%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU918^5 : 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 : n018.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 08:29:35 AM UTC 2026
% Result : Theorem 3.17s 2.06s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 11 ~; 0 |; 1 &; 28 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 12 ^; 15 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(1,conjecture,
( ( a != b )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ( ^ [C: $i] : ( A @ ( B @ C ) ) )
= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM197_pme) ).
thf(2,negated_conjecture,
~ ( ( a != b )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ( ^ [C: $i] : ( A @ ( B @ C ) ) )
= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( a != b )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ( ^ [C: $i] : ( A @ ( B @ C ) ) )
= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $i,A: $i > $i] :
( ( a != b )
& ( ( ^ [C: $i] : ( A @ ( B @ C ) ) )
= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
a != b,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
a != b,
inference(lifteq,[status(thm)],[5]) ).
thf(6,plain,
! [B: $i > $i,A: $i > $i] :
( ( ^ [C: $i] : ( A @ ( B @ C ) ) )
= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [B: $i > $i,A: $i > $i] :
( ( ^ [C: $i] : ( A @ ( B @ C ) ) )
= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
! [C: $i,B: $i > $i,A: $i > $i] :
( ( A @ ( B @ C ) )
= ( B @ ( A @ C ) ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(10,plain,
$false,
inference(simplifyReflect,[status(thm)],[7,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU918^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n018.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 14:48:11 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 ...
% 1.16/0.95 % [INFO] Parsing done (183ms).
% 1.16/0.96 % [INFO] Running in sequential loop mode.
% 1.72/1.35 % [INFO] eprover registered as external prover.
% 1.72/1.36 % [INFO] Scanning for conjecture ...
% 1.90/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.90/1.47 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.90/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.48 % [INFO] Type checking passed.
% 1.90/1.48 % [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 ...
% 3.17/2.05 % [INFO] Killing All external provers ...
% 3.17/2.06 % Time passed: 1715ms (effective reasoning time: 1084ms)
% 3.17/2.06 % 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)>
% 3.17/2.06 % Axioms used in derivation (0):
% 3.17/2.06 % No. of inferences in proof: 10
% 3.17/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1715 ms resp. 1084 ms w/o parsing
% 3.17/2.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.17/2.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------