%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP089-1 : 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 : n006.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 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 39 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 135 ( 80 ~; 55 |; 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(A,B),divide(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]) ).
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_58,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_58]) ).
cnf(c_59,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_59]) ).
cnf(c_60,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_61,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_60]) ).
cnf(c_62,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_61]) ).
cnf(c_63,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_62]) ).
cnf(c_64,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_63]) ).
cnf(c_65,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_64]) ).
cnf(c_66,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_65]) ).
cnf(c_67,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_66]) ).
cnf(c_68,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_67]) ).
cnf(c_69,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_68]) ).
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_69]) ).
cnf(c_10,plain,
divide(A,divide(B,divide(C,divide(divide(A,D),divide(B,D))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_70,plain,
divide(A,B) = divide(divide(A,divide(B,C)),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_12,plain,
divide(divide(A,divide(B,C)),C) = divide(A,B),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_15,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_20,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_25,plain,
divide(A,divide(B,inverse(divide(divide(A,C),divide(B,C))))) = divide(D,D),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_71,plain,
divide(A,divide(A,divide(B,divide(C,C)))) = B,
inference(paramod,[status(thm)],[c_20,c_1]) ).
cnf(c_26,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_20,c_71]) ).
cnf(c_72,plain,
divide(A,B) = divide(divide(A,C),divide(B,C)),
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_30,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
divide(A,divide(B,inverse(divide(A,B)))) = divide(D,D),
inference(paramod,[status(thm)],[c_30,c_25]) ).
cnf(c_31,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_15,c_73]) ).
cnf(c_34,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_31,c_9]) ).
cnf(c_74,plain,
A = inverse(divide(divide(B,B),A)),
inference(paramod,[status(thm)],[c_26,c_5]) ).
cnf(c_75,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_5,c_74]) ).
cnf(c_38,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_75]) ).
cnf(c_76,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_38,c_34]) ).
cnf(c_39,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_76]) ).
cnf(c_40,plain,
divide(divide(A,B),A) = inverse(B),
inference(paramod,[status(thm)],[c_12,c_5]) ).
cnf(c_44,plain,
divide(divide(A,divide(B,C)),D) = divide(A,divide(B,divide(C,D))),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_77,plain,
divide(divide(A,B),C) = divide(divide(A,divide(B,divide(D,C))),D),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_78,plain,
divide(divide(A,B),C) = divide(A,divide(B,divide(divide(D,C),D))),
inference(paramod,[status(thm)],[c_44,c_77]) ).
cnf(c_45,plain,
divide(divide(A,B),C) = divide(A,divide(B,inverse(C))),
inference(paramod,[status(thm)],[c_40,c_78]) ).
cnf(c_46,plain,
divide(A,divide(B,inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_45,c_40]) ).
cnf(c_79,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),inverse(inverse(c3)))) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(paramod,[status(thm)],[c_45,c_39]) ).
cnf(c_80,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(paramod,[status(thm)],[c_38,c_79]) ).
cnf(c_47,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,inverse(divide(b3,inverse(c3)))) != divide(a3,divide(inverse(b3),c3)) ),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_81,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_15,c_26]) ).
cnf(c_48,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_49,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_48,c_47]) ).
cnf(c_50,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_46,c_26]) ).
cnf(c_82,plain,
( divide(a4,inverse(b4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_50,c_49]) ).
cnf(c_53,plain,
divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3)),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,plain,
inverse(divide(A,inverse(B))) = divide(inverse(A),B),
inference(paramod,[status(thm)],[c_50,c_48]) ).
cnf(c_55,plain,
divide(inverse(A),B) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_48,c_83]) ).
cnf(c_84,plain,
divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3)),
inference(paramod,[status(thm)],[c_55,c_53]) ).
cnf(c_57,plain,
$false,
inference(copy,[status(thm)],[c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP089-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n006.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 14:21:55 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3094470 was started by sandbox2 on n006,
% 0.16/0.43 % Fri Sep 25 14:21:55 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.16/0.46
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 31.
% 0.16/0.46 % Level of proof is 10.
% 0.16/0.46 % Maximum clause weight is 75.000.
% 0.16/0.46 % Given clauses 17.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------