%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP090-1 : 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 : n003.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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 52 ( 32 unt; 0 def)
% Number of atoms : 106 ( 105 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 131 ( 77 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 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 : 69 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,divide(VAR_1,VAR_2)),divide(VAR_0,VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,divide(B,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]) ).
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(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_5,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_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
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_6,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_76]) ).
cnf(c_7,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_77,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_7,c_6]) ).
cnf(c_78,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_7,c_77]) ).
cnf(c_79,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_7,c_78]) ).
cnf(c_80,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_7,c_79]) ).
cnf(c_81,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_4,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
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_81]) ).
cnf(c_83,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_7,c_82]) ).
cnf(c_84,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_7,c_83]) ).
cnf(c_85,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_7,c_84]) ).
cnf(c_86,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_7,c_85]) ).
cnf(c_8,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_7,c_86]) ).
cnf(c_9,plain,
divide(divide(A,B),divide(A,divide(C,divide(D,B)))) = divide(C,D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(A,divide(divide(B,divide(C,A)),B)) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
divide(divide(divide(A,divide(B,C)),divide(divide(A,B),D)),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_14,plain,
inverse(divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_17,plain,
divide(divide(A,B),divide(divide(C,D),C)) = divide(A,divide(B,D)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_31,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_4,c_14]) ).
cnf(c_87,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
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_31,c_8]) ).
cnf(c_33,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_88,plain,
inverse(A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_14,c_31]) ).
cnf(c_34,plain,
divide(divide(A,B),A) = inverse(B),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_37,plain,
divide(divide(A,B),inverse(C)) = divide(A,divide(B,C)),
inference(paramod,[status(thm)],[c_34,c_17]) ).
cnf(c_38,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_34,c_10]) ).
cnf(c_41,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_37,c_33]) ).
cnf(c_89,plain,
divide(A,inverse(inverse(A))) = divide(B,B),
inference(paramod,[status(thm)],[c_4,c_38]) ).
cnf(c_45,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_31,c_89]) ).
cnf(c_47,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_90,plain,
divide(divide(divide(A,divide(B,C)),inverse(B)),C) = A,
inference(paramod,[status(thm)],[c_34,c_11]) ).
cnf(c_91,plain,
divide(divide(A,divide(divide(B,C),B)),C) = A,
inference(paramod,[status(thm)],[c_37,c_90]) ).
cnf(c_55,plain,
divide(divide(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_34,c_91]) ).
cnf(c_67,plain,
divide(inverse(A),B) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_34,c_55]) ).
cnf(c_68,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_55,c_38]) ).
cnf(c_69,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_38,c_55]) ).
cnf(c_92,plain,
( divide(a4,inverse(b4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(paramod,[status(thm)],[c_68,c_47]) ).
cnf(c_70,plain,
divide(a3,divide(inverse(b3),c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_93,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_69,c_34]) ).
cnf(c_71,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_71,c_70]) ).
cnf(c_95,plain,
divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3)),
inference(paramod,[status(thm)],[c_67,c_94]) ).
cnf(c_75,plain,
$false,
inference(copy,[status(thm)],[c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP090-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:23:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 368060 was started by sandbox2 on n003,
% 0.08/0.35 % Fri Sep 25 14:23:37 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 28.
% 0.08/0.38 % Level of proof is 9.
% 0.08/0.38 % Maximum clause weight is 40.000.
% 0.08/0.38 % Given clauses 20.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------