%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP470-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:29:47 AM UTC 2026
% Result : Unsatisfiable 7.39s 1.32s
% Output : CNFRefutation 7.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 3
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 212 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(inverse(divide(VAR_0,divide(VAR_1,divide(VAR_2,VAR_3)))),divide(divide(VAR_3,VAR_2),VAR_0)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(inverse(divide(A,divide(B,divide(C,D)))),divide(divide(D,C),A)) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,inverse(VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_3,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_3998,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_2,c_3998]) ).
cnf(c_5,plain,
divide(inverse(divide(A,divide(B,C))),divide(divide(divide(divide(D,E),F),inverse(divide(F,divide(C,divide(E,D))))),A)) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_3999,plain,
divide(inverse(divide(A,B)),divide(divide(C,divide(D,E)),A)) = inverse(divide(C,divide(B,divide(E,D)))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(divide(A,divide(B,divide(C,D)))) = divide(inverse(divide(E,B)),divide(divide(A,divide(D,C)),E)),
inference(copy,[status(thm)],[c_3999]) ).
cnf(c_7,plain,
divide(inverse(A),divide(divide(B,C),inverse(divide(divide(C,B),divide(A,divide(D,E)))))) = divide(E,D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
divide(inverse(divide(A,divide(B,divide(divide(divide(C,D),E),inverse(divide(E,divide(F,divide(D,C)))))))),divide(F,A)) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_24,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,divide(D,E)),A)),divide(divide(D,E),C)) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_28,plain,
inverse(divide(A,divide(divide(B,divide(divide(C,D),A)),divide(D,C)))) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_64,plain,
inverse(inverse(divide(A,divide(B,divide(inverse(divide(divide(C,D),B)),divide(D,C)))))) = A,
inference(paramod,[status(thm)],[c_6,c_28]) ).
cnf(c_4000,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(divide(inverse(divide(E,divide(D,divide(F,V6)))),divide(divide(V6,F),E)),C)) = B,
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_80,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,C)) = B,
inference(paramod,[status(thm)],[c_1,c_4000]) ).
cnf(c_4001,plain,
divide(inverse(A),divide(divide(B,C),inverse(divide(divide(C,B),divide(A,divide(D,E)))))) = divide(divide(divide(F,V6),inverse(divide(divide(V6,F),divide(V7,divide(E,D))))),inverse(V7)),
inference(paramod,[status(thm)],[c_7,c_7]) ).
cnf(c_4002,plain,
divide(E,D) = divide(divide(divide(F,V6),inverse(divide(divide(V6,F),divide(V7,divide(E,D))))),inverse(V7)),
inference(paramod,[status(thm)],[c_7,c_4001]) ).
cnf(c_142,plain,
divide(divide(divide(A,B),inverse(divide(divide(B,A),divide(C,divide(D,E))))),inverse(C)) = divide(D,E),
inference(copy,[status(thm)],[c_4002]) ).
cnf(c_4003,plain,
divide(divide(divide(A,B),inverse(divide(divide(B,A),divide(C,D)))),inverse(C)) = divide(inverse(divide(E,divide(D,divide(F,V6)))),divide(divide(V6,F),E)),
inference(paramod,[status(thm)],[c_1,c_142]) ).
cnf(c_190,plain,
divide(divide(divide(A,B),inverse(divide(divide(B,A),divide(C,D)))),inverse(C)) = D,
inference(paramod,[status(thm)],[c_1,c_4003]) ).
cnf(c_249,plain,
divide(divide(divide(divide(divide(A,B),C),inverse(divide(C,D))),inverse(D)),inverse(B)) = A,
inference(paramod,[status(thm)],[c_80,c_190]) ).
cnf(c_304,plain,
divide(divide(A,inverse(B)),inverse(inverse(divide(C,D)))) = divide(divide(A,divide(inverse(D),B)),C),
inference(paramod,[status(thm)],[c_249,c_249]) ).
cnf(c_4004,plain,
divide(inverse(divide(A,B)),divide(C,A)) = divide(inverse(divide(D,B)),divide(divide(inverse(divide(E,divide(C,divide(F,V6)))),divide(divide(V6,F),E)),D)),
inference(paramod,[status(thm)],[c_80,c_8]) ).
cnf(c_345,plain,
divide(inverse(divide(A,B)),divide(C,A)) = divide(inverse(divide(D,B)),divide(C,D)),
inference(paramod,[status(thm)],[c_1,c_4004]) ).
cnf(c_4005,plain,
divide(inverse(A),divide(divide(B,C),inverse(divide(divide(C,B),divide(A,divide(divide(D,divide(inverse(E),F)),V6)))))) = divide(inverse(inverse(divide(V6,E))),divide(D,inverse(F))),
inference(paramod,[status(thm)],[c_304,c_7]) ).
cnf(c_4006,plain,
divide(V6,divide(D,divide(inverse(E),F))) = divide(inverse(inverse(divide(V6,E))),divide(D,inverse(F))),
inference(paramod,[status(thm)],[c_7,c_4005]) ).
cnf(c_525,plain,
divide(inverse(inverse(divide(A,B))),divide(C,inverse(D))) = divide(A,divide(C,divide(inverse(B),D))),
inference(copy,[status(thm)],[c_4006]) ).
cnf(c_632,plain,
inverse(divide(inverse(inverse(divide(A,B))),divide(divide(C,divide(divide(D,inverse(B)),A)),inverse(D)))) = C,
inference(paramod,[status(thm)],[c_525,c_28]) ).
cnf(c_639,plain,
inverse(inverse(divide(inverse(inverse(divide(A,divide(divide(B,C),D)))),divide(D,inverse(divide(C,B)))))) = A,
inference(paramod,[status(thm)],[c_525,c_64]) ).
cnf(c_4007,plain,
inverse(inverse(divide(inverse(inverse(A)),divide(B,inverse(divide(inverse(divide(C,divide(D,divide(E,F)))),divide(divide(F,E),C))))))) = inverse(divide(B,divide(A,D))),
inference(paramod,[status(thm)],[c_5,c_639]) ).
cnf(c_1066,plain,
inverse(inverse(divide(inverse(inverse(A)),divide(B,inverse(C))))) = inverse(divide(B,divide(A,C))),
inference(paramod,[status(thm)],[c_1,c_4007]) ).
cnf(c_4008,plain,
inverse(A) = inverse(divide(divide(A,divide(divide(B,inverse(C)),D)),divide(divide(D,C),B))),
inference(paramod,[status(thm)],[c_632,c_1066]) ).
cnf(c_1324,plain,
inverse(divide(divide(A,divide(divide(B,inverse(C)),D)),divide(divide(D,C),B))) = inverse(A),
inference(copy,[status(thm)],[c_4008]) ).
cnf(c_1360,plain,
divide(divide(divide(divide(divide(A,inverse(B)),C),D),inverse(D)),inverse(divide(C,B))) = A,
inference(paramod,[status(thm)],[c_1324,c_190]) ).
cnf(c_1480,plain,
divide(A,inverse(divide(inverse(divide(inverse(B),C)),B))) = divide(A,inverse(C)),
inference(paramod,[status(thm)],[c_249,c_1360]) ).
cnf(c_4009,plain,
divide(divide(inverse(divide(A,inverse(B))),divide(divide(C,D),A)),divide(D,C)) = inverse(divide(inverse(divide(inverse(E),B)),E)),
inference(paramod,[status(thm)],[c_1480,c_80]) ).
cnf(c_4010,plain,
inverse(B) = inverse(divide(inverse(divide(inverse(E),B)),E)),
inference(paramod,[status(thm)],[c_80,c_4009]) ).
cnf(c_1588,plain,
inverse(divide(inverse(divide(inverse(A),B)),A)) = inverse(B),
inference(copy,[status(thm)],[c_4010]) ).
cnf(c_1895,plain,
inverse(divide(inverse(A),divide(inverse(B),A))) = inverse(B),
inference(paramod,[status(thm)],[c_1588,c_1588]) ).
cnf(c_4011,plain,
inverse(divide(inverse(A),divide(B,A))) = inverse(divide(C,divide(divide(B,divide(divide(D,E),C)),divide(E,D)))),
inference(paramod,[status(thm)],[c_28,c_1895]) ).
cnf(c_1910,plain,
inverse(divide(inverse(A),divide(B,A))) = B,
inference(paramod,[status(thm)],[c_28,c_4011]) ).
cnf(c_2085,plain,
divide(A,divide(divide(B,C),inverse(divide(C,B)))) = A,
inference(paramod,[status(thm)],[c_1910,c_1]) ).
cnf(c_4012,plain,
inverse(A) = inverse(divide(A,divide(B,B))),
inference(paramod,[status(thm)],[c_1910,c_1066]) ).
cnf(c_2135,plain,
inverse(divide(A,divide(B,B))) = inverse(A),
inference(copy,[status(thm)],[c_4012]) ).
cnf(c_4013,plain,
divide(inverse(divide(A,B)),divide(divide(C,D),inverse(divide(D,C)))) = divide(B,A),
inference(paramod,[status(thm)],[c_2135,c_7]) ).
cnf(c_2912,plain,
inverse(divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_2085,c_4013]) ).
cnf(c_4014,plain,
divide(divide(divide(A,B),inverse(divide(B,A))),inverse(C)) = C,
inference(paramod,[status(thm)],[c_2135,c_190]) ).
cnf(c_2915,plain,
divide(divide(divide(A,B),divide(A,B)),inverse(C)) = C,
inference(paramod,[status(thm)],[c_2912,c_4014]) ).
cnf(c_4015,plain,
inverse(divide(inverse(divide(A,B)),divide(C,A))) = inverse(inverse(divide(C,B))),
inference(paramod,[status(thm)],[c_345,c_2135]) ).
cnf(c_4016,plain,
inverse(divide(divide(B,A),divide(C,A))) = inverse(inverse(divide(C,B))),
inference(paramod,[status(thm)],[c_2912,c_4015]) ).
cnf(c_4017,plain,
divide(divide(C,A),divide(B,A)) = inverse(inverse(divide(C,B))),
inference(paramod,[status(thm)],[c_2912,c_4016]) ).
cnf(c_4018,plain,
divide(divide(C,A),divide(B,A)) = inverse(divide(B,C)),
inference(paramod,[status(thm)],[c_2912,c_4017]) ).
cnf(c_2924,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(paramod,[status(thm)],[c_2912,c_4018]) ).
cnf(c_3996,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_2924,c_2915]) ).
cnf(c_3997,plain,
$false,
inference(resolve,[status(thm)],[c_3996,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP470-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:55:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1031880 was started by sandbox on n010,
% 0.09/0.36 % Fri Sep 25 14:55:59 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 7.39/1.32
% 7.39/1.32 % SZS status Unsatisfiable for theBenchmark
% 7.39/1.32
% 7.39/1.32 % Proof 1 at 0.81 (+ 0.12) seconds.
% 7.39/1.32 % Length of proof is 34.
% 7.39/1.32 % Level of proof is 19.
% 7.39/1.32 % Maximum clause weight is 25.000.
% 7.39/1.32 % Given clauses 36.
% 7.39/1.32
% 7.39/1.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------