%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP521-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:30:16 AM UTC 2026
% Result : Unsatisfiable 0.04s 15.36s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(VAR_1,divide(VAR_2,divide(VAR_0,VAR_1)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(B,divide(C,divide(A,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_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_5,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_6,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
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_47,plain,
divide(inverse(b1),inverse(b1)) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_8,plain,
divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_7,c_47]) ).
cnf(c_48,plain,
divide(divide(A,A),divide(B,divide(C,inverse(B)))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_11,plain,
inverse(divide(A,divide(B,inverse(A)))) = B,
inference(paramod,[status(thm)],[c_4,c_48]) ).
cnf(c_29,plain,
inverse(divide(A,inverse(inverse(A)))) = divide(B,B),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_45,plain,
inverse(divide(A,inverse(inverse(A)))) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_29,c_8]) ).
cnf(c_46,plain,
$false,
inference(resolve,[status(thm)],[c_45,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP521-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/15.34 % Computer : n012.cluster.edu
% 0.04/15.34 % Model : x86_64 x86_64
% 0.04/15.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.34 % Memory : 8046.5625MB
% 0.04/15.34 % OS : Linux 6.8.0-71-generic
% 0.04/15.34 % CPULimit : 300
% 0.04/15.34 % WCLimit : 300
% 0.04/15.34 % DateTime : Fri Sep 25 14:57:57 UTC 2026
% 0.04/15.34 % CPUTime :
% 0.04/15.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/15.34 % Process 2376535 was started by sandbox2 on n012,
% 0.04/15.34 % Fri Sep 25 14:57:57 2026
% 0.04/15.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/15.35
% 0.04/15.35 % From the command line: assign(max_seconds, 300).
% 0.04/15.36
% 0.04/15.36 % SZS status Unsatisfiable for theBenchmark
% 0.04/15.36
% 0.04/15.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/15.36 % Length of proof is 12.
% 0.04/15.36 % Level of proof is 5.
% 0.04/15.36 % Maximum clause weight is 12.000.
% 0.04/15.36 % Given clauses 8.
% 0.04/15.36
% 0.04/15.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------