%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP052-1 : 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 : n001.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 07:19:53 AM UTC 2026
% Result : Unsatisfiable 51.71s 26.89s
% Output : Refutation 51.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 377 ( 9 ~; 7 |; 0 &; 361 @)
% ( 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 : 11 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(a1_decl,type,
a1: $i ).
thf(b1_decl,type,
b1: $i ).
thf(b2_decl,type,
b2: $i ).
thf(a2_decl,type,
a2: $i ).
thf(a3_decl,type,
a3: $i ).
thf(b3_decl,type,
b3: $i ).
thf(c3_decl,type,
c3: $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/sandbox/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(12,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(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( C @ multiply ) )
= ( A @ ( B @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse ) ),
inference(pattern_uni,[status(thm)],[12:[bind(A,$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(21,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)],[13]) ).
thf(74,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)],[21,7]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ inverse @ ( C @ ( C @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( B @ multiply ) @ ( C @ inverse @ ( B @ multiply ) @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$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(106,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)],[75]) ).
thf(79,plain,
! [G: $i,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 ) )
!= ( G @ ( E @ inverse @ ( G @ ( G @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse @ ( F @ multiply ) ) )
| ( C
= ( D @ ( E @ ( D @ inverse @ ( G @ inverse @ ( F @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ ( D @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse ) ) ),
inference(paramod_ordered,[status(thm)],[7,21]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ ( A @ inverse @ ( D @ inverse @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ ( A @ inverse @ multiply ) @ multiply ) @ multiply ) @ inverse )
= B ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( I @ ( M @ inverse @ ( K @ multiply ) @ inverse @ multiply ) )),bind(F,$thf( K )),bind(G,$thf( M ))]]) ).
thf(108,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)],[80]) ).
thf(1,negated_conjecture,
( ( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) )
| ( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 )
| ( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
thf(3,plain,
( ( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) )
| ( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 )
| ( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(999,plain,
$false,
inference(e,[status(thm)],[106,6,21,7,108,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP052-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.14/0.39 % Computer : n001.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 14:25:40 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.14 % [INFO] Parsing done (170ms).
% 1.33/1.15 % [INFO] Running in sequential loop mode.
% 1.87/1.55 % [INFO] eprover registered as external prover.
% 1.87/1.56 % [INFO] Scanning for conjecture ...
% 2.10/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.10/1.68 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.10/1.69 % [INFO] Problem is propositional (TPTP CNF).
% 2.10/1.69 % [INFO] Type checking passed.
% 2.27/1.70 % [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 ...
% 51.71/26.89 % External prover 'e' found a proof!
% 51.71/26.89 % [INFO] Killing All external provers ...
% 51.71/26.89 % Time passed: 26352ms (effective reasoning time: 25724ms)
% 51.71/26.89 % Axioms used in derivation (1): single_axiom
% 51.71/26.89 % No. of inferences in proof: 15
% 51.71/26.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 26352 ms resp. 25724 ms w/o parsing
% 51.89/26.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 51.89/26.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------