%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU787_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : Sun Sep 27 08:40:18 AM UTC 2026
% Result : Theorem 3.53s 2.38s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 2 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 154 ( 2 ~; 2 |; 0 &; 110 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(binunion_decl,type,
binunion: $i > $i > $i ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(breln1_decl,type,
breln1: $i > $i > $o ).
thf(breln1unionE_decl,type,
breln1unionE: $o ).
thf(1,conjecture,
( breln1unionE
=> ! [A: $i,B: $i] :
( ( B @ ( A @ breln1 ) )
=> ! [C: $i] :
( ( C @ ( A @ breln1 ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ ( E @ in ) )
=> ( ( C @ ( B @ binunion ) @ ( E @ ( D @ kpair ) @ in ) )
=> ! [F: $o] :
( ( ( B @ ( E @ ( D @ kpair ) @ in ) )
=> F )
=> ( ( ( C @ ( E @ ( D @ kpair ) @ in ) )
=> F )
=> F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionEcases) ).
thf(2,negated_conjecture,
~ ( breln1unionE
=> ! [A: $i,B: $i] :
( ( B @ ( A @ breln1 ) )
=> ! [C: $i] :
( ( C @ ( A @ breln1 ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ ( E @ in ) )
=> ( ( C @ ( B @ binunion ) @ ( E @ ( D @ kpair ) @ in ) )
=> ! [F: $o] :
( ( ( B @ ( E @ ( D @ kpair ) @ in ) )
=> F )
=> ( ( ( C @ ( E @ ( D @ kpair ) @ in ) )
=> F )
=> F ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( breln1unionE
=> ! [A: $i,B: $i] :
( ( B @ ( A @ breln1 ) )
=> ! [C: $i] :
( ( C @ ( A @ breln1 ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ ( E @ in ) )
=> ( ( C @ ( B @ binunion ) @ ( E @ ( D @ kpair ) @ in ) )
=> ! [F: $o] :
( ( ( B @ ( E @ ( D @ kpair ) @ in ) )
=> F )
=> ( ( ( C @ ( E @ ( D @ kpair ) @ in ) )
=> F )
=> F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( breln1unionE
= ( ! [A: $i,B: $i] :
( ( B @ ( A @ breln1 ) )
=> ! [C: $i] :
( ( C @ ( A @ breln1 ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ ( E @ in ) )
=> ( ( C @ ( B @ binunion ) @ ( E @ ( D @ kpair ) @ in ) )
=> ( ( C @ ( E @ ( D @ kpair ) @ in ) )
| ( B @ ( E @ ( D @ kpair ) @ in ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionE) ).
thf(15,plain,
( breln1unionE
= ( ! [A: $i,B: $i] :
( ( B @ ( A @ breln1 ) )
=> ! [C: $i] :
( ( C @ ( A @ breln1 ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ ( E @ in ) )
=> ( ( C @ ( B @ binunion ) @ ( E @ ( D @ kpair ) @ in ) )
=> ( ( C @ ( E @ ( D @ kpair ) @ in ) )
| ( B @ ( E @ ( D @ kpair ) @ in ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[4,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU787_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.09 % 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
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 10:29:17 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.83/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.19 % [INFO] Parsing done (188ms).
% 1.36/1.21 % [INFO] Running in sequential loop mode.
% 2.02/1.61 % [INFO] eprover registered as external prover.
% 2.02/1.62 % [INFO] Scanning for conjecture ...
% 2.22/1.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.22/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.40/1.80 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.40/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.81 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.40/1.81 % [INFO] Type checking passed.
% 2.40/1.82 % [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 ...
% 3.53/2.37 % External prover 'e' found a proof!
% 3.53/2.37 % [INFO] Killing All external provers ...
% 3.53/2.37 % Time passed: 1816ms (effective reasoning time: 1161ms)
% 3.53/2.37 % 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)>
% 3.53/2.37 % Axioms used in derivation (1): breln1unionE
% 3.53/2.37 % No. of inferences in proof: 6
% 3.53/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1816 ms resp. 1161 ms w/o parsing
% 3.79/2.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.79/2.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------