%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP472-1 : 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 07:29:47 AM UTC 2026
% Result : Unsatisfiable 2.03s 0.79s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 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 : 147 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(divide(inverse(divide(VAR_0,VAR_1)),divide(divide(VAR_2,VAR_3),VAR_0)),divide(VAR_3,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,C)) = 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_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_3,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_843,plain,
divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_844,plain,
divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)),
inference(paramod,[status(thm)],[c_2,c_843]) ).
cnf(c_4,plain,
divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(copy,[status(thm)],[c_844]) ).
cnf(c_5,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(F,E),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
divide(divide(inverse(divide(divide(A,B),C)),D),divide(divide(divide(B,A),E),inverse(divide(E,D)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(E),divide(divide(F,V6),divide(inverse(divide(V7,E)),divide(divide(B,A),V7)))))),divide(D,C)) = divide(V6,F),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_845,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(divide(V6,V7),divide(inverse(V8),divide(divide(V7,V6),divide(inverse(divide(V9,V8)),divide(divide(F,E),V9))))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_846,plain,
divide(F,E) = divide(divide(V6,V7),divide(inverse(V8),divide(divide(V7,V6),divide(inverse(divide(V9,V8)),divide(divide(F,E),V9))))),
inference(paramod,[status(thm)],[c_5,c_845]) ).
cnf(c_20,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(divide(E,F),D))))) = divide(E,F),
inference(copy,[status(thm)],[c_846]) ).
cnf(c_847,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(E,D))))) = divide(divide(inverse(divide(F,E)),divide(divide(V6,V7),F)),divide(V7,V6)),
inference(paramod,[status(thm)],[c_1,c_20]) ).
cnf(c_107,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(E,D))))) = E,
inference(paramod,[status(thm)],[c_1,c_847]) ).
cnf(c_232,plain,
divide(divide(inverse(divide(A,B)),divide(B,A)),divide(C,D)) = divide(D,C),
inference(paramod,[status(thm)],[c_107,c_9]) ).
cnf(c_241,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(divide(E,F)),divide(F,E)))),divide(D,C)) = divide(B,A),
inference(paramod,[status(thm)],[c_232,c_1]) ).
cnf(c_254,plain,
divide(divide(inverse(divide(A,B)),divide(B,A)),divide(inverse(b1),inverse(b1))) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_232,c_4]) ).
cnf(c_848,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(divide(F,E),divide(inverse(divide(V6,V7)),divide(V7,V6))),
inference(paramod,[status(thm)],[c_232,c_5]) ).
cnf(c_849,plain,
divide(F,E) = divide(divide(F,E),divide(inverse(divide(V6,V7)),divide(V7,V6))),
inference(paramod,[status(thm)],[c_5,c_848]) ).
cnf(c_258,plain,
divide(divide(A,B),divide(inverse(divide(C,D)),divide(D,C))) = divide(A,B),
inference(copy,[status(thm)],[c_849]) ).
cnf(c_355,plain,
divide(divide(inverse(divide(A,B)),divide(C,D)),divide(D,C)) = divide(B,A),
inference(paramod,[status(thm)],[c_258,c_241]) ).
cnf(c_850,plain,
divide(divide(inverse(divide(divide(inverse(divide(A,B)),divide(B,A)),C)),divide(D,E)),divide(E,D)) = C,
inference(paramod,[status(thm)],[c_258,c_1]) ).
cnf(c_357,plain,
divide(A,divide(inverse(divide(B,C)),divide(C,B))) = A,
inference(paramod,[status(thm)],[c_355,c_850]) ).
cnf(c_385,plain,
divide(divide(A,B),divide(inverse(C),divide(B,A))) = C,
inference(paramod,[status(thm)],[c_258,c_107]) ).
cnf(c_851,plain,
divide(inverse(divide(divide(A,B),C)),divide(divide(divide(B,A),D),inverse(divide(D,divide(inverse(divide(E,F)),divide(F,E)))))) = C,
inference(paramod,[status(thm)],[c_357,c_7]) ).
cnf(c_401,plain,
divide(inverse(divide(divide(A,B),C)),divide(divide(divide(B,A),D),inverse(D))) = C,
inference(paramod,[status(thm)],[c_357,c_851]) ).
cnf(c_616,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(D,E))),divide(C,B)) = divide(inverse(A),divide(E,D)),
inference(paramod,[status(thm)],[c_385,c_1]) ).
cnf(c_852,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(E),divide(F,E)))),divide(D,C)) = divide(divide(B,A),F),
inference(paramod,[status(thm)],[c_385,c_9]) ).
cnf(c_657,plain,
divide(inverse(divide(A,B)),divide(divide(C,D),inverse(D))) = divide(divide(B,A),C),
inference(paramod,[status(thm)],[c_616,c_852]) ).
cnf(c_676,plain,
divide(A,divide(inverse(B),divide(divide(inverse(B),divide(C,D)),divide(D,C)))) = A,
inference(paramod,[status(thm)],[c_385,c_357]) ).
cnf(c_690,plain,
divide(divide(inverse(A),divide(divide(inverse(A),divide(B,C)),divide(C,B))),divide(inverse(b1),inverse(b1))) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_385,c_254]) ).
cnf(c_815,plain,
divide(divide(A,divide(B,C)),divide(C,B)) = A,
inference(paramod,[status(thm)],[c_657,c_401]) ).
cnf(c_836,plain,
divide(divide(inverse(A),inverse(A)),divide(inverse(b1),inverse(b1))) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_815,c_690]) ).
cnf(c_841,plain,
divide(A,divide(inverse(B),inverse(B))) = A,
inference(paramod,[status(thm)],[c_815,c_676]) ).
cnf(c_842,plain,
$false,
inference(resolve,[status(thm)],[c_841,c_836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP472-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n014.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Fri Sep 25 14:55:32 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 506767 was started by sandbox2 on n014,
% 0.17/0.45 % Fri Sep 25 14:55:32 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 2.03/0.79
% 2.03/0.79 % SZS status Unsatisfiable for theBenchmark
% 2.03/0.79
% 2.03/0.79 % Proof 1 at 0.27 (+ 0.05) seconds.
% 2.03/0.79 % Length of proof is 25.
% 2.03/0.79 % Level of proof is 11.
% 2.03/0.79 % Maximum clause weight is 34.000.
% 2.03/0.79 % Given clauses 19.
% 2.03/0.79
% 2.03/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------