%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV001-1 : 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 : 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 08:57:54 AM UTC 2026
% Result : Unsatisfiable 3.78s 2.78s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 254 ( 44 ~; 44 |; 0 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(q1_decl,type,
q1: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(q4_decl,type,
q4: $i > $i > $i > $o ).
thf(less_or_equalish_decl,type,
less_or_equalish: $i > $i > $o ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(q2_decl,type,
q2: $i > $i > $i > $o ).
thf(q3_decl,type,
q3: $i > $i > $i > $o ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ less_or_equalish ) )
| ~ ( C @ ( A @ less_or_equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_substitution1) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ less_or_equalish ) )
| ~ ( C @ ( A @ less_or_equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ less_or_equalish ) )
| ~ ( A @ ( C @ less_or_equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_substitution2) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ less_or_equalish ) )
| ~ ( A @ ( C @ less_or_equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equalish ) )
| ( B @ ( A @ less_or_equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_less_or_equal) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equalish ) )
| ( B @ ( A @ less_or_equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less_or_equalish ) )
| ~ ( C @ ( B @ less_or_equalish ) )
| ~ ( B @ ( A @ less_or_equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_or_equal) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less_or_equalish ) )
| ~ ( C @ ( B @ less_or_equalish ) )
| ~ ( B @ ( A @ less_or_equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( a @ ( A @ less_or_equalish ) )
| ~ ( A @ ( b @ less_or_equalish ) )
| ~ ( A @ ( a @ less_or_equalish ) )
| ~ ( A @ ( b @ ( a @ q4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(16,plain,
! [A: $i] :
( ~ ( a @ ( A @ less_or_equalish ) )
| ~ ( A @ ( b @ less_or_equalish ) )
| ~ ( A @ ( a @ less_or_equalish ) )
| ~ ( A @ ( b @ ( a @ q4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ q3 ) ) )
| ( B @ ( A @ less_or_equalish ) )
| ~ ( C @ ( B @ ( A @ q1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ q3 ) ) )
| ( B @ ( A @ less_or_equalish ) )
| ~ ( C @ ( B @ ( A @ q1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ q4 ) ) )
| ~ ( C @ ( B @ ( A @ q3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ q4 ) ) )
| ~ ( C @ ( B @ ( A @ q3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
c @ ( b @ ( a @ q1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(15,plain,
c @ ( b @ ( a @ q1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ q2 ) ) )
| ~ ( B @ ( A @ less_or_equalish ) )
| ~ ( C @ ( B @ ( A @ q1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ q2 ) ) )
| ~ ( B @ ( A @ less_or_equalish ) )
| ~ ( C @ ( B @ ( A @ q1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ less_or_equalish ) )
| ( B @ ( A @ less_or_equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_less_or_equal) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ less_or_equalish ) )
| ( B @ ( A @ less_or_equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( A @ q4 ) ) )
| ~ ( C @ ( B @ ( A @ q2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( A @ q4 ) ) )
| ~ ( C @ ( B @ ( A @ q2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( A @ ( B @ less_or_equalish ) )
| ~ ( B @ ( A @ less_or_equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_implies_equal) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( A @ ( B @ less_or_equalish ) )
| ~ ( B @ ( A @ less_or_equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i] : ( A @ ( A @ less_or_equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_reflexivity) ).
thf(32,plain,
! [A: $i] : ( A @ ( A @ less_or_equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( b @ ( A @ less_or_equalish ) )
| ~ ( A @ ( b @ less_or_equalish ) )
| ~ ( A @ ( a @ less_or_equalish ) )
| ~ ( A @ ( b @ ( a @ q4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(17,plain,
! [A: $i] :
( ~ ( b @ ( A @ less_or_equalish ) )
| ~ ( A @ ( b @ less_or_equalish ) )
| ~ ( A @ ( a @ less_or_equalish ) )
| ~ ( A @ ( b @ ( a @ q4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[20,22,39,35,16,26,30,15,24,37,28,33,32,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % 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
% 0.21/0.45 % Computer : n009.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Sat Sep 26 13:04:45 UTC 2026
% 0.21/0.45 % CPUTime :
% 0.21/0.45 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
% 1.42/1.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.60 % [INFO] Parsing done (278ms).
% 1.92/1.62 % [INFO] Running in sequential loop mode.
% 2.48/2.06 % [INFO] eprover registered as external prover.
% 2.48/2.07 % [INFO] Scanning for conjecture ...
% 2.68/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.78/2.21 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.78/2.23 % [INFO] Problem is propositional (TPTP CNF).
% 2.78/2.23 % [INFO] Type checking passed.
% 2.78/2.24 % [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 ...
% 3.78/2.78 % External prover 'e' found a proof!
% 3.78/2.78 % [INFO] Killing All external provers ...
% 3.78/2.78 % Time passed: 2114ms (effective reasoning time: 1150ms)
% 3.78/2.78 % Axioms used in derivation (11): equal_implies_less_or_equal, clause_2, less_or_equal_substitution1, clause_1, less_or_equal_implies_equal, less_or_equal_substitution2, clause_4, clause_3, transitivity_of_less_or_equal, all_less_or_equal, less_or_equal_reflexivity
% 3.78/2.78 % No. of inferences in proof: 29
% 3.78/2.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2114 ms resp. 1150 ms w/o parsing
% 4.03/2.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.03/2.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------