%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO067-1 : 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 : n009.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 06:55:12 AM UTC 2026
% Result : Unsatisfiable 1.78s 0.64s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 2
% Syntax : Number of formulae : 125 ( 125 unt; 0 def)
% Number of atoms : 125 ( 124 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 608 ( 11 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_1,axiom,
multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)),
file('theBenchmark.p',prove_tba_axioms_1) ).
cnf(c_2,plain,
multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)),
inference(clausify,[status(thm)],[prove_tba_axioms_1]) ).
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_1029,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_1029]) ).
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_1030,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_1030]) ).
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_1031,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_1032,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_1031]) ).
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_1032]) ).
cnf(c_1033,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_1034,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_1033]) ).
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_1034]) ).
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_1035,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_1035]) ).
cnf(c_1036,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_1037,plain,
B = multiply(inverse(V7),B,V7),
inference(paramod,[status(thm)],[c_1,c_1036]) ).
cnf(c_245,plain,
multiply(inverse(A),B,A) = B,
inference(copy,[status(thm)],[c_1037]) ).
cnf(c_1038,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_1039,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_1038]) ).
cnf(c_258,plain,
multiply(A,inverse(multiply(B,inverse(B),C)),C) = A,
inference(paramod,[status(thm)],[c_245,c_1039]) ).
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_1040,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_1040]) ).
cnf(c_1041,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_1041]) ).
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_1042,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_1042]) ).
cnf(c_1043,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_1043]) ).
cnf(c_1044,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_1045,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_1044]) ).
cnf(c_1046,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_1045]) ).
cnf(c_1047,plain,
multiply(A,inverse(C),D) = multiply(inverse(C),multiply(D,inverse(A),C),A),
inference(paramod,[status(thm)],[c_473,c_1046]) ).
cnf(c_484,plain,
multiply(inverse(A),multiply(B,inverse(C),A),C) = multiply(C,inverse(A),B),
inference(copy,[status(thm)],[c_1047]) ).
cnf(c_1048,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_1049,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_1048]) ).
cnf(c_1050,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_1049]) ).
cnf(c_1051,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_1050]) ).
cnf(c_1052,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_1051]) ).
cnf(c_1053,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_1052]) ).
cnf(c_1054,plain,
multiply(A,B,C) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_475,c_1053]) ).
cnf(c_489,plain,
multiply(A,multiply(B,inverse(multiply(C,A,D)),D),C) = multiply(C,A,B),
inference(copy,[status(thm)],[c_1054]) ).
cnf(c_1055,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_1055]) ).
cnf(c_1056,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_1056]) ).
cnf(c_1057,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_1057]) ).
cnf(c_1058,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_1059,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_1058]) ).
cnf(c_1060,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_1059]) ).
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_1060]) ).
cnf(c_1061,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_1062,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_1061]) ).
cnf(c_1063,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_1062]) ).
cnf(c_1064,plain,
multiply(inverse(inverse(A)),inverse(multiply(C,V9,B)),multiply(C,V9,B)) = A,
inference(paramod,[status(thm)],[c_475,c_1063]) ).
cnf(c_555,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_475,c_1064]) ).
cnf(c_567,plain,
multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)),
inference(paramod,[status(thm)],[c_525,c_2]) ).
cnf(c_1065,plain,
multiply(inverse(A),inverse(B),B) = multiply(B,inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_245,c_484]) ).
cnf(c_1066,plain,
inverse(A) = multiply(B,inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_475,c_1065]) ).
cnf(c_568,plain,
multiply(A,inverse(B),inverse(B)) = inverse(B),
inference(copy,[status(thm)],[c_1066]) ).
cnf(c_1067,plain,
multiply(inverse(inverse(A)),inverse(A),A) = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_568,c_484]) ).
cnf(c_1068,plain,
multiply(A,inverse(A),A) = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_555,c_1067]) ).
cnf(c_1069,plain,
A = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_506,c_1068]) ).
cnf(c_1070,plain,
A = multiply(A,A,B),
inference(paramod,[status(thm)],[c_555,c_1069]) ).
cnf(c_571,plain,
multiply(A,A,B) = A,
inference(copy,[status(thm)],[c_1070]) ).
cnf(c_1071,plain,
multiply(inverse(A),inverse(B),B) = multiply(B,inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_571,c_484]) ).
cnf(c_1072,plain,
inverse(A) = multiply(B,inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_475,c_1071]) ).
cnf(c_574,plain,
multiply(A,inverse(B),inverse(A)) = inverse(B),
inference(copy,[status(thm)],[c_1072]) ).
cnf(c_1073,plain,
multiply(inverse(inverse(A)),inverse(B),B) = multiply(B,inverse(inverse(A)),A),
inference(paramod,[status(thm)],[c_574,c_484]) ).
cnf(c_1074,plain,
multiply(A,inverse(B),B) = multiply(B,inverse(inverse(A)),A),
inference(paramod,[status(thm)],[c_555,c_1073]) ).
cnf(c_1075,plain,
A = multiply(B,inverse(inverse(A)),A),
inference(paramod,[status(thm)],[c_475,c_1074]) ).
cnf(c_1076,plain,
A = multiply(B,A,A),
inference(paramod,[status(thm)],[c_555,c_1075]) ).
cnf(c_579,plain,
multiply(A,B,B) = B,
inference(copy,[status(thm)],[c_1076]) ).
cnf(c_1077,plain,
multiply(A,B,C) = multiply(C,A,multiply(C,A,B)),
inference(paramod,[status(thm)],[c_506,c_489]) ).
cnf(c_580,plain,
multiply(A,B,multiply(A,B,C)) = multiply(B,C,A),
inference(copy,[status(thm)],[c_1077]) ).
cnf(c_1078,plain,
multiply(A,multiply(B,inverse(A),A),C) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_579,c_489]) ).
cnf(c_594,plain,
multiply(A,B,C) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_475,c_1078]) ).
cnf(c_1079,plain,
multiply(e,multiply(a,c,b),d) != multiply(d,e,multiply(a,b,c)),
inference(paramod,[status(thm)],[c_594,c_567]) ).
cnf(c_595,plain,
multiply(d,e,multiply(a,c,b)) != multiply(d,e,multiply(a,b,c)),
inference(paramod,[status(thm)],[c_594,c_1079]) ).
cnf(c_610,plain,
multiply(A,B,A) = A,
inference(paramod,[status(thm)],[c_594,c_571]) ).
cnf(c_1080,plain,
multiply(A,B,C) = multiply(multiply(C,A,B),C,A),
inference(paramod,[status(thm)],[c_580,c_594]) ).
cnf(c_1081,plain,
multiply(A,B,C) = multiply(A,multiply(C,A,B),C),
inference(paramod,[status(thm)],[c_594,c_1080]) ).
cnf(c_640,plain,
multiply(A,multiply(B,A,C),B) = multiply(A,C,B),
inference(copy,[status(thm)],[c_1081]) ).
cnf(c_642,plain,
multiply(A,B,multiply(B,C,A)) = multiply(B,C,A),
inference(paramod,[status(thm)],[c_594,c_580]) ).
cnf(c_645,plain,
multiply(A,multiply(B,C,A),C) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_594,c_640]) ).
cnf(c_1082,plain,
multiply(A,multiply(B,A,C),multiply(A,C,B)) = multiply(multiply(B,A,C),B,A),
inference(paramod,[status(thm)],[c_640,c_580]) ).
cnf(c_1083,plain,
multiply(A,multiply(B,A,C),multiply(A,C,B)) = multiply(A,multiply(B,A,C),B),
inference(paramod,[status(thm)],[c_594,c_1082]) ).
cnf(c_647,plain,
multiply(A,multiply(B,A,C),multiply(A,C,B)) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_640,c_1083]) ).
cnf(c_698,plain,
multiply(A,multiply(B,A,C),multiply(C,B,A)) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_594,c_647]) ).
cnf(c_703,plain,
multiply(A,multiply(A,B,C),multiply(B,C,A)) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_594,c_698]) ).
cnf(c_1084,plain,
multiply(A,B,multiply(C,A,D)) = multiply(A,multiply(D,B,A),C),
inference(paramod,[status(thm)],[c_579,c_525]) ).
cnf(c_809,plain,
multiply(A,multiply(B,C,A),D) = multiply(A,C,multiply(D,A,B)),
inference(copy,[status(thm)],[c_1084]) ).
cnf(c_1085,plain,
multiply(A,multiply(multiply(B,A,C),B,C),B) = multiply(B,A,multiply(B,A,C)),
inference(paramod,[status(thm)],[c_525,c_642]) ).
cnf(c_1086,plain,
multiply(A,multiply(C,multiply(B,A,C),B),B) = multiply(B,A,multiply(B,A,C)),
inference(paramod,[status(thm)],[c_594,c_1085]) ).
cnf(c_1087,plain,
multiply(A,multiply(C,A,multiply(B,C,B)),B) = multiply(B,A,multiply(B,A,C)),
inference(paramod,[status(thm)],[c_809,c_1086]) ).
cnf(c_1088,plain,
multiply(A,multiply(C,A,B),B) = multiply(B,A,multiply(B,A,C)),
inference(paramod,[status(thm)],[c_610,c_1087]) ).
cnf(c_838,plain,
multiply(A,multiply(B,A,C),C) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_580,c_1088]) ).
cnf(c_1089,plain,
multiply(multiply(multiply(A,B,C),C,B),A,multiply(multiply(A,B,C),C,C)) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_703,c_525]) ).
cnf(c_1090,plain,
multiply(multiply(B,multiply(A,B,C),C),A,multiply(multiply(A,B,C),C,C)) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_594,c_1089]) ).
cnf(c_1091,plain,
multiply(multiply(B,A,C),A,multiply(multiply(A,B,C),C,C)) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_838,c_1090]) ).
cnf(c_1092,plain,
multiply(multiply(B,A,C),A,C) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_579,c_1091]) ).
cnf(c_1093,plain,
multiply(C,multiply(B,A,C),A) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_594,c_1092]) ).
cnf(c_865,plain,
multiply(A,B,C) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_645,c_1093]) ).
cnf(c_1094,plain,
multiply(d,e,multiply(a,b,c)) != multiply(d,e,multiply(a,b,c)),
inference(paramod,[status(thm)],[c_865,c_595]) ).
cnf(c_1028,plain,
$false,
inference(copy,[status(thm)],[c_1094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO067-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:41:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1310831 was started by sandbox on n009,
% 0.09/0.36 % Sat Sep 26 22:41:59 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 1.78/0.64
% 1.78/0.64 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 1.78/0.64
% 1.78/0.64 % SZS status Unsatisfiable for theBenchmark
% 1.78/0.64
% 1.78/0.64 % Proof 1 at 0.21 (+ 0.05) seconds.
% 1.78/0.64 % Length of proof is 57.
% 1.78/0.64 % Level of proof is 25.
% 1.78/0.64 % Maximum clause weight is 97.000.
% 1.78/0.64 % Given clauses 68.
% 1.78/0.64
% 1.78/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------