%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET724^4 : TPTP v9.3.1. Released v3.6.0.
% 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 08:23:07 AM UTC 2026
% Result : Theorem 4.09s 2.38s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 16 unt; 0 typ; 6 def)
% Number of atoms : 44 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 90 ( 15 ~; 2 |; 8 &; 59 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 24 ^; 20 !; 5 ?; 53 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(fun_composition_decl,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(fun_surjective_decl,type,
fun_surjective: ( $i > $i ) > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(fun_composition_def,definition,
( fun_composition
= ( ^ [A: $i > $i,B: $i > $i,C: $i] : ( B @ ( A @ C ) ) ) ) ).
thf(fun_surjective_def,definition,
( fun_surjective
= ( ^ [A: $i > $i] :
! [B: $i] :
? [C: $i] :
( B
= ( A @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
~ ! [B: $i > $i,C: $i > $i] :
( ( ( ( ^ [D: $i] : ( B @ ( A @ D ) ) )
= ( ^ [D: $i] : ( C @ ( A @ D ) ) ) )
& ! [D: $i] :
? [E: $i] :
( D
= ( A @ E ) ) )
=> ( B = C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
~ ! [B: $i > $i] :
( ( ( ( ^ [C: $i] : ( A @ ( sk1 @ C ) ) )
= ( ^ [C: $i] : ( B @ ( sk1 @ C ) ) ) )
& ! [C: $i] :
? [D: $i] :
( C
= ( sk1 @ D ) ) )
=> ( A = B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i] :
~ ( ( ( ( ^ [B: $i] : ( sk2 @ ( sk1 @ B ) ) )
= ( ^ [B: $i] : ( A @ ( sk1 @ B ) ) ) )
& ! [B: $i] :
? [C: $i] :
( B
= ( sk1 @ C ) ) )
=> ( sk2 = A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( sk1 @ B ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i,B: $i > $i,C: $i > $i] :
( ( ( ( fun_composition @ A @ B )
= ( fun_composition @ A @ C ) )
& ( fun_surjective @ A ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i,B: $i > $i,C: $i > $i] :
( ( ( ( fun_composition @ A @ B )
= ( fun_composition @ A @ C ) )
& ( fun_surjective @ A ) )
=> ( B = C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i,B: $i > $i,C: $i > $i] :
( ( ( ( ^ [D: $i] : ( B @ ( A @ D ) ) )
= ( ^ [D: $i] : ( C @ ( A @ D ) ) ) )
& ! [D: $i] :
? [E: $i] :
( D
= ( A @ E ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( sk2 @ ( sk1 @ B ) ) )
= ( ^ [B: $i] : ( sk3 @ ( sk1 @ B ) ) ) )
& ( A
= ( sk1 @ ( sk4 @ A ) ) )
& ( sk2 != sk3 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
sk2 != sk3,
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
sk3 != sk2,
inference(lifteq,[status(thm)],[7]) ).
thf(6,plain,
! [A: $i] :
( A
= ( sk1 @ ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ( sk1 @ ( sk4 @ A ) )
= A ),
inference(lifteq,[status(thm)],[6]) ).
thf(5,plain,
( ( ^ [A: $i] : ( sk2 @ ( sk1 @ A ) ) )
= ( ^ [A: $i] : ( sk3 @ ( sk1 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( ^ [A: $i] : ( sk3 @ ( sk1 @ A ) ) )
= ( ^ [A: $i] : ( sk2 @ ( sk1 @ A ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(13,plain,
( ( ( ^ [A: $i] : ( sk2 @ ( sk1 @ A ) ) )
!= sk2 )
| ( ( ^ [A: $i] : ( sk3 @ ( sk1 @ A ) ) )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[8,10]) ).
thf(16,plain,
( ( sk1
!= ( ^ [A: $i] : A ) )
| ( sk1
!= ( ^ [A: $i] : A ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(17,plain,
( sk1
!= ( ^ [A: $i] : A ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
( ( sk1 @ sk6 )
!= sk6 ),
inference(func_ext,[status(esa)],[17]) ).
thf(11,plain,
( ( sk3 @ sk5 )
!= ( sk2 @ sk5 ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[10,9,17,3,18,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET724^4 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.11/0.22 % Computer : n008.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 13:41:24 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.88/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.00 % [INFO] Parsing done (203ms).
% 1.19/1.02 % [INFO] Running in sequential loop mode.
% 2.06/1.41 % [INFO] eprover registered as external prover.
% 2.06/1.42 % [INFO] Scanning for conjecture ...
% 2.23/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.57 % [INFO] Type checking passed.
% 2.23/1.58 % [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 ...
% 4.09/2.38 % External prover 'e' found a proof!
% 4.09/2.38 % [INFO] Killing All external provers ...
% 4.09/2.38 % Time passed: 2027ms (effective reasoning time: 1357ms)
% 4.09/2.38 % 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)>
% 4.09/2.38 % Axioms used in derivation (0):
% 4.09/2.38 % No. of inferences in proof: 16
% 4.09/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2027 ms resp. 1357 ms w/o parsing
% 4.37/2.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.37/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------