%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET557^1 : 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 : n013.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 08:22:56 AM UTC 2026
% Result : Theorem 7.06s 3.55s
% Output : Refutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 30 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 58 ( 15 ~; 4 |; 0 &; 39 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 5 ^; 15 !; 9 ?; 31 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i > $i > $o ).
thf(sk2_decl,type,
sk2: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $o] :
@+[B: $i] :
( ( sk1 @ B )
= A ) ) ) ).
thf(1,conjecture,
~ ? [A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjectiveCantorThm) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
! [A: $i > $o] :
( ( sk1 @ ( sk2 @ A ) )
= A ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [A: $i > $o] :
( ( sk1 @ ( sk2 @ A ) )
= A ),
inference(lifteq,[status(thm)],[5]) ).
thf(7,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ ( sk2 @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[6]) ).
thf(8,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk1 @ ( sk2 @ A ) @ B )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(21,plain,
! [A: $i] :
( ~ ( sk1
@ ( sk2
@ ^ [B: $i] : $false )
@ A )
| $false ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(43,plain,
! [A: $i] :
~ ( sk1
@ ( sk2
@ ^ [B: $i] : $false )
@ A ),
inference(simp,[status(thm)],[21]) ).
thf(19,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk1 @ ( sk2 @ A ) @ B )
| ( ( A @ B )
!= ( ~ ( sk1 @ ( sk2 @ A ) @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(36,plain,
~ ( sk1
@ ( sk2
@ ^ [A: $i] :
~ ( sk1 @ A @ A ) )
@ ( sk2
@ ^ [A: $i] :
~ ( sk1 @ A @ A ) ) ),
inference(pre_uni,[status(thm)],[19:[bind(A,$thf( ^ [C: $i] : ~ ( sk1 @ C @ C ) )),bind(B,$thf( sk2 @ ^ [C: $i] : ~ ( sk1 @ C @ C ) ))]]) ).
thf(97,plain,
$false,
inference(e,[status(thm)],[6,7,3,43,8,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET557^1 : 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
% 0.13/0.23 % Computer : n013.cluster.edu
% 0.13/0.23 % Model : x86_64 x86_64
% 0.13/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.23 % Memory : 8046.5625MB
% 0.13/0.23 % OS : Linux 6.8.0-71-generic
% 0.13/0.24 % CPULimit : 300
% 0.13/0.24 % WCLimit : 300
% 0.13/0.24 % DateTime : Tue Sep 29 13:37:06 UTC 2026
% 0.13/0.24 % CPUTime :
% 0.13/0.24 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
% 1.15/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.21 % [INFO] Parsing done (243ms).
% 1.65/1.23 % [INFO] Running in sequential loop mode.
% 2.37/1.71 % [INFO] eprover registered as external prover.
% 2.37/1.72 % [INFO] Scanning for conjecture ...
% 2.54/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.54/1.86 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.54/1.86 % [INFO] Problem is higher-order (TPTP THF).
% 2.54/1.87 % [INFO] Type checking passed.
% 2.54/1.87 % [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 ...
% 7.06/3.54 % External prover 'e' found a proof!
% 7.06/3.54 % [INFO] Killing All external provers ...
% 7.06/3.54 % Time passed: 3107ms (effective reasoning time: 2301ms)
% 7.06/3.54 % 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)>
% 7.06/3.54 % Axioms used in derivation (0):
% 7.06/3.54 % No. of inferences in proof: 13
% 7.06/3.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3107 ms resp. 2301 ms w/o parsing
% 7.41/3.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.41/3.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------