%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP422-1 : TPTP v9.3.1. Released v2.6.0.
% 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 : n003.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 07:20:58 AM UTC 2026
% Result : Unsatisfiable 150.78s 73.23s
% Output : Refutation 150.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 49 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 805 ( 32 ~; 18 |; 0 &; 755 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 117 ( 0 ^; 117 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(b2_decl,type,
b2: $i ).
thf(a2_decl,type,
a2: $i ).
thf(1,negated_conjecture,
( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
thf(3,plain,
( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,plain,
( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 ),
inference(lifteq,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= B ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( F @ inverse @ multiply ) @ ( E @ inverse @ multiply ) @ inverse ) )
| ( ( F @ ( D @ multiply ) @ ( B @ ( D @ multiply ) @ inverse @ multiply ) @ inverse )
= E ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ ( C @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse @ ( C @ ( C @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[9:[bind(A,$thf( W @ inverse )),bind(B,$thf( L )),bind(C,$thf( W @ ( W @ inverse @ multiply ) @ inverse )),bind(D,$thf( D )),bind(E,$thf( W @ ( W @ inverse @ multiply ) @ inverse @ ( W @ ( W @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse @ ( W @ ( W @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ ( L @ inverse @ multiply ) @ inverse @ ( W @ inverse @ multiply ) )),bind(F,$thf( W ))]]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ ( C @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse @ ( C @ ( C @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(42,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ ( C @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse @ ( C @ ( C @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( F @ inverse @ multiply ) @ ( E @ inverse @ multiply ) @ inverse @ ( D @ multiply ) ) )
| ( ( F @ ( D @ multiply ) @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse )
= E ) ),
inference(paramod_ordered,[status(thm)],[23,7]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse )
= B ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( J )),bind(D,$thf( J @ inverse )),bind(E,$thf( B )),bind(F,$thf( J @ ( J @ inverse @ multiply ) @ inverse ))]]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse )
= B ),
inference(simp,[status(thm)],[43]) ).
thf(164,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( F @ inverse @ multiply ) @ ( E @ inverse @ multiply ) @ inverse ) )
| ( ( F @ ( D @ multiply ) @ ( B @ ( D @ multiply ) @ inverse @ multiply ) @ inverse )
= E ) ),
inference(paramod_ordered,[status(thm)],[136,7]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( M )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( N @ ( M @ multiply ) @ ( L @ ( M @ multiply ) @ inverse @ multiply ) @ inverse )),bind(F,$thf( N ))]]) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse ) ),
inference(simp,[status(thm)],[165]) ).
thf(399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( b2 @ ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[272,5]) ).
thf(584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[399]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( b2 @ ( B @ multiply ) @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( B @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[8]) ).
thf(314,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( F @ inverse @ multiply ) @ ( E @ inverse @ multiply ) @ inverse ) )
| ( ( F @ ( D @ multiply ) @ ( B @ ( D @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( E @ multiply ) @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[136,21]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( M )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( N @ ( M @ multiply ) @ ( L @ ( M @ multiply ) @ inverse @ multiply ) @ inverse )),bind(F,$thf( N ))]]) ).
thf(350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[315]) ).
thf(204,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( F @ ( F @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ inverse @ ( F @ ( F @ inverse @ multiply ) @ inverse @ inverse @ multiply ) @ ( E @ inverse @ multiply ) @ inverse ) )
| ( ( B @ ( F @ inverse @ multiply ) )
= ( F @ ( D @ multiply ) @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse ) ) ),
inference(paramod_ordered,[status(thm)],[136,23]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ inverse @ multiply ) )
= ( D @ ( A @ multiply ) @ ( D @ ( D @ inverse @ multiply ) @ inverse @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( M )),bind(B,$thf( L )),bind(C,$thf( Q @ ( Q @ inverse @ multiply ) @ inverse )),bind(D,$thf( D )),bind(E,$thf( Q @ ( Q @ inverse @ multiply ) @ inverse @ ( M @ multiply ) @ ( L @ ( M @ multiply ) @ inverse @ multiply ) @ inverse )),bind(F,$thf( Q ))]]) ).
thf(263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ inverse @ multiply ) )
= ( D @ ( A @ multiply ) @ ( D @ ( D @ inverse @ multiply ) @ inverse @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse ) ),
inference(simp,[status(thm)],[205]) ).
thf(18,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( F @ inverse @ multiply ) @ ( E @ inverse @ multiply ) @ inverse @ ( D @ multiply ) @ inverse ) )
| ( ( F @ ( D @ multiply ) @ ( B @ multiply ) @ inverse )
= E ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(19,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( F @ inverse @ multiply ) @ ( E @ inverse @ multiply ) @ inverse @ ( D @ multiply ) ) )
| ( ( F @ ( D @ multiply ) @ ( B @ multiply ) @ inverse )
= E ) ),
inference(simp,[status(thm)],[18]) ).
thf(422,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( H @ ( G @ multiply ) @ ( F @ ( G @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( ( H @ ( E @ multiply ) @ ( F @ ( E @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[272,350]) ).
thf(423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ multiply ) @ ( A @ ( D @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( C @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( B )),bind(G,$thf( A )),bind(H,$thf( D ))]]) ).
thf(630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ multiply ) @ ( A @ ( D @ multiply ) @ inverse @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( C @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[423]) ).
thf(4030,plain,
$false,
inference(e,[status(thm)],[5,6,584,350,7,3,263,23,272,19,136,630,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP422-1 : TPTP v9.3.1. Released v2.6.0.
% 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
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 14:55:08 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.87/1.07 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/1.29 % [INFO] Parsing done (211ms).
% 1.20/1.30 % [INFO] Running in sequential loop mode.
% 1.79/1.80 % [INFO] eprover registered as external prover.
% 1.79/1.81 % [INFO] Scanning for conjecture ...
% 1.94/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.94/1.95 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.94/1.96 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.97 % [INFO] Type checking passed.
% 1.94/1.97 % [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 ...
% 150.78/73.23 % External prover 'e' found a proof!
% 150.78/73.23 % [INFO] Killing All external provers ...
% 150.78/73.23 % Time passed: 72739ms (effective reasoning time: 71921ms)
% 150.78/73.23 % Axioms used in derivation (1): single_axiom
% 150.78/73.23 % No. of inferences in proof: 32
% 150.78/73.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 72739 ms resp. 71921 ms w/o parsing
% 150.78/73.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 150.78/73.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------