%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP410-1 : 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 : n015.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 07:29:08 AM UTC 2026
% Result : Unsatisfiable 17.52s 2.63s
% Output : CNFRefutation 17.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 16 ( 3 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 : 262 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(inverse(multiply(VAR_0,inverse(multiply(VAR_1,VAR_2)))),multiply(VAR_0,inverse(VAR_2))),inverse(multiply(inverse(VAR_2),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B,
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_5034,plain,
multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_3,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(copy,[status(thm)],[c_5034]) ).
cnf(c_4,plain,
multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(inverse(C),C))) = inverse(C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5035,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D)))))))),multiply(A,inverse(multiply(E,inverse(D))))),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,inverse(D))))) = inverse(multiply(E,inverse(multiply(C,D)))),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_6,plain,
inverse(multiply(A,inverse(multiply(B,C)))) = multiply(multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))))),multiply(D,inverse(multiply(A,inverse(C))))),inverse(multiply(inverse(multiply(A,inverse(C))),multiply(A,inverse(C))))),
inference(copy,[status(thm)],[c_5035]) ).
cnf(c_8,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))),multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = inverse(inverse(multiply(inverse(C),C))),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_9,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))),multiply(A,inverse(C))) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_13,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_15,plain,
multiply(multiply(inverse(multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(D,multiply(inverse(C),C))))),inverse(C)),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))) = D,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_5036,plain,
multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_33,plain,
inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(A,inverse(C))))),inverse(multiply(inverse(multiply(A,inverse(C))),multiply(A,inverse(C))))),
inference(copy,[status(thm)],[c_5036]) ).
cnf(c_5037,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))),multiply(C,inverse(D)))))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_38,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(paramod,[status(thm)],[c_9,c_5037]) ).
cnf(c_5038,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(C,F)))),multiply(E,inverse(F))),inverse(multiply(inverse(F),F)))))),
inference(paramod,[status(thm)],[c_1,c_38]) ).
cnf(c_42,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_5038]) ).
cnf(c_5039,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(D))) = multiply(inverse(multiply(E,inverse(multiply(inverse(C),C)))),multiply(E,inverse(D))),
inference(paramod,[status(thm)],[c_1,c_42]) ).
cnf(c_55,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C))) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,B)))),multiply(E,inverse(B))),inverse(C))),
inference(copy,[status(thm)],[c_5039]) ).
cnf(c_57,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))),multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(E))) = multiply(inverse(multiply(F,inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))),multiply(F,inverse(E))),
inference(paramod,[status(thm)],[c_3,c_42]) ).
cnf(c_61,plain,
multiply(inverse(multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(D))),inverse(C)) = multiply(inverse(multiply(E,inverse(D))),multiply(E,inverse(multiply(inverse(C),C)))),
inference(paramod,[status(thm)],[c_4,c_42]) ).
cnf(c_71,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_1,c_55]) ).
cnf(c_5040,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(D),D)))))),multiply(B,inverse(inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D)))))))),multiply(A,inverse(multiply(E,inverse(D))))),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,inverse(D))))),multiply(E,inverse(D))) = C,
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_88,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))),multiply(C,inverse(D))) = B,
inference(paramod,[status(thm)],[c_1,c_5040]) ).
cnf(c_5041,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(multiply(inverse(C),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_1,c_71]) ).
cnf(c_109,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_1,c_5041]) ).
cnf(c_166,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(D),D))) = B,
inference(paramod,[status(thm)],[c_109,c_1]) ).
cnf(c_167,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(paramod,[status(thm)],[c_109,c_2]) ).
cnf(c_193,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(inverse(B)),inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_109,c_42]) ).
cnf(c_218,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))),multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(E),E))) = inverse(inverse(multiply(inverse(C),C))),
inference(paramod,[status(thm)],[c_109,c_8]) ).
cnf(c_5042,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))),multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = inverse(inverse(multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_109,c_8]) ).
cnf(c_219,plain,
inverse(inverse(multiply(inverse(A),A))) = inverse(inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_218,c_5042]) ).
cnf(c_298,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C))),inverse(multiply(inverse(D),D))) = inverse(C),
inference(paramod,[status(thm)],[c_109,c_166]) ).
cnf(c_309,plain,
multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(D))),inverse(multiply(inverse(E),E))) = inverse(D),
inference(paramod,[status(thm)],[c_166,c_166]) ).
cnf(c_316,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(inverse(B)),inverse(B))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_193,c_109]) ).
cnf(c_5043,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(inverse(C)),inverse(C))))),inverse(multiply(inverse(D),D))) = inverse(multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_316,c_166]) ).
cnf(c_356,plain,
inverse(multiply(inverse(inverse(A)),inverse(A))) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_298,c_5043]) ).
cnf(c_371,plain,
inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),B)))) = inverse(multiply(inverse(C),C)),
inference(paramod,[status(thm)],[c_219,c_356]) ).
cnf(c_451,plain,
multiply(multiply(inverse(multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(D,multiply(inverse(C),C))))),inverse(C)),inverse(multiply(inverse(E),E))) = D,
inference(paramod,[status(thm)],[c_109,c_15]) ).
cnf(c_5044,plain,
multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(multiply(inverse(B),multiply(multiply(inverse(multiply(C,inverse(multiply(B,D)))),multiply(C,inverse(D))),inverse(D))),inverse(multiply(A,multiply(inverse(D),D))))),inverse(D)),inverse(multiply(inverse(D),D)))),inverse(multiply(inverse(E),E))) = inverse(multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_15,c_166]) ).
cnf(c_5045,plain,
multiply(multiply(inverse(A),A),inverse(multiply(inverse(E),E))) = inverse(multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_451,c_5044]) ).
cnf(c_463,plain,
inverse(multiply(inverse(A),A)) = multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))),
inference(copy,[status(thm)],[c_5045]) ).
cnf(c_5046,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),C)))) = multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(E),E)))),multiply(D,inverse(multiply(A,inverse(C))))),inverse(multiply(inverse(multiply(A,inverse(C))),multiply(A,inverse(C))))),
inference(paramod,[status(thm)],[c_463,c_33]) ).
cnf(c_1092,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),C)))) = inverse(multiply(A,inverse(C))),
inference(paramod,[status(thm)],[c_298,c_5046]) ).
cnf(c_1277,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),C))),inverse(D))) = multiply(inverse(multiply(E,inverse(C))),multiply(E,inverse(D))),
inference(paramod,[status(thm)],[c_1092,c_193]) ).
cnf(c_5047,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),B)))),multiply(A,inverse(B)))),inverse(multiply(inverse(C),C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(D,inverse(multiply(inverse(E),E)))),
inference(paramod,[status(thm)],[c_463,c_57]) ).
cnf(c_2262,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B)))),inverse(multiply(inverse(C),C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(D,inverse(multiply(inverse(E),E)))),
inference(paramod,[status(thm)],[c_1092,c_5047]) ).
cnf(c_5048,plain,
multiply(inverse(multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(inverse(D),D)))),inverse(C)) = multiply(inverse(multiply(E,inverse(multiply(inverse(inverse(multiply(inverse(F),F))),inverse(multiply(inverse(V6),V6)))))),multiply(E,inverse(multiply(inverse(C),C)))),
inference(paramod,[status(thm)],[c_371,c_61]) ).
cnf(c_5049,plain,
multiply(inverse(inverse(C)),inverse(C)) = multiply(inverse(multiply(E,inverse(multiply(inverse(inverse(multiply(inverse(F),F))),inverse(multiply(inverse(V6),V6)))))),multiply(E,inverse(multiply(inverse(C),C)))),
inference(paramod,[status(thm)],[c_309,c_5048]) ).
cnf(c_2437,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C)))))),multiply(A,inverse(multiply(inverse(D),D)))) = multiply(inverse(inverse(D)),inverse(D)),
inference(copy,[status(thm)],[c_5049]) ).
cnf(c_5050,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B)))),inverse(multiply(inverse(C),C))) = multiply(inverse(inverse(E)),inverse(E)),
inference(paramod,[status(thm)],[c_2437,c_2262]) ).
cnf(c_2466,plain,
multiply(inverse(inverse(A)),inverse(A)) = multiply(inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(C)))),inverse(multiply(inverse(D),D))),
inference(copy,[status(thm)],[c_5050]) ).
cnf(c_5051,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(D,inverse(multiply(C,E)))),multiply(D,inverse(E))),inverse(multiply(inverse(F),F)))),multiply(multiply(inverse(multiply(D,inverse(multiply(C,E)))),multiply(D,inverse(E))),inverse(multiply(inverse(F),F)))))),multiply(multiply(inverse(multiply(D,inverse(multiply(C,E)))),multiply(D,inverse(E))),inverse(multiply(inverse(F),F)))) = B,
inference(paramod,[status(thm)],[c_166,c_88]) ).
cnf(c_5052,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))),inverse(multiply(inverse(C),multiply(multiply(inverse(multiply(D,inverse(multiply(C,E)))),multiply(D,inverse(E))),inverse(multiply(inverse(F),F)))))),multiply(multiply(inverse(multiply(D,inverse(multiply(C,E)))),multiply(D,inverse(E))),inverse(multiply(inverse(F),F)))) = B,
inference(paramod,[status(thm)],[c_166,c_5051]) ).
cnf(c_5053,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),multiply(multiply(inverse(multiply(D,inverse(multiply(C,E)))),multiply(D,inverse(E))),inverse(multiply(inverse(F),F)))) = B,
inference(paramod,[status(thm)],[c_166,c_5052]) ).
cnf(c_4265,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C) = B,
inference(paramod,[status(thm)],[c_166,c_5053]) ).
cnf(c_5054,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))),multiply(C,inverse(D))) = multiply(inverse(multiply(inverse(E),E)),B),
inference(paramod,[status(thm)],[c_1092,c_88]) ).
cnf(c_5055,plain,
B = multiply(inverse(multiply(inverse(E),E)),B),
inference(paramod,[status(thm)],[c_4265,c_5054]) ).
cnf(c_4305,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(copy,[status(thm)],[c_5055]) ).
cnf(c_5056,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(inverse(C)),inverse(D))) = multiply(inverse(multiply(E,inverse(C))),multiply(E,inverse(D))),
inference(paramod,[status(thm)],[c_4305,c_1277]) ).
cnf(c_5057,plain,
multiply(inverse(inverse(C)),inverse(D)) = multiply(inverse(multiply(E,inverse(C))),multiply(E,inverse(D))),
inference(paramod,[status(thm)],[c_4305,c_5056]) ).
cnf(c_4461,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(inverse(B)),inverse(C)),
inference(copy,[status(thm)],[c_5057]) ).
cnf(c_5058,plain,
multiply(inverse(inverse(A)),inverse(A)) = multiply(inverse(multiply(inverse(inverse(C)),inverse(C))),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_4461,c_2466]) ).
cnf(c_5059,plain,
multiply(inverse(inverse(A)),inverse(A)) = inverse(multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_4305,c_5058]) ).
cnf(c_4612,plain,
inverse(multiply(inverse(A),A)) = multiply(inverse(inverse(B)),inverse(B)),
inference(copy,[status(thm)],[c_5059]) ).
cnf(c_5060,plain,
multiply(inverse(multiply(inverse(A),A)),a2) != a2,
inference(paramod,[status(thm)],[c_4612,c_167]) ).
cnf(c_5061,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_4305,c_5060]) ).
cnf(c_5033,plain,
$false,
inference(copy,[status(thm)],[c_5061]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP410-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:55:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1653330 was started by sandbox on n015,
% 0.10/0.37 % Fri Sep 25 14:55:42 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 17.52/2.63
% 17.52/2.63 % SZS status Unsatisfiable for theBenchmark
% 17.52/2.63
% 17.52/2.63 % Proof 1 at 1.76 (+ 0.34) seconds.
% 17.52/2.63 % Length of proof is 40.
% 17.52/2.63 % Level of proof is 15.
% 17.52/2.63 % Maximum clause weight is 100.000.
% 17.52/2.63 % Given clauses 99.
% 17.52/2.63
% 17.52/2.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
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