%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP094-1 : 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 : n026.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 07:27:19 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 76 ( 51 unt; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 156 ( 91 ~; 65 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 : 137 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,divide(VAR_0,VAR_1)),divide(divide(VAR_1,VAR_2),VAR_0)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C,
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(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_6,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_77,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(divide(identity,a1),a1) != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_78,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(divide(identity,a1),divide(identity,a1)) != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_2,c_77]) ).
cnf(c_79,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_5,c_78]) ).
cnf(c_80,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != multiply(divide(identity,b1),b1) ),
inference(paramod,[status(thm)],[c_3,c_79]) ).
cnf(c_81,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != divide(divide(identity,b1),divide(identity,b1)) ),
inference(paramod,[status(thm)],[c_2,c_80]) ).
cnf(c_82,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_5,c_81]) ).
cnf(c_83,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(divide(identity,b2),b2),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_3,c_82]) ).
cnf(c_84,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(divide(identity,b2),divide(identity,b2)),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_83]) ).
cnf(c_85,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_5,c_84]) ).
cnf(c_86,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_85]) ).
cnf(c_87,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_86]) ).
cnf(c_88,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_87]) ).
cnf(c_89,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_88]) ).
cnf(c_90,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_89]) ).
cnf(c_91,plain,
( divide(a4,divide(identity,b4)) != multiply(b4,a4)
| 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_90]) ).
cnf(c_92,plain,
( divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4))
| 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_91]) ).
cnf(c_93,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| 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(copy,[status(thm)],[c_92]) ).
cnf(c_7,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| 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_93]) ).
cnf(c_8,plain,
divide(divide(identity,A),divide(divide(divide(divide(B,A),C),D),divide(identity,divide(C,B)))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(identity,divide(A,divide(identity,divide(B,C)))),divide(D,A)) = divide(divide(C,D),B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(divide(identity,divide(divide(divide(A,B),C),identity)),B) = divide(C,A),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_94,plain,
divide(divide(identity,identity),divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_94]) ).
cnf(c_95,plain,
divide(divide(identity,divide(divide(A,B),A)),identity) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_13,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_11,c_95]) ).
cnf(c_14,plain,
divide(divide(identity,divide(divide(A,B),C)),B) = divide(C,A),
inference(paramod,[status(thm)],[c_13,c_10]) ).
cnf(c_96,plain,
divide(divide(identity,divide(A,divide(identity,B))),divide(C,A)) = divide(divide(divide(divide(D,B),E),C),divide(identity,divide(E,D))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_15,plain,
divide(divide(divide(divide(A,B),C),D),divide(identity,divide(C,A))) = divide(divide(identity,divide(E,divide(identity,B))),divide(D,E)),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_20,plain,
divide(divide(identity,A),divide(identity,divide(identity,divide(B,C)))) = divide(divide(C,A),B),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_23,plain,
divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_29,plain,
divide(identity,divide(A,divide(identity,divide(B,C)))) = divide(divide(C,A),B),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_30,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_97,plain,
divide(identity,divide(A,divide(identity,B))) = divide(divide(divide(divide(C,B),D),A),divide(identity,divide(D,C))),
inference(paramod,[status(thm)],[c_8,c_11]) ).
cnf(c_34,plain,
divide(divide(divide(divide(A,B),C),D),divide(identity,divide(C,A))) = divide(identity,divide(D,divide(identity,B))),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_98,plain,
divide(identity,divide(A,identity)) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_99,plain,
divide(identity,A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_13,c_98]) ).
cnf(c_35,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_37,plain,
divide(divide(divide(A,B),C),divide(D,B)) = divide(divide(A,D),C),
inference(paramod,[status(thm)],[c_29,c_9]) ).
cnf(c_39,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_30,c_23]) ).
cnf(c_40,plain,
divide(divide(identity,A),divide(B,C)) = divide(divide(C,A),B),
inference(paramod,[status(thm)],[c_39,c_20]) ).
cnf(c_100,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| 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_39,c_7]) ).
cnf(c_41,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_101,plain,
divide(identity,divide(D,divide(identity,B))) = divide(divide(identity,divide(E,divide(identity,B))),divide(D,E)),
inference(paramod,[status(thm)],[c_34,c_15]) ).
cnf(c_102,plain,
divide(identity,divide(D,divide(identity,B))) = divide(divide(E,divide(E,divide(identity,B))),D),
inference(paramod,[status(thm)],[c_40,c_101]) ).
cnf(c_42,plain,
divide(identity,divide(A,divide(identity,B))) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_39,c_102]) ).
cnf(c_47,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)) ),
inference(paramod,[status(thm)],[c_42,c_41]) ).
cnf(c_49,plain,
divide(divide(identity,divide(A,B)),C) = divide(divide(B,C),A),
inference(paramod,[status(thm)],[c_42,c_29]) ).
cnf(c_50,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(paramod,[status(thm)],[c_49,c_14]) ).
cnf(c_103,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_39,c_35]) ).
cnf(c_51,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_103]) ).
cnf(c_52,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(paramod,[status(thm)],[c_51,c_49]) ).
cnf(c_53,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,b3),c3)) ),
inference(paramod,[status(thm)],[c_52,c_47]) ).
cnf(c_56,plain,
divide(divide(A,B),divide(identity,C)) = divide(A,divide(B,C)),
inference(paramod,[status(thm)],[c_35,c_50]) ).
cnf(c_60,plain,
divide(divide(A,divide(B,C)),divide(D,B)) = divide(A,divide(D,C)),
inference(paramod,[status(thm)],[c_50,c_50]) ).
cnf(c_104,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(a3,divide(divide(identity,b3),c3)) != divide(a3,divide(divide(identity,b3),c3)) ),
inference(paramod,[status(thm)],[c_56,c_53]) ).
cnf(c_61,plain,
divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4)),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_105,plain,
divide(divide(divide(A,B),C),divide(identity,D)) = divide(divide(A,divide(B,D)),C),
inference(paramod,[status(thm)],[c_35,c_37]) ).
cnf(c_106,plain,
divide(divide(A,B),divide(C,D)) = divide(divide(A,divide(B,D)),C),
inference(paramod,[status(thm)],[c_56,c_105]) ).
cnf(c_66,plain,
divide(divide(A,divide(B,C)),D) = divide(divide(A,B),divide(D,C)),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_107,plain,
divide(identity,divide(divide(A,B),C)) = divide(divide(B,D),divide(divide(A,D),C)),
inference(paramod,[status(thm)],[c_37,c_51]) ).
cnf(c_108,plain,
divide(C,divide(A,B)) = divide(divide(B,D),divide(divide(A,D),C)),
inference(paramod,[status(thm)],[c_51,c_107]) ).
cnf(c_67,plain,
divide(divide(A,B),divide(divide(C,B),D)) = divide(D,divide(C,A)),
inference(copy,[status(thm)],[c_108]) ).
cnf(c_109,plain,
divide(divide(A,B),divide(divide(D,B),C)) = divide(A,divide(D,C)),
inference(paramod,[status(thm)],[c_66,c_60]) ).
cnf(c_75,plain,
divide(A,divide(B,C)) = divide(C,divide(B,A)),
inference(paramod,[status(thm)],[c_67,c_109]) ).
cnf(c_76,plain,
$false,
inference(resolve,[status(thm)],[c_75,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP094-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:24:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2727721 was started by sandbox on n026,
% 0.11/0.37 % Fri Sep 25 14:24:39 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 38.
% 0.11/0.38 % Level of proof is 13.
% 0.11/0.38 % Maximum clause weight is 107.000.
% 0.11/0.38 % Given clauses 13.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------