%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO179^5 : 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 : n004.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 08:45:20 AM UTC 2026
% Result : Theorem 4.27s 2.39s
% Output : Refutation 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 0 equ; 0 cnn)
% Maximal formula atoms : 36 ( 27 avg)
% Number of connectives : 323 ( 2 ~; 48 |; 54 &; 216 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 0 !; 18 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(cG_decl,type,
cG: $i > $i > $o ).
thf(cR_decl,type,
cR: $i > $i > $o ).
thf(cF_decl,type,
cF: $i ).
thf(cE_decl,type,
cE: $i ).
thf(cD_decl,type,
cD: $i ).
thf(cC_decl,type,
cC: $i ).
thf(cB_decl,type,
cB: $i ).
thf(cA_decl,type,
cA: $i ).
thf(1,conjecture,
( ( ( ( cR @ cA @ cB )
| ( cG @ cA @ cB ) )
& ( ( cR @ cA @ cC )
| ( cG @ cA @ cC ) )
& ( ( cR @ cA @ cD )
| ( cG @ cA @ cD ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cR @ cA @ cF )
| ( cG @ cA @ cF ) )
& ( ( cR @ cB @ cC )
| ( cG @ cB @ cC ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cE )
| ( cG @ cB @ cE ) )
& ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cC @ cD )
| ( cG @ cC @ cD ) )
& ( ( cR @ cC @ cE )
| ( cG @ cC @ cE ) )
& ( ( cR @ cC @ cF )
| ( cG @ cC @ cF ) )
& ( ( cR @ cD @ cE )
| ( cG @ cD @ cE ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cR @ cE @ cF )
| ( cG @ cE @ cF ) ) )
=> ( ? [A: $i,B: $i,C: $i] :
( ( cR @ A @ B )
& ( cR @ A @ C )
& ( cR @ B @ C ) )
| ? [A: $i,B: $i,C: $i] :
( ( cG @ A @ B )
& ( cG @ A @ C )
& ( cG @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSIX_THEOREM_B) ).
thf(2,negated_conjecture,
~ ( ( ( ( cR @ cA @ cB )
| ( cG @ cA @ cB ) )
& ( ( cR @ cA @ cC )
| ( cG @ cA @ cC ) )
& ( ( cR @ cA @ cD )
| ( cG @ cA @ cD ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cR @ cA @ cF )
| ( cG @ cA @ cF ) )
& ( ( cR @ cB @ cC )
| ( cG @ cB @ cC ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cE )
| ( cG @ cB @ cE ) )
& ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cC @ cD )
| ( cG @ cC @ cD ) )
& ( ( cR @ cC @ cE )
| ( cG @ cC @ cE ) )
& ( ( cR @ cC @ cF )
| ( cG @ cC @ cF ) )
& ( ( cR @ cD @ cE )
| ( cG @ cD @ cE ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cR @ cE @ cF )
| ( cG @ cE @ cF ) ) )
=> ( ? [A: $i,B: $i,C: $i] :
( ( cR @ A @ B )
& ( cR @ A @ C )
& ( cR @ B @ C ) )
| ? [A: $i,B: $i,C: $i] :
( ( cG @ A @ B )
& ( cG @ A @ C )
& ( cG @ B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( ( cR @ cA @ cB )
| ( cG @ cA @ cB ) )
& ( ( cR @ cA @ cC )
| ( cG @ cA @ cC ) )
& ( ( cR @ cA @ cD )
| ( cG @ cA @ cD ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cR @ cA @ cF )
| ( cG @ cA @ cF ) )
& ( ( cR @ cB @ cC )
| ( cG @ cB @ cC ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cE )
| ( cG @ cB @ cE ) )
& ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cC @ cD )
| ( cG @ cC @ cD ) )
& ( ( cR @ cC @ cE )
| ( cG @ cC @ cE ) )
& ( ( cR @ cC @ cF )
| ( cG @ cC @ cF ) )
& ( ( cR @ cD @ cE )
| ( cG @ cD @ cE ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cR @ cE @ cF )
| ( cG @ cE @ cF ) ) )
=> ( ? [A: $i,B: $i,C: $i] :
( ( cR @ A @ B )
& ( cR @ A @ C )
& ( cR @ B @ C ) )
| ? [A: $i,B: $i,C: $i] :
( ( cG @ A @ B )
& ( cG @ A @ C )
& ( cG @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(77,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO179^5 : 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
% 0.11/0.22 % Computer : n004.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 16:37:07 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (200ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 2.05/1.42 % [INFO] eprover registered as external prover.
% 2.05/1.43 % [INFO] Scanning for conjecture ...
% 2.25/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.45/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.45/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.45/1.60 % [INFO] Type checking passed.
% 2.45/1.61 % [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 ...
% 4.27/2.39 % External prover 'e' found a proof!
% 4.27/2.39 % [INFO] Killing All external provers ...
% 4.27/2.39 % Time passed: 2026ms (effective reasoning time: 1373ms)
% 4.27/2.39 % 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)>
% 4.27/2.39 % Axioms used in derivation (0):
% 4.27/2.39 % No. of inferences in proof: 4
% 4.27/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2026 ms resp. 1373 ms w/o parsing
% 4.56/2.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.56/2.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------