%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET872+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 : n009.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 08:31:14 AM UTC 2026
% Result : Theorem 3.68s 8.32s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 23 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 128 ( 6 ~; 5 |; 7 &; 86 @)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 40 !; 4 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(8,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(74,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(13,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ singleton @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ singleton @ subset ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ singleton @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(79,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
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/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(15,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(76,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(39,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(81,plain,
$false,
inference(e,[status(thm)],[74,13,66,18,11,79,15,76,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET872+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/5.49 % Computer : n009.cluster.edu
% 0.16/5.49 % Model : x86_64 x86_64
% 0.16/5.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.49 % Memory : 8046.5625MB
% 0.16/5.49 % OS : Linux 6.8.0-71-generic
% 0.16/5.49 % CPULimit : 300
% 0.16/5.49 % WCLimit : 300
% 0.16/5.49 % DateTime : Sat Sep 26 08:23:34 UTC 2026
% 0.16/5.50 % CPUTime :
% 0.19/5.50 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
% 0.93/6.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/6.60 % [INFO] Parsing done (280ms).
% 1.30/6.62 % [INFO] Running in sequential loop mode.
% 1.90/7.20 % [INFO] eprover registered as external prover.
% 1.94/7.21 % [INFO] Scanning for conjecture ...
% 2.08/7.35 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.19/7.40 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.19/7.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/7.44 % [INFO] Type checking passed.
% 2.19/7.45 % [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 ...
% 3.68/8.32 % External prover 'e' found a proof!
% 3.68/8.32 % [INFO] Killing All external provers ...
% 3.68/8.32 % Time passed: 2571ms (effective reasoning time: 1693ms)
% 3.68/8.32 % 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)>
% 3.68/8.32 % Axioms used in derivation (8): d1_tarski, d2_tarski, commutativity_k2_tarski, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, d3_tarski, reflexivity_r1_tarski
% 3.68/8.32 % No. of inferences in proof: 20
% 3.68/8.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2571 ms resp. 1693 ms w/o parsing
% 3.81/8.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.81/8.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------