%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:26:55 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 43 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 36 ~; 22 |; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(divide(identity,VAR_1),VAR_2),divide(divide(divide(VAR_0,VAR_0),VAR_0),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),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,axiom,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_6,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_72,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(divide(identity,a1),a1) != identity ),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_73,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| divide(divide(identity,a1),divide(identity,a1)) != identity ),
inference(paramod,[status(thm)],[c_2,c_72]) ).
cnf(c_74,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_5,c_73]) ).
cnf(c_75,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_74]) ).
cnf(c_76,plain,
( multiply(divide(a3,divide(identity,b3)),c3) != multiply(a3,multiply(b3,c3))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_75]) ).
cnf(c_77,plain,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,multiply(b3,c3))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_76]) ).
cnf(c_78,plain,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,divide(b3,divide(identity,c3)))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_77]) ).
cnf(c_79,plain,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_78]) ).
cnf(c_7,plain,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2 ),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_8,plain,
divide(A,divide(divide(divide(identity,B),C),divide(divide(identity,A),C))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_80,plain,
inverse(divide(divide(divide(identity,A),B),divide(divide(identity,identity),B))) = A,
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_81,plain,
inverse(divide(divide(divide(identity,A),B),divide(identity,B))) = A,
inference(paramod,[status(thm)],[c_5,c_80]) ).
cnf(c_10,plain,
divide(identity,divide(divide(divide(identity,A),B),divide(identity,B))) = A,
inference(paramod,[status(thm)],[c_3,c_81]) ).
cnf(c_12,plain,
divide(A,divide(identity,divide(divide(identity,A),divide(identity,B)))) = B,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_13,plain,
divide(A,divide(divide(divide(identity,B),divide(identity,A)),identity)) = B,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_14,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_17,plain,
divide(A,divide(divide(identity,B),divide(identity,A))) = B,
inference(paramod,[status(thm)],[c_14,c_13]) ).
cnf(c_82,plain,
divide(identity,divide(divide(divide(identity,A),identity),identity)) = A,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_83,plain,
divide(identity,divide(divide(identity,A),identity)) = A,
inference(paramod,[status(thm)],[c_14,c_82]) ).
cnf(c_19,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_14,c_83]) ).
cnf(c_84,plain,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_19,c_7]) ).
cnf(c_23,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_24,plain,
divide(A,divide(divide(B,C),divide(divide(identity,A),C))) = divide(identity,B),
inference(paramod,[status(thm)],[c_19,c_8]) ).
cnf(c_29,plain,
divide(A,divide(B,divide(identity,A))) = divide(identity,B),
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_31,plain,
divide(divide(identity,A),divide(B,A)) = divide(identity,B),
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_85,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = divide(identity,divide(identity,B)),
inference(paramod,[status(thm)],[c_31,c_31]) ).
cnf(c_33,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = B,
inference(paramod,[status(thm)],[c_19,c_85]) ).
cnf(c_39,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(paramod,[status(thm)],[c_33,c_12]) ).
cnf(c_40,plain,
divide(divide(A,divide(identity,B)),B) = A,
inference(paramod,[status(thm)],[c_19,c_39]) ).
cnf(c_86,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_39,c_29]) ).
cnf(c_41,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_42,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)),
inference(paramod,[status(thm)],[c_41,c_23]) ).
cnf(c_87,plain,
divide(identity,divide(identity,A)) = divide(divide(divide(A,B),divide(divide(identity,C),B)),C),
inference(paramod,[status(thm)],[c_24,c_41]) ).
cnf(c_88,plain,
divide(A,identity) = divide(divide(divide(A,B),divide(divide(identity,C),B)),C),
inference(paramod,[status(thm)],[c_41,c_87]) ).
cnf(c_89,plain,
A = divide(divide(divide(A,B),divide(divide(identity,C),B)),C),
inference(paramod,[status(thm)],[c_14,c_88]) ).
cnf(c_50,plain,
divide(divide(divide(A,B),divide(divide(identity,C),B)),C) = A,
inference(copy,[status(thm)],[c_89]) ).
cnf(c_90,plain,
divide(A,B) = divide(identity,divide(divide(B,C),divide(divide(identity,divide(identity,A)),C))),
inference(paramod,[status(thm)],[c_50,c_29]) ).
cnf(c_91,plain,
divide(A,B) = divide(identity,divide(divide(B,C),divide(divide(A,identity),C))),
inference(paramod,[status(thm)],[c_41,c_90]) ).
cnf(c_92,plain,
divide(A,B) = divide(identity,divide(divide(B,C),divide(A,C))),
inference(paramod,[status(thm)],[c_14,c_91]) ).
cnf(c_93,plain,
divide(A,B) = divide(divide(A,C),divide(B,C)),
inference(paramod,[status(thm)],[c_41,c_92]) ).
cnf(c_62,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
divide(A,divide(B,C)) = divide(divide(A,divide(identity,C)),B),
inference(paramod,[status(thm)],[c_40,c_62]) ).
cnf(c_70,plain,
divide(divide(A,divide(identity,B)),C) = divide(A,divide(C,B)),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_71,plain,
$false,
inference(resolve,[status(thm)],[c_70,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n013.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:20:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 600010 was started by sandbox on n013,
% 0.09/0.35 % Fri Sep 25 14:20:06 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.38 % Length of proof is 27.
% 0.13/0.38 % Level of proof is 13.
% 0.13/0.38 % Maximum clause weight is 86.000.
% 0.13/0.38 % Given clauses 24.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------