%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n010.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 09:16:31 AM UTC 2026
% Result : Unsatisfiable 4.23s 2.55s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 53 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 444 ( 60 ~; 88 |; 0 &; 296 @)
% ( 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 : 9 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_decl,type,
element: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(k_decl,type,
k: $i ).
thf(f_decl,type,
f: $i > $i ).
thf(m_decl,type,
m: $i ).
thf(g_decl,type,
g: $i > $i ).
thf(n_decl,type,
n: $i ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetryish) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,negated_conjecture,
~ ( k @ ( n @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_20) ).
thf(41,plain,
~ ( k @ ( n @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element ) )
| ~ ( A @ ( C @ element ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitutionish1) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element ) )
| ~ ( A @ ( C @ element ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivityish) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,negated_conjecture,
! [B: $i,A: $i] :
( ( m @ ( B @ equalish ) )
| ( m @ ( B @ element ) )
| ( m @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) )
| ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( m @ ( B @ equalish ) )
| ( m @ ( B @ element ) )
| ( m @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) )
| ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,negated_conjecture,
! [A: $i] :
( ( k @ ( A @ equalish ) )
| ( k @ ( A @ element ) )
| ~ ( m @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
thf(35,plain,
! [A: $i] :
( ( k @ ( A @ equalish ) )
| ( k @ ( A @ element ) )
| ~ ( m @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( a @ ( A @ equalish ) )
| ( k @ ( A @ equalish ) )
| ~ ( a @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_3) ).
thf(31,plain,
! [A: $i] :
( ( a @ ( A @ equalish ) )
| ( k @ ( A @ equalish ) )
| ~ ( a @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,negated_conjecture,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ( A @ ( A @ g @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
thf(43,plain,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ( A @ ( A @ g @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ~ ( m @ ( A @ f @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
thf(40,plain,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ~ ( m @ ( A @ f @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element ) )
| ~ ( C @ ( A @ equalish ) )
| ~ ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitutionish2) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element ) )
| ~ ( C @ ( A @ equalish ) )
| ~ ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(16,negated_conjecture,
~ ( a @ ( n @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_18) ).
thf(42,plain,
~ ( a @ ( n @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,negated_conjecture,
~ ( n @ ( m @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_19) ).
thf(37,plain,
~ ( n @ ( m @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ~ ( A @ ( A @ f @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_6) ).
thf(46,plain,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ~ ( A @ ( A @ f @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,negated_conjecture,
! [A: $i] :
( ( k @ ( A @ equalish ) )
| ( k @ ( A @ element ) )
| ~ ( n @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
thf(29,plain,
! [A: $i] :
( ( k @ ( A @ equalish ) )
| ( k @ ( A @ element ) )
| ~ ( n @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,negated_conjecture,
k @ ( m @ equalish ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_23) ).
thf(33,plain,
k @ ( m @ equalish ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,negated_conjecture,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ( A @ g @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
thf(28,plain,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ( A @ g @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,negated_conjecture,
! [B: $i,A: $i] :
( ( n @ ( B @ equalish ) )
| ~ ( n @ ( B @ element ) )
| ( n @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) )
| ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( n @ ( B @ equalish ) )
| ~ ( n @ ( B @ element ) )
| ( n @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) )
| ~ ( A @ ( B @ element ) )
| ~ ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,negated_conjecture,
~ ( a @ ( m @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_21) ).
thf(45,plain,
~ ( a @ ( m @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ( A @ ( A @ f @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_8) ).
thf(32,plain,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ( A @ ( A @ f @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ~ ( A @ ( A @ g @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
thf(34,plain,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ~ ( A @ ( A @ g @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,negated_conjecture,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ~ ( n @ ( A @ g @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
thf(44,plain,
! [A: $i] :
( ( n @ ( A @ equalish ) )
| ( n @ ( A @ element ) )
| ~ ( n @ ( A @ g @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ( A @ f @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_7) ).
thf(27,plain,
! [A: $i] :
( ( m @ ( A @ equalish ) )
| ~ ( m @ ( A @ element ) )
| ( A @ f @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ( a @ ( A @ equalish ) )
| ( a @ ( A @ element ) )
| ~ ( k @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_4) ).
thf(36,plain,
! [A: $i] :
( ( a @ ( A @ equalish ) )
| ( a @ ( A @ element ) )
| ~ ( k @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,negated_conjecture,
~ ( a @ ( k @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_22) ).
thf(30,plain,
~ ( a @ ( k @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,negated_conjecture,
! [A: $i] :
( ( k @ ( A @ equalish ) )
| ( m @ ( A @ equalish ) )
| ( n @ ( A @ equalish ) )
| ~ ( k @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).
thf(47,plain,
! [A: $i] :
( ( k @ ( A @ equalish ) )
| ( m @ ( A @ equalish ) )
| ( n @ ( A @ equalish ) )
| ~ ( k @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivityish) ).
thf(68,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(81,plain,
$false,
inference(e,[status(thm)],[69,41,73,71,39,35,31,43,40,75,42,37,46,29,33,28,38,45,32,34,44,27,36,30,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.14/0.39 % Computer : n010.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 17:05:00 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.19 % [INFO] Parsing done (203ms).
% 1.43/1.20 % [INFO] Running in sequential loop mode.
% 2.12/1.62 % [INFO] eprover registered as external prover.
% 2.12/1.63 % [INFO] Scanning for conjecture ...
% 2.30/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.48/1.83 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.48/1.84 % [INFO] Problem is propositional (TPTP CNF).
% 2.48/1.84 % [INFO] Type checking passed.
% 2.48/1.85 % [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 ...
% 4.23/2.55 % External prover 'e' found a proof!
% 4.23/2.55 % [INFO] Killing All external provers ...
% 4.23/2.55 % Time passed: 2009ms (effective reasoning time: 1339ms)
% 4.23/2.55 % Axioms used in derivation (5): transitivityish, element_substitutionish1, symmetryish, reflexivityish, element_substitutionish2
% 4.23/2.55 % No. of inferences in proof: 53
% 4.23/2.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2009 ms resp. 1339 ms w/o parsing
% 4.63/2.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.63/2.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------