%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET931+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 : n005.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 08:31:22 AM UTC 2026
% Result : Theorem 3.22s 1.81s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 37 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 159 ( 39 ~; 0 |; 24 &; 86 @)
% ( 4 <=>; 6 =>; 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; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 26 !; 4 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $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] :
( ( ( C @ ( B @ unordered_pair ) @ ( A @ set_difference ) )
= empty_set )
<=> ~ ( ( A
!= ( C @ ( B @ unordered_pair ) ) )
& ( A
!= ( C @ singleton ) )
& ( A
!= ( B @ singleton ) )
& ( A != empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ unordered_pair ) @ ( A @ set_difference ) )
= empty_set )
<=> ~ ( ( A
!= ( C @ ( B @ unordered_pair ) ) )
& ( A
!= ( C @ singleton ) )
& ( A
!= ( B @ singleton ) )
& ( A != empty_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ unordered_pair ) ) )
& ( A
!= ( C @ singleton ) )
& ( A
!= ( B @ singleton ) )
& ( A != empty_set ) )
=> ( ( C @ ( B @ unordered_pair ) @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( C @ ( B @ unordered_pair ) @ ( A @ set_difference ) )
= empty_set )
=> ~ ( ( A
!= ( C @ ( B @ unordered_pair ) ) )
& ( A
!= ( C @ singleton ) )
& ( A
!= ( B @ singleton ) )
& ( A != empty_set ) ) ) ),
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(53,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(27,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(48,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(30,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(50,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ subset ) )
<=> ~ ( ( A
!= ( C @ ( B @ unordered_pair ) ) )
& ( A
!= ( C @ singleton ) )
& ( A
!= ( B @ singleton ) )
& ( A != empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ unordered_pair ) ) )
& ( A
!= ( C @ singleton ) )
& ( A
!= ( B @ singleton ) )
& ( A != empty_set ) )
=> ( C @ ( B @ unordered_pair ) @ ( A @ subset ) ) )
& ( ( C @ ( B @ unordered_pair ) @ ( A @ subset ) )
=> ~ ( ( A
!= ( C @ ( B @ unordered_pair ) ) )
& ( A
!= ( C @ singleton ) )
& ( A
!= ( B @ singleton ) )
& ( A != empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(69,plain,
$false,
inference(e,[status(thm)],[10,53,27,48,55,30,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET931+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
% 0.14/0.38 % Computer : n005.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sat Sep 26 08:26:17 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.74/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.97/0.80 % [INFO] Parsing done (96ms).
% 0.97/0.81 % [INFO] Running in sequential loop mode.
% 1.14/1.01 % [INFO] eprover registered as external prover.
% 1.14/1.02 % [INFO] Scanning for conjecture ...
% 1.46/1.07 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.46/1.09 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.46/1.10 % [INFO] Problem is first-order (TPTP FOF).
% 1.46/1.10 % [INFO] Type checking passed.
% 1.46/1.11 % [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 ...
% 3.22/1.81 % External prover 'e' found a proof!
% 3.22/1.81 % [INFO] Killing All external provers ...
% 3.22/1.81 % Time passed: 1321ms (effective reasoning time: 997ms)
% 3.22/1.81 % 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)>
% 3.22/1.81 % Axioms used in derivation (7): fc1_xboole_0, l46_zfmisc_1, t37_xboole_1, commutativity_k2_tarski, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0
% 3.22/1.81 % No. of inferences in proof: 18
% 3.22/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1321 ms resp. 997 ms w/o parsing
% 3.22/1.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.22/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------