%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP534-1 : 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 : 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 07:30:18 AM UTC 2026
% Result : Unsatisfiable 0.17s 5.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 39 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,divide(divide(VAR_0,VAR_1),VAR_2)),VAR_1) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,divide(divide(A,B),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_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_7,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_8,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_9,plain,
divide(identity,A) = inverse(A),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_32,plain,
multiply(divide(inverse(b2),divide(identity,b2)),a2) != a2,
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_33,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_9,c_32]) ).
cnf(c_34,plain,
multiply(identity,a2) != a2,
inference(paramod,[status(thm)],[c_6,c_33]) ).
cnf(c_35,plain,
divide(identity,divide(identity,a2)) != a2,
inference(paramod,[status(thm)],[c_8,c_34]) ).
cnf(c_36,plain,
divide(identity,inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_9,c_35]) ).
cnf(c_10,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_9,c_36]) ).
cnf(c_12,plain,
divide(divide(divide(A,divide(divide(A,B),C)),divide(C,D)),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_37,plain,
divide(divide(A,divide(identity,B)),A) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_14,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_9,c_37]) ).
cnf(c_38,plain,
divide(identity,A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_39,plain,
inverse(A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_9,c_38]) ).
cnf(c_24,plain,
divide(divide(A,B),A) = inverse(B),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_30,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_24,c_14]) ).
cnf(c_31,plain,
$false,
inference(resolve,[status(thm)],[c_30,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP534-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n001.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Fri Sep 25 15:04:46 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.44 % Process 3616894 was started by sandbox2 on n001,
% 0.17/5.44 % Fri Sep 25 15:04:46 2026
% 0.17/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.45
% 0.17/5.45 % From the command line: assign(max_seconds, 300).
% 0.17/5.46
% 0.17/5.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.46
% 0.17/5.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/5.46 % Length of proof is 15.
% 0.17/5.46 % Level of proof is 5.
% 0.17/5.46 % Maximum clause weight is 15.000.
% 0.17/5.46 % Given clauses 6.
% 0.17/5.46
% 0.17/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------