%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP404-1 : 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 : 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 07:20:55 AM UTC 2026
% Result : Unsatisfiable 94.45s 37.43s
% Output : Refutation 83.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 68 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 130 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1806 ( 98 ~; 63 |; 0 &;1645 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 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 : 264 ( 0 ^; 264 !; 0 ?; 264 :)
% 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] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ 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 @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( F @ ( E @ ( D @ multiply ) @ inverse @ multiply ) ) )
| ( ( E @ ( E @ inverse @ multiply ) @ ( E @ multiply ) @ inverse @ ( C @ inverse @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
= ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( A @ ( D @ ( C @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( U @ ( T @ multiply ) @ inverse )),bind(B,$thf( Z )),bind(C,$thf( O )),bind(D,$thf( T )),bind(E,$thf( U )),bind(F,$thf( Z @ ( Z @ inverse @ multiply ) @ ( Z @ multiply ) @ inverse @ ( O @ ( Z @ ( U @ ( T @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse ))]]) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
= ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( A @ ( D @ ( C @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse ) ),
inference(simp,[status(thm)],[15]) ).
thf(164,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
!= ( F @ ( F @ inverse @ multiply ) @ ( F @ multiply ) @ inverse @ ( G @ ( F @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( E @ multiply ) ) )
| ( ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( A @ ( D @ ( C @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
= G ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( A @ ( D @ multiply ) @ inverse @ multiply ) @ ( B @ ( A @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
= C ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( I @ ( C @ ( K @ multiply ) @ inverse @ multiply ) )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( K )),bind(F,$thf( C )),bind(G,$thf( I ))]]) ).
thf(297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( A @ ( D @ multiply ) @ inverse @ multiply ) @ ( B @ ( A @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
= C ),
inference(simp,[status(thm)],[165]) ).
thf(178,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( A @ ( D @ ( C @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ ( F @ multiply ) @ inverse @ ( G @ ( F @ ( E @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) @ ( E @ multiply ) )
= G ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) @ ( C @ ( B @ multiply ) @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( J @ ( I @ multiply ) @ inverse )),bind(F,$thf( D )),bind(G,$thf( A ))]]) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) @ ( C @ ( B @ multiply ) @ inverse @ multiply ) )
= A ),
inference(simp,[status(thm)],[179]) ).
thf(1839,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( A @ ( D @ multiply ) @ inverse @ multiply ) @ ( B @ ( A @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( G @ ( G @ inverse @ multiply ) @ ( G @ multiply ) @ inverse @ ( E @ inverse @ multiply ) @ inverse ) )
| ( ( C @ ( F @ multiply ) @ ( G @ ( F @ multiply ) @ inverse @ multiply ) )
= E ) ),
inference(paramod_ordered,[status(thm)],[297,303]) ).
thf(1840,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) )
= ( C @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ ( B @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[1839:[bind(A,$thf( T )),bind(B,$thf( L )),bind(C,$thf( Q )),bind(D,$thf( S )),bind(E,$thf( Q @ ( T @ ( S @ multiply ) @ inverse @ multiply ) @ ( L @ ( T @ ( S @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) )),bind(F,$thf( F )),bind(G,$thf( L ))]]) ).
thf(1944,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) )
= ( C @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ ( B @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) ) ),
inference(simp,[status(thm)],[1840]) ).
thf(3378,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ ( B @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) )
!= ( H @ ( F @ ( I @ multiply ) @ inverse @ multiply ) @ ( G @ ( F @ ( I @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) ) )
| ( ( G @ ( G @ inverse @ multiply ) @ ( G @ multiply ) @ inverse @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
= H ) ),
inference(paramod_ordered,[status(thm)],[1944,297]) ).
thf(3379,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
= C ),
inference(pattern_uni,[status(thm)],[3378:[bind(A,$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( B )),bind(H,$thf( C )),bind(I,$thf( D ))]]) ).
thf(4401,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ ( F @ multiply ) @ inverse @ ( D @ inverse @ multiply ) @ inverse ) )
| ( ( C @ ( E @ multiply ) @ ( F @ ( E @ multiply ) @ inverse @ multiply ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[3379,303]) ).
thf(4402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) )
= ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[4401:[bind(A,$thf( L )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ multiply ) @ ( K @ ( L @ multiply ) @ inverse @ multiply ) )),bind(E,$thf( E )),bind(F,$thf( K ))]]) ).
thf(4575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) )
= ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) ) ),
inference(simp,[status(thm)],[4402]) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) @ ( C @ ( B @ multiply ) @ inverse @ multiply ) )
!= ( b2 @ ( b2 @ inverse @ multiply ) ) )
| ( ( a2 @ ( A @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[303,5]) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
!= b2 )
| ( ( C @ ( B @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( A @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[1312]) ).
thf(2376,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( F @ ( F @ inverse @ multiply ) @ ( F @ multiply ) @ inverse @ ( D @ inverse @ multiply ) @ inverse @ ( E @ multiply ) ) )
| ( C != b2 )
| ( ( F @ ( E @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( D @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[7,1517]) ).
thf(2377,plain,
! [C: $i,B: $i,A: $i] :
( ( A != b2 )
| ( ( C @ ( B @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( A @ ( C @ ( B @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(pattern_uni,[status(thm)],[2376:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( H )),bind(D,$thf( H @ ( K @ ( J @ multiply ) @ inverse @ multiply ) )),bind(E,$thf( J )),bind(F,$thf( K ))]]) ).
thf(2521,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( b2 @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[2377]) ).
thf(2547,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= b2 )
| ( ( a2 @ ( b2 @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[2521]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) ) )
| ( C != a2 ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( a2 @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 )
| ( A
!= ( b2 @ ( b2 @ inverse @ multiply ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( a2 @ ( A @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 ),
inference(simp,[status(thm)],[22]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( a2 @ ( D @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) ) )
| ( ( C @ inverse )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[7,27]) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse ) )
| ( A
!= ( a2 @ ( D @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( ( C @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[34]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( B @ ( A @ ( a2 @ ( C @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse ) )
| ( ( B @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[39]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( b2 @ ( b2 @ inverse @ multiply ) ) )
| ( ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( a2 @ ( D @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[7,27]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= b2 )
| ( A
!= ( b2 @ inverse ) )
| ( ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( a2 @ ( D @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[33]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( B @ ( A @ ( b2 @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= b2 )
| ( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( a2 @ ( C @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[37]) ).
thf(4277,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( F @ ( F @ inverse @ multiply ) @ ( F @ multiply ) @ inverse @ ( D @ inverse @ multiply ) @ inverse ) )
| ( ( C @ ( E @ multiply ) )
!= b2 )
| ( ( F @ ( E @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( D @ multiply ) )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[3379,1517]) ).
thf(4278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ multiply ) )
!= b2 )
| ( ( B @ ( A @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(pattern_uni,[status(thm)],[4277:[bind(A,$thf( L )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ multiply ) @ ( K @ ( L @ multiply ) @ inverse @ multiply ) )),bind(E,$thf( E )),bind(F,$thf( K ))]]) ).
thf(4649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ multiply ) )
!= b2 )
| ( ( B @ ( A @ multiply ) @ inverse )
!= ( b2 @ inverse ) )
| ( ( a2 @ ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[4278]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ 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 @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= b2 )
| ( A
!= ( b2 @ inverse ) )
| ( ( a2 @ ( C @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[9]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( B @ ( A @ ( b2 @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= b2 )
| ( ( a2 @ ( B @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[18]) ).
thf(16,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( E @ ( E @ inverse @ multiply ) @ ( E @ multiply ) ) )
| ( ( C @ inverse @ ( F @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(19,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( E @ ( E @ inverse @ multiply ) ) )
| ( A != E )
| ( ( C @ inverse @ ( F @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(simp,[status(thm)],[16]) ).
thf(25,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( B @ ( A @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( D @ ( D @ inverse @ multiply ) ) )
| ( ( B @ inverse @ ( E @ ( D @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( C @ multiply ) )
= E ) ),
inference(simp,[status(thm)],[19]) ).
thf(6720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ multiply ) )
!= b2 )
| ( ( B @ ( A @ multiply ) )
!= b2 )
| ( ( a2 @ ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) @ multiply ) )
!= a2 ) ),
inference(simp,[status(thm)],[4649]) ).
thf(1311,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) @ ( C @ ( B @ multiply ) @ inverse @ multiply ) )
!= ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) ) )
| ( A != a2 ) ),
inference(paramod_ordered,[status(thm)],[303,5]) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( a2 @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= a2 )
| ( ( B @ ( A @ multiply ) @ inverse )
!= ( b2 @ ( b2 @ inverse @ multiply ) ) ) ),
inference(simp,[status(thm)],[1311]) ).
thf(1612,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( a2 @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= a2 )
| ( ( B @ ( A @ multiply ) @ inverse )
!= ( b2 @ ( b2 @ inverse @ multiply ) ) ) ),
inference(simp,[status(thm)],[1489]) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( D @ ( D @ inverse @ multiply ) ) )
| ( ( C @ ( D @ multiply ) @ inverse @ ( a2 @ ( D @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[7,27]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= D )
| ( A
!= ( D @ inverse ) )
| ( ( C @ ( D @ multiply ) @ inverse @ ( a2 @ ( D @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[35]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( B @ ( A @ ( C @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= C )
| ( ( B @ ( C @ multiply ) @ inverse @ ( a2 @ ( C @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[38]) ).
thf(4859,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ inverse @ multiply ) )
!= ( G @ ( I @ ( H @ multiply ) @ inverse @ multiply ) @ ( F @ ( I @ ( H @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) ) )
| ( ( D @ ( C @ multiply ) @ ( B @ ( C @ multiply ) @ inverse @ multiply ) )
= ( G @ ( E @ multiply ) @ ( F @ ( E @ multiply ) @ inverse @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[4575,1944]) ).
thf(4860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) )
= ( C @ ( D @ multiply ) @ ( A @ ( D @ multiply ) @ inverse @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[4859:[bind(A,$thf( L @ ( K @ multiply ) @ inverse )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( B )),bind(G,$thf( D )),bind(H,$thf( K )),bind(I,$thf( L ))]]) ).
thf(5495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( A @ ( B @ multiply ) @ inverse @ multiply ) )
= ( C @ ( D @ multiply ) @ ( A @ ( D @ multiply ) @ inverse @ multiply ) ) ),
inference(simp,[status(thm)],[4860]) ).
thf(455,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse @ ( A @ ( D @ ( C @ ( B @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( E @ ( E @ inverse @ multiply ) @ ( E @ multiply ) @ inverse @ ( F @ ( E @ ( a2 @ ( G @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( ( C @ ( C @ inverse @ multiply ) @ ( C @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ multiply ) )
!= ( G @ ( G @ inverse @ multiply ) @ ( G @ multiply ) @ inverse ) )
| ( ( F @ inverse )
!= a2 ) ),
inference(paramod_ordered,[status(thm)],[29,45]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( ( a2 @ ( a2 @ inverse @ multiply ) @ ( a2 @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) )
!= ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse ) )
| ( ( A @ inverse )
!= a2 ) ),
inference(pattern_uni,[status(thm)],[455:[bind(A,$thf( A )),bind(B,$thf( J @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse )),bind(C,$thf( a2 )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( A )),bind(G,$thf( J ))]]) ).
thf(517,plain,
! [B: $i,A: $i] :
( ( ( a2 @ ( a2 @ inverse @ multiply ) @ ( a2 @ multiply ) @ inverse @ ( A @ inverse @ multiply ) @ inverse @ ( B @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) @ inverse @ multiply ) )
!= ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse ) )
| ( ( A @ inverse )
!= a2 ) ),
inference(simp,[status(thm)],[456]) ).
thf(11,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( E @ ( E @ inverse @ multiply ) ) )
| ( ( C @ ( E @ multiply ) @ inverse @ ( F @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(20,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= E )
| ( A
!= ( E @ inverse ) )
| ( ( C @ ( E @ multiply ) @ inverse @ ( F @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( D @ multiply ) )
= F ) ),
inference(simp,[status(thm)],[11]) ).
thf(26,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( B @ ( A @ ( D @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= D )
| ( ( B @ ( D @ multiply ) @ inverse @ ( E @ ( D @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( C @ multiply ) )
= E ) ),
inference(simp,[status(thm)],[20]) ).
thf(10,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ ( A @ multiply ) )
!= ( E @ ( E @ inverse @ multiply ) @ ( E @ multiply ) @ inverse @ ( F @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) ) )
| ( ( C @ 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 @ ( B @ inverse @ multiply ) @ ( B @ multiply ) @ inverse @ ( C @ ( B @ ( A @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( E @ ( E @ inverse @ multiply ) @ ( E @ multiply ) @ inverse ) )
| ( A
!= ( F @ ( E @ ( D @ multiply ) @ inverse @ multiply ) @ inverse ) )
| ( ( C @ inverse @ ( D @ multiply ) )
= F ) ),
inference(simp,[status(thm)],[10]) ).
thf(23,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) @ ( A @ multiply ) @ inverse @ ( B @ ( A @ ( E @ ( D @ ( C @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse @ multiply ) @ inverse )
!= ( D @ ( D @ inverse @ multiply ) @ ( D @ multiply ) @ inverse ) )
| ( ( B @ inverse @ ( C @ multiply ) )
= E ) ),
inference(simp,[status(thm)],[17]) ).
thf(11032,plain,
$false,
inference(e,[status(thm)],[5,4575,29,6,2547,45,43,1517,4649,3379,1944,24,25,6720,1612,44,27,2521,7,303,3,5495,517,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP404-1 : TPTP v9.3.1. Released v2.6.0.
% 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
% 0.16/5.42 % Computer : n001.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Fri Sep 25 14:58:01 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 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
% 0.19/5.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/5.81 % [INFO] Parsing done (87ms).
% 0.19/5.82 % [INFO] Running in sequential loop mode.
% 0.19/6.01 % [INFO] eprover registered as external prover.
% 0.19/6.02 % [INFO] Scanning for conjecture ...
% 1.39/6.06 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.39/6.07 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.39/6.08 % [INFO] Problem is propositional (TPTP CNF).
% 1.39/6.08 % [INFO] Type checking passed.
% 1.39/6.08 % [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 ...
% 94.45/37.43 % External prover 'e' found a proof!
% 94.45/37.43 % [INFO] Killing All external provers ...
% 94.45/37.43 % Time passed: 31918ms (effective reasoning time: 31608ms)
% 94.45/37.43 % Axioms used in derivation (1): single_axiom
% 94.45/37.43 % No. of inferences in proof: 68
% 94.45/37.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 31918 ms resp. 31608 ms w/o parsing
% 83.69/37.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 83.69/37.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------