%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP528-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 07:30:17 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.63s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 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 : 58 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(A,B),divide(C,B))) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(divide(VAR_2,VAR_2),VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_4,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_3]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_5,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_6,plain,
multiply(b,a) != multiply(a,b),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_7,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_59,plain,
divide(b,inverse(a)) != multiply(a,b),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_8,plain,
divide(b,inverse(a)) != divide(a,inverse(b)),
inference(paramod,[status(thm)],[c_7,c_59]) ).
cnf(c_9,plain,
divide(A,divide(B,divide(C,divide(divide(A,D),divide(B,D))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_60,plain,
divide(A,B) = divide(divide(A,divide(B,C)),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
divide(divide(A,divide(B,C)),C) = divide(A,B),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_19,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_61,plain,
divide(A,divide(A,divide(B,divide(C,C)))) = B,
inference(paramod,[status(thm)],[c_19,c_1]) ).
cnf(c_27,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_19,c_61]) ).
cnf(c_38,plain,
divide(divide(A,B),A) = inverse(B),
inference(paramod,[status(thm)],[c_11,c_4]) ).
cnf(c_42,plain,
divide(divide(A,divide(B,C)),D) = divide(A,divide(B,divide(C,D))),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_62,plain,
divide(divide(A,B),C) = divide(divide(A,divide(B,divide(D,C))),D),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_63,plain,
divide(divide(A,B),C) = divide(A,divide(B,divide(divide(D,C),D))),
inference(paramod,[status(thm)],[c_42,c_62]) ).
cnf(c_43,plain,
divide(divide(A,B),C) = divide(A,divide(B,inverse(C))),
inference(paramod,[status(thm)],[c_38,c_63]) ).
cnf(c_44,plain,
divide(A,divide(B,inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_43,c_38]) ).
cnf(c_57,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_44,c_27]) ).
cnf(c_58,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP528-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.60 % Computer : n026.cluster.edu
% 0.09/0.60 % Model : x86_64 x86_64
% 0.09/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.60 % Memory : 8046.5625MB
% 0.09/0.60 % OS : Linux 6.8.0-71-generic
% 0.09/0.60 % CPULimit : 300
% 0.09/0.60 % WCLimit : 300
% 0.09/0.60 % DateTime : Fri Sep 25 15:01:11 UTC 2026
% 0.09/0.61 % CPUTime :
% 0.09/0.61 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.61 % Process 2828479 was started by sandbox2 on n026,
% 0.09/0.61 % Fri Sep 25 15:01:11 2026
% 0.09/0.61 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.61
% 0.09/0.61 % From the command line: assign(max_seconds, 300).
% 0.14/0.63
% 0.14/0.63 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.63
% 0.14/0.63 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.63 % Length of proof is 18.
% 0.14/0.63 % Level of proof is 6.
% 0.14/0.63 % Maximum clause weight is 15.000.
% 0.14/0.63 % Given clauses 21.
% 0.14/0.63
% 0.14/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------