%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO300^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n014.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 08:45:33 AM UTC 2026
% Result : Theorem 3.16s 2.12s
% Output : Refutation 3.48s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
~ ( ! [B: ( $i > $i ) > $i] : ( A @ B @ B )
=> ? [B: ( $i > $i ) > $i] :
( A
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ) ) ) ).
thf(1,conjecture,
! [A: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [B: ( $i > $i ) > $i] :
( ! [C: ( $i > $i ) > $i] : ( A @ C @ C )
=> ( A
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUNIFTHM1) ).
thf(2,negated_conjecture,
~ ! [A: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [B: ( $i > $i ) > $i] :
( ! [C: ( $i > $i ) > $i] : ( A @ C @ C )
=> ( A
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [B: ( $i > $i ) > $i] :
( ! [C: ( $i > $i ) > $i] : ( A @ C @ C )
=> ( A
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [B: ( $i > $i ) > $i] : ( A @ B @ B )
=> ? [B: ( $i > $i ) > $i] :
( A
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [B: ( $i > $i ) > $i,A: ( $i > $i ) > $i] :
( ( sk1 @ A @ A )
& ~ ( sk1
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [A: ( $i > $i ) > $i] : ( sk1 @ A @ A ),
inference(cnfConj,[status(thm)],[5]) ).
thf(7,plain,
! [A: ( $i > $i ) > $i] :
~ ( sk1
@ ^ [B: $i > $i] :
( B
@ ( A
@ ^ [C: $i] : C ) )
@ A ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
! [A: ( $i > $i ) > $i] :
~ ( sk1
@ ^ [B: $i > $i] :
( B
@ ( A
@ ^ [C: $i] : C ) )
@ A ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
! [B: ( $i > $i ) > $i,A: ( $i > $i ) > $i] :
( ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(10,plain,
! [B: ( $i > $i ) > $i,A: ( $i > $i ) > $i] :
( ( sk1 @ A @ A )
!= ( sk1
@ ^ [C: $i > $i] :
( C
@ ( B
@ ^ [D: $i] : D ) )
@ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
! [A: ( $i > $i ) > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : C ) )
!= A ),
inference(pre_uni,[status(thm)],[10:[bind(A,$thf( ^ [D: $i > $i] : ( D @ ( C @ ^ [E: $i] : E ) ) )),bind(B,$thf( ^ [D: $i > $i] : ( D @ ( C @ D ) ) ))]]) ).
thf(12,plain,
! [A: ( $i > $i ) > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : C ) )
!= A ),
inference(pre_uni,[status(thm)],[11:[]]) ).
thf(13,plain,
! [A: ( $i > $i ) > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : C ) )
!= A ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
! [A: ( $i > $i ) > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : C ) )
!= A ),
inference(flex_uni,[status(thm)],[13:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO300^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.11/0.21 % Computer : n014.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:44:14 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (174ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.73/1.39 % [INFO] eprover registered as external prover.
% 1.91/1.40 % [INFO] Scanning for conjecture ...
% 1.91/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.53 % [INFO] Type checking passed.
% 2.09/1.53 % [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 ...
% 3.16/2.12 % [INFO] Killing All external provers ...
% 3.16/2.12 % Time passed: 1764ms (effective reasoning time: 1127ms)
% 3.16/2.12 % 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)>
% 3.16/2.12 % Axioms used in derivation (0):
% 3.16/2.12 % No. of inferences in proof: 14
% 3.16/2.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1764 ms resp. 1127 ms w/o parsing
% 3.48/2.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.48/2.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------