%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP088-1 : 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 : n018.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 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 71 ( 50 unt; 0 def)
% Number of atoms : 124 ( 123 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 128 ( 75 ~; 53 |; 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(VAR_1,divide(VAR_2,divide(VAR_0,VAR_1)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(B,divide(C,divide(A,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]) ).
cnf(c_3,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(copy,[status(thm)],[c_2]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_4,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_5,plain,
divide(divide(A,A),B) = inverse(B),
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_117,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_6]) ).
cnf(c_7,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_117]) ).
cnf(c_118,plain,
divide(A,inverse(C)) = multiply(A,C),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_8,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_119,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_8,c_7]) ).
cnf(c_120,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)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_119]) ).
cnf(c_121,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
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_120]) ).
cnf(c_122,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_121]) ).
cnf(c_123,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_5,c_122]) ).
cnf(c_124,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_123]) ).
cnf(c_125,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_124]) ).
cnf(c_126,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3)))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_125]) ).
cnf(c_127,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
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_126]) ).
cnf(c_128,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
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_127]) ).
cnf(c_9,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
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_8,c_128]) ).
cnf(c_10,plain,
divide(A,divide(divide(B,divide(C,divide(A,B))),divide(D,C))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
divide(A,divide(divide(B,divide(C,A)),B)) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_129,plain,
divide(divide(A,A),divide(B,divide(C,inverse(B)))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_12,plain,
inverse(divide(A,divide(B,inverse(A)))) = B,
inference(paramod,[status(thm)],[c_5,c_129]) ).
cnf(c_14,plain,
divide(A,inverse(divide(B,divide(A,divide(C,C))))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_15,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_26,plain,
divide(A,divide(A,divide(B,divide(C,divide(D,divide(D,C)))))) = B,
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_30,plain,
divide(inverse(inverse(divide(A,A))),B) = inverse(B),
inference(paramod,[status(thm)],[c_15,c_5]) ).
cnf(c_35,plain,
inverse(divide(A,inverse(inverse(A)))) = divide(B,B),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_38,plain,
inverse(inverse(divide(A,inverse(inverse(divide(B,B)))))) = A,
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_41,plain,
divide(A,divide(divide(B,inverse(divide(A,B))),divide(C,inverse(inverse(divide(D,D)))))) = C,
inference(paramod,[status(thm)],[c_30,c_10]) ).
cnf(c_48,plain,
divide(A,divide(A,divide(B,inverse(divide(C,inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_35,c_1]) ).
cnf(c_49,plain,
divide(A,divide(B,inverse(divide(C,inverse(inverse(C)))))) = divide(A,B),
inference(paramod,[status(thm)],[c_35,c_1]) ).
cnf(c_64,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_35,c_35]) ).
cnf(c_66,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_49,c_48]) ).
cnf(c_67,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(resolve,[status(thm)],[c_64,c_9]) ).
cnf(c_130,plain,
divide(A,divide(A,divide(B,divide(C,C)))) = B,
inference(paramod,[status(thm)],[c_66,c_26]) ).
cnf(c_68,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_66,c_130]) ).
cnf(c_73,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_68,c_14]) ).
cnf(c_131,plain,
divide(A,divide(A,divide(C,inverse(inverse(divide(D,D)))))) = C,
inference(paramod,[status(thm)],[c_73,c_41]) ).
cnf(c_75,plain,
divide(A,inverse(inverse(divide(B,B)))) = A,
inference(paramod,[status(thm)],[c_66,c_131]) ).
cnf(c_78,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_75,c_38]) ).
cnf(c_132,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_78,c_67]) ).
cnf(c_79,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_132]) ).
cnf(c_133,plain,
divide(A,B) = divide(divide(A,C),divide(B,C)),
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_82,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_90,plain,
divide(divide(A,B),divide(A,C)) = divide(D,divide(B,divide(C,D))),
inference(paramod,[status(thm)],[c_10,c_11]) ).
cnf(c_134,plain,
divide(A,B) = divide(C,divide(B,divide(A,C))),
inference(paramod,[status(thm)],[c_1,c_66]) ).
cnf(c_95,plain,
divide(A,divide(B,divide(C,A))) = divide(C,B),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_99,plain,
divide(divide(A,B),divide(A,C)) = divide(C,B),
inference(paramod,[status(thm)],[c_95,c_90]) ).
cnf(c_135,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_73,c_66]) ).
cnf(c_104,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_105,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_66,c_73]) ).
cnf(c_106,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) ),
inference(paramod,[status(thm)],[c_104,c_79]) ).
cnf(c_136,plain,
divide(A,divide(B,inverse(C))) = divide(divide(A,C),B),
inference(paramod,[status(thm)],[c_105,c_82]) ).
cnf(c_112,plain,
divide(divide(A,B),C) = divide(A,divide(C,inverse(B))),
inference(copy,[status(thm)],[c_136]) ).
cnf(c_137,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),inverse(inverse(b3)))) != divide(a3,divide(inverse(c3),b3)) ),
inference(paramod,[status(thm)],[c_112,c_106]) ).
cnf(c_138,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(c3),b3)) ),
inference(paramod,[status(thm)],[c_78,c_137]) ).
cnf(c_113,plain,
divide(b4,inverse(a4)) != divide(a4,inverse(b4)),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_139,plain,
divide(A,divide(divide(A,C),inverse(B))) = divide(C,B),
inference(paramod,[status(thm)],[c_112,c_99]) ).
cnf(c_140,plain,
divide(A,divide(A,divide(inverse(B),inverse(C)))) = divide(C,B),
inference(paramod,[status(thm)],[c_112,c_139]) ).
cnf(c_114,plain,
divide(inverse(A),inverse(B)) = divide(B,A),
inference(paramod,[status(thm)],[c_66,c_140]) ).
cnf(c_141,plain,
multiply(A,B) = divide(inverse(inverse(B)),inverse(A)),
inference(paramod,[status(thm)],[c_114,c_8]) ).
cnf(c_142,plain,
divide(A,inverse(B)) = divide(inverse(inverse(B)),inverse(A)),
inference(paramod,[status(thm)],[c_8,c_141]) ).
cnf(c_115,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_78,c_142]) ).
cnf(c_116,plain,
$false,
inference(resolve,[status(thm)],[c_115,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n018.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 14:23:35 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2150038 was started by sandbox2 on n018,
% 0.18/0.43 % Fri Sep 25 14:23:35 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.49
% 0.18/0.49 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.18/0.49
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.49
% 0.18/0.49 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.18/0.49 % Length of proof is 41.
% 0.18/0.49 % Level of proof is 13.
% 0.18/0.49 % Maximum clause weight is 75.000.
% 0.18/0.49 % Given clauses 23.
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------