%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP406-1 : 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 : n014.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 07:28:57 AM UTC 2026
% Result : Unsatisfiable 2.65s 0.80s
% Output : CNFRefutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 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 : 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 : 87 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,inverse(multiply(inverse(multiply(inverse(multiply(VAR_0,VAR_1)),VAR_2)),multiply(inverse(VAR_1),multiply(inverse(VAR_1),VAR_1))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = 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_480,plain,
multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),multiply(inverse(C),C))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),B)),multiply(inverse(D),multiply(inverse(D),D)))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(D),multiply(inverse(B),multiply(inverse(B),B))))),
inference(copy,[status(thm)],[c_480]) ).
cnf(c_6,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(inverse(B),multiply(inverse(B),B)))))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_7,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(A,B)),D))),multiply(inverse(C),multiply(inverse(C),C)))) = D,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_481,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),A)),multiply(inverse(D),multiply(inverse(D),D)))))),E))),multiply(inverse(B),multiply(inverse(B),B)))) = E,
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_11,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C))),multiply(inverse(B),multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_1,c_481]) ).
cnf(c_482,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(multiply(D,E)),B)),multiply(inverse(multiply(D,E)),C)),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_14,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(A,B)),D)) = multiply(inverse(multiply(E,C)),multiply(E,D)),
inference(copy,[status(thm)],[c_482]) ).
cnf(c_483,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),multiply(inverse(multiply(C,D)),A))),multiply(inverse(E),multiply(inverse(E),E)))),F))),multiply(inverse(B),multiply(inverse(B),B)))) = F,
inference(paramod,[status(thm)],[c_7,c_7]) ).
cnf(c_15,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(B),multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_11,c_483]) ).
cnf(c_34,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_14,c_14]) ).
cnf(c_47,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(C,D)),multiply(C,multiply(inverse(B),B)))))) = multiply(inverse(B),D),
inference(paramod,[status(thm)],[c_34,c_6]) ).
cnf(c_484,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(E,multiply(inverse(C),multiply(inverse(C),C)))),multiply(E,D)),
inference(paramod,[status(thm)],[c_15,c_34]) ).
cnf(c_55,plain,
multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)),
inference(copy,[status(thm)],[c_484]) ).
cnf(c_485,plain,
multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),multiply(B,inverse(D))))),multiply(A,inverse(multiply(inverse(multiply(E,multiply(inverse(C),multiply(inverse(C),C)))),multiply(E,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(D)))),multiply(inverse(multiply(B,C)),multiply(B,inverse(D))))))))) = D,
inference(paramod,[status(thm)],[c_55,c_6]) ).
cnf(c_302,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(B),B))) = C,
inference(paramod,[status(thm)],[c_47,c_485]) ).
cnf(c_304,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)),
inference(paramod,[status(thm)],[c_15,c_55]) ).
cnf(c_377,plain,
multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),multiply(inverse(D),multiply(inverse(D),D)))),
inference(paramod,[status(thm)],[c_302,c_304]) ).
cnf(c_486,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),multiply(inverse(C),multiply(inverse(C),C)))) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_377,c_3]) ).
cnf(c_479,plain,
$false,
inference(resolve,[status(thm)],[c_377,c_486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP406-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 : Fri Sep 25 14:51:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 497563 was started by sandbox on n014,
% 0.12/0.36 % Fri Sep 25 14:51:48 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 2.65/0.80
% 2.65/0.80 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 2.65/0.80
% 2.65/0.80 % SZS status Unsatisfiable for theBenchmark
% 2.65/0.80
% 2.65/0.80 % Proof 1 at 0.30 (+ 0.07) seconds.
% 2.65/0.80 % Length of proof is 16.
% 2.65/0.80 % Level of proof is 8.
% 2.65/0.80 % Maximum clause weight is 86.000.
% 2.65/0.80 % Given clauses 32.
% 2.65/0.80
% 2.65/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------