%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU614^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n008.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 08:28:46 AM UTC 2026
% Result : Theorem 4.07s 2.47s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 93 ( 7 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 359 ( 62 ~; 45 |; 11 &; 212 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 44 !; 0 ?; 47 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(symdiff_decl,type,
symdiff: $i > $i > $i ).
thf(symdiffE_decl,type,
symdiffE: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(symdiffE_def,definition,
( symdiffE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( symdiff @ A @ B ) )
=> ! [D: $o] :
( ( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> D ) )
=> ( ( ~ ( in @ C @ A )
=> ( ( in @ C @ B )
=> D ) )
=> D ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ~ ( in @ C @ ( symdiff @ A @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ B @ sk1 )
=> ( ( in @ B @ A )
=> ~ ( in @ B @ ( symdiff @ sk1 @ A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( in @ A @ sk1 )
=> ( ( in @ A @ sk2 )
=> ~ ( in @ A @ ( symdiff @ sk1 @ sk2 ) ) ) ) ) ) ).
thf(1,conjecture,
( symdiffE
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ~ ( in @ C @ ( symdiff @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(2,negated_conjecture,
~ ( symdiffE
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ~ ( in @ C @ ( symdiff @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( symdiff @ A @ B ) )
=> ! [D: $o] :
( ( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> D ) )
=> ( ( ~ ( in @ C @ A )
=> ( ( in @ C @ B )
=> D ) )
=> D ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ~ ( in @ C @ ( symdiff @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ( in @ C @ A )
| ~ ( in @ C @ A )
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ( in @ C @ A )
| ~ D
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ ( in @ C @ B )
| ~ ( in @ C @ A )
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ ( in @ C @ B )
| ( in @ C @ B )
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ ( in @ C @ B )
| ~ D
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ D
| ~ ( in @ C @ A )
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ D
| ( in @ C @ B )
| D )
& ( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ D
| ~ D
| D )
& ( in @ sk3 @ sk1 )
& ( in @ sk3 @ sk2 )
& ( in @ sk3 @ ( symdiff @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
in @ sk3 @ ( symdiff @ sk1 @ sk2 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ ( in @ C @ B )
| ~ ( in @ C @ A )
| D ),
inference(cnfConj,[status(thm)],[4]) ).
thf(54,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( symdiff @ A @ B ) )
| ~ ( in @ C @ B )
| ~ ( in @ C @ A )
| ( D
!= ( ~ ( in @ C @ ( symdiff @ A @ B ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( symdiff @ B @ C ) )
| ~ ( in @ A @ C )
| ~ ( in @ A @ B ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( F )),bind(D,$thf( ~ ( in @ F @ ( symdiff @ H @ I ) ) ))]]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( symdiff @ B @ C ) )
| ~ ( in @ A @ C )
| ~ ( in @ A @ B ) ),
inference(simp,[status(thm)],[68]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( in @ A @ C )
| ~ ( in @ A @ B )
| ( ( in @ sk3 @ ( symdiff @ sk1 @ sk2 ) )
!= ( in @ A @ ( symdiff @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,75]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ A @ B )
| ( ( in @ sk3 @ ( symdiff @ sk1 @ sk2 ) )
!= ( in @ A @ ( symdiff @ B @ C ) ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
( ~ ( in @ sk3 @ sk2 )
| ~ ( in @ sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(9,plain,
in @ sk3 @ sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
in @ sk3 @ sk1,
inference(cnfConj,[status(thm)],[4]) ).
thf(137,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[96,9,12]) ).
thf(138,plain,
$false,
inference(simp,[status(thm)],[137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU614^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:58:54 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (185ms).
% 1.19/0.99 % [INFO] Running in sequential loop mode.
% 1.77/1.38 % [INFO] eprover registered as external prover.
% 1.77/1.39 % [INFO] Scanning for conjecture ...
% 1.93/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.11/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.11/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.53 % [INFO] Type checking passed.
% 2.11/1.54 % [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 ...
% 4.07/2.46 % [INFO] Killing All external provers ...
% 4.07/2.47 % Time passed: 2124ms (effective reasoning time: 1472ms)
% 4.07/2.47 % 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)>
% 4.07/2.47 % Axioms used in derivation (0):
% 4.07/2.47 % No. of inferences in proof: 16
% 4.07/2.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2124 ms resp. 1472 ms w/o parsing
% 4.37/2.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.37/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------