%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP540-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 07:30:19 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,VAR_1),divide(divide(VAR_0,VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,B),divide(divide(A,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(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_5,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_6,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_5]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_7,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_8,plain,
multiply(b,a) != multiply(a,b),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_9,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_10,plain,
divide(identity,A) = inverse(A),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_85,plain,
divide(b,divide(identity,a)) != multiply(a,b),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_86,plain,
divide(b,inverse(a)) != multiply(a,b),
inference(paramod,[status(thm)],[c_10,c_85]) ).
cnf(c_87,plain,
divide(b,inverse(a)) != divide(a,divide(identity,b)),
inference(paramod,[status(thm)],[c_9,c_86]) ).
cnf(c_11,plain,
divide(b,inverse(a)) != divide(a,inverse(b)),
inference(paramod,[status(thm)],[c_10,c_87]) ).
cnf(c_13,plain,
divide(A,divide(divide(divide(B,C),D),divide(divide(B,A),C))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_88,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_16,plain,
inverse(divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_10,c_88]) ).
cnf(c_18,plain,
divide(divide(A,divide(A,B)),identity) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_89,plain,
divide(inverse(A),divide(divide(identity,B),A)) = B,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_19,plain,
divide(inverse(A),divide(inverse(B),A)) = B,
inference(paramod,[status(thm)],[c_10,c_89]) ).
cnf(c_31,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_38,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_31,c_18]) ).
cnf(c_51,plain,
inverse(divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_38,c_16]) ).
cnf(c_90,plain,
divide(b,inverse(a)) != inverse(divide(inverse(b),a)),
inference(paramod,[status(thm)],[c_51,c_11]) ).
cnf(c_74,plain,
inverse(divide(inverse(b),a)) != divide(b,inverse(a)),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_78,plain,
divide(inverse(A),B) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_19,c_38]) ).
cnf(c_83,plain,
inverse(divide(inverse(a),b)) != divide(b,inverse(a)),
inference(paramod,[status(thm)],[c_78,c_74]) ).
cnf(c_84,plain,
$false,
inference(resolve,[status(thm)],[c_83,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP540-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.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 15:05:10 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 3618042 was started by sandbox on n001,
% 0.14/0.37 % Fri Sep 25 15:05:10 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.38 % Length of proof is 22.
% 0.14/0.38 % Level of proof is 7.
% 0.14/0.38 % Maximum clause weight is 15.000.
% 0.14/0.38 % Given clauses 14.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------