%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU709^2 : 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 : n014.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 08:29:05 AM UTC 2026
% Result : Theorem 2.84s 1.21s
% Output : Refutation 2.84s
% 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 : 56 ( 15 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 143 ( 4 ~; 0 |; 0 &; 102 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-4 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(setadjoinIL_decl,type,
setadjoinIL: $o ).
thf(in__Cong_decl,type,
in__Cong: $o ).
thf(secondinupair_decl,type,
secondinupair: $o ).
thf(if_decl,type,
if: $i > $o > $i > $i > $i ).
thf(iftrue_decl,type,
iftrue: $o ).
thf(iffalse_decl,type,
iffalse: $o ).
thf(setadjoinIL_def,definition,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(secondinupair_def,definition,
( secondinupair
= ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(iftrue_def,definition,
( iftrue
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( if @ A @ B @ C @ D )
= C ) ) ) ) ) ) ).
thf(iffalse_def,definition,
( iffalse
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ B
=> ( ( if @ A @ B @ C @ D )
= D ) ) ) ) ) ) ).
thf(1,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(2,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( if @ A @ B @ C @ D )
= C ) ) ) )
=> ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ B
=> ( ( if @ A @ B @ C @ D )
= D ) ) ) )
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU709^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % 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
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:12:59 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 0.69/0.47 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.57 % [INFO] Parsing done (101ms).
% 0.94/0.58 % [INFO] Running in sequential loop mode.
% 1.27/0.76 % [INFO] eprover registered as external prover.
% 1.27/0.77 % [INFO] Scanning for conjecture ...
% 1.52/0.83 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.52/0.85 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.52/0.85 % [INFO] Problem is higher-order (TPTP THF).
% 1.52/0.85 % [INFO] Type checking passed.
% 1.52/0.85 % [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 ...
% 2.84/1.21 % External prover 'e' found a proof!
% 2.84/1.21 % [INFO] Killing All external provers ...
% 2.84/1.21 % Time passed: 951ms (effective reasoning time: 631ms)
% 2.84/1.21 % 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)>
% 2.84/1.21 % Axioms used in derivation (0):
% 2.84/1.21 % No. of inferences in proof: 4
% 2.84/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 951 ms resp. 631 ms w/o parsing
% 2.84/1.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.84/1.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------