%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 07:29:10 AM UTC 2026
% Result : Unsatisfiable 11.57s 1.98s
% Output : CNFRefutation 11.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of formulae : 112 ( 112 unt; 0 def)
% Number of atoms : 112 ( 111 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 21 ( 4 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 377 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(multiply(VAR_0,inverse(multiply(inverse(multiply(inverse(multiply(VAR_1,VAR_0)),multiply(VAR_1,inverse(VAR_2)))),inverse(multiply(inverse(VAR_0),VAR_0)))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_2,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_4,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,inverse(C)))),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(inverse(C))))),inverse(multiply(inverse(A),A))))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_14,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A))))))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_24,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(inverse(C))))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_48,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(C))))))),inverse(multiply(inverse(B),B))) = C,
inference(paramod,[status(thm)],[c_24,c_1]) ).
cnf(c_2483,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(inverse(E),E)))))))),
inference(paramod,[status(thm)],[c_24,c_4]) ).
cnf(c_2484,plain,
C = multiply(D,inverse(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(inverse(E),E)))))))),
inference(paramod,[status(thm)],[c_1,c_2483]) ).
cnf(c_71,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(B),B)))))))) = C,
inference(copy,[status(thm)],[c_2484]) ).
cnf(c_82,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,C)))))),inverse(multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_24,c_14]) ).
cnf(c_96,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_24,c_24]) ).
cnf(c_104,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(D))))))),A)),D)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_48,c_1]) ).
cnf(c_2485,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),multiply(D,inverse(E)))),inverse(multiply(inverse(C),C))))))))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,E))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_4,c_48]) ).
cnf(c_115,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_1,c_2485]) ).
cnf(c_2486,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),E)),inverse(multiply(inverse(C),C))))))))),inverse(multiply(inverse(A),A)))))) = multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),inverse(multiply(inverse(F),F))))),
inference(paramod,[status(thm)],[c_71,c_4]) ).
cnf(c_143,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_2486]) ).
cnf(c_2487,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B)))))))) = inverse(inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),D)),C)),inverse(multiply(inverse(D),D))))))),
inference(paramod,[status(thm)],[c_71,c_71]) ).
cnf(c_166,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),A)),D)),inverse(multiply(inverse(A),A))))))) = multiply(B,inverse(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(inverse(C),C)))))))),
inference(copy,[status(thm)],[c_2487]) ).
cnf(c_204,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,C)))))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(C,D)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = D,
inference(paramod,[status(thm)],[c_82,c_71]) ).
cnf(c_2488,plain,
inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))),multiply(inverse(multiply(inverse(multiply(D,A)),multiply(D,C))),E))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = E,
inference(paramod,[status(thm)],[c_115,c_14]) ).
cnf(c_220,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),E)),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))) = E,
inference(paramod,[status(thm)],[c_166,c_2488]) ).
cnf(c_2489,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(B,C)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,A)),multiply(E,inverse(inverse(multiply(A,B)))))),D)),C)),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_82,c_143]) ).
cnf(c_277,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,D)))))),A)),E)),inverse(multiply(inverse(A),A))))) = multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(multiply(D,E)),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))),
inference(copy,[status(thm)],[c_2489]) ).
cnf(c_286,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = multiply(inverse(A),A),
inference(paramod,[status(thm)],[c_277,c_104]) ).
cnf(c_299,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))))))))) = C,
inference(paramod,[status(thm)],[c_286,c_14]) ).
cnf(c_308,plain,
multiply(inverse(multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),inverse(C))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = C,
inference(paramod,[status(thm)],[c_286,c_48]) ).
cnf(c_376,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),C)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_286,c_96]) ).
cnf(c_2490,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),A)),D)),inverse(multiply(inverse(A),A))))))) = inverse(inverse(multiply(multiply(B,E),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)),inverse(multiply(inverse(multiply(B,E)),multiply(B,E)))))))),
inference(paramod,[status(thm)],[c_220,c_14]) ).
cnf(c_2491,plain,
multiply(B,inverse(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(inverse(C),C)))))))) = inverse(inverse(multiply(multiply(B,E),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)),inverse(multiply(inverse(multiply(B,E)),multiply(B,E)))))))),
inference(paramod,[status(thm)],[c_166,c_2490]) ).
cnf(c_403,plain,
inverse(inverse(multiply(multiply(A,B),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),E)),inverse(multiply(inverse(multiply(A,B)),multiply(A,B)))))))) = multiply(A,inverse(inverse(multiply(D,inverse(multiply(inverse(E),inverse(multiply(inverse(D),D)))))))),
inference(copy,[status(thm)],[c_2491]) ).
cnf(c_2492,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(inverse(C),C)))))))) = D,
inference(paramod,[status(thm)],[c_143,c_220]) ).
cnf(c_451,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B))))))))) = C,
inference(paramod,[status(thm)],[c_166,c_2492]) ).
cnf(c_2493,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),A)),B),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(D),D)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))),multiply(C,B))),E)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),B)),multiply(inverse(multiply(inverse(A),A)),B))))))))) = E,
inference(paramod,[status(thm)],[c_286,c_220]) ).
cnf(c_452,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),inverse(multiply(inverse(C),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))))))))) = C,
inference(paramod,[status(thm)],[c_403,c_2493]) ).
cnf(c_2494,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),multiply(D,inverse(E)))),inverse(multiply(inverse(C),C)))))))) = multiply(inverse(multiply(F,B)),multiply(F,E)),
inference(paramod,[status(thm)],[c_4,c_451]) ).
cnf(c_472,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_1,c_2494]) ).
cnf(c_485,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_286,c_451]) ).
cnf(c_550,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))),a2) != a2,
inference(paramod,[status(thm)],[c_485,c_2]) ).
cnf(c_2495,plain,
multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(A))))))),inverse(multiply(inverse(C),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_48,c_485]) ).
cnf(c_603,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_48,c_2495]) ).
cnf(c_2496,plain,
multiply(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(A))))))),inverse(multiply(inverse(C),C)))),a2) != a2,
inference(paramod,[status(thm)],[c_48,c_550]) ).
cnf(c_695,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(paramod,[status(thm)],[c_48,c_2496]) ).
cnf(c_703,plain,
multiply(multiply(A,multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,inverse(A)))),inverse(multiply(inverse(B),B)))))),a2) != a2,
inference(paramod,[status(thm)],[c_1,c_695]) ).
cnf(c_740,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))))),multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,C))),inverse(multiply(inverse(D),D)))))),a2) != a2,
inference(paramod,[status(thm)],[c_14,c_703]) ).
cnf(c_767,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(A)),inverse(A))))))) = A,
inference(paramod,[status(thm)],[c_603,c_1]) ).
cnf(c_785,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(A),A))))))) = A,
inference(paramod,[status(thm)],[c_603,c_14]) ).
cnf(c_792,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),B)),multiply(inverse(D),D))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_603,c_24]) ).
cnf(c_807,plain,
multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,A))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_603,c_115]) ).
cnf(c_830,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_603,c_472]) ).
cnf(c_831,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,A)),
inference(paramod,[status(thm)],[c_603,c_472]) ).
cnf(c_843,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C))))))) = A,
inference(paramod,[status(thm)],[c_603,c_785]) ).
cnf(c_859,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_830,c_603]) ).
cnf(c_997,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C)))))) = A,
inference(paramod,[status(thm)],[c_603,c_767]) ).
cnf(c_2497,plain,
multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(C)),inverse(C))))))),multiply(inverse(D),D)) = multiply(C,multiply(inverse(C),A)),
inference(paramod,[status(thm)],[c_767,c_831]) ).
cnf(c_1024,plain,
multiply(A,multiply(inverse(B),B)) = multiply(C,multiply(inverse(C),A)),
inference(paramod,[status(thm)],[c_997,c_2497]) ).
cnf(c_2498,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),inverse(multiply(inverse(C),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))))))) = C,
inference(paramod,[status(thm)],[c_997,c_452]) ).
cnf(c_1029,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),C))))) = C,
inference(paramod,[status(thm)],[c_997,c_2498]) ).
cnf(c_2499,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),C)),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_997,c_376]) ).
cnf(c_1030,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(multiply(inverse(B),B),C))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_997,c_2499]) ).
cnf(c_2500,plain,
multiply(inverse(inverse(C)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = C,
inference(paramod,[status(thm)],[c_1029,c_308]) ).
cnf(c_1034,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))) = A,
inference(paramod,[status(thm)],[c_997,c_2500]) ).
cnf(c_2501,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))))))) = C,
inference(paramod,[status(thm)],[c_1034,c_299]) ).
cnf(c_1036,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))))) = C,
inference(paramod,[status(thm)],[c_997,c_2501]) ).
cnf(c_2502,plain,
multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_1024,c_603]) ).
cnf(c_1049,plain,
multiply(inverse(A),A) = multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),C)))),
inference(copy,[status(thm)],[c_2502]) ).
cnf(c_1095,plain,
multiply(A,multiply(inverse(A),B)) = multiply(C,multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_1024,c_1024]) ).
cnf(c_2503,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D))))))))) = A,
inference(paramod,[status(thm)],[c_997,c_843]) ).
cnf(c_1283,plain,
inverse(inverse(multiply(A,multiply(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_997,c_2503]) ).
cnf(c_2504,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D)))))))) = A,
inference(paramod,[status(thm)],[c_997,c_997]) ).
cnf(c_1335,plain,
inverse(multiply(inverse(A),multiply(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_997,c_2504]) ).
cnf(c_2505,plain,
multiply(multiply(inverse(A),B),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,A))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_1335,c_807]) ).
cnf(c_1397,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(inverse(B),B))) = multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))),
inference(copy,[status(thm)],[c_2505]) ).
cnf(c_1400,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(multiply(inverse(inverse(inverse(C))),B),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_1335,c_792]) ).
cnf(c_2506,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(C),A),inverse(multiply(inverse(A),A)))))),multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,C))),inverse(multiply(inverse(D),D)))))),a2) != a2,
inference(paramod,[status(thm)],[c_1397,c_740]) ).
cnf(c_1510,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(B),A),inverse(multiply(inverse(A),A)))))),multiply(C,inverse(multiply(multiply(inverse(B),C),inverse(multiply(inverse(C),C)))))),a2) != a2,
inference(paramod,[status(thm)],[c_1397,c_2506]) ).
cnf(c_1744,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(multiply(inverse(B),B),C))) = multiply(multiply(inverse(inverse(inverse(C))),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_1400,c_1030]) ).
cnf(c_1776,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,B))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D)))),E)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = E,
inference(paramod,[status(thm)],[c_843,c_204]) ).
cnf(c_1793,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(multiply(inverse(D),D),E)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = E,
inference(paramod,[status(thm)],[c_859,c_204]) ).
cnf(c_1922,plain,
inverse(inverse(multiply(A,multiply(inverse(A),B)))) = B,
inference(paramod,[status(thm)],[c_1024,c_1283]) ).
cnf(c_1966,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = multiply(inverse(C),B),
inference(paramod,[status(thm)],[c_472,c_1335]) ).
cnf(c_2052,plain,
multiply(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),inverse(multiply(inverse(B),B))),inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_1966,c_1793]) ).
cnf(c_2057,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C)))),D)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))))) = D,
inference(paramod,[status(thm)],[c_1966,c_1776]) ).
cnf(c_2507,plain,
inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,C)))) = C,
inference(paramod,[status(thm)],[c_830,c_1922]) ).
cnf(c_2213,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_1966,c_2507]) ).
cnf(c_2241,plain,
inverse(inverse(multiply(A,multiply(B,multiply(inverse(B),C))))) = multiply(inverse(inverse(A)),C),
inference(paramod,[status(thm)],[c_1095,c_1922]) ).
cnf(c_2508,plain,
inverse(inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),C))))))) = A,
inference(paramod,[status(thm)],[c_1049,c_1922]) ).
cnf(c_2245,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_2241,c_2508]) ).
cnf(c_2509,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(multiply(inverse(B),B),D)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))))) = D,
inference(paramod,[status(thm)],[c_2213,c_2057]) ).
cnf(c_2510,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(multiply(inverse(B),B),D)),inverse(multiply(inverse(A),A)))))))) = D,
inference(paramod,[status(thm)],[c_2245,c_2509]) ).
cnf(c_2306,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),multiply(multiply(inverse(B),B),C))))) = C,
inference(paramod,[status(thm)],[c_2213,c_2510]) ).
cnf(c_2511,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_2245,c_2052]) ).
cnf(c_2512,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_2245,c_2511]) ).
cnf(c_2513,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_2245,c_2512]) ).
cnf(c_2514,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = D,
inference(paramod,[status(thm)],[c_2245,c_2513]) ).
cnf(c_2515,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(B),B)))))))) = D,
inference(paramod,[status(thm)],[c_2245,c_2514]) ).
cnf(c_2309,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(multiply(inverse(C),C),D))))) = D,
inference(paramod,[status(thm)],[c_2213,c_2515]) ).
cnf(c_2516,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B)))),multiply(multiply(inverse(B),B),C))) = multiply(multiply(inverse(inverse(inverse(C))),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_2245,c_1744]) ).
cnf(c_2517,plain,
inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C))) = multiply(multiply(inverse(inverse(inverse(C))),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_2213,c_2516]) ).
cnf(c_2518,plain,
inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C))) = multiply(inverse(C),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_2245,c_2517]) ).
cnf(c_2331,plain,
inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C))) = multiply(inverse(C),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_2245,c_2518]) ).
cnf(c_2519,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B)))),multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))))) = C,
inference(paramod,[status(thm)],[c_2245,c_1036]) ).
cnf(c_2520,plain,
inverse(inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))))) = C,
inference(paramod,[status(thm)],[c_2213,c_2519]) ).
cnf(c_2521,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),C)),inverse(multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_2331,c_2520]) ).
cnf(c_2419,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(paramod,[status(thm)],[c_2213,c_2521]) ).
cnf(c_2522,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(multiply(inverse(C),C),D)))) = D,
inference(paramod,[status(thm)],[c_2419,c_2309]) ).
cnf(c_2478,plain,
inverse(inverse(multiply(multiply(inverse(A),A),B))) = B,
inference(paramod,[status(thm)],[c_2419,c_2522]) ).
cnf(c_2523,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(multiply(inverse(B),B),C)))) = C,
inference(paramod,[status(thm)],[c_2419,c_2306]) ).
cnf(c_2481,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(paramod,[status(thm)],[c_2478,c_2523]) ).
cnf(c_2482,plain,
$false,
inference(resolve,[status(thm)],[c_2481,c_1510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:55:25 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2811917 was started by sandbox on n026,
% 0.17/0.43 % Fri Sep 25 14:55:25 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 11.57/1.98
% 11.57/1.98 % SZS status Unsatisfiable for theBenchmark
% 11.57/1.98
% 11.57/1.98 % Proof 1 at 1.34 (+ 0.18) seconds.
% 11.57/1.98 % Length of proof is 69.
% 11.57/1.98 % Level of proof is 20.
% 11.57/1.98 % Maximum clause weight is 96.000.
% 11.57/1.98 % Given clauses 57.
% 11.57/1.98
% 11.57/1.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------