%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LDA002-1 : 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 : n015.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 08:00:08 AM UTC 2026
% Result : Unsatisfiable 3.35s 1.80s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 74 ( 2 ~; 0 |; 0 &; 72 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(v_decl,type,
v: $i ).
thf(b_decl,type,
b: $i ).
thf(n2_decl,type,
n2: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n3_decl,type,
n3: $i ).
thf(u_decl,type,
u: $i ).
thf(u1_decl,type,
u1: $i ).
thf(u2_decl,type,
u2: $i ).
thf(u3_decl,type,
u3: $i ).
thf(uu_decl,type,
uu: $i ).
thf(6,axiom,
( u1
= ( n1 @ ( u @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(24,plain,
( u1
= ( n1 @ ( u @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
( n3
= ( n1 @ ( n2 @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(20,plain,
( n3
= ( n1 @ ( n2 @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
( u3
= ( n3 @ ( u @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
thf(28,plain,
( u3
= ( n3 @ ( u @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( v @ ( a @ f ) )
!= ( v @ ( b @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(13,plain,
( ( v @ ( a @ f ) )
!= ( v @ ( b @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
( u
= ( n2 @ ( n2 @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(22,plain,
( u
= ( n2 @ ( n2 @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
( n2
= ( n1 @ ( n1 @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(18,plain,
( n2
= ( n1 @ ( n1 @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,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(16,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(7,axiom,
( u2
= ( n2 @ ( u @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
thf(26,plain,
( u2
= ( n2 @ ( u @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
( a
= ( u2 @ ( n2 @ ( n3 @ f ) @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
thf(32,plain,
( a
= ( u2 @ ( n2 @ ( n3 @ f ) @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
( b
= ( u3 @ ( u1 @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
thf(34,plain,
( b
= ( u3 @ ( u1 @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
( v
= ( uu @ ( uu @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
thf(36,plain,
( v
= ( uu @ ( uu @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
( uu
= ( u @ ( u @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
thf(30,plain,
( uu
= ( u @ ( u @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(104,plain,
$false,
inference(e,[status(thm)],[24,20,28,13,22,18,16,26,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 23:58:13 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.58/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.78 % [INFO] Parsing done (89ms).
% 0.71/0.79 % [INFO] Running in sequential loop mode.
% 1.11/0.98 % [INFO] eprover registered as external prover.
% 1.11/0.99 % [INFO] Scanning for conjecture ...
% 1.40/1.08 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.40/1.11 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.40/1.13 % [INFO] Problem is propositional (TPTP CNF).
% 1.57/1.13 % [INFO] Type checking passed.
% 1.57/1.14 % [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 ...
% 3.35/1.80 % External prover 'e' found a proof!
% 3.35/1.80 % [INFO] Killing All external provers ...
% 3.35/1.80 % Time passed: 1320ms (effective reasoning time: 1011ms)
% 3.35/1.80 % Axioms used in derivation (11): clause_5, clause_2, clause_8, clause_9, clause_4, clause_6, a1, clause_7, clause_10, clause_11, clause_3
% 3.35/1.80 % No. of inferences in proof: 25
% 3.35/1.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1320 ms resp. 1011 ms w/o parsing
% 3.35/1.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.35/1.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------