%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP424-1 : 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 07:29:25 AM UTC 2026
% Result : Unsatisfiable 0.04s 0.34s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 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 : 11 ( 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 : 43 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(inverse(multiply(inverse(multiply(VAR_0,inverse(multiply(inverse(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(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B,
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,
multiply(inverse(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(inverse(B),C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(C),C)))),C)))),multiply(A,inverse(C))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_10,plain,
multiply(inverse(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(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(D),D)))),D))),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_14,plain,
multiply(inverse(multiply(inverse(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_10,c_6]) ).
cnf(c_21,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_14,c_6]) ).
cnf(c_40,plain,
multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(multiply(D,inverse(E))))) = multiply(inverse(multiply(F,inverse(multiply(inverse(C),C)))),multiply(F,inverse(multiply(D,inverse(E))))),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_24,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(E),multiply(inverse(multiply(inverse(multiply(F,inverse(multiply(inverse(E),B)))),multiply(F,inverse(B)))),inverse(multiply(C,inverse(D))))),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_33,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(B))))),multiply(A,inverse(multiply(inverse(inverse(B)),inverse(B))))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_41,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(B))))),multiply(A,inverse(multiply(inverse(inverse(B)),inverse(B))))) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_33,c_3]) ).
cnf(c_39,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP424-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 14:53:05 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.31 % Process 2363624 was started by sandbox on n012,
% 0.04/0.31 % Fri Sep 25 14:53:05 2026
% 0.04/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 0.04/0.34
% 0.04/0.34 % SZS status Unsatisfiable for theBenchmark
% 0.04/0.34
% 0.04/0.34 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.04/0.34 % Length of proof is 11.
% 0.04/0.34 % Level of proof is 8.
% 0.04/0.34 % Maximum clause weight is 90.000.
% 0.04/0.34 % Given clauses 19.
% 0.04/0.34
% 0.04/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------