%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 06:55:10 AM UTC 2026
% Result : Unsatisfiable 4.95s 1.07s
% Output : CNFRefutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 2
% Syntax : Number of formulae : 157 ( 145 unt; 0 def)
% Number of atoms : 190 ( 189 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 82 ( 49 ~; 33 |; 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 : 698 ( 13 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,axiom,
( multiply(inverse(b),b,a) != a
| multiply(a,a,b) != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)) ),
file('theBenchmark.p',prove_tba_axioms) ).
cnf(c_2,plain,
( multiply(inverse(b),b,a) != a
| multiply(a,a,b) != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)) ),
inference(clausify,[status(thm)],[prove_tba_axioms]) ).
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_26,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),multiply(F,inverse(multiply(E,inverse(E),V6)),V6),multiply(C,D,inverse(E)))),multiply(D,F,C)) = B,
inference(paramod,[status(thm)],[c_10,c_1]) ).
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_1034,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_1034]) ).
cnf(c_33,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,inverse(D),E),inverse(multiply(D,inverse(D),E)),multiply(D,inverse(D),F))),F) = multiply(B,multiply(C,inverse(multiply(A,B,V6)),V6),A),
inference(paramod,[status(thm)],[c_10,c_3]) ).
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_1035,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_1035]) ).
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_1036,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_1037,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_1036]) ).
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_1037]) ).
cnf(c_1038,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_1039,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_1038]) ).
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_1039]) ).
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_195,plain,
multiply(multiply(multiply(inverse(A),inverse(A),A),multiply(inverse(A),inverse(multiply(A,inverse(A),B)),B),multiply(C,inverse(C),D)),inverse(multiply(multiply(E,inverse(E),F),inverse(multiply(E,inverse(E),F)),multiply(E,inverse(E),V6))),V6) = multiply(multiply(inverse(A),inverse(multiply(A,inverse(A),B)),B),D,multiply(inverse(A),inverse(A),A)),
inference(paramod,[status(thm)],[c_26,c_33]) ).
cnf(c_1040,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_1040]) ).
cnf(c_1041,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_1042,plain,
B = multiply(inverse(V7),B,V7),
inference(paramod,[status(thm)],[c_1,c_1041]) ).
cnf(c_245,plain,
multiply(inverse(A),B,A) = B,
inference(copy,[status(thm)],[c_1042]) ).
cnf(c_1043,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_1044,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_1043]) ).
cnf(c_258,plain,
multiply(A,inverse(multiply(B,inverse(B),C)),C) = A,
inference(paramod,[status(thm)],[c_245,c_1044]) ).
cnf(c_1045,plain,
multiply(multiply(inverse(A),multiply(inverse(A),inverse(multiply(A,inverse(A),B)),B),multiply(C,inverse(C),D)),inverse(multiply(multiply(E,inverse(E),F),inverse(multiply(E,inverse(E),F)),multiply(E,inverse(E),V6))),V6) = multiply(multiply(inverse(A),inverse(multiply(A,inverse(A),B)),B),D,multiply(inverse(A),inverse(A),A)),
inference(paramod,[status(thm)],[c_245,c_195]) ).
cnf(c_1046,plain,
multiply(multiply(inverse(A),inverse(A),multiply(C,inverse(C),D)),inverse(multiply(multiply(E,inverse(E),F),inverse(multiply(E,inverse(E),F)),multiply(E,inverse(E),V6))),V6) = multiply(multiply(inverse(A),inverse(multiply(A,inverse(A),B)),B),D,multiply(inverse(A),inverse(A),A)),
inference(paramod,[status(thm)],[c_258,c_1045]) ).
cnf(c_1047,plain,
multiply(multiply(inverse(A),inverse(A),multiply(C,inverse(C),D)),inverse(multiply(multiply(E,inverse(E),F),inverse(multiply(E,inverse(E),F)),multiply(E,inverse(E),V6))),V6) = multiply(inverse(A),D,multiply(inverse(A),inverse(A),A)),
inference(paramod,[status(thm)],[c_258,c_1046]) ).
cnf(c_311,plain,
multiply(multiply(inverse(A),inverse(A),multiply(B,inverse(B),C)),inverse(multiply(multiply(D,inverse(D),E),inverse(multiply(D,inverse(D),E)),multiply(D,inverse(D),F))),F) = multiply(inverse(A),C,inverse(A)),
inference(paramod,[status(thm)],[c_245,c_1047]) ).
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_1048,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_1048]) ).
cnf(c_1049,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_1049]) ).
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_1050,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_1050]) ).
cnf(c_1051,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_1051]) ).
cnf(c_1052,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_1053,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_1052]) ).
cnf(c_1054,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_1053]) ).
cnf(c_1055,plain,
multiply(A,inverse(C),D) = multiply(inverse(C),multiply(D,inverse(A),C),A),
inference(paramod,[status(thm)],[c_473,c_1054]) ).
cnf(c_484,plain,
multiply(inverse(A),multiply(B,inverse(C),A),C) = multiply(C,inverse(A),B),
inference(copy,[status(thm)],[c_1055]) ).
cnf(c_1056,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_1057,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_1056]) ).
cnf(c_1058,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_1057]) ).
cnf(c_1059,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_1058]) ).
cnf(c_1060,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_1059]) ).
cnf(c_1061,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_1060]) ).
cnf(c_1062,plain,
multiply(A,B,C) = multiply(B,multiply(C,inverse(multiply(A,B,V7)),V7),A),
inference(paramod,[status(thm)],[c_475,c_1061]) ).
cnf(c_489,plain,
multiply(A,multiply(B,inverse(multiply(C,A,D)),D),C) = multiply(C,A,B),
inference(copy,[status(thm)],[c_1062]) ).
cnf(c_1063,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_1063]) ).
cnf(c_1064,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_1064]) ).
cnf(c_1065,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_1065]) ).
cnf(c_1066,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_1067,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_1066]) ).
cnf(c_1068,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_1067]) ).
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_1068]) ).
cnf(c_1069,plain,
multiply(multiply(inverse(A),inverse(A),C),inverse(multiply(multiply(D,inverse(D),E),inverse(multiply(D,inverse(D),E)),multiply(D,inverse(D),F))),F) = multiply(inverse(A),C,inverse(A)),
inference(paramod,[status(thm)],[c_506,c_311]) ).
cnf(c_1070,plain,
multiply(multiply(inverse(A),inverse(A),C),inverse(multiply(E,inverse(multiply(D,inverse(D),E)),multiply(D,inverse(D),F))),F) = multiply(inverse(A),C,inverse(A)),
inference(paramod,[status(thm)],[c_506,c_1069]) ).
cnf(c_1071,plain,
multiply(multiply(inverse(A),inverse(A),C),inverse(multiply(E,inverse(E),multiply(D,inverse(D),F))),F) = multiply(inverse(A),C,inverse(A)),
inference(paramod,[status(thm)],[c_506,c_1070]) ).
cnf(c_1072,plain,
multiply(multiply(inverse(A),inverse(A),C),inverse(multiply(E,inverse(E),F)),F) = multiply(inverse(A),C,inverse(A)),
inference(paramod,[status(thm)],[c_506,c_1071]) ).
cnf(c_1073,plain,
multiply(multiply(inverse(A),inverse(A),C),inverse(F),F) = multiply(inverse(A),C,inverse(A)),
inference(paramod,[status(thm)],[c_506,c_1072]) ).
cnf(c_527,plain,
multiply(inverse(A),inverse(A),B) = multiply(inverse(A),B,inverse(A)),
inference(paramod,[status(thm)],[c_475,c_1073]) ).
cnf(c_1074,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_1075,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_1074]) ).
cnf(c_1076,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_1075]) ).
cnf(c_1077,plain,
multiply(inverse(inverse(A)),inverse(multiply(C,V9,B)),multiply(C,V9,B)) = A,
inference(paramod,[status(thm)],[c_475,c_1076]) ).
cnf(c_555,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_475,c_1077]) ).
cnf(c_567,plain,
( multiply(inverse(b),b,a) != a
| multiply(a,a,b) != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramod,[status(thm)],[c_525,c_2]) ).
cnf(c_1078,plain,
multiply(inverse(A),inverse(B),B) = multiply(B,inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_245,c_484]) ).
cnf(c_1079,plain,
inverse(A) = multiply(B,inverse(A),inverse(A)),
inference(paramod,[status(thm)],[c_475,c_1078]) ).
cnf(c_568,plain,
multiply(A,inverse(B),inverse(B)) = inverse(B),
inference(copy,[status(thm)],[c_1079]) ).
cnf(c_570,plain,
multiply(inverse(A),A,B) = multiply(B,inverse(A),B),
inference(paramod,[status(thm)],[c_506,c_484]) ).
cnf(c_571,plain,
( multiply(a,inverse(b),a) != a
| multiply(a,a,b) != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramod,[status(thm)],[c_570,c_567]) ).
cnf(c_1080,plain,
multiply(inverse(inverse(A)),inverse(A),A) = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_568,c_484]) ).
cnf(c_1081,plain,
multiply(A,inverse(A),A) = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_555,c_1080]) ).
cnf(c_1082,plain,
A = multiply(A,inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_506,c_1081]) ).
cnf(c_1083,plain,
A = multiply(A,A,B),
inference(paramod,[status(thm)],[c_555,c_1082]) ).
cnf(c_572,plain,
multiply(A,A,B) = A,
inference(copy,[status(thm)],[c_1083]) ).
cnf(c_1084,plain,
( multiply(a,inverse(b),a) != a
| a != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramod,[status(thm)],[c_572,c_571]) ).
cnf(c_573,plain,
( multiply(a,inverse(b),a) != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(copy,[status(thm)],[c_1084]) ).
cnf(c_1085,plain,
inverse(A) = multiply(inverse(A),B,inverse(A)),
inference(paramod,[status(thm)],[c_572,c_527]) ).
cnf(c_575,plain,
multiply(inverse(A),B,inverse(A)) = inverse(A),
inference(copy,[status(thm)],[c_1085]) ).
cnf(c_1086,plain,
multiply(inverse(A),inverse(B),B) = multiply(B,inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_572,c_484]) ).
cnf(c_1087,plain,
inverse(A) = multiply(B,inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_475,c_1086]) ).
cnf(c_576,plain,
multiply(A,inverse(B),inverse(A)) = inverse(B),
inference(copy,[status(thm)],[c_1087]) ).
cnf(c_1088,plain,
multiply(inverse(inverse(A)),inverse(A),B) = multiply(B,inverse(inverse(A)),inverse(A)),
inference(paramod,[status(thm)],[c_575,c_484]) ).
cnf(c_1089,plain,
multiply(A,inverse(A),B) = multiply(B,inverse(inverse(A)),inverse(A)),
inference(paramod,[status(thm)],[c_555,c_1088]) ).
cnf(c_1090,plain,
B = multiply(B,inverse(inverse(A)),inverse(A)),
inference(paramod,[status(thm)],[c_506,c_1089]) ).
cnf(c_1091,plain,
B = multiply(B,A,inverse(A)),
inference(paramod,[status(thm)],[c_555,c_1090]) ).
cnf(c_578,plain,
multiply(A,B,inverse(B)) = A,
inference(copy,[status(thm)],[c_1091]) ).
cnf(c_1092,plain,
( multiply(a,inverse(b),a) != a
| a != a
| multiply(b,a,a) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramod,[status(thm)],[c_578,c_573]) ).
cnf(c_580,plain,
( multiply(a,inverse(b),a) != a
| multiply(b,a,a) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(copy,[status(thm)],[c_1092]) ).
cnf(c_1093,plain,
multiply(inverse(inverse(A)),inverse(B),B) = multiply(B,inverse(inverse(A)),A),
inference(paramod,[status(thm)],[c_576,c_484]) ).
cnf(c_1094,plain,
multiply(A,inverse(B),B) = multiply(B,inverse(inverse(A)),A),
inference(paramod,[status(thm)],[c_555,c_1093]) ).
cnf(c_1095,plain,
A = multiply(B,inverse(inverse(A)),A),
inference(paramod,[status(thm)],[c_475,c_1094]) ).
cnf(c_1096,plain,
A = multiply(B,A,A),
inference(paramod,[status(thm)],[c_555,c_1095]) ).
cnf(c_582,plain,
multiply(A,B,B) = B,
inference(copy,[status(thm)],[c_1096]) ).
cnf(c_1097,plain,
( multiply(a,inverse(b),a) != a
| a != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramod,[status(thm)],[c_582,c_580]) ).
cnf(c_583,plain,
( multiply(a,inverse(b),a) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(copy,[status(thm)],[c_1097]) ).
cnf(c_1098,plain,
multiply(A,B,C) = multiply(C,A,multiply(C,A,B)),
inference(paramod,[status(thm)],[c_506,c_489]) ).
cnf(c_584,plain,
multiply(A,B,multiply(A,B,C)) = multiply(B,C,A),
inference(copy,[status(thm)],[c_1098]) ).
cnf(c_589,plain,
multiply(A,inverse(B),C) = multiply(C,A,inverse(B)),
inference(paramod,[status(thm)],[c_575,c_489]) ).
cnf(c_1099,plain,
( multiply(a,a,inverse(b)) != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramod,[status(thm)],[c_589,c_583]) ).
cnf(c_1100,plain,
( a != a
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramod,[status(thm)],[c_572,c_1099]) ).
cnf(c_597,plain,
multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)),
inference(copy,[status(thm)],[c_1100]) ).
cnf(c_1101,plain,
multiply(A,multiply(B,inverse(A),A),C) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_582,c_489]) ).
cnf(c_599,plain,
multiply(A,B,C) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_475,c_1101]) ).
cnf(c_1102,plain,
multiply(e,multiply(a,c,b),d) != multiply(d,e,multiply(a,b,c)),
inference(paramod,[status(thm)],[c_599,c_597]) ).
cnf(c_600,plain,
multiply(d,e,multiply(a,c,b)) != multiply(d,e,multiply(a,b,c)),
inference(paramod,[status(thm)],[c_599,c_1102]) ).
cnf(c_615,plain,
multiply(A,B,A) = A,
inference(paramod,[status(thm)],[c_599,c_572]) ).
cnf(c_1103,plain,
multiply(A,B,C) = multiply(multiply(C,A,B),C,A),
inference(paramod,[status(thm)],[c_584,c_599]) ).
cnf(c_1104,plain,
multiply(A,B,C) = multiply(A,multiply(C,A,B),C),
inference(paramod,[status(thm)],[c_599,c_1103]) ).
cnf(c_645,plain,
multiply(A,multiply(B,A,C),B) = multiply(A,C,B),
inference(copy,[status(thm)],[c_1104]) ).
cnf(c_647,plain,
multiply(A,B,multiply(B,C,A)) = multiply(B,C,A),
inference(paramod,[status(thm)],[c_599,c_584]) ).
cnf(c_650,plain,
multiply(A,multiply(B,C,A),C) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_599,c_645]) ).
cnf(c_1105,plain,
multiply(A,multiply(B,A,C),multiply(A,C,B)) = multiply(multiply(B,A,C),B,A),
inference(paramod,[status(thm)],[c_645,c_584]) ).
cnf(c_1106,plain,
multiply(A,multiply(B,A,C),multiply(A,C,B)) = multiply(A,multiply(B,A,C),B),
inference(paramod,[status(thm)],[c_599,c_1105]) ).
cnf(c_652,plain,
multiply(A,multiply(B,A,C),multiply(A,C,B)) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_645,c_1106]) ).
cnf(c_703,plain,
multiply(A,multiply(B,A,C),multiply(C,B,A)) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_599,c_652]) ).
cnf(c_708,plain,
multiply(A,multiply(A,B,C),multiply(B,C,A)) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_599,c_703]) ).
cnf(c_1107,plain,
multiply(A,B,multiply(C,A,D)) = multiply(A,multiply(D,B,A),C),
inference(paramod,[status(thm)],[c_582,c_525]) ).
cnf(c_814,plain,
multiply(A,multiply(B,C,A),D) = multiply(A,C,multiply(D,A,B)),
inference(copy,[status(thm)],[c_1107]) ).
cnf(c_1108,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_647]) ).
cnf(c_1109,plain,
multiply(A,multiply(C,multiply(B,A,C),B),B) = multiply(B,A,multiply(B,A,C)),
inference(paramod,[status(thm)],[c_599,c_1108]) ).
cnf(c_1110,plain,
multiply(A,multiply(C,A,multiply(B,C,B)),B) = multiply(B,A,multiply(B,A,C)),
inference(paramod,[status(thm)],[c_814,c_1109]) ).
cnf(c_1111,plain,
multiply(A,multiply(C,A,B),B) = multiply(B,A,multiply(B,A,C)),
inference(paramod,[status(thm)],[c_615,c_1110]) ).
cnf(c_843,plain,
multiply(A,multiply(B,A,C),C) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_584,c_1111]) ).
cnf(c_1112,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_708,c_525]) ).
cnf(c_1113,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_599,c_1112]) ).
cnf(c_1114,plain,
multiply(multiply(B,A,C),A,multiply(multiply(A,B,C),C,C)) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_843,c_1113]) ).
cnf(c_1115,plain,
multiply(multiply(B,A,C),A,C) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_582,c_1114]) ).
cnf(c_1116,plain,
multiply(C,multiply(B,A,C),A) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_599,c_1115]) ).
cnf(c_870,plain,
multiply(A,B,C) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_650,c_1116]) ).
cnf(c_1117,plain,
multiply(d,e,multiply(a,b,c)) != multiply(d,e,multiply(a,b,c)),
inference(paramod,[status(thm)],[c_870,c_600]) ).
cnf(c_1033,plain,
$false,
inference(copy,[status(thm)],[c_1117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 22:40:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2113423 was started by sandbox2 on n026,
% 0.08/0.35 % Sat Sep 26 22:40:41 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 4.95/1.07
% 4.95/1.07 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 4.95/1.07
% 4.95/1.07 % SZS status Unsatisfiable for theBenchmark
% 4.95/1.07
% 4.95/1.07 % Proof 1 at 0.55 (+ 0.13) seconds.
% 4.95/1.07 % Length of proof is 71.
% 4.95/1.07 % Level of proof is 25.
% 4.95/1.07 % Maximum clause weight is 97.000.
% 4.95/1.07 % Given clauses 69.
% 4.95/1.07
% 4.95/1.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------