%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% 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 : 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 07:20:56 AM UTC 2026
% Result : Unsatisfiable 87.06s 33.22s
% Output : Refutation 87.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 52 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 842 ( 37 ~; 19 |; 0 &; 786 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 107 ( 0 ^; 107 !; 0 ?; 107 :)
% 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(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
= C ),
inference(lifteq,[status(thm)],[6]) ).
thf(14,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( F @ ( E @ inverse @ ( D @ multiply ) @ inverse @ multiply ) ) )
| ( ( E @ ( C @ inverse @ ( E @ ( E @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( C @ multiply ) )
= ( A @ ( B @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( ZB @ inverse @ ( Z @ multiply ) @ inverse )),bind(B,$thf( M )),bind(C,$thf( U )),bind(D,$thf( Z )),bind(E,$thf( ZB )),bind(F,$thf( M @ ( U @ ( M @ inverse @ ( ZB @ inverse @ ( Z @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( M @ ( M @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse ))]]) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( C @ multiply ) )
= ( A @ ( B @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse ) ),
inference(simp,[status(thm)],[15]) ).
thf(238,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= ( F @ ( G @ ( F @ inverse @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ ( F @ ( F @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse ) )
| ( ( D @ ( B @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( C @ multiply ) @ ( E @ multiply ) )
= G ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ inverse @ ( C @ ( C @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( B @ multiply ) @ ( C @ inverse @ ( B @ multiply ) @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( I )),bind(D,$thf( K )),bind(E,$thf( K @ inverse @ ( I @ multiply ) @ inverse )),bind(F,$thf( A )),bind(G,$thf( B ))]]) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ inverse @ ( C @ ( C @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( B @ multiply ) @ ( C @ inverse @ ( B @ multiply ) @ inverse @ multiply ) )
= A ),
inference(simp,[status(thm)],[239]) ).
thf(1,negated_conjecture,
( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 ),
file('/export/starexec/sandbox2/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(8,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) ) )
| ( C != a2 ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( a2 @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(221,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( C @ multiply ) )
!= ( F @ ( G @ ( F @ inverse @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ ( F @ ( F @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( E @ multiply ) ) )
| ( ( A @ ( B @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
= G ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
= B ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( A )),bind(B,$thf( I @ ( M @ inverse @ ( K @ multiply ) @ inverse @ multiply ) )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( K )),bind(F,$thf( M )),bind(G,$thf( I ))]]) ).
thf(435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
= B ),
inference(simp,[status(thm)],[222]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( ( B @ ( a2 @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= a2 )
| ( A
!= ( b2 @ ( b2 @ inverse @ multiply ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( a2 @ ( A @ inverse @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= a2 ),
inference(simp,[status(thm)],[22]) ).
thf(10,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( F @ ( E @ inverse @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ ( E @ ( E @ inverse @ multiply ) @ multiply ) ) )
| ( ( E @ ( C @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(17,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= ( F @ ( E @ inverse @ ( D @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( A
!= ( E @ ( E @ inverse @ multiply ) ) )
| ( ( E @ ( C @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(simp,[status(thm)],[10]) ).
thf(23,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= ( E @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( ( D @ ( B @ multiply ) @ inverse @ ( C @ multiply ) )
= E ) ),
inference(simp,[status(thm)],[17]) ).
thf(200,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= ( F @ ( a2 @ ( F @ inverse @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ ( F @ ( F @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse ) )
| ( ( D @ ( B @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( C @ multiply ) @ ( E @ multiply ) )
!= ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,21]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( B @ ( a2 @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) )
!= ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( A )),bind(B,$thf( a2 )),bind(C,$thf( H )),bind(D,$thf( J )),bind(E,$thf( J @ inverse @ ( H @ multiply ) @ inverse )),bind(F,$thf( A ))]]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( B @ ( a2 @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) )
!= ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(449,plain,
! [B: $i,A: $i] :
( ( ( B @ ( a2 @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
!= a2 )
| ( ( B @ inverse @ ( A @ multiply ) @ inverse )
!= ( b2 @ ( b2 @ inverse @ multiply ) ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( b2 @ ( b2 @ inverse @ multiply ) ) )
| ( ( D @ ( a2 @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[7,27]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= b2 )
| ( A
!= ( b2 @ inverse ) )
| ( ( D @ ( a2 @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[33]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ inverse @ ( b2 @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= b2 )
| ( ( C @ ( a2 @ ( C @ inverse @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ ( C @ ( C @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[37]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( b2 @ ( b2 @ inverse @ multiply ) ) )
| ( ( a2 @ ( C @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ ( B @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= b2 )
| ( A
!= ( b2 @ inverse ) )
| ( ( a2 @ ( C @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[9]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ inverse @ ( b2 @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
!= b2 )
| ( ( a2 @ ( B @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[18]) ).
thf(4873,plain,
$false,
inference(e,[status(thm)],[29,443,6,21,435,27,7,3,23,5,449,42,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % 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
% 0.09/0.34 % Computer : n012.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 14:52:37 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 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
% 0.50/0.62 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.71 % [INFO] Parsing done (81ms).
% 0.66/0.71 % [INFO] Running in sequential loop mode.
% 0.80/0.89 % [INFO] eprover registered as external prover.
% 0.80/0.89 % [INFO] Scanning for conjecture ...
% 0.96/0.93 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 0.96/0.94 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 0.96/0.95 % [INFO] Problem is propositional (TPTP CNF).
% 0.96/0.95 % [INFO] Type checking passed.
% 0.96/0.95 % [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 ...
% 87.06/33.21 % External prover 'e' found a proof!
% 87.06/33.21 % [INFO] Killing All external provers ...
% 87.06/33.21 % Time passed: 32796ms (effective reasoning time: 32498ms)
% 87.06/33.22 % Axioms used in derivation (1): single_axiom
% 87.06/33.22 % No. of inferences in proof: 34
% 87.06/33.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32796 ms resp. 32498 ms w/o parsing
% 87.06/33.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 87.06/33.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------