%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP415-1 : 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 : n017.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 07:20:57 AM UTC 2026
% Result : Unsatisfiable 48.78s 20.19s
% Output : Refutation 48.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 604 ( 23 ~; 11 |; 0 &; 570 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 77 ( 0 ^; 77 !; 0 ?; 77 :)
% 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(1,negated_conjecture,
( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
thf(3,plain,
( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,plain,
( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( b1 @ ( b1 @ inverse @ multiply ) )
!= ( a1 @ ( a1 @ inverse @ multiply ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(8,plain,
( ( b1 != a1 )
| ( ( b1 @ inverse )
!= ( a1 @ inverse ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(287,plain,
( ( b1 != a1 )
| ( b1 != a1 ) ),
inference(simp,[status(thm)],[8]) ).
thf(293,plain,
b1 != a1,
inference(simp,[status(thm)],[287]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
= C ),
inference(lifteq,[status(thm)],[6]) ).
thf(13,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
!= ( F @ inverse ) )
| ( ( D @ ( D @ inverse @ multiply ) @ inverse @ ( C @ ( E @ multiply ) @ ( D @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ multiply ) @ inverse )
= F ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(14,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( D @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
= ( E @ ( E @ inverse @ multiply ) @ inverse @ ( D @ inverse @ ( C @ multiply ) @ ( E @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( E @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( W )),bind(B,$thf( R )),bind(C,$thf( T )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( W @ ( W @ inverse @ multiply ) @ inverse @ ( T @ inverse @ ( R @ multiply ) @ ( W @ ( R @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( W @ multiply ) ))]]) ).
thf(29,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( D @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
= ( E @ ( E @ inverse @ multiply ) @ inverse @ ( D @ inverse @ ( C @ multiply ) @ ( E @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( E @ multiply ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(48,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( E @ inverse @ multiply ) @ inverse @ ( D @ inverse @ ( C @ multiply ) @ ( E @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( E @ multiply ) )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( H @ inverse @ ( G @ multiply ) @ ( F @ ( G @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( F @ multiply ) ) )
| ( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( D @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ inverse )
= H ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ inverse )
= C ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( E )),bind(G,$thf( C )),bind(H,$thf( D ))]]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ inverse )
= C ),
inference(simp,[status(thm)],[49]) ).
thf(38,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( D @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ inverse @ ( H @ inverse @ ( G @ multiply ) @ ( F @ ( G @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( F @ multiply ) @ inverse ) )
| ( ( E @ ( E @ inverse @ multiply ) @ inverse @ ( D @ inverse @ ( C @ multiply ) @ ( E @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( E @ multiply ) )
= H ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ inverse @ ( C @ inverse @ inverse @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
= C ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( I @ inverse )),bind(E,$thf( E )),bind(F,$thf( A )),bind(G,$thf( B )),bind(H,$thf( I ))]]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ inverse @ ( C @ inverse @ inverse @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
= C ),
inference(simp,[status(thm)],[39]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ inverse @ ( C @ inverse @ inverse @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) )
| ( C
!= ( a1 @ ( a1 @ inverse @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,5]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ inverse @ ( a1 @ ( a1 @ inverse @ multiply ) @ inverse @ inverse @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= b1 )
| ( B
!= ( b1 @ inverse ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(285,plain,
! [A: $i] :
( ( b1 @ inverse @ ( b1 @ inverse @ inverse @ multiply ) @ inverse @ ( a1 @ ( a1 @ inverse @ multiply ) @ inverse @ inverse @ ( A @ multiply ) @ ( b1 @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= b1 ),
inference(simp,[status(thm)],[251]) ).
thf(12,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
!= ( D @ ( D @ inverse @ multiply ) @ inverse @ ( F @ inverse @ ( E @ multiply ) @ ( D @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( ( C @ ( D @ multiply ) @ inverse )
= F ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(22,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( D @ ( D @ inverse @ multiply ) @ inverse @ ( F @ inverse @ ( E @ multiply ) @ ( D @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) ) )
| ( ( C @ ( D @ multiply ) @ inverse )
= F ) ),
inference(simp,[status(thm)],[12]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse )
!= ( b1 @ inverse ) )
| ( ( b1 @ ( C @ multiply ) )
!= ( a1 @ ( a1 @ inverse @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ inverse @ ( C @ inverse @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= b1 )
| ( ( b1 @ ( C @ multiply ) )
!= ( a1 @ ( a1 @ inverse @ multiply ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(1893,plain,
$false,
inference(e,[status(thm)],[5,293,6,137,285,134,22,7,3,20,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP415-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.08 % 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
% 0.16/0.42 % Computer : n017.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 14:48:03 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 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
% 1.07/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.28 % [INFO] Parsing done (161ms).
% 1.35/1.29 % [INFO] Running in sequential loop mode.
% 1.90/1.69 % [INFO] eprover registered as external prover.
% 2.08/1.70 % [INFO] Scanning for conjecture ...
% 2.08/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.24/1.81 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.24/1.82 % [INFO] Problem is propositional (TPTP CNF).
% 2.24/1.83 % [INFO] Type checking passed.
% 2.24/1.83 % [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 ...
% 48.78/20.19 % External prover 'e' found a proof!
% 48.78/20.19 % [INFO] Killing All external provers ...
% 48.78/20.19 % Time passed: 19560ms (effective reasoning time: 18891ms)
% 48.78/20.19 % Axioms used in derivation (1): single_axiom
% 48.78/20.19 % No. of inferences in proof: 27
% 48.78/20.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19560 ms resp. 18891 ms w/o parsing
% 48.97/20.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.97/20.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------