%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n003.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 09:16:30 AM UTC 2026
% Result : Unsatisfiable 4.85s 3.15s
% Output : Refutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 56 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 204 ( 38 ~; 66 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(m_decl,type,
m: $i ).
thf(n_decl,type,
n: $i ).
thf(k_decl,type,
k: $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(g_decl,type,
g: $i > $i ).
thf(10,negated_conjecture,
! [A: $i] :
( ( ( A @ g )
!= A )
| ( n @ ( A @ element ) )
| ( A = n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
thf(18,plain,
! [A: $i] :
( ( ( A @ g )
!= A )
| ( n @ ( A @ element ) )
| ( A = n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ( ( A @ f )
!= m )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
thf(31,plain,
! [A: $i] :
( ( ( A @ f )
!= m )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
n != k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
thf(24,plain,
n != k,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ g @ element ) )
| ( n @ ( A @ element ) )
| ( A = n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( A @ g @ element ) )
| ( n @ ( A @ element ) )
| ( A = n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
m != n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_1) ).
thf(20,plain,
m != n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,negated_conjecture,
! [A: $i] :
( ( A @ g @ ( A @ element ) )
| ( n @ ( A @ element ) )
| ( A = n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
thf(29,plain,
! [A: $i] :
( ( A @ g @ ( A @ element ) )
| ( n @ ( A @ element ) )
| ( A = n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,negated_conjecture,
! [A: $i] :
( ~ ( k @ ( A @ element ) )
| ( A = n )
| ( A = m )
| ( A = k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
thf(28,plain,
! [A: $i] :
( ~ ( k @ ( A @ element ) )
| ( A = n )
| ( A = m )
| ( A = k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ( A @ f @ ( A @ element ) )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
thf(21,plain,
! [A: $i] :
( ( A @ f @ ( A @ element ) )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,negated_conjecture,
! [A: $i] :
( ( k @ ( A @ element ) )
| ( A != n )
| ( A = k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
thf(32,plain,
! [A: $i] :
( ( k @ ( A @ element ) )
| ( A != n )
| ( A = k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ( ( A @ f )
!= A )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
thf(17,plain,
! [A: $i] :
( ( ( A @ f )
!= A )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ( ( A @ g )
!= n )
| ( n @ ( A @ element ) )
| ( A = n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
thf(22,plain,
! [A: $i] :
( ( ( A @ g )
!= n )
| ( n @ ( A @ element ) )
| ( A = n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
k != m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
thf(27,plain,
k != m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ f @ element ) )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( A @ f @ element ) )
| ~ ( m @ ( A @ element ) )
| ( A = m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) )
| ( B = A )
| ( B = n )
| ~ ( n @ ( A @ element ) )
| ( A = n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) )
| ( B = A )
| ( B = n )
| ~ ( n @ ( A @ element ) )
| ( A = n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) )
| ( B = A )
| ( B = m )
| ( m @ ( A @ element ) )
| ( A = m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) )
| ( B = A )
| ( B = m )
| ( m @ ( A @ element ) )
| ( A = m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,negated_conjecture,
! [A: $i] :
( ( k @ ( A @ element ) )
| ( A != m )
| ( A = k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
thf(19,plain,
! [A: $i] :
( ( k @ ( A @ element ) )
| ( A != m )
| ( A = k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[18,31,24,25,20,29,28,21,32,17,22,27,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.14/0.53 % Computer : n003.cluster.edu
% 0.14/0.53 % Model : x86_64 x86_64
% 0.14/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.53 % Memory : 8046.5625MB
% 0.14/0.53 % OS : Linux 6.8.0-71-generic
% 0.14/0.54 % CPULimit : 300
% 0.14/0.54 % WCLimit : 300
% 0.14/0.54 % DateTime : Sat Sep 26 17:05:54 UTC 2026
% 0.14/0.54 % CPUTime :
% 0.14/0.54 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
% 1.09/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.47 % [INFO] Parsing done (266ms).
% 1.41/1.49 % [INFO] Running in sequential loop mode.
% 2.53/2.06 % [INFO] eprover registered as external prover.
% 2.53/2.07 % [INFO] Scanning for conjecture ...
% 2.82/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.00/2.33 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.00/2.33 % [INFO] Problem is propositional (TPTP CNF).
% 3.00/2.33 % [INFO] Type checking passed.
% 3.00/2.34 % [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 ...
% 4.85/3.15 % External prover 'e' found a proof!
% 4.85/3.15 % [INFO] Killing All external provers ...
% 4.85/3.15 % Time passed: 2475ms (effective reasoning time: 1647ms)
% 4.85/3.15 % Axioms used in derivation (0):
% 4.85/3.15 % No. of inferences in proof: 33
% 4.85/3.15 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2475 ms resp. 1647 ms w/o parsing
% 5.25/3.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.25/3.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------