%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ROB021-1 : 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 : 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 08:26:47 AM UTC 2026
% Result : Unsatisfiable 5.28s 3.26s
% Output : Refutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 76 ( 4 ~; 2 |; 0 &; 70 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(add_decl,type,
add: $i > $i > $i ).
thf(negate_decl,type,
negate: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(1,negated_conjecture,
( ( b @ negate @ ( a @ negate @ add ) @ negate @ ( b @ negate @ ( a @ add ) @ negate @ add ) )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
thf(6,plain,
( ( b @ negate @ ( a @ negate @ add ) @ negate @ ( b @ negate @ ( a @ add ) @ negate @ add ) )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ negate )
!= ( B @ negate ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',negative_equality_implies_positive_equality) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ negate )
!= ( B @ negate ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[6,9,13,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ROB021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.20/0.47 % Computer : n009.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.48 % WCLimit : 300
% 0.20/0.48 % DateTime : Sat Sep 26 06:16:16 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 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
% 1.44/1.33 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.98/1.61 % [INFO] Parsing done (272ms).
% 1.98/1.63 % [INFO] Running in sequential loop mode.
% 2.96/2.25 % [INFO] eprover registered as external prover.
% 2.96/2.26 % [INFO] Scanning for conjecture ...
% 3.17/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.35/2.42 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.35/2.44 % [INFO] Problem is propositional (TPTP CNF).
% 3.35/2.45 % [INFO] Type checking passed.
% 3.35/2.46 % [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 ...
% 5.28/3.25 % External prover 'e' found a proof!
% 5.28/3.25 % [INFO] Killing All external provers ...
% 5.28/3.25 % Time passed: 2562ms (effective reasoning time: 1610ms)
% 5.28/3.25 % Axioms used in derivation (4): commutativity_of_add, robbins_axiom, associativity_of_add, negative_equality_implies_positive_equality
% 5.28/3.25 % No. of inferences in proof: 11
% 5.28/3.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2562 ms resp. 1610 ms w/o parsing
% 5.52/3.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.52/3.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------