%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU995^5 : 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 : n002.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 08:29:41 AM UTC 2026
% Result : Theorem 4.11s 2.06s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 67 ( 17 ~; 1 |; 1 &; 44 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 1 ^; 29 !; 3 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(cV_decl,type,
cV: $i ).
thf(cU_decl,type,
cU: $i ).
thf(1,conjecture,
( ( cU != cV )
=> ? [A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
~ ! [B: $i > $i,C: $i > $i] :
( ( A @ B @ C )
= ( A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM24_pme) ).
thf(2,negated_conjecture,
~ ( ( cU != cV )
=> ? [A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
~ ! [B: $i > $i,C: $i > $i] :
( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( cU != cV )
=> ? [A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
~ ! [B: $i > $i,C: $i > $i] :
( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( cU != cV )
=> ~ ! [A: ( $i > $i ) > ( $i > $i ) > $i > $i,B: $i > $i,C: $i > $i] :
( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [C: $i > $i,B: $i > $i,A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
( ( cU != cV )
& ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [C: $i > $i,B: $i > $i,A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
( ( A @ B @ C )
= ( A @ C @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
! [C: $i > $i,B: $i > $i,A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
( ( A @ B @ C )
= ( A @ C @ B ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
! [D: $i,C: $i > $i,B: $i > $i,A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
( ( A @ B @ C @ D )
= ( A @ C @ B @ D ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(6,plain,
cU != cV,
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
cU != cV,
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [D: $i,C: $i > $i,B: $i > $i,A: ( $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( A @ C @ B @ D )
!= cV )
| ( ( A @ B @ C @ D )
!= cU ) ),
inference(paramod_ordered,[status(thm)],[10,8]) ).
thf(16,plain,
! [C: ( $i > $i ) > ( $i > $i ) > $i > $i,B: $i,A: $i > $i] :
( ( A
@ ( C
@ ^ [D: $i] : cU
@ A
@ B ) )
!= cV ),
inference(pre_uni,[status(thm)],[11:[bind(A,$thf( ^ [F: $i > $i] : ^ [G: $i > $i] : ^ [H: $i] : ( G @ ( F @ F @ G @ H ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: $i] : cU ))]]) ).
thf(22,plain,
$false,
inference(pre_uni,[status(thm)],[16:[bind(A,$thf( ^ [D: $i] : D )),bind(B,$thf( A )),bind(C,$thf( ^ [D: $i > $i] : ^ [E: $i > $i] : ^ [F: $i] : cV ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU995^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8046.5625MB
% 0.11/0.31 % OS : Linux 6.8.0-71-generic
% 0.11/0.31 % CPULimit : 300
% 0.30/0.31 % WCLimit : 300
% 0.30/0.31 % DateTime : Tue Sep 29 14:58:37 UTC 2026
% 0.30/0.31 % CPUTime :
% 0.30/0.31 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
% 1.00/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/0.91 % [INFO] Parsing done (142ms).
% 1.43/0.92 % [INFO] Running in sequential loop mode.
% 1.94/1.29 % [INFO] eprover registered as external prover.
% 2.16/1.30 % [INFO] Scanning for conjecture ...
% 2.32/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.32/1.47 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.32/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 2.32/1.48 % [INFO] Type checking passed.
% 2.32/1.49 % [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 ...
% 4.11/2.05 % [INFO] Killing All external provers ...
% 4.11/2.05 % Time passed: 1611ms (effective reasoning time: 1128ms)
% 4.11/2.05 % 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)>
% 4.11/2.06 % Axioms used in derivation (0):
% 4.11/2.06 % No. of inferences in proof: 13
% 4.11/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1611 ms resp. 1128 ms w/o parsing
% 4.11/2.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.11/2.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------