%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP466-1 : 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 : n017.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 07:29:47 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 35 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(divide(VAR_0,VAR_0),divide(VAR_1,divide(divide(VAR_2,divide(VAR_3,VAR_1)),inverse(VAR_3)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = C,
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_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_3,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_21,plain,
divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_22,plain,
divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_4,plain,
divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_6,plain,
divide(divide(A,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,inverse(D)))) = divide(E,E),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_23,plain,
multiply(inverse(A),A) = divide(divide(B,B),divide(divide(divide(C,divide(D,E)),inverse(D)),divide(C,inverse(E)))),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_18,plain,
divide(inverse(A),inverse(A)) = divide(divide(B,B),divide(divide(divide(C,divide(D,E)),inverse(D)),divide(C,inverse(E)))),
inference(paramod,[status(thm)],[c_2,c_23]) ).
cnf(c_24,plain,
divide(divide(A,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,inverse(D)))) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_19,plain,
divide(inverse(a1),inverse(a1)) != divide(divide(A,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,inverse(D)))),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_20,plain,
$false,
inference(resolve,[status(thm)],[c_19,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP466-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 14:50:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2563212 was started by sandbox on n017,
% 0.10/0.36 % Fri Sep 25 14:50:47 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 8.
% 0.13/0.37 % Level of proof is 3.
% 0.13/0.37 % Maximum clause weight is 23.000.
% 0.13/0.37 % Given clauses 5.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------