%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP539-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:30:19 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 68 ( 68 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 18 ( 18 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,VAR_1),divide(divide(VAR_0,VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,B),divide(divide(A,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]) ).
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(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_5,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_6,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_5]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_7,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_8,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_9,plain,
divide(identity,A) = inverse(A),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_115,plain,
multiply(divide(a3,divide(identity,b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_116,plain,
multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_9,c_115]) ).
cnf(c_117,plain,
divide(divide(a3,inverse(b3)),divide(identity,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_8,c_116]) ).
cnf(c_118,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_9,c_117]) ).
cnf(c_119,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,divide(identity,c3))),
inference(paramod,[status(thm)],[c_8,c_118]) ).
cnf(c_120,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3))),
inference(paramod,[status(thm)],[c_9,c_119]) ).
cnf(c_121,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(identity,divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_8,c_120]) ).
cnf(c_10,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_9,c_121]) ).
cnf(c_12,plain,
divide(A,divide(divide(divide(B,C),D),divide(divide(B,A),C))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_122,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_15,plain,
inverse(divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_9,c_122]) ).
cnf(c_17,plain,
divide(divide(A,divide(A,B)),identity) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_123,plain,
divide(inverse(A),divide(divide(identity,B),A)) = B,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_18,plain,
divide(inverse(A),divide(inverse(B),A)) = B,
inference(paramod,[status(thm)],[c_9,c_123]) ).
cnf(c_124,plain,
divide(A,divide(B,divide(divide(C,A),D))) = divide(divide(C,B),D),
inference(paramod,[status(thm)],[c_1,c_12]) ).
cnf(c_23,plain,
divide(divide(A,B),C) = divide(D,divide(B,divide(divide(A,D),C))),
inference(copy,[status(thm)],[c_124]) ).
cnf(c_125,plain,
divide(A,divide(divide(identity,B),divide(divide(C,A),C))) = B,
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_26,plain,
divide(A,divide(inverse(B),divide(divide(C,A),C))) = B,
inference(paramod,[status(thm)],[c_9,c_125]) ).
cnf(c_30,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_126,plain,
divide(A,divide(B,divide(divide(C,A),D))) = divide(divide(divide(E,F),B),divide(divide(E,divide(C,D)),F)),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_33,plain,
divide(divide(divide(A,B),C),divide(divide(A,divide(D,E)),B)) = divide(F,divide(C,divide(divide(D,F),E))),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_37,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_30,c_17]) ).
cnf(c_127,plain,
A = inverse(divide(identity,A)),
inference(paramod,[status(thm)],[c_37,c_9]) ).
cnf(c_128,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_9,c_127]) ).
cnf(c_42,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_128]) ).
cnf(c_129,plain,
inverse(divide(A,B)) = divide(divide(divide(C,D),A),divide(divide(C,B),D)),
inference(paramod,[status(thm)],[c_12,c_15]) ).
cnf(c_49,plain,
divide(divide(divide(A,B),C),divide(divide(A,D),B)) = inverse(divide(C,D)),
inference(copy,[status(thm)],[c_129]) ).
cnf(c_50,plain,
inverse(divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_37,c_15]) ).
cnf(c_130,plain,
inverse(A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_15,c_42]) ).
cnf(c_51,plain,
divide(divide(A,B),A) = inverse(B),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_131,plain,
inverse(divide(C,divide(D,E))) = divide(F,divide(C,divide(divide(D,F),E))),
inference(paramod,[status(thm)],[c_49,c_33]) ).
cnf(c_55,plain,
divide(A,divide(B,divide(divide(C,A),D))) = inverse(divide(B,divide(C,D))),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_59,plain,
divide(A,divide(inverse(B),inverse(A))) = B,
inference(paramod,[status(thm)],[c_51,c_26]) ).
cnf(c_60,plain,
divide(divide(A,B),C) = inverse(divide(B,divide(A,C))),
inference(paramod,[status(thm)],[c_55,c_23]) ).
cnf(c_72,plain,
inverse(divide(inverse(b3),divide(a3,inverse(c3)))) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_60,c_10]) ).
cnf(c_132,plain,
inverse(divide(inverse(b3),divide(a3,inverse(c3)))) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_50,c_72]) ).
cnf(c_75,plain,
divide(a3,divide(inverse(c3),b3)) != inverse(divide(inverse(b3),divide(a3,inverse(c3)))),
inference(copy,[status(thm)],[c_132]) ).
cnf(c_80,plain,
divide(inverse(A),B) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_18,c_37]) ).
cnf(c_133,plain,
divide(a3,divide(inverse(b3),c3)) != inverse(divide(inverse(b3),divide(a3,inverse(c3)))),
inference(paramod,[status(thm)],[c_80,c_75]) ).
cnf(c_87,plain,
inverse(divide(inverse(b3),divide(a3,inverse(c3)))) != divide(a3,divide(inverse(b3),c3)),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_91,plain,
divide(A,divide(B,inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_42,c_59]) ).
cnf(c_134,plain,
divide(inverse(A),B) = inverse(divide(A,divide(identity,B))),
inference(paramod,[status(thm)],[c_9,c_60]) ).
cnf(c_94,plain,
divide(inverse(A),B) = inverse(divide(A,inverse(B))),
inference(paramod,[status(thm)],[c_9,c_134]) ).
cnf(c_135,plain,
inverse(inverse(divide(b3,inverse(divide(a3,inverse(c3)))))) != divide(a3,divide(inverse(b3),c3)),
inference(paramod,[status(thm)],[c_94,c_87]) ).
cnf(c_136,plain,
divide(b3,inverse(divide(a3,inverse(c3)))) != divide(a3,divide(inverse(b3),c3)),
inference(paramod,[status(thm)],[c_42,c_135]) ).
cnf(c_103,plain,
divide(b3,inverse(divide(a3,inverse(c3)))) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_94,c_136]) ).
cnf(c_109,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_91,c_37]) ).
cnf(c_137,plain,
divide(divide(A,inverse(B)),C) = inverse(divide(inverse(A),divide(B,C))),
inference(paramod,[status(thm)],[c_109,c_60]) ).
cnf(c_138,plain,
inverse(divide(inverse(B),divide(A,C))) = inverse(divide(inverse(A),divide(B,C))),
inference(paramod,[status(thm)],[c_60,c_137]) ).
cnf(c_139,plain,
inverse(inverse(divide(B,inverse(divide(A,C))))) = inverse(divide(inverse(A),divide(B,C))),
inference(paramod,[status(thm)],[c_94,c_138]) ).
cnf(c_140,plain,
divide(B,inverse(divide(A,C))) = inverse(divide(inverse(A),divide(B,C))),
inference(paramod,[status(thm)],[c_42,c_139]) ).
cnf(c_141,plain,
divide(B,inverse(divide(A,C))) = inverse(inverse(divide(A,inverse(divide(B,C))))),
inference(paramod,[status(thm)],[c_94,c_140]) ).
cnf(c_113,plain,
divide(A,inverse(divide(B,C))) = divide(B,inverse(divide(A,C))),
inference(paramod,[status(thm)],[c_42,c_141]) ).
cnf(c_114,plain,
$false,
inference(resolve,[status(thm)],[c_113,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP539-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:59:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 517791 was started by sandbox2 on n014,
% 0.10/0.37 % Fri Sep 25 14:59:17 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.41
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.41
% 0.10/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.41 % Length of proof is 36.
% 0.10/0.41 % Level of proof is 11.
% 0.10/0.41 % Maximum clause weight is 23.000.
% 0.10/0.41 % Given clauses 20.
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------