%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO317^5 : TPTP v9.3.1. Released v4.0.0.
% 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 08:45:35 AM UTC 2026
% Result : Theorem 4.35s 2.49s
% Output : Refutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 45 ( 9 equ; 3 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 146 ( 12 ~; 8 |; 20 &; 93 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 1 ^; 31 !; 6 ?; 39 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cP_decl,type,
cP: $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(cEQ_decl,type,
cEQ: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ ( f @ B ) )
=> ( cP @ B ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i] : ( cEQ @ A @ A )
& ! [A: $i,B: $i] :
( ( ( cEQ @ A @ B )
& ( cP @ A ) )
=> ( cP @ B ) )
& ( cP @ a )
& ! [A: $i,B: $i] :
( ( cEQ @ ( f @ A ) @ ( f @ B ) )
=> ( cEQ @ A @ B ) ) )
=> ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ ( f @ B ) )
=> ( cP @ B ) )
& ? [B: $i] : ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM304) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] : ( cEQ @ A @ A )
& ! [A: $i,B: $i] :
( ( ( cEQ @ A @ B )
& ( cP @ A ) )
=> ( cP @ B ) )
& ( cP @ a )
& ! [A: $i,B: $i] :
( ( cEQ @ ( f @ A ) @ ( f @ B ) )
=> ( cEQ @ A @ B ) ) )
=> ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ ( f @ B ) )
=> ( cP @ B ) )
& ? [B: $i] : ( A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] : ( cEQ @ A @ A )
& ! [A: $i,B: $i] :
( ( ( cEQ @ A @ B )
& ( cP @ A ) )
=> ( cP @ B ) )
& ( cP @ a )
& ! [A: $i,B: $i] :
( ( cEQ @ ( f @ A ) @ ( f @ B ) )
=> ( cEQ @ A @ B ) ) )
=> ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ ( f @ B ) )
=> ( cP @ B ) )
& ? [B: $i] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( cEQ @ A @ A )
& ( ~ ( cEQ @ B @ C )
| ~ ( cP @ B )
| ( cP @ C ) )
& ( cP @ a )
& ( ~ ( cEQ @ ( f @ D ) @ ( f @ E ) )
| ( cEQ @ D @ E ) )
& ( ( F @ ( f @ ( sk1 @ F ) ) )
| ~ ( F @ G ) )
& ( ~ ( cP @ ( sk1 @ F ) )
| ~ ( F @ G ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [B: $i,A: $i > $o] :
( ( A @ ( f @ ( sk1 @ A ) ) )
| ~ ( A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: $i] :
( ( A
= ( f @ ( sk1 @ ( (=) @ $i @ A ) ) ) )
| ( A != A ) ),
inference(replace_leibeq,[status(thm)],[7:[bind(A,$thf( (=) @ $i @ B ))]]) ).
thf(15,plain,
! [A: $i] :
( ( A
= ( f @ ( sk1 @ ( (=) @ $i @ A ) ) ) )
| ( A != A ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(16,plain,
! [A: $i] :
( A
= ( f @ ( sk1 @ ( (=) @ $i @ A ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(5,plain,
! [A: $i] : ( cEQ @ A @ A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
cP @ a,
inference(cnfConj,[status(thm)],[4]) ).
thf(59,plain,
$false,
inference(e,[status(thm)],[3,16,5,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO317^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.21 % Computer : n009.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:45:15 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.06/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (191ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 2.06/1.43 % [INFO] eprover registered as external prover.
% 2.06/1.44 % [INFO] Scanning for conjecture ...
% 2.24/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.58 % [INFO] Type checking passed.
% 2.24/1.59 % [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 ...
% 4.35/2.49 % External prover 'e' found a proof!
% 4.35/2.49 % [INFO] Killing All external provers ...
% 4.35/2.49 % Time passed: 2127ms (effective reasoning time: 1471ms)
% 4.35/2.49 % 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)>
% 4.35/2.49 % Axioms used in derivation (0):
% 4.35/2.49 % No. of inferences in proof: 11
% 4.35/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2127 ms resp. 1471 ms w/o parsing
% 4.58/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.58/2.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------