%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP554-1 : 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 : n011.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 07:30:21 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,inverse(divide(VAR_1,divide(VAR_0,VAR_2)))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,inverse(VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_3,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_76,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_2,c_76]) ).
cnf(c_5,plain,
divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_77,plain,
divide(divide(A,inverse(B)),C) = divide(D,inverse(divide(B,divide(D,divide(A,C))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
divide(A,inverse(divide(B,divide(A,divide(C,D))))) = divide(divide(C,inverse(B)),D),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_10,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_11,plain,
divide(divide(divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),inverse(divide(E,D))),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_78,plain,
divide(A,inverse(B)) = divide(C,inverse(divide(B,divide(C,A)))),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_15,plain,
divide(A,inverse(divide(B,divide(A,C)))) = divide(C,inverse(B)),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_79,plain,
divide(A,inverse(B)) = divide(divide(C,inverse(divide(D,divide(C,A)))),inverse(divide(B,D))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_80,plain,
divide(A,inverse(B)) = divide(divide(A,inverse(D)),inverse(divide(B,D))),
inference(paramod,[status(thm)],[c_15,c_79]) ).
cnf(c_18,plain,
divide(divide(A,inverse(B)),inverse(divide(C,B))) = divide(A,inverse(C)),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_81,plain,
divide(divide(divide(divide(divide(C,inverse(B)),inverse(divide(D,B))),inverse(divide(E,D))),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_15,c_11]) ).
cnf(c_82,plain,
divide(divide(divide(divide(C,inverse(D)),inverse(divide(E,D))),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_18,c_81]) ).
cnf(c_83,plain,
divide(divide(divide(C,inverse(E)),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_18,c_82]) ).
cnf(c_21,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_18,c_83]) ).
cnf(c_84,plain,
divide(divide(C,D),inverse(B)) = divide(divide(C,inverse(B)),D),
inference(paramod,[status(thm)],[c_15,c_6]) ).
cnf(c_22,plain,
divide(divide(A,inverse(B)),C) = divide(divide(A,C),inverse(B)),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
divide(divide(inverse(b2),inverse(a2)),inverse(b2)) != a2,
inference(paramod,[status(thm)],[c_22,c_4]) ).
cnf(c_86,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_21,c_85]) ).
cnf(c_75,plain,
$false,
inference(copy,[status(thm)],[c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP554-1 : 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 : n011.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
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:59:45 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2303356 was started by sandbox on n011,
% 0.11/0.37 % Fri Sep 25 14:59:45 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 13.
% 0.11/0.38 % Level of proof is 6.
% 0.11/0.38 % Maximum clause weight is 27.000.
% 0.11/0.38 % Given clauses 14.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------