%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP442-1 : 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 : 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 07:29:43 AM UTC 2026
% Result : Unsatisfiable 7.60s 1.44s
% Output : CNFRefutation 7.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of formulae : 41 ( 41 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 14 ( 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 : 170 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : inverse(multiply(VAR_0,multiply(VAR_1,multiply(multiply(VAR_2,inverse(VAR_2)),inverse(multiply(VAR_3,multiply(VAR_0,VAR_1))))))) = VAR_3,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(A,multiply(B,multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(A,B))))))) = D,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_2,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_3,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_4,plain,
inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,A)))),multiply(multiply(E,inverse(E)),C)))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))),multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(F,inverse(F)),C)))) = D,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_1944,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(multiply(multiply(C,inverse(C)),D),multiply(multiply(E,inverse(E)),F)))) = multiply(multiply(V6,inverse(V6)),inverse(multiply(B,multiply(D,F)))),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_6,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))) = inverse(multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(multiply(F,inverse(F)),C),multiply(multiply(V6,inverse(V6)),D)))),
inference(copy,[status(thm)],[c_1944]) ).
cnf(c_7,plain,
inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,inverse(C)),D),multiply(multiply(multiply(E,inverse(E)),A),multiply(multiply(F,inverse(F)),B))))))) = D,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_8,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(F,inverse(F)),C)))))))) = D,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_10,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,C)))) = D,
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_11,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))) = multiply(multiply(E,inverse(E)),inverse(multiply(B,multiply(C,D)))),
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_1945,plain,
inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,multiply(multiply(F,inverse(F)),inverse(multiply(A,multiply(B,C))))))),multiply(multiply(V6,inverse(V6)),E)))) = multiply(V7,inverse(V7)),
inference(paramod,[status(thm)],[c_11,c_4]) ).
cnf(c_14,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_4,c_1945]) ).
cnf(c_16,plain,
inverse(multiply(A,multiply(inverse(A),multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,inverse(D)))))))) = C,
inference(paramod,[status(thm)],[c_14,c_1]) ).
cnf(c_17,plain,
multiply(multiply(A,multiply(B,multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(A,B)))))),D) = multiply(E,inverse(E)),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_18,plain,
inverse(multiply(inverse(A),multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,inverse(D))))),multiply(multiply(E,inverse(E)),C)))) = A,
inference(paramod,[status(thm)],[c_14,c_4]) ).
cnf(c_21,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(C))))),multiply(multiply(multiply(D,inverse(D)),B),multiply(multiply(E,inverse(E)),F)))) = inverse(F),
inference(paramod,[status(thm)],[c_14,c_5]) ).
cnf(c_906,plain,
inverse(multiply(A,multiply(inverse(A),B))) = inverse(multiply(C,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_10,c_16]) ).
cnf(c_935,plain,
multiply(multiply(A,multiply(inverse(A),B)),inverse(multiply(C,multiply(inverse(C),B)))) = multiply(D,inverse(D)),
inference(paramod,[status(thm)],[c_906,c_14]) ).
cnf(c_1946,plain,
inverse(multiply(inverse(multiply(A,multiply(inverse(A),B))),multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,inverse(E))))),multiply(multiply(F,inverse(F)),D)))) = multiply(V6,multiply(inverse(V6),B)),
inference(paramod,[status(thm)],[c_935,c_4]) ).
cnf(c_1216,plain,
multiply(A,multiply(inverse(A),B)) = multiply(C,multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_18,c_1946]) ).
cnf(c_1947,plain,
multiply(A,multiply(B,inverse(B))) = multiply(C,multiply(inverse(C),inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_14,c_1216]) ).
cnf(c_1294,plain,
multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,multiply(C,inverse(C))),
inference(copy,[status(thm)],[c_1947]) ).
cnf(c_1948,plain,
multiply(A,multiply(inverse(A),inverse(inverse(multiply(B,multiply(C,multiply(multiply(D,inverse(D)),inverse(multiply(multiply(E,inverse(E)),multiply(B,C)))))))))) = multiply(F,inverse(F)),
inference(paramod,[status(thm)],[c_17,c_1294]) ).
cnf(c_1489,plain,
multiply(A,multiply(inverse(A),inverse(multiply(B,inverse(B))))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_1,c_1948]) ).
cnf(c_1949,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(C))))),multiply(multiply(multiply(D,inverse(D)),B),multiply(multiply(E,inverse(E)),F)))) = multiply(inverse(F),inverse(multiply(V6,inverse(V6)))),
inference(paramod,[status(thm)],[c_1489,c_5]) ).
cnf(c_1950,plain,
inverse(F) = multiply(inverse(F),inverse(multiply(V6,inverse(V6)))),
inference(paramod,[status(thm)],[c_21,c_1949]) ).
cnf(c_1508,plain,
multiply(inverse(A),inverse(multiply(B,inverse(B)))) = inverse(A),
inference(copy,[status(thm)],[c_1950]) ).
cnf(c_1951,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = inverse(multiply(C,multiply(D,multiply(multiply(E,inverse(E)),inverse(multiply(A,multiply(C,D))))))),
inference(paramod,[status(thm)],[c_1,c_1508]) ).
cnf(c_1533,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_1,c_1951]) ).
cnf(c_1571,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))) = inverse(multiply(D,inverse(D))),
inference(paramod,[status(thm)],[c_1533,c_10]) ).
cnf(c_1952,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,inverse(multiply(B,multiply(multiply(multiply(F,inverse(F)),D),multiply(multiply(V6,inverse(V6)),E))))))))))) = inverse(multiply(V7,inverse(V7))),
inference(paramod,[status(thm)],[c_8,c_1571]) ).
cnf(c_1605,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),B))) = inverse(multiply(C,inverse(C))),
inference(paramod,[status(thm)],[c_8,c_1952]) ).
cnf(c_1783,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),B))) = multiply(multiply(C,inverse(C)),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_1605,c_1605]) ).
cnf(c_1953,plain,
inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,inverse(C)),inverse(multiply(inverse(D),D))),multiply(multiply(multiply(E,inverse(E)),A),multiply(multiply(F,inverse(F)),B))))))) = inverse(multiply(inverse(V6),V6)),
inference(paramod,[status(thm)],[c_1783,c_7]) ).
cnf(c_1842,plain,
inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_7,c_1953]) ).
cnf(c_1954,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,inverse(D))))),multiply(multiply(E,inverse(E)),C)))) = multiply(inverse(F),F),
inference(paramod,[status(thm)],[c_1842,c_18]) ).
cnf(c_1942,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_18,c_1954]) ).
cnf(c_1943,plain,
$false,
inference(resolve,[status(thm)],[c_1942,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP442-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n009.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 14:54:28 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1882521 was started by sandbox2 on n009,
% 0.15/0.42 % Fri Sep 25 14:54:28 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 7.60/1.44
% 7.60/1.44 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 7.60/1.44
% 7.60/1.44 % SZS status Unsatisfiable for theBenchmark
% 7.60/1.44
% 7.60/1.44 % Proof 1 at 0.74 (+ 0.24) seconds.
% 7.60/1.44 % Length of proof is 28.
% 7.60/1.44 % Level of proof is 18.
% 7.60/1.44 % Maximum clause weight is 97.000.
% 7.60/1.44 % Given clauses 54.
% 7.60/1.44
% 7.60/1.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------