%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO010^1 : 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 : n009.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 08:45:00 AM UTC 2026
% Result : Theorem 3.84s 2.30s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 30 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 14 ~; 5 |; 5 &; 39 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 10 ^; 12 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq_decl,type,
leibeq: $i > $i > $o ).
thf(p_decl,type,
p: ( $i > $i ) > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(leibeq_def,definition,
( leibeq
= ( ^ [A: $i,B: $i] :
! [C: $i > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i] : ( leibeq @ ( f @ A ) @ A )
& ( p
@ ^ [A: $i] : A ) )
=> ( p @ f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] : ( leibeq @ ( f @ A ) @ A )
& ( p
@ ^ [A: $i] : A ) )
=> ( p @ f ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i,B: $i > $o] :
( ( B @ ( f @ A ) )
=> ( B @ A ) )
& ( p
@ ^ [A: $i] : A ) )
=> ( p @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i] :
( ( ~ ( B @ ( f @ A ) )
| ( B @ A ) )
& ( p
@ ^ [C: $i] : C )
& ~ ( p @ f ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( p
@ ^ [A: $i] : A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( p @ f ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ~ $true
| ( ( p @ f )
!= ( p
@ ^ [A: $i] : A ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(12,plain,
( ( p @ f )
!= ( p
@ ^ [A: $i] : A ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
( f
!= ( ^ [A: $i] : A ) ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
( ( f @ sk1 )
!= sk1 ),
inference(func_ext,[status(esa)],[13]) ).
thf(5,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( f @ A ) )
| ( B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i] :
( ( ( f @ A )
!= ( f @ A ) )
| ( ( f @ A )
= A ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ ( f @ A ) ))]]) ).
thf(9,plain,
! [A: $i] :
( ( ( f @ A )
!= ( f @ A ) )
| ( ( f @ A )
= A ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
! [A: $i] :
( ( f @ A )
= A ),
inference(simp,[status(thm)],[9]) ).
thf(63,plain,
sk1 != sk1,
inference(rewrite,[status(thm)],[14,10]) ).
thf(64,plain,
$false,
inference(simp,[status(thm)],[63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO010^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:21:15 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.85/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.95 % [INFO] Parsing done (178ms).
% 1.17/0.96 % [INFO] Running in sequential loop mode.
% 1.72/1.37 % [INFO] eprover registered as external prover.
% 1.72/1.38 % [INFO] Scanning for conjecture ...
% 1.91/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.50 % [INFO] Type checking passed.
% 2.04/1.51 % [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 ...
% 3.56/2.29 % [INFO] Killing All external provers ...
% 3.56/2.30 % Time passed: 1954ms (effective reasoning time: 1322ms)
% 3.56/2.30 % 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)>
% 3.84/2.30 % Axioms used in derivation (0):
% 3.84/2.30 % No. of inferences in proof: 16
% 3.84/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1954 ms resp. 1322 ms w/o parsing
% 3.84/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.84/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------