%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP415-1 : 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 : n012.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 07:29:10 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.46s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 16 ( 4 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 : 104 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(multiply(VAR_0,inverse(multiply(inverse(multiply(inverse(multiply(VAR_1,VAR_0)),multiply(VAR_1,inverse(VAR_2)))),inverse(multiply(inverse(VAR_0),VAR_0)))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = C,
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_5,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,inverse(C)))),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_12,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(inverse(C))))),inverse(multiply(inverse(A),A))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_15,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A))))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_25,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(inverse(C))))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_49,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(C))))))),inverse(multiply(inverse(B),B))) = C,
inference(paramod,[status(thm)],[c_25,c_1]) ).
cnf(c_553,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(inverse(E),E)))))))),
inference(paramod,[status(thm)],[c_25,c_5]) ).
cnf(c_554,plain,
C = multiply(D,inverse(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(inverse(E),E)))))))),
inference(paramod,[status(thm)],[c_1,c_553]) ).
cnf(c_72,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(B),B)))))))) = C,
inference(copy,[status(thm)],[c_554]) ).
cnf(c_83,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,C)))))),inverse(multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_25,c_15]) ).
cnf(c_105,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(D))))))),A)),D)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_49,c_1]) ).
cnf(c_555,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),multiply(D,inverse(E)))),inverse(multiply(inverse(C),C))))))))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,E))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_5,c_49]) ).
cnf(c_116,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_1,c_555]) ).
cnf(c_556,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),E)),inverse(multiply(inverse(C),C))))))))),inverse(multiply(inverse(A),A)))))) = multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),inverse(multiply(inverse(F),F))))),
inference(paramod,[status(thm)],[c_72,c_5]) ).
cnf(c_144,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_556]) ).
cnf(c_557,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B)))))))) = inverse(inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),D)),C)),inverse(multiply(inverse(D),D))))))),
inference(paramod,[status(thm)],[c_72,c_72]) ).
cnf(c_167,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),A)),D)),inverse(multiply(inverse(A),A))))))) = multiply(B,inverse(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(inverse(C),C)))))))),
inference(copy,[status(thm)],[c_557]) ).
cnf(c_558,plain,
inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))),multiply(inverse(multiply(inverse(multiply(D,A)),multiply(D,C))),E))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = E,
inference(paramod,[status(thm)],[c_116,c_15]) ).
cnf(c_221,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),E)),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))) = E,
inference(paramod,[status(thm)],[c_167,c_558]) ).
cnf(c_559,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(B,C)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,A)),multiply(E,inverse(inverse(multiply(A,B)))))),D)),C)),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_83,c_144]) ).
cnf(c_278,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,D)))))),A)),E)),inverse(multiply(inverse(A),A))))) = multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(multiply(D,E)),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))),
inference(copy,[status(thm)],[c_559]) ).
cnf(c_287,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = multiply(inverse(A),A),
inference(paramod,[status(thm)],[c_278,c_105]) ).
cnf(c_560,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(inverse(C),C)))))))) = D,
inference(paramod,[status(thm)],[c_144,c_221]) ).
cnf(c_452,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B))))))))) = C,
inference(paramod,[status(thm)],[c_167,c_560]) ).
cnf(c_486,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_287,c_452]) ).
cnf(c_551,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_486,c_3]) ).
cnf(c_552,plain,
$false,
inference(resolve,[status(thm)],[c_551,c_486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP415-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Fri Sep 25 14:52:36 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 2362727 was started by sandbox on n012,
% 0.02/0.30 % Fri Sep 25 14:52:36 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.23/0.46
% 0.23/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.46
% 0.23/0.46 % Proof 1 at 0.12 (+ 0.02) seconds.
% 0.23/0.46 % Length of proof is 21.
% 0.23/0.46 % Level of proof is 10.
% 0.23/0.46 % Maximum clause weight is 54.000.
% 0.23/0.46 % Given clauses 22.
% 0.23/0.46
% 0.23/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------