%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO227^5 : 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 : n005.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 08:45:26 AM UTC 2026
% Result : Theorem 4.38s 2.40s
% Output : Refutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 24 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 136 ( 34 ~; 16 |; 12 &; 65 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 21 !; 3 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_decl,type,
c: $i ).
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(c_less__decl,type,
c_less_: $i > $i > $o ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( c_less_ @ A @ B )
=> ( A != B ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE4_W_AX) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( c_less_ @ A @ B )
=> ( A != B ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( c_less_ @ A @ B )
=> ( A != B ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [A: $i > $o] :
( ~ ( A @ a )
& ( A @ b )
& ~ ( A @ c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( ~ ( c_less_ @ A @ B )
| ( A != B ) )
& ( c_less_ @ a @ b )
& ( c_less_ @ b @ c )
& ( ( C @ a )
| ~ ( C @ b )
| ( C @ c ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [A: $i > $o] :
( ( A @ a )
| ~ ( A @ b )
| ( A @ c ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ( b = a )
| ( b != b )
| ( b = c ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (=) @ $i @ b ))]]) ).
thf(12,plain,
( ( a = b )
| ( b != b )
| ( b = c ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(13,plain,
( ( a = b )
| ( b = c ) ),
inference(simp,[status(thm)],[12]) ).
thf(6,plain,
c_less_ @ a @ b,
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( c_less_ @ A @ B )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( c_less_ @ A @ B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(11,plain,
! [A: $i] :
~ ( c_less_ @ A @ A ),
inference(simp,[status(thm)],[10]) ).
thf(15,plain,
! [A: $i] :
( ~ $true
| ( ( c_less_ @ a @ b )
!= ( c_less_ @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,11]) ).
thf(16,plain,
! [A: $i] :
( ( c_less_ @ a @ b )
!= ( c_less_ @ A @ A ) ),
inference(simp,[status(thm)],[15]) ).
thf(19,plain,
! [A: $i] :
( ( a != A )
| ( b != A ) ),
inference(simp,[status(thm)],[16]) ).
thf(21,plain,
a != b,
inference(simp,[status(thm)],[19]) ).
thf(7,plain,
c_less_ @ b @ c,
inference(cnfConj,[status(thm)],[4]) ).
thf(17,plain,
! [A: $i] :
( ~ $true
| ( ( c_less_ @ b @ c )
!= ( c_less_ @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,11]) ).
thf(18,plain,
! [A: $i] :
( ( c_less_ @ b @ c )
!= ( c_less_ @ A @ A ) ),
inference(simp,[status(thm)],[17]) ).
thf(20,plain,
! [A: $i] :
( ( b != A )
| ( c != A ) ),
inference(simp,[status(thm)],[18]) ).
thf(22,plain,
b != c,
inference(simp,[status(thm)],[20]) ).
thf(80,plain,
$false,
inference(simplifyReflect,[status(thm)],[13,21,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO227^5 : 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
% 0.09/0.21 % Computer : n005.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:40:01 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.91/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.99 % [INFO] Parsing done (191ms).
% 1.26/1.00 % [INFO] Running in sequential loop mode.
% 2.05/1.41 % [INFO] eprover registered as external prover.
% 2.05/1.42 % [INFO] Scanning for conjecture ...
% 2.24/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.55 % [INFO] Type checking passed.
% 2.24/1.56 % [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 ...
% 4.13/2.39 % [INFO] Killing All external provers ...
% 4.38/2.40 % Time passed: 2033ms (effective reasoning time: 1385ms)
% 4.38/2.40 % 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)>
% 4.38/2.40 % Axioms used in derivation (0):
% 4.38/2.40 % No. of inferences in proof: 22
% 4.38/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2033 ms resp. 1385 ms w/o parsing
% 4.38/2.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.38/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------