%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n012.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 07:20:27 AM UTC 2026
% Result : Unsatisfiable 3.23s 1.60s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 102 ( 2 ~; 0 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(identity_decl,type,
identity: $i ).
thf(left_division_decl,type,
left_division: $i > $i > $i ).
thf(right_division_decl,type,
right_division: $i > $i > $i ).
thf(right_inverse_decl,type,
right_inverse: $i > $i ).
thf(left_inverse_decl,type,
left_inverse: $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) @ right_division ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) @ right_division ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ left_division ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_division_multiply) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ left_division ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( A @ left_inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ left_inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ right_division ) @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ right_division ) @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ left_division ) @ ( A @ multiply ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_left_division) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ left_division ) @ ( A @ multiply ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( identity @ ( A @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(16,plain,
! [A: $i] :
( ( identity @ ( A @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( b @ ( c @ ( b @ ( a @ multiply ) @ multiply ) @ multiply ) )
!= ( b @ ( c @ multiply ) @ ( b @ multiply ) @ ( a @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang2) ).
thf(11,plain,
( ( b @ ( c @ ( b @ ( a @ multiply ) @ multiply ) @ multiply ) )
!= ( b @ ( c @ multiply ) @ ( b @ multiply ) @ ( a @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ right_inverse @ ( A @ multiply ) )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(26,plain,
! [A: $i] :
( ( A @ right_inverse @ ( A @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ multiply ) @ ( A @ multiply ) @ multiply ) )
= ( A @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang1) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ multiply ) @ ( A @ multiply ) @ multiply ) )
= ( A @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(319,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,22,18,16,11,26,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % 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
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Fri Sep 25 14:36:52 UTC 2026
% 0.08/0.32 % CPUTime :
% 0.08/0.32 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
% 0.38/0.60 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.50/0.68 % [INFO] Parsing done (82ms).
% 0.50/0.69 % [INFO] Running in sequential loop mode.
% 0.81/0.87 % [INFO] eprover registered as external prover.
% 0.81/0.87 % [INFO] Scanning for conjecture ...
% 0.98/0.91 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 0.98/0.92 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 0.98/0.93 % [INFO] Problem is propositional (TPTP CNF).
% 0.98/0.93 % [INFO] Type checking passed.
% 0.98/0.94 % [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 ...
% 3.23/1.60 % External prover 'e' found a proof!
% 3.23/1.60 % [INFO] Killing All external provers ...
% 3.23/1.60 % Time passed: 1200ms (effective reasoning time: 909ms)
% 3.23/1.60 % Axioms used in derivation (9): left_division_multiply, moufang1, left_identity, right_division_multiply, multiply_left_division, left_inverse, right_identity, right_inverse, multiply_right_division
% 3.23/1.60 % No. of inferences in proof: 21
% 3.23/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1200 ms resp. 909 ms w/o parsing
% 3.23/1.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.23/1.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------