%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LDA007-3 : 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 : n020.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 3.09s 2.24s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 50 ( 2 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 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(tt_decl,type,
tt: $i ).
thf(ts_decl,type,
ts: $i ).
thf(s_decl,type,
s: $i ).
thf(k_decl,type,
k: $i ).
thf(7,axiom,
( tsk
= ( k @ ( ts @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(21,plain,
( tsk
= ( k @ ( ts @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
( tt
= ( t @ ( t @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(13,plain,
( tt
= ( t @ ( t @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
( tt_ts
= ( ts @ ( tt @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(17,plain,
( tt_ts
= ( ts @ ( tt @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( A @ f ) )
= ( C @ ( A @ f ) @ ( B @ ( A @ f ) @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(11,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)],[2]) ).
thf(1,negated_conjecture,
( ( tsk @ ( t @ f ) )
!= ( tk @ ( tt_ts @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(8,plain,
( ( tsk @ ( t @ f ) )
!= ( tk @ ( tt_ts @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
( tk
= ( k @ ( t @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(19,plain,
( tk
= ( k @ ( t @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
( ts
= ( s @ ( t @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(15,plain,
( ts
= ( s @ ( t @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
$false,
inference(e,[status(thm)],[21,13,17,11,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA007-3 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 23:56:49 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.15 % [INFO] Parsing done (182ms).
% 1.22/1.17 % [INFO] Running in sequential loop mode.
% 1.72/1.56 % [INFO] eprover registered as external prover.
% 1.72/1.57 % [INFO] Scanning for conjecture ...
% 1.90/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.90/1.69 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.90/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.06/1.70 % [INFO] Type checking passed.
% 2.06/1.71 % [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 ...
% 3.09/2.23 % External prover 'e' found a proof!
% 3.09/2.23 % [INFO] Killing All external provers ...
% 3.09/2.23 % Time passed: 1700ms (effective reasoning time: 1057ms)
% 3.09/2.24 % Axioms used in derivation (6): clause_5, clause_2, clause_1, clause_4, a1, clause_3
% 3.09/2.24 % No. of inferences in proof: 15
% 3.09/2.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1700 ms resp. 1057 ms w/o parsing
% 3.09/2.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.09/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------