%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% 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 : n007.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 08:00:09 AM UTC 2026
% Result : Unsatisfiable 4.66s 2.68s
% Output : Refutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 186 ( 10 ~; 10 |; 0 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i > $i ).
thf(t_decl,type,
t: $i ).
thf(tsk_decl,type,
tsk: $i ).
thf(tt_ts_decl,type,
tt_ts: $i ).
thf(tk_decl,type,
tk: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(a_decl,type,
a: $i > $i > $i ).
thf(critical_point_decl,type,
critical_point: $i > $i ).
thf(k_decl,type,
k: $i ).
thf(ts_decl,type,
ts: $i ).
thf(sk_decl,type,
sk: $i ).
thf(s_decl,type,
s: $i ).
thf(ttk_decl,type,
ttk: $i ).
thf(tt_decl,type,
tt: $i ).
thf(stk_decl,type,
stk: $i ).
thf(st_decl,type,
st: $i ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( A @ f ) )
= ( C @ ( A @ f ) @ ( B @ ( A @ f ) @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( A @ f ) )
= ( C @ ( A @ f ) @ ( B @ ( A @ f ) @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
( ts
= ( s @ ( t @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(52,plain,
( ts
= ( s @ ( t @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
( stk
= ( k @ ( st @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
thf(61,plain,
( stk
= ( k @ ( st @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ a ) @ ( A @ less ) )
| ( B @ critical_point @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ a ) @ ( A @ less ) )
| ( B @ critical_point @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
( sk
= ( k @ ( s @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
thf(44,plain,
( sk
= ( k @ ( s @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
( tk
= ( k @ ( t @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
thf(54,plain,
( tk
= ( k @ ( t @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ f ) @ a ) )
= B )
| ( ( B @ ( A @ a ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ f ) @ a ) )
= B )
| ( ( B @ ( A @ a ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f ) @ critical_point )
= ( B @ critical_point @ ( A @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f ) @ critical_point )
= ( B @ critical_point @ ( A @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ a ) @ ( A @ a ) )
= ( C @ ( A @ a ) @ ( B @ ( A @ f ) @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1a) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ a ) @ ( A @ a ) )
= ( C @ ( A @ a ) @ ( B @ ( A @ f ) @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
thf(24,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
( ttk
= ( k @ ( tt @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
thf(46,plain,
( ttk
= ( k @ ( tt @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ a ) @ ( A @ ( C @ a ) @ less ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b4) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ a ) @ ( A @ ( C @ a ) @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
( k
= ( t @ critical_point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(38,plain,
( k
= ( t @ critical_point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( tsk @ ( t @ f ) )
!= ( tk @ ( tt_ts @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(21,plain,
( ( tsk @ ( t @ f ) )
!= ( tk @ ( tt_ts @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
( tt
= ( t @ ( t @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
thf(48,plain,
( tt
= ( t @ ( t @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
( st
= ( t @ ( s @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(63,plain,
( st
= ( t @ ( s @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
( tt_ts
= ( ts @ ( tt @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(50,plain,
( tt_ts
= ( ts @ ( tt @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ a ) )
= A )
| ~ ( B @ critical_point @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ a ) )
= A )
| ~ ( B @ critical_point @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
( tsk
= ( k @ ( ts @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
thf(40,plain,
( tsk
= ( k @ ( ts @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ a ) @ ( A @ less ) )
| ( A
= ( A @ ( B @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ a ) @ ( A @ less ) )
| ( A
= ( A @ ( B @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(104,plain,
$false,
inference(e,[status(thm)],[56,52,61,34,44,54,58,36,42,24,46,29,38,21,48,63,50,31,40,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.12 % 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
% 0.26/0.51 % Computer : n007.cluster.edu
% 0.26/0.51 % Model : x86_64 x86_64
% 0.26/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.51 % Memory : 8046.5625MB
% 0.26/0.51 % OS : Linux 6.8.0-71-generic
% 0.26/0.51 % CPULimit : 300
% 0.26/0.51 % WCLimit : 300
% 0.26/0.51 % DateTime : Fri Sep 25 23:53:55 UTC 2026
% 0.26/0.51 % CPUTime :
% 0.26/0.51 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
% 1.17/1.09 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.60/1.39 % [INFO] Parsing done (290ms).
% 1.81/1.41 % [INFO] Running in sequential loop mode.
% 2.41/1.86 % [INFO] eprover registered as external prover.
% 2.41/1.87 % [INFO] Scanning for conjecture ...
% 2.63/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.63/2.02 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.93/2.05 % [INFO] Problem is propositional (TPTP CNF).
% 2.93/2.05 % [INFO] Type checking passed.
% 2.93/2.06 % [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 ...
% 4.66/2.67 % External prover 'e' found a proof!
% 4.66/2.67 % [INFO] Killing All external provers ...
% 4.66/2.67 % Time passed: 2027ms (effective reasoning time: 1255ms)
% 4.66/2.68 % Axioms used in derivation (19): clause_2, clause_1, clause_8, b4, clause_9, clause_6, a1, clause_3, a2, c3, clause_5, a1a, c2, b1, c1, clause_7, clause_10, clause_4, d2
% 4.66/2.68 % No. of inferences in proof: 41
% 4.66/2.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2027 ms resp. 1255 ms w/o parsing
% 5.18/2.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.18/2.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------