%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 06:55:13 AM UTC 2026
% Result : Unsatisfiable 1.91s 0.67s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 2
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 507 ( 7 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] : multiply(multiply(VAR_0,inverse(VAR_0),VAR_1),inverse(multiply(multiply(VAR_2,VAR_3,VAR_4),VAR_5,multiply(VAR_2,VAR_3,VAR_6))),multiply(VAR_3,multiply(VAR_6,VAR_5,VAR_4),VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C)) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_tba_axioms_4,axiom,
multiply(a,a,b) != a,
file('theBenchmark.p',prove_tba_axioms_4) ).
cnf(c_2,plain,
multiply(a,a,b) != a,
inference(clausify,[status(thm)],[prove_tba_axioms_4]) ).
cnf(c_3,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(E,multiply(V7,V6,F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V8)),V8),A),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,multiply(E,multiply(F,V6,V7),V8)),inverse(multiply(multiply(V8,E,V7),V6,multiply(V8,E,F))),multiply(C,D,multiply(V9,inverse(V9),V10)))),multiply(D,V10,C)) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
multiply(inverse(A),multiply(B,inverse(multiply(A,inverse(A),C)),C),A) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_20,plain,
multiply(A,multiply(B,inverse(multiply(C,A,D)),D),C) = multiply(A,multiply(B,inverse(multiply(C,A,E)),E),C),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_27,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,inverse(C),D),inverse(multiply(C,inverse(C),D)),multiply(C,inverse(C),E))),E) = B,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_572,plain,
multiply(A,inverse(multiply(multiply(B,C,D),E,multiply(B,C,F))),multiply(C,multiply(F,E,D),B)) = multiply(multiply(A,inverse(multiply(V6,inverse(V6),V7)),V7),multiply(V6,inverse(multiply(inverse(V6),multiply(A,inverse(multiply(V6,inverse(V6),V7)),V7),V8)),V8),inverse(V6)),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_29,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(B,inverse(multiply(inverse(B),multiply(A,inverse(multiply(B,inverse(B),C)),C),D)),D),inverse(B)) = multiply(A,inverse(multiply(multiply(E,F,V6),V7,multiply(E,F,V8))),multiply(F,multiply(V8,V7,V6),E)),
inference(copy,[status(thm)],[c_572]) ).
cnf(c_45,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,E,F),inverse(multiply(D,E,F)),multiply(D,E,V6))),multiply(E,multiply(V6,inverse(multiply(D,E,V7)),V7),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V8)),V8),A),
inference(paramod,[status(thm)],[c_20,c_3]) ).
cnf(c_573,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(D,inverse(A),B),inverse(B)) = multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(D,inverse(multiply(inverse(B),multiply(A,inverse(multiply(B,inverse(B),C)),C),E)),E),inverse(B)),
inference(paramod,[status(thm)],[c_10,c_20]) ).
cnf(c_47,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(D,inverse(multiply(inverse(B),multiply(A,inverse(multiply(B,inverse(B),C)),C),E)),E),inverse(B)) = multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(D,inverse(A),B),inverse(B)),
inference(copy,[status(thm)],[c_573]) ).
cnf(c_49,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(E,multiply(V7,V6,F),D)),
inference(paramod,[status(thm)],[c_47,c_29]) ).
cnf(c_574,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(inverse(C),multiply(D,inverse(multiply(C,inverse(C),E)),E),C),inverse(D),multiply(inverse(C),multiply(D,inverse(multiply(C,inverse(C),E)),E),C))),multiply(D,inverse(multiply(multiply(F,V6,V7),V8,multiply(F,V6,V9))),multiply(V6,multiply(V9,V8,V7),F))) = B,
inference(paramod,[status(thm)],[c_49,c_1]) ).
cnf(c_575,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(D,inverse(D),multiply(inverse(C),multiply(D,inverse(multiply(C,inverse(C),E)),E),C))),multiply(D,inverse(multiply(multiply(F,V6,V7),V8,multiply(F,V6,V9))),multiply(V6,multiply(V9,V8,V7),F))) = B,
inference(paramod,[status(thm)],[c_10,c_574]) ).
cnf(c_69,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),C)),multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(E,multiply(V7,V6,F),D))) = B,
inference(paramod,[status(thm)],[c_10,c_575]) ).
cnf(c_576,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(inverse(D),multiply(E,inverse(multiply(D,inverse(D),F)),F),D),inverse(E),multiply(inverse(D),multiply(E,inverse(multiply(D,inverse(D),F)),F),D))),multiply(E,inverse(multiply(multiply(V6,V7,V8),V9,multiply(V6,V7,V10))),multiply(V7,multiply(V10,V9,V8),V6))) = multiply(B,multiply(C,inverse(multiply(A,B,V11)),V11),A),
inference(paramod,[status(thm)],[c_49,c_3]) ).
cnf(c_577,plain,
multiply(multiply(A,B,C),inverse(multiply(E,inverse(E),multiply(inverse(D),multiply(E,inverse(multiply(D,inverse(D),F)),F),D))),multiply(E,inverse(multiply(multiply(V6,V7,V8),V9,multiply(V6,V7,V10))),multiply(V7,multiply(V10,V9,V8),V6))) = multiply(B,multiply(C,inverse(multiply(A,B,V11)),V11),A),
inference(paramod,[status(thm)],[c_10,c_576]) ).
cnf(c_75,plain,
multiply(multiply(A,B,C),inverse(multiply(D,inverse(D),D)),multiply(D,inverse(multiply(multiply(E,F,V6),V7,multiply(E,F,V8))),multiply(F,multiply(V8,V7,V6),E))) = multiply(B,multiply(C,inverse(multiply(A,B,V9)),V9),A),
inference(paramod,[status(thm)],[c_10,c_577]) ).
cnf(c_80,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(multiply(D,E,F),inverse(multiply(D,E,F)),multiply(D,E,V6))),multiply(multiply(D,E,V6),inverse(multiply(multiply(V7,V8,V9),V10,multiply(V7,V8,V11))),multiply(V8,multiply(V11,V10,V9),V7))),
inference(paramod,[status(thm)],[c_3,c_49]) ).
cnf(c_109,plain,
multiply(inverse(multiply(A,inverse(A),A)),multiply(B,inverse(A),multiply(A,inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C))),multiply(A,inverse(A),A)) = B,
inference(paramod,[status(thm)],[c_69,c_10]) ).
cnf(c_125,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),C)),multiply(multiply(C,inverse(multiply(D,inverse(D),E)),E),multiply(D,inverse(C),D),inverse(D))) = B,
inference(paramod,[status(thm)],[c_49,c_69]) ).
cnf(c_156,plain,
multiply(multiply(A,multiply(multiply(B,C,D),inverse(multiply(multiply(B,C,E),A,F)),F),multiply(B,C,E)),inverse(multiply(V6,inverse(V6),V6)),multiply(multiply(V6,inverse(multiply(V7,inverse(V7),V8)),V8),multiply(V7,inverse(V6),V7),inverse(V7))) = multiply(C,multiply(D,A,E),B),
inference(paramod,[status(thm)],[c_3,c_125]) ).
cnf(c_578,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(inverse(C),multiply(multiply(D,inverse(D),multiply(E,inverse(E),F)),inverse(multiply(C,inverse(C),V6)),V6),C)),multiply(inverse(D),F,D)) = B,
inference(paramod,[status(thm)],[c_27,c_6]) ).
cnf(c_240,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),multiply(D,inverse(D),E))),multiply(inverse(C),E,C)) = B,
inference(paramod,[status(thm)],[c_10,c_578]) ).
cnf(c_579,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C)) = multiply(inverse(V7),B,V7),
inference(paramod,[status(thm)],[c_240,c_1]) ).
cnf(c_580,plain,
B = multiply(inverse(V7),B,V7),
inference(paramod,[status(thm)],[c_1,c_579]) ).
cnf(c_245,plain,
multiply(inverse(A),B,A) = B,
inference(copy,[status(thm)],[c_580]) ).
cnf(c_581,plain,
multiply(inverse(multiply(A,inverse(A),multiply(B,inverse(B),C))),multiply(D,inverse(multiply(B,inverse(B),C)),multiply(inverse(A),C,A)),multiply(A,inverse(A),multiply(B,inverse(B),C))) = D,
inference(paramod,[status(thm)],[c_240,c_10]) ).
cnf(c_582,plain,
multiply(inverse(multiply(A,inverse(A),multiply(B,inverse(B),C))),multiply(D,inverse(multiply(B,inverse(B),C)),C),multiply(A,inverse(A),multiply(B,inverse(B),C))) = D,
inference(paramod,[status(thm)],[c_245,c_581]) ).
cnf(c_258,plain,
multiply(A,inverse(multiply(B,inverse(B),C)),C) = A,
inference(paramod,[status(thm)],[c_245,c_582]) ).
cnf(c_319,plain,
multiply(A,inverse(B),multiply(B,inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C))) = A,
inference(paramod,[status(thm)],[c_245,c_109]) ).
cnf(c_352,plain,
multiply(multiply(A,multiply(multiply(B,C,D),inverse(multiply(multiply(B,C,E),A,F)),F),multiply(B,C,E)),inverse(multiply(V6,inverse(V6),V6)),multiply(V6,multiply(V7,inverse(V6),V7),inverse(V7))) = multiply(C,multiply(D,A,E),B),
inference(paramod,[status(thm)],[c_258,c_156]) ).
cnf(c_381,plain,
multiply(A,multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(multiply(C,D,E),inverse(multiply(C,D,E)),multiply(C,D,F))),multiply(multiply(C,D,F),inverse(multiply(multiply(V6,V7,V8),V9,multiply(V6,V7,V10))),multiply(V7,multiply(V10,V9,V8),V6))),
inference(paramod,[status(thm)],[c_258,c_80]) ).
cnf(c_425,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(B,C,multiply(D,multiply(E,F,V6),V7)),inverse(multiply(multiply(V7,D,V6),F,multiply(V7,D,E))),multiply(B,C,multiply(V8,inverse(V8),V9)))),multiply(C,V9,B)) = A,
inference(paramod,[status(thm)],[c_245,c_6]) ).
cnf(c_435,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),inverse(multiply(F,inverse(F),E)),multiply(C,D,V6))),multiply(D,V6,C)) = B,
inference(paramod,[status(thm)],[c_258,c_1]) ).
cnf(c_440,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,E,F),inverse(multiply(V6,inverse(V6),F)),multiply(D,E,V7))),multiply(E,V7,D)) = multiply(B,multiply(C,inverse(multiply(A,B,V8)),V8),A),
inference(paramod,[status(thm)],[c_258,c_3]) ).
cnf(c_583,plain,
multiply(inverse(multiply(A,inverse(A),B)),multiply(C,inverse(D),B),D) = multiply(inverse(multiply(A,inverse(A),B)),multiply(C,inverse(multiply(D,inverse(multiply(A,inverse(A),B)),E)),E),D),
inference(paramod,[status(thm)],[c_258,c_20]) ).
cnf(c_442,plain,
multiply(inverse(multiply(A,inverse(A),B)),multiply(C,inverse(multiply(D,inverse(multiply(A,inverse(A),B)),E)),E),D) = multiply(inverse(multiply(A,inverse(A),B)),multiply(C,inverse(D),B),D),
inference(copy,[status(thm)],[c_583]) ).
cnf(c_584,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,inverse(multiply(E,inverse(E),F)),V6),inverse(multiply(D,inverse(multiply(E,inverse(E),F)),V6)),D)),multiply(inverse(multiply(E,inverse(E),F)),multiply(F,inverse(multiply(D,inverse(multiply(E,inverse(E),F)),V7)),V7),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V8)),V8),A),
inference(paramod,[status(thm)],[c_258,c_45]) ).
cnf(c_458,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,inverse(multiply(E,inverse(E),F)),V6),inverse(multiply(D,inverse(multiply(E,inverse(E),F)),V6)),D)),multiply(inverse(multiply(E,inverse(E),F)),multiply(F,inverse(D),F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_442,c_584]) ).
cnf(c_465,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B),C)),D),inverse(multiply(E,inverse(E),E)),multiply(E,inverse(multiply(multiply(F,V6,V7),V8,multiply(F,V6,V9))),multiply(V6,multiply(V9,V8,V7),F))) = multiply(inverse(multiply(B,inverse(B),C)),multiply(D,inverse(A),C),A),
inference(paramod,[status(thm)],[c_258,c_75]) ).
cnf(c_585,plain,
inverse(A) = inverse(multiply(B,inverse(B),A)),
inference(paramod,[status(thm)],[c_258,c_245]) ).
cnf(c_473,plain,
inverse(multiply(A,inverse(A),B)) = inverse(B),
inference(copy,[status(thm)],[c_585]) ).
cnf(c_586,plain,
multiply(A,inverse(multiply(B,inverse(B),C)),C) = A,
inference(paramod,[status(thm)],[c_258,c_258]) ).
cnf(c_475,plain,
multiply(A,inverse(B),B) = A,
inference(paramod,[status(thm)],[c_473,c_586]) ).
cnf(c_587,plain,
multiply(multiply(A,inverse(C),D),inverse(multiply(E,inverse(E),E)),multiply(E,inverse(multiply(multiply(F,V6,V7),V8,multiply(F,V6,V9))),multiply(V6,multiply(V9,V8,V7),F))) = multiply(inverse(multiply(B,inverse(B),C)),multiply(D,inverse(A),C),A),
inference(paramod,[status(thm)],[c_473,c_465]) ).
cnf(c_588,plain,
multiply(multiply(A,inverse(C),D),inverse(E),multiply(E,inverse(multiply(multiply(F,V6,V7),V8,multiply(F,V6,V9))),multiply(V6,multiply(V9,V8,V7),F))) = multiply(inverse(multiply(B,inverse(B),C)),multiply(D,inverse(A),C),A),
inference(paramod,[status(thm)],[c_475,c_587]) ).
cnf(c_589,plain,
multiply(A,inverse(C),D) = multiply(inverse(multiply(B,inverse(B),C)),multiply(D,inverse(A),C),A),
inference(paramod,[status(thm)],[c_319,c_588]) ).
cnf(c_590,plain,
multiply(A,inverse(C),D) = multiply(inverse(C),multiply(D,inverse(A),C),A),
inference(paramod,[status(thm)],[c_473,c_589]) ).
cnf(c_484,plain,
multiply(inverse(A),multiply(B,inverse(C),A),C) = multiply(C,inverse(A),B),
inference(copy,[status(thm)],[c_590]) ).
cnf(c_591,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,inverse(F),V6),inverse(multiply(D,inverse(multiply(E,inverse(E),F)),V6)),D)),multiply(inverse(multiply(E,inverse(E),F)),multiply(F,inverse(D),F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_473,c_458]) ).
cnf(c_592,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,inverse(F),V6),inverse(multiply(D,inverse(F),V6)),D)),multiply(inverse(multiply(E,inverse(E),F)),multiply(F,inverse(D),F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_473,c_591]) ).
cnf(c_593,plain,
multiply(multiply(A,B,C),inverse(D),multiply(inverse(multiply(E,inverse(E),F)),multiply(F,inverse(D),F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_473,c_592]) ).
cnf(c_594,plain,
multiply(multiply(A,B,C),inverse(D),multiply(inverse(F),multiply(F,inverse(D),F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_473,c_593]) ).
cnf(c_595,plain,
multiply(multiply(A,B,C),inverse(D),multiply(D,inverse(F),F)) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_484,c_594]) ).
cnf(c_596,plain,
multiply(multiply(A,B,C),inverse(D),D) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_475,c_595]) ).
cnf(c_597,plain,
multiply(A,B,C) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_475,c_596]) ).
cnf(c_489,plain,
multiply(A,multiply(B,inverse(multiply(C,A,D)),D),C) = multiply(C,A,B),
inference(copy,[status(thm)],[c_597]) ).
cnf(c_598,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,E,F),inverse(F),multiply(D,E,V7))),multiply(E,V7,D)) = multiply(B,multiply(C,inverse(multiply(A,B,V8)),V8),A),
inference(paramod,[status(thm)],[c_473,c_440]) ).
cnf(c_502,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,E,F),inverse(F),multiply(D,E,V6))),multiply(E,V6,D)) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_489,c_598]) ).
cnf(c_599,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),inverse(E),multiply(C,D,V6))),multiply(D,V6,C)) = B,
inference(paramod,[status(thm)],[c_473,c_435]) ).
cnf(c_506,plain,
multiply(A,inverse(A),B) = B,
inference(paramod,[status(thm)],[c_502,c_599]) ).
cnf(c_600,plain,
multiply(A,multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(C,D,F)),multiply(multiply(C,D,F),inverse(multiply(multiply(V6,V7,V8),V9,multiply(V6,V7,V10))),multiply(V7,multiply(V10,V9,V8),V6))),
inference(paramod,[status(thm)],[c_506,c_381]) ).
cnf(c_518,plain,
multiply(A,multiply(B,inverse(A),B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_319,c_600]) ).
cnf(c_601,plain,
multiply(multiply(multiply(B,C,E),A,multiply(B,C,D)),inverse(multiply(V6,inverse(V6),V6)),multiply(V6,multiply(V7,inverse(V6),V7),inverse(V7))) = multiply(C,multiply(D,A,E),B),
inference(paramod,[status(thm)],[c_489,c_352]) ).
cnf(c_602,plain,
multiply(multiply(multiply(B,C,E),A,multiply(B,C,D)),inverse(V6),multiply(V6,multiply(V7,inverse(V6),V7),inverse(V7))) = multiply(C,multiply(D,A,E),B),
inference(paramod,[status(thm)],[c_506,c_601]) ).
cnf(c_603,plain,
multiply(multiply(multiply(B,C,E),A,multiply(B,C,D)),inverse(V6),V6) = multiply(C,multiply(D,A,E),B),
inference(paramod,[status(thm)],[c_518,c_602]) ).
cnf(c_525,plain,
multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(B,multiply(E,D,C),A),
inference(paramod,[status(thm)],[c_475,c_603]) ).
cnf(c_604,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(B,C,multiply(D,multiply(E,F,V6),V7)),inverse(multiply(D,multiply(E,F,V6),V7)),multiply(B,C,multiply(V8,inverse(V8),V9)))),multiply(C,V9,B)) = A,
inference(paramod,[status(thm)],[c_525,c_425]) ).
cnf(c_605,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(B,C,multiply(D,multiply(E,F,V6),V7)),inverse(multiply(D,multiply(E,F,V6),V7)),multiply(B,C,V9))),multiply(C,V9,B)) = A,
inference(paramod,[status(thm)],[c_506,c_604]) ).
cnf(c_606,plain,
multiply(inverse(inverse(A)),inverse(multiply(C,multiply(V9,inverse(multiply(D,multiply(E,F,V6),V7)),multiply(D,multiply(E,F,V6),V7)),B)),multiply(C,V9,B)) = A,
inference(paramod,[status(thm)],[c_525,c_605]) ).
cnf(c_607,plain,
multiply(inverse(inverse(A)),inverse(multiply(C,V9,B)),multiply(C,V9,B)) = A,
inference(paramod,[status(thm)],[c_475,c_606]) ).
cnf(c_555,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_475,c_607]) ).
cnf(c_608,plain,
multiply(inverse(A),inverse(B),B) = multiply(B,inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_245,c_484]) ).
cnf(c_609,plain,
inverse(A) = multiply(B,inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_475,c_608]) ).
cnf(c_567,plain,
multiply(A,inverse(B),inverse(B)) = inverse(B),
inference(copy,[status(thm)],[c_609]) ).
cnf(c_610,plain,
multiply(inverse(inverse(A)),inverse(A),A) = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_567,c_484]) ).
cnf(c_611,plain,
multiply(A,inverse(A),A) = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_555,c_610]) ).
cnf(c_612,plain,
A = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_506,c_611]) ).
cnf(c_613,plain,
A = multiply(A,A,B),
inference(paramod,[status(thm)],[c_555,c_612]) ).
cnf(c_570,plain,
multiply(A,A,B) = A,
inference(copy,[status(thm)],[c_613]) ).
cnf(c_571,plain,
$false,
inference(resolve,[status(thm)],[c_570,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 22:42:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 90246 was started by sandbox2 on n014,
% 0.10/0.38 % Sat Sep 26 22:42:47 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 1.91/0.67
% 1.91/0.67 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.91/0.67
% 1.91/0.67 % SZS status Unsatisfiable for theBenchmark
% 1.91/0.67
% 1.91/0.67 % Proof 1 at 0.22 (+ 0.05) seconds.
% 1.91/0.67 % Length of proof is 41.
% 1.91/0.67 % Level of proof is 17.
% 1.91/0.67 % Maximum clause weight is 97.000.
% 1.91/0.67 % Given clauses 32.
% 1.91/0.67
% 1.91/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------