%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 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 : n009.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 06:45:53 AM UTC 2026
% Result : Unsatisfiable 3.29s 3.01s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 124 ( 24 ~; 24 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(d2_decl,type,
d2: $i > $o ).
thf(f_decl,type,
f: $i > $i > $i ).
thf(d1_decl,type,
d1: $i > $o ).
thf(c_decl,type,
c: $i > $o ).
thf(a1_decl,type,
a1: $i ).
thf(a2_decl,type,
a2: $i ).
thf(a3_decl,type,
a3: $i ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ d2 )
| ~ ( A @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
thf(24,plain,
! [A: $i] :
( ~ ( A @ d2 )
| ~ ( A @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ d2 )
| ~ ( A @ d2 )
| ( B @ ( A @ f ) @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_3) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( B @ d2 )
| ~ ( A @ d2 )
| ( B @ ( A @ f ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
a1 @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_c_not_empty) ).
thf(28,plain,
a1 @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ d1 )
| ~ ( A @ d1 )
| ( B @ ( A @ f ) @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( B @ d1 )
| ~ ( A @ d1 )
| ( B @ ( A @ f ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ d1 )
| ~ ( A @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
thf(22,plain,
! [A: $i] :
( ~ ( A @ d1 )
| ~ ( A @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ c )
| ~ ( A @ c )
| ( B @ ( A @ f ) @ d1 )
| ( B @ ( A @ f ) @ d2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( B @ c )
| ~ ( A @ c )
| ( B @ ( A @ f ) @ d1 )
| ( B @ ( A @ f ) @ d2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( A @ f ) )
= ( C @ ( B @ ( A @ f ) @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( A @ f ) )
= ( C @ ( B @ ( A @ f ) @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ d2 )
| ~ ( A @ d1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_d1_d2) ).
thf(26,plain,
! [A: $i] :
( ~ ( A @ d2 )
| ~ ( A @ d1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
a3 @ d2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d2_not_empty) ).
thf(30,plain,
a3 @ d2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ d2 )
| ( A @ d1 )
| ( A @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
thf(20,plain,
! [A: $i] :
( ( A @ d2 )
| ( A @ d1 )
| ( A @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
a2 @ d1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d1_not_empty) ).
thf(29,plain,
a2 @ d1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[24,14,28,13,22,12,18,26,30,20,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 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
% 0.13/0.47 % Computer : n009.cluster.edu
% 0.13/0.47 % Model : x86_64 x86_64
% 0.13/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.47 % Memory : 8046.5625MB
% 0.13/0.47 % OS : Linux 6.8.0-71-generic
% 0.13/0.47 % CPULimit : 300
% 0.13/0.47 % WCLimit : 300
% 0.13/0.47 % DateTime : Sat Sep 26 20:58:15 UTC 2026
% 0.13/0.47 % CPUTime :
% 0.13/0.47 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
% 0.80/1.29 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/1.48 % [INFO] Parsing done (193ms).
% 1.11/1.50 % [INFO] Running in sequential loop mode.
% 1.62/1.87 % [INFO] eprover registered as external prover.
% 1.62/1.87 % [INFO] Scanning for conjecture ...
% 1.78/2.01 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 1.97/2.08 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.97/2.09 % [INFO] Problem is propositional (TPTP CNF).
% 1.97/2.09 % [INFO] Type checking passed.
% 1.97/2.10 % [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 ...
% 3.29/3.00 % External prover 'e' found a proof!
% 3.29/3.00 % [INFO] Killing All external provers ...
% 3.29/3.00 % Time passed: 2309ms (effective reasoning time: 1503ms)
% 3.29/3.00 % Axioms used in derivation (8): partition_c_not_empty, partitions_union, partition_d2_not_empty, partitions_exclusive_c_d1, partition_d1_not_empty, partitions_exclusive_c_d2, f_is_associative, partitions_exclusive_d1_d2
% 3.29/3.01 % No. of inferences in proof: 23
% 3.29/3.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2309 ms resp. 1503 ms w/o parsing
% 3.70/3.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.70/3.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------