%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP091-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:27:18 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 5
% Syntax : Number of formulae : 78 ( 38 unt; 0 def)
% Number of atoms : 176 ( 175 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 240 ( 142 ~; 98 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 69 ( 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,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_7,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_68,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_8,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_9,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_10,plain,
divide(identity,A) = inverse(A),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_69,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(inverse(b1),divide(identity,b1)) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_70,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(inverse(b1),inverse(b1)) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_10,c_69]) ).
cnf(c_71,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_6,c_70]) ).
cnf(c_72,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != divide(inverse(a1),divide(identity,a1)) ),
inference(paramod,[status(thm)],[c_9,c_71]) ).
cnf(c_73,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_10,c_72]) ).
cnf(c_74,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_6,c_73]) ).
cnf(c_75,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(inverse(b2),divide(identity,b2)),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_74]) ).
cnf(c_76,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(inverse(b2),inverse(b2)),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_75]) ).
cnf(c_77,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_6,c_76]) ).
cnf(c_78,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_77]) ).
cnf(c_79,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(identity,inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_78]) ).
cnf(c_80,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_79]) ).
cnf(c_81,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(divide(a3,divide(identity,b3)),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_80]) ).
cnf(c_82,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_81]) ).
cnf(c_83,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),divide(identity,c3)) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_82]) ).
cnf(c_84,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_83]) ).
cnf(c_85,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,divide(identity,c3)))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_84]) ).
cnf(c_86,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3)))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_85]) ).
cnf(c_87,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(identity,divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_86]) ).
cnf(c_88,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_87]) ).
cnf(c_89,plain,
( divide(b4,divide(identity,a4)) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_88]) ).
cnf(c_90,plain,
( divide(b4,inverse(a4)) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_89]) ).
cnf(c_91,plain,
( divide(b4,inverse(a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_9,c_90]) ).
cnf(c_92,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_10,c_91]) ).
cnf(c_11,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2 ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_13,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_14,plain,
divide(divide(A,B),divide(divide(A,C),B)) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_93,plain,
divide(divide(A,divide(identity,B)),A) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_15,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_10,c_93]) ).
cnf(c_94,plain,
divide(divide(identity,divide(inverse(A),B)),A) = B,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_17,plain,
divide(inverse(divide(inverse(A),B)),A) = B,
inference(paramod,[status(thm)],[c_10,c_94]) ).
cnf(c_23,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_95,plain,
divide(identity,A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_96,plain,
inverse(A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_10,c_95]) ).
cnf(c_25,plain,
divide(divide(A,B),A) = inverse(B),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_31,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_25,c_15]) ).
cnf(c_97,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_31,c_11]) ).
cnf(c_32,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_34,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(paramod,[status(thm)],[c_23,c_1]) ).
cnf(c_98,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_41,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_10,c_98]) ).
cnf(c_99,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_23,c_25]) ).
cnf(c_46,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_48,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_23,c_41]) ).
cnf(c_53,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| inverse(divide(inverse(c3),divide(a3,inverse(b3)))) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(paramod,[status(thm)],[c_46,c_32]) ).
cnf(c_58,plain,
divide(inverse(A),B) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_23,c_17]) ).
cnf(c_62,plain,
divide(inverse(A),B) = inverse(divide(A,inverse(B))),
inference(paramod,[status(thm)],[c_48,c_17]) ).
cnf(c_100,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| inverse(inverse(divide(c3,inverse(divide(a3,inverse(b3)))))) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(paramod,[status(thm)],[c_62,c_53]) ).
cnf(c_63,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(c3,inverse(divide(a3,inverse(b3)))) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(paramod,[status(thm)],[c_31,c_100]) ).
cnf(c_101,plain,
inverse(divide(A,inverse(B))) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_62,c_58]) ).
cnf(c_65,plain,
inverse(divide(A,inverse(B))) = inverse(divide(B,inverse(A))),
inference(paramod,[status(thm)],[c_62,c_101]) ).
cnf(c_102,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(c3,inverse(divide(a3,inverse(b3)))) != inverse(divide(inverse(divide(b3,inverse(c3))),a3)) ),
inference(paramod,[status(thm)],[c_46,c_63]) ).
cnf(c_103,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(c3,inverse(divide(a3,inverse(b3)))) != inverse(inverse(divide(divide(b3,inverse(c3)),inverse(a3)))) ),
inference(paramod,[status(thm)],[c_62,c_102]) ).
cnf(c_104,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(c3,inverse(divide(a3,inverse(b3)))) != inverse(inverse(divide(divide(b3,inverse(a3)),inverse(c3)))) ),
inference(paramod,[status(thm)],[c_34,c_103]) ).
cnf(c_105,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(c3,inverse(divide(a3,inverse(b3)))) != inverse(inverse(divide(c3,inverse(divide(b3,inverse(a3)))))) ),
inference(paramod,[status(thm)],[c_65,c_104]) ).
cnf(c_106,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(c3,inverse(divide(a3,inverse(b3)))) != inverse(inverse(divide(c3,inverse(divide(a3,inverse(b3)))))) ),
inference(paramod,[status(thm)],[c_65,c_105]) ).
cnf(c_107,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(c3,inverse(divide(a3,inverse(b3)))) != divide(c3,inverse(divide(a3,inverse(b3)))) ),
inference(paramod,[status(thm)],[c_31,c_106]) ).
cnf(c_66,plain,
divide(b4,inverse(a4)) != divide(a4,inverse(b4)),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_108,plain,
inverse(divide(inverse(a4),b4)) != divide(a4,inverse(b4)),
inference(paramod,[status(thm)],[c_46,c_66]) ).
cnf(c_109,plain,
inverse(inverse(divide(a4,inverse(b4)))) != divide(a4,inverse(b4)),
inference(paramod,[status(thm)],[c_62,c_108]) ).
cnf(c_110,plain,
divide(a4,inverse(b4)) != divide(a4,inverse(b4)),
inference(paramod,[status(thm)],[c_31,c_109]) ).
cnf(c_67,plain,
$false,
inference(copy,[status(thm)],[c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP091-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.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 14:26:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2587002 was started by sandbox on n016,
% 0.10/0.37 % Fri Sep 25 14:26:43 2026
% 0.10/0.37 % 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).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 30.
% 0.14/0.39 % Level of proof is 9.
% 0.14/0.39 % Maximum clause weight is 35.000.
% 0.14/0.39 % Given clauses 19.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------