%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU653^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : Wed Sep 30 08:28:55 AM UTC 2026
% Result : Theorem 3.78s 2.19s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 49 ( 29 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 208 ( 2 ~; 2 |; 0 &; 176 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(secondinupair_decl,type,
secondinupair: $o ).
thf(upairset2E_decl,type,
upairset2E: $o ).
thf(setukpairinjL2_decl,type,
setukpairinjL2: $o ).
thf(setukpairinjR1_decl,type,
setukpairinjR1: $o ).
thf(upairequniteq_decl,type,
upairequniteq: $o ).
thf(secondinupair_def,definition,
( secondinupair
= ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(upairset2E_def,definition,
( upairset2E
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) ) ) ) ).
thf(setukpairinjL2_def,definition,
( setukpairinjL2
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( A = C ) ) ) ) ).
thf(setukpairinjR1_def,definition,
( setukpairinjR1
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( ( C = D )
=> ( B = D ) ) ) ) ) ).
thf(upairequniteq_def,definition,
( upairequniteq
= ( ! [A: $i,B: $i,C: $i] :
( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
= ( setadjoin @ C @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(1,conjecture,
( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( B = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(2,negated_conjecture,
~ ( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( B = D ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( A = C ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( ( C = D )
=> ( B = D ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
= ( setadjoin @ C @ emptyset ) )
=> ( A = B ) )
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( B = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU653^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:03:00 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.98 % [INFO] Parsing done (183ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.88/1.38 % [INFO] eprover registered as external prover.
% 1.88/1.39 % [INFO] Scanning for conjecture ...
% 2.32/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.32/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.32/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.32/1.57 % [INFO] Type checking passed.
% 2.32/1.58 % [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 ...
% 3.78/2.19 % External prover 'e' found a proof!
% 3.78/2.19 % [INFO] Killing All external provers ...
% 3.78/2.19 % Time passed: 1846ms (effective reasoning time: 1194ms)
% 3.78/2.19 % 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)>
% 3.78/2.19 % Axioms used in derivation (0):
% 3.78/2.19 % No. of inferences in proof: 4
% 3.78/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1846 ms resp. 1194 ms w/o parsing
% 3.96/2.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.96/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------