%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP607-1 : 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 : n001.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 07:30:28 AM UTC 2026
% Result : Unsatisfiable 0.16s 10.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 3
% Syntax : Number of formulae : 94 ( 94 unt; 0 def)
% Number of atoms : 94 ( 93 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 28 ( 28 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 180 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(VAR_0,inverse(double_divide(inverse(VAR_1),double_divide(VAR_0,VAR_2))))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = inverse(double_divide(VAR_1,VAR_0)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(clausify,[status(thm)],[multiply]) ).
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_3,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_113,plain,
multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_114,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_113]) ).
cnf(c_115,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3))),
inference(paramod,[status(thm)],[c_2,c_114]) ).
cnf(c_116,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_2,c_115]) ).
cnf(c_4,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_5,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_117,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(D,inverse(double_divide(inverse(B),double_divide(D,double_divide(A,C))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,double_divide(C,D))))) = double_divide(inverse(double_divide(C,inverse(B))),D),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_7,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),A))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_118,plain,
double_divide(inverse(A),inverse(B)) = double_divide(C,inverse(double_divide(inverse(B),double_divide(C,A)))),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_13,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = double_divide(inverse(C),inverse(B)),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_119,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(C,inverse(double_divide(inverse(D),double_divide(C,A))))),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_120,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(inverse(A),inverse(D))),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_13,c_119]) ).
cnf(c_16,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(double_divide(inverse(C),B))) = double_divide(inverse(A),inverse(C)),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_17,plain,
double_divide(inverse(inverse(double_divide(inverse(A),B))),inverse(A)) = B,
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_121,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(C),inverse(B))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_122,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(C),inverse(D))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_16,c_121]) ).
cnf(c_19,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B,
inference(paramod,[status(thm)],[c_16,c_122]) ).
cnf(c_123,plain,
double_divide(inverse(double_divide(C,D)),inverse(B)) = double_divide(inverse(double_divide(C,inverse(B))),D),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_20,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(inverse(double_divide(A,C)),inverse(B)),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_27,plain,
double_divide(inverse(double_divide(inverse(A),A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_20,c_19]) ).
cnf(c_33,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_27,c_10]) ).
cnf(c_124,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(A),A)),inverse(B))),inverse(C)) = double_divide(inverse(C),inverse(B)),
inference(paramod,[status(thm)],[c_27,c_20]) ).
cnf(c_36,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_27,c_124]) ).
cnf(c_125,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(A,inverse(B)))),inverse(B))),inverse(C)) = C,
inference(paramod,[status(thm)],[c_20,c_27]) ).
cnf(c_37,plain,
double_divide(inverse(double_divide(inverse(A),inverse(double_divide(B,double_divide(B,inverse(A)))))),inverse(C)) = C,
inference(paramod,[status(thm)],[c_36,c_125]) ).
cnf(c_38,plain,
double_divide(inverse(A),inverse(inverse(A))) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_36,c_33]) ).
cnf(c_40,plain,
double_divide(inverse(A),inverse(inverse(double_divide(inverse(A),B)))) = B,
inference(paramod,[status(thm)],[c_36,c_17]) ).
cnf(c_126,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(C)))) = double_divide(inverse(double_divide(B,inverse(A))),inverse(C)),
inference(paramod,[status(thm)],[c_36,c_20]) ).
cnf(c_47,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) = double_divide(inverse(B),inverse(double_divide(A,inverse(C)))),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_127,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(C)) = double_divide(inverse(double_divide(inverse(C),inverse(A))),inverse(B)),
inference(paramod,[status(thm)],[c_36,c_20]) ).
cnf(c_128,plain,
double_divide(inverse(B),inverse(double_divide(inverse(A),inverse(C)))) = double_divide(inverse(double_divide(inverse(C),inverse(A))),inverse(B)),
inference(paramod,[status(thm)],[c_47,c_127]) ).
cnf(c_129,plain,
double_divide(inverse(B),inverse(double_divide(inverse(A),inverse(C)))) = double_divide(inverse(A),inverse(double_divide(inverse(C),inverse(B)))),
inference(paramod,[status(thm)],[c_47,c_128]) ).
cnf(c_48,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(C)))) = double_divide(inverse(C),inverse(double_divide(inverse(A),inverse(B)))),
inference(copy,[status(thm)],[c_129]) ).
cnf(c_49,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(inverse(B),inverse(double_divide(A,C))),
inference(paramod,[status(thm)],[c_36,c_20]) ).
cnf(c_50,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_36,c_27]) ).
cnf(c_52,plain,
double_divide(inverse(double_divide(A,double_divide(A,inverse(B)))),inverse(double_divide(inverse(B),inverse(C)))) = C,
inference(paramod,[status(thm)],[c_49,c_37]) ).
cnf(c_130,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),C))) = double_divide(inverse(inverse(double_divide(inverse(C),A))),inverse(B)),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_60,plain,
double_divide(inverse(inverse(double_divide(inverse(A),B))),inverse(C)) = double_divide(inverse(B),inverse(double_divide(inverse(C),A))),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_131,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(inverse(C),inverse(D))))) = double_divide(inverse(inverse(double_divide(inverse(D),double_divide(A,C)))),inverse(B)),
inference(paramod,[status(thm)],[c_13,c_13]) ).
cnf(c_132,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(inverse(C),inverse(D))))) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_60,c_131]) ).
cnf(c_62,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))) = double_divide(A,inverse(double_divide(inverse(C),double_divide(inverse(B),inverse(D))))),
inference(copy,[status(thm)],[c_132]) ).
cnf(c_133,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(inverse(double_divide(A,inverse(B))),inverse(inverse(C)))))) = C,
inference(paramod,[status(thm)],[c_62,c_52]) ).
cnf(c_63,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(inverse(B),inverse(double_divide(A,inverse(inverse(C)))))))) = C,
inference(paramod,[status(thm)],[c_49,c_133]) ).
cnf(c_134,plain,
double_divide(inverse(inverse(inverse(A))),inverse(double_divide(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_38,c_10]) ).
cnf(c_65,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_50,c_134]) ).
cnf(c_71,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(inverse(B),inverse(double_divide(A,C)))))) = C,
inference(paramod,[status(thm)],[c_65,c_63]) ).
cnf(c_77,plain,
double_divide(inverse(A),double_divide(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_65,c_40]) ).
cnf(c_135,plain,
double_divide(A,inverse(inverse(double_divide(A,C)))) = C,
inference(paramod,[status(thm)],[c_77,c_71]) ).
cnf(c_79,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_65,c_135]) ).
cnf(c_81,plain,
double_divide(inverse(A),inverse(double_divide(B,A))) = inverse(B),
inference(paramod,[status(thm)],[c_65,c_10]) ).
cnf(c_136,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),inverse(inverse(A))),
inference(paramod,[status(thm)],[c_65,c_36]) ).
cnf(c_137,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),A),
inference(paramod,[status(thm)],[c_65,c_136]) ).
cnf(c_82,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_138,plain,
inverse(double_divide(a3,inverse(double_divide(c3,b3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_82,c_4]) ).
cnf(c_88,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3)))),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_139,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_65,c_82]) ).
cnf(c_90,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_65,c_139]) ).
cnf(c_140,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3)))),
inference(paramod,[status(thm)],[c_90,c_88]) ).
cnf(c_92,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_90,c_140]) ).
cnf(c_141,plain,
double_divide(inverse(A),inverse(B)) = inverse(double_divide(B,A)),
inference(paramod,[status(thm)],[c_81,c_79]) ).
cnf(c_101,plain,
inverse(double_divide(A,B)) = double_divide(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_142,plain,
inverse(double_divide(c3,double_divide(inverse(b3),inverse(a3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_101,c_92]) ).
cnf(c_143,plain,
inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_90,c_142]) ).
cnf(c_144,plain,
double_divide(inverse(double_divide(inverse(a3),inverse(b3))),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_101,c_143]) ).
cnf(c_145,plain,
double_divide(double_divide(inverse(inverse(b3)),inverse(inverse(a3))),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_101,c_144]) ).
cnf(c_146,plain,
double_divide(double_divide(b3,inverse(inverse(a3))),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_65,c_145]) ).
cnf(c_147,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_65,c_146]) ).
cnf(c_148,plain,
double_divide(double_divide(a3,b3),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_90,c_147]) ).
cnf(c_149,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_90,c_148]) ).
cnf(c_150,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,double_divide(inverse(c3),inverse(b3)))),
inference(paramod,[status(thm)],[c_101,c_149]) ).
cnf(c_151,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,double_divide(inverse(b3),inverse(c3)))),
inference(paramod,[status(thm)],[c_90,c_150]) ).
cnf(c_152,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(double_divide(inverse(b3),inverse(c3))),inverse(a3)),
inference(paramod,[status(thm)],[c_101,c_151]) ).
cnf(c_153,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(inverse(inverse(c3)),inverse(inverse(b3))),inverse(a3)),
inference(paramod,[status(thm)],[c_101,c_152]) ).
cnf(c_154,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(c3,inverse(inverse(b3))),inverse(a3)),
inference(paramod,[status(thm)],[c_65,c_153]) ).
cnf(c_155,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(c3,b3),inverse(a3)),
inference(paramod,[status(thm)],[c_65,c_154]) ).
cnf(c_156,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),inverse(a3)),
inference(paramod,[status(thm)],[c_90,c_155]) ).
cnf(c_106,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_90,c_156]) ).
cnf(c_157,plain,
double_divide(inverse(A),double_divide(inverse(inverse(C)),inverse(inverse(B)))) = double_divide(inverse(C),inverse(double_divide(inverse(A),inverse(B)))),
inference(paramod,[status(thm)],[c_101,c_48]) ).
cnf(c_158,plain,
double_divide(inverse(A),double_divide(C,inverse(inverse(B)))) = double_divide(inverse(C),inverse(double_divide(inverse(A),inverse(B)))),
inference(paramod,[status(thm)],[c_65,c_157]) ).
cnf(c_159,plain,
double_divide(inverse(A),double_divide(C,B)) = double_divide(inverse(C),inverse(double_divide(inverse(A),inverse(B)))),
inference(paramod,[status(thm)],[c_65,c_158]) ).
cnf(c_160,plain,
double_divide(inverse(A),double_divide(C,B)) = double_divide(inverse(C),double_divide(inverse(inverse(B)),inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_101,c_159]) ).
cnf(c_161,plain,
double_divide(inverse(A),double_divide(C,B)) = double_divide(inverse(C),double_divide(B,inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_65,c_160]) ).
cnf(c_162,plain,
double_divide(inverse(A),double_divide(C,B)) = double_divide(inverse(C),double_divide(B,A)),
inference(paramod,[status(thm)],[c_65,c_161]) ).
cnf(c_111,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_163,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_112,plain,
$false,
inference(resolve,[status(thm)],[c_111,c_163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP607-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.44 % Computer : n001.cluster.edu
% 0.16/10.44 % Model : x86_64 x86_64
% 0.16/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.44 % Memory : 8046.5625MB
% 0.16/10.44 % OS : Linux 6.8.0-71-generic
% 0.16/10.44 % CPULimit : 300
% 0.16/10.44 % WCLimit : 300
% 0.16/10.44 % DateTime : Fri Sep 25 15:07:51 UTC 2026
% 0.16/10.44 % CPUTime :
% 0.16/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/10.45 % Process 3626410 was started by sandbox2 on n001,
% 0.16/10.45 % Fri Sep 25 15:07:51 2026
% 0.16/10.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/10.45
% 0.16/10.45 % From the command line: assign(max_seconds, 300).
% 0.16/10.50
% 0.16/10.50 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.16/10.50
% 0.16/10.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/10.50
% 0.16/10.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.16/10.50 % Length of proof is 40.
% 0.16/10.50 % Level of proof is 15.
% 0.16/10.50 % Maximum clause weight is 85.000.
% 0.16/10.50 % Given clauses 21.
% 0.16/10.50
% 0.16/10.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
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