%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET887+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 : 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 08:31:16 AM UTC 2026
% Result : Theorem 6.27s 8.62s
% Output : Refutation 6.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 46 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 190 ( 39 ~; 5 |; 24 &; 104 @)
% ( 4 <=>; 14 =>; 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 : 61 ( 0 ^; 57 !; 4 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(88,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ unordered_pair ) @ ( B @ ( A @ unordered_pair ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ unordered_pair ) @ ( B @ ( A @ unordered_pair ) @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ unordered_pair ) @ ( B @ ( A @ unordered_pair ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
thf(64,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)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(86,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(81,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(63,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(83,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(27,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ( ( A = empty_set )
=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(96,plain,
$false,
inference(e,[status(thm)],[88,24,14,92,64,86,81,63,36,83,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.22/5.48 % Computer : n010.cluster.edu
% 0.22/5.48 % Model : x86_64 x86_64
% 0.22/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.48 % Memory : 8046.5625MB
% 0.22/5.48 % OS : Linux 6.8.0-71-generic
% 0.22/5.48 % CPULimit : 300
% 0.22/5.48 % WCLimit : 300
% 0.22/5.48 % DateTime : Sat Sep 26 08:25:06 UTC 2026
% 0.22/5.49 % CPUTime :
% 0.22/5.49 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
% 1.45/6.32 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.01/6.61 % [INFO] Parsing done (289ms).
% 2.01/6.64 % [INFO] Running in sequential loop mode.
% 3.01/7.26 % [INFO] eprover registered as external prover.
% 3.01/7.27 % [INFO] Scanning for conjecture ...
% 3.40/7.42 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.40/7.47 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.58/7.51 % [INFO] Problem is first-order (TPTP FOF).
% 3.58/7.52 % [INFO] Type checking passed.
% 3.58/7.53 % [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 ...
% 6.27/8.62 % External prover 'e' found a proof!
% 6.27/8.62 % [INFO] Killing All external provers ...
% 6.27/8.62 % Time passed: 2928ms (effective reasoning time: 1975ms)
% 6.27/8.62 % 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)>
% 6.27/8.62 % Axioms used in derivation (11): fc1_xboole_0, l46_zfmisc_1, d2_tarski, d1_xboole_0, t8_zfmisc_1, commutativity_k2_tarski, reflexivity_r1_tarski, rc1_xboole_0, t10_zfmisc_1, rc2_xboole_0, antisymmetry_r2_hidden
% 6.27/8.62 % No. of inferences in proof: 26
% 6.27/8.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2928 ms resp. 1975 ms w/o parsing
% 6.51/8.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.51/8.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------