killing All external provers ...
% 5.55/3.32 % Time passed: 2636ms (effective reasoning time: 1708ms)
% 5.55/3.32 % 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)>
% 5.55/3.32 % Axioms used in derivation (11): fc1_xboole_0, fc2_xboole_0, commutativity_k2_xboole_0, fc3_xboole_0, l4_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0, l1_zfmisc_1, idempotence_k2_xboole_0, t7_xboole_1
% 5.55/3.32 % No. of inferences in proof: 26
% 5.55/3.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2636 ms resp. 1708 ms w/o parsing
% 5.55/3.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.55/3.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------