%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP067-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 41 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 38 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 63 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,VAR_0),divide(VAR_0,divide(VAR_1,divide(divide(identity,VAR_0),VAR_2)))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),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_46,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_47,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_46]) ).
cnf(c_48,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_5,c_47]) ).
cnf(c_49,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_48]) ).
cnf(c_50,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_49]) ).
cnf(c_51,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_50]) ).
cnf(c_52,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_51]) ).
cnf(c_53,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_52]) ).
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_53]) ).
cnf(c_8,plain,
divide(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),C) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
divide(divide(identity,divide(identity,divide(A,divide(identity,B)))),B) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_14,plain,
divide(divide(identity,divide(identity,divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_16,plain,
divide(divide(identity,divide(A,B)),C) = divide(identity,divide(identity,divide(B,divide(identity,divide(divide(identity,A),C))))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_54,plain,
divide(divide(identity,divide(identity,A)),B) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_55,plain,
divide(identity,divide(identity,divide(A,divide(identity,divide(divide(identity,identity),B))))) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_16,c_54]) ).
cnf(c_17,plain,
divide(identity,divide(identity,divide(A,divide(identity,divide(identity,B))))) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_5,c_55]) ).
cnf(c_56,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,divide(divide(identity,identity),identity))))) = A,
inference(paramod,[status(thm)],[c_16,c_14]) ).
cnf(c_57,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,divide(identity,identity))))) = A,
inference(paramod,[status(thm)],[c_5,c_56]) ).
cnf(c_58,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,identity)))) = A,
inference(paramod,[status(thm)],[c_5,c_57]) ).
cnf(c_18,plain,
divide(identity,divide(identity,divide(divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_5,c_58]) ).
cnf(c_59,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,B)),divide(identity,divide(divide(identity,identity),B))))) = A,
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_20,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,B)),divide(identity,divide(identity,B))))) = A,
inference(paramod,[status(thm)],[c_5,c_59]) ).
cnf(c_25,plain,
divide(identity,divide(identity,divide(A,divide(identity,divide(identity,B))))) = divide(identity,divide(B,divide(A,identity))),
inference(paramod,[status(thm)],[c_5,c_17]) ).
cnf(c_60,plain,
divide(identity,divide(identity,divide(divide(divide(identity,A),divide(identity,B)),divide(identity,divide(identity,B))))) = divide(identity,divide(A,identity)),
inference(paramod,[status(thm)],[c_5,c_17]) ).
cnf(c_61,plain,
divide(identity,A) = divide(identity,divide(A,identity)),
inference(paramod,[status(thm)],[c_20,c_60]) ).
cnf(c_26,plain,
divide(identity,divide(A,identity)) = divide(identity,A),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_26,c_18]) ).
cnf(c_30,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_26,c_62]) ).
cnf(c_63,plain,
divide(identity,divide(identity,divide(A,B))) = divide(identity,divide(B,divide(A,identity))),
inference(paramod,[status(thm)],[c_30,c_25]) ).
cnf(c_64,plain,
divide(A,B) = divide(identity,divide(B,divide(A,identity))),
inference(paramod,[status(thm)],[c_30,c_63]) ).
cnf(c_33,plain,
divide(identity,divide(A,divide(B,identity))) = divide(B,A),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_38,plain,
divide(divide(identity,divide(A,B)),C) = divide(B,divide(identity,divide(divide(identity,A),C))),
inference(paramod,[status(thm)],[c_30,c_16]) ).
cnf(c_65,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_30,c_7]) ).
cnf(c_39,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_66,plain,
divide(identity,divide(identity,A)) = divide(A,identity),
inference(paramod,[status(thm)],[c_26,c_30]) ).
cnf(c_67,plain,
A = divide(A,identity),
inference(paramod,[status(thm)],[c_30,c_66]) ).
cnf(c_40,plain,
divide(A,identity) = A,
inference(copy,[status(thm)],[c_67]) ).
cnf(c_41,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_40,c_33]) ).
cnf(c_68,plain,
divide(divide(identity,divide(divide(identity,b3),a3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_69,plain,
divide(a3,divide(identity,divide(divide(identity,divide(identity,b3)),divide(identity,c3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_38,c_68]) ).
cnf(c_70,plain,
divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_30,c_69]) ).
cnf(c_45,plain,
$false,
inference(copy,[status(thm)],[c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP067-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:20:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3678475 was started by sandbox2 on n005,
% 0.17/0.43 % Fri Sep 25 14:20:32 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/0.46 % Length of proof is 23.
% 0.17/0.46 % Level of proof is 10.
% 0.17/0.46 % Maximum clause weight is 100.000.
% 0.17/0.46 % Given clauses 13.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------