%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP542-1 : 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 : n020.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 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 : 8 ( 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 : 60 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,divide(divide(divide(VAR_0,VAR_1),VAR_2),VAR_0)),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(identity,VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = divide(identity,VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(identity,A),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_5,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_4]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_35,plain,
multiply(multiply(divide(identity,b2),b2),a2) != a2,
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_36,plain,
multiply(divide(divide(identity,b2),divide(identity,b2)),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_35]) ).
cnf(c_37,plain,
multiply(identity,a2) != a2,
inference(paramod,[status(thm)],[c_5,c_36]) ).
cnf(c_7,plain,
divide(identity,divide(identity,a2)) != a2,
inference(paramod,[status(thm)],[c_2,c_37]) ).
cnf(c_38,plain,
divide(divide(identity,divide(A,identity)),B) = divide(divide(divide(C,A),B),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,divide(B,identity)),C),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_39,plain,
divide(divide(identity,divide(divide(A,B),divide(identity,divide(divide(divide(C,A),D),C)))),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(divide(identity,divide(divide(A,B),divide(identity,divide(divide(identity,divide(A,identity)),C)))),B) = C,
inference(paramod,[status(thm)],[c_9,c_39]) ).
cnf(c_11,plain,
divide(divide(identity,divide(divide(identity,divide(A,identity)),B)),B) = A,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_40,plain,
divide(divide(identity,identity),divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_17,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_40]) ).
cnf(c_19,plain,
divide(divide(identity,divide(divide(identity,divide(divide(identity,divide(A,identity)),B)),C)),C) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_9,c_11]) ).
cnf(c_20,plain,
divide(divide(identity,divide(divide(identity,A),B)),B) = divide(identity,divide(divide(identity,divide(A,identity)),identity)),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_21,plain,
divide(divide(identity,A),identity) = divide(identity,divide(A,identity)),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_41,plain,
divide(identity,divide(divide(identity,divide(divide(divide(identity,divide(A,identity)),B),identity)),identity)) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_20,c_19]) ).
cnf(c_42,plain,
divide(identity,divide(divide(identity,divide(divide(identity,divide(divide(A,identity),identity)),B)),identity)) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_9,c_41]) ).
cnf(c_43,plain,
divide(identity,divide(identity,divide(divide(divide(identity,divide(divide(A,identity),identity)),B),identity))) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_21,c_42]) ).
cnf(c_22,plain,
divide(identity,divide(identity,divide(divide(identity,divide(divide(divide(A,identity),identity),identity)),B))) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_9,c_43]) ).
cnf(c_44,plain,
divide(identity,divide(divide(identity,divide(divide(A,identity),identity)),identity)) = A,
inference(paramod,[status(thm)],[c_20,c_11]) ).
cnf(c_45,plain,
divide(identity,divide(identity,divide(divide(divide(A,identity),identity),identity))) = A,
inference(paramod,[status(thm)],[c_21,c_44]) ).
cnf(c_23,plain,
divide(divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_17,c_45]) ).
cnf(c_25,plain,
divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B))) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_23,c_22]) ).
cnf(c_46,plain,
divide(divide(identity,divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B)))),A) = B,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_32,plain,
divide(divide(identity,divide(divide(identity,A),B)),A) = B,
inference(paramod,[status(thm)],[c_25,c_46]) ).
cnf(c_47,plain,
divide(divide(identity,divide(divide(identity,A),divide(identity,divide(divide(identity,identity),B)))),A) = B,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_48,plain,
divide(divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B)))),A) = B,
inference(paramod,[status(thm)],[c_5,c_47]) ).
cnf(c_33,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_32,c_48]) ).
cnf(c_34,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP542-1 : 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 : n020.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 15:00:04 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 3209540 was started by sandbox on n020,
% 0.10/0.36 % Fri Sep 25 15:00:04 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 20.
% 0.10/0.38 % Level of proof is 8.
% 0.10/0.38 % Maximum clause weight is 21.000.
% 0.10/0.38 % Given clauses 11.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------