%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET741^4 : TPTP v9.3.1. Released v3.6.0.
% 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 : n010.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 4.30s 2.36s
% Output : Refutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 28 ( 14 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 70 ( 2 ~; 0 |; 8 &; 54 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-3 aty)
% Number of variables : 29 ( 6 ^; 19 !; 4 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(fun_composition_decl,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(fun_injective_decl,type,
fun_injective: ( $i > $i ) > $o ).
thf(fun_surjective_decl,type,
fun_surjective: ( $i > $i ) > $o ).
thf(fun_bijective_decl,type,
fun_bijective: ( $i > $i ) > $o ).
thf(fun_composition_def,definition,
( fun_composition
= ( ^ [A: $i > $i,B: $i > $i,C: $i] : ( B @ ( A @ C ) ) ) ) ).
thf(fun_injective_def,definition,
( fun_injective
= ( ^ [A: $i > $i] :
! [B: $i,C: $i] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ) ).
thf(fun_surjective_def,definition,
( fun_surjective
= ( ^ [A: $i > $i] :
! [B: $i] :
? [C: $i] :
( B
= ( A @ C ) ) ) ) ).
thf(fun_bijective_def,definition,
( fun_bijective
= ( ^ [A: $i > $i] :
( ( fun_injective @ A )
& ( fun_surjective @ A ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i,B: $i > $i,C: $i > $i] :
( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ A @ B ) @ C ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ B @ C ) @ A ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ C @ A ) @ B ) ) )
=> ( fun_bijective @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i,B: $i > $i,C: $i > $i] :
( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ A @ B ) @ C ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ B @ C ) @ A ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ C @ A ) @ B ) ) )
=> ( fun_bijective @ C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i,B: $i > $i,C: $i > $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( B @ ( A @ D ) ) )
= ( C @ ( B @ ( A @ E ) ) ) )
=> ( D = E ) )
& ! [D: $i] :
? [E: $i] :
( D
= ( A @ ( C @ ( B @ E ) ) ) )
& ! [D: $i] :
? [E: $i] :
( D
= ( B @ ( A @ ( C @ E ) ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( ( C @ D )
= ( C @ E ) )
=> ( D = E ) )
& ! [D: $i] :
? [E: $i] :
( D
= ( C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET741^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n010.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:41:18 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.04/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.07 % [INFO] Parsing done (235ms).
% 1.46/1.08 % [INFO] Running in sequential loop mode.
% 2.30/1.55 % [INFO] eprover registered as external prover.
% 2.30/1.56 % [INFO] Scanning for conjecture ...
% 2.54/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.78/1.71 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.78/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 2.78/1.72 % [INFO] Type checking passed.
% 2.78/1.72 % [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 ...
% 4.30/2.36 % External prover 'e' found a proof!
% 4.30/2.36 % [INFO] Killing All external provers ...
% 4.30/2.36 % Time passed: 1991ms (effective reasoning time: 1265ms)
% 4.30/2.36 % 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)>
% 4.30/2.36 % Axioms used in derivation (0):
% 4.30/2.36 % No. of inferences in proof: 4
% 4.30/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1991 ms resp. 1265 ms w/o parsing
% 4.57/2.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.57/2.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------