%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 51 unt; 0 def)
% Number of atoms : 139 ( 138 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 161 ( 97 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 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 : 86 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,divide(divide(divide(VAR_0,VAR_1),VAR_2),VAR_0)),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,divide(divide(divide(A,B),C),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(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_75,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_76,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_75]) ).
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
| identity != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_5,c_76]) ).
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
| identity != multiply(divide(identity,b1),b1) ),
inference(paramod,[status(thm)],[c_3,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 != divide(divide(identity,b1),divide(identity,b1)) ),
inference(paramod,[status(thm)],[c_2,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 != identity ),
inference(paramod,[status(thm)],[c_5,c_79]) ).
cnf(c_81,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_80]) ).
cnf(c_82,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_81]) ).
cnf(c_83,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_82]) ).
cnf(c_84,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_83]) ).
cnf(c_85,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_84]) ).
cnf(c_86,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_85]) ).
cnf(c_87,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_86]) ).
cnf(c_88,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_87]) ).
cnf(c_89,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_88]) ).
cnf(c_90,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_89]) ).
cnf(c_91,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_90]) ).
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_91]) ).
cnf(c_8,plain,
divide(divide(identity,divide(divide(A,B),divide(identity,divide(divide(divide(C,A),D),C)))),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_17,plain,
divide(divide(identity,divide(divide(A,B),divide(identity,divide(identity,C)))),B) = divide(C,A),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_92,plain,
divide(divide(identity,identity),divide(divide(divide(A,identity),B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_18,plain,
divide(identity,divide(divide(divide(A,identity),B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_92]) ).
cnf(c_21,plain,
divide(divide(identity,divide(A,identity)),divide(B,A)) = divide(identity,B),
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_93,plain,
multiply(divide(identity,divide(identity,identity)),A) = A,
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_94,plain,
multiply(divide(identity,identity),A) = A,
inference(paramod,[status(thm)],[c_5,c_93]) ).
cnf(c_95,plain,
multiply(identity,A) = A,
inference(paramod,[status(thm)],[c_5,c_94]) ).
cnf(c_22,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_2,c_95]) ).
cnf(c_96,plain,
divide(divide(identity,divide(identity,A)),identity) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_23,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_22,c_96]) ).
cnf(c_24,plain,
divide(divide(identity,divide(divide(A,B),C)),B) = divide(C,A),
inference(paramod,[status(thm)],[c_22,c_17]) ).
cnf(c_26,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_22,c_11]) ).
cnf(c_97,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_26,c_7]) ).
cnf(c_27,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_97]) ).
cnf(c_28,plain,
divide(divide(identity,A),divide(B,A)) = divide(identity,B),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_30,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_23,c_18]) ).
cnf(c_34,plain,
divide(divide(identity,A),divide(identity,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_28,c_26]) ).
cnf(c_35,plain,
divide(A,divide(B,divide(identity,A))) = divide(identity,B),
inference(paramod,[status(thm)],[c_26,c_28]) ).
cnf(c_37,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,A)),
inference(paramod,[status(thm)],[c_26,c_34]) ).
cnf(c_38,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_26,c_34]) ).
cnf(c_98,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(c3,divide(identity,divide(a3,divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_37,c_27]) ).
cnf(c_99,plain,
( divide(a4,divide(identity,b4)) != divide(a4,divide(identity,b4))
| divide(c3,divide(identity,divide(a3,divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_37,c_98]) ).
cnf(c_39,plain,
divide(c3,divide(identity,divide(a3,divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_40,plain,
divide(divide(identity,A),divide(divide(B,A),C)) = divide(C,B),
inference(paramod,[status(thm)],[c_38,c_24]) ).
cnf(c_100,plain,
divide(identity,A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_30,c_26]) ).
cnf(c_41,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_42,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_26,c_30]) ).
cnf(c_101,plain,
divide(c3,divide(divide(identity,b3),a3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_42,c_39]) ).
cnf(c_102,plain,
divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_38,c_101]) ).
cnf(c_103,plain,
divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(divide(identity,c3),b3)),
inference(paramod,[status(thm)],[c_42,c_102]) ).
cnf(c_43,plain,
divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(divide(identity,b3),c3)),
inference(paramod,[status(thm)],[c_38,c_103]) ).
cnf(c_48,plain,
divide(divide(identity,A),divide(B,C)) = divide(divide(C,B),A),
inference(paramod,[status(thm)],[c_42,c_34]) ).
cnf(c_49,plain,
divide(divide(A,divide(B,C)),C) = divide(A,B),
inference(paramod,[status(thm)],[c_48,c_40]) ).
cnf(c_55,plain,
divide(divide(A,divide(identity,B)),C) = divide(A,divide(C,B)),
inference(paramod,[status(thm)],[c_41,c_49]) ).
cnf(c_104,plain,
divide(A,divide(B,C)) = divide(identity,divide(B,divide(C,divide(identity,A)))),
inference(paramod,[status(thm)],[c_49,c_35]) ).
cnf(c_105,plain,
divide(A,divide(B,C)) = divide(divide(C,divide(identity,A)),B),
inference(paramod,[status(thm)],[c_42,c_104]) ).
cnf(c_59,plain,
divide(A,divide(B,C)) = divide(C,divide(B,A)),
inference(paramod,[status(thm)],[c_55,c_105]) ).
cnf(c_62,plain,
divide(b3,divide(divide(identity,a3),c3)) != divide(a3,divide(divide(identity,b3),c3)),
inference(paramod,[status(thm)],[c_59,c_43]) ).
cnf(c_106,plain,
divide(identity,divide(A,divide(B,C))) = divide(divide(B,A),C),
inference(paramod,[status(thm)],[c_59,c_42]) ).
cnf(c_66,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(paramod,[status(thm)],[c_42,c_106]) ).
cnf(c_107,plain,
divide(b3,divide(divide(identity,a3),c3)) != divide(c3,divide(divide(identity,b3),a3)),
inference(paramod,[status(thm)],[c_59,c_62]) ).
cnf(c_108,plain,
divide(b3,divide(divide(identity,a3),c3)) != divide(c3,divide(divide(identity,a3),b3)),
inference(paramod,[status(thm)],[c_66,c_107]) ).
cnf(c_109,plain,
divide(b3,divide(divide(identity,a3),c3)) != divide(b3,divide(divide(identity,a3),c3)),
inference(paramod,[status(thm)],[c_59,c_108]) ).
cnf(c_74,plain,
$false,
inference(copy,[status(thm)],[c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 14:21:58 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1789222 was started by sandbox2 on n009,
% 0.19/0.45 % Fri Sep 25 14:21:58 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.50
% 0.19/0.50 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 0.19/0.50
% 0.19/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.50
% 0.19/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.19/0.50 % Length of proof is 35.
% 0.19/0.50 % Level of proof is 13.
% 0.19/0.50 % Maximum clause weight is 107.000.
% 0.19/0.50 % Given clauses 22.
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------