%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP553-1 : 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 : n018.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 07:30:21 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 84 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,inverse(divide(VAR_1,divide(VAR_0,VAR_2)))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,inverse(divide(B,divide(A,C)))),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_48,plain,
divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_49,plain,
divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)),
inference(paramod,[status(thm)],[c_2,c_48]) ).
cnf(c_4,plain,
divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_5,plain,
divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_11,plain,
divide(divide(divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),inverse(divide(E,D))),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_13,plain,
divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(D)),C) = divide(divide(E,inverse(divide(F,divide(E,B)))),inverse(divide(D,F))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_50,plain,
divide(A,inverse(B)) = divide(C,inverse(divide(B,divide(C,A)))),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_15,plain,
divide(A,inverse(divide(B,divide(A,C)))) = divide(C,inverse(B)),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_51,plain,
divide(A,inverse(B)) = divide(divide(C,inverse(divide(D,divide(C,A)))),inverse(divide(B,D))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_52,plain,
divide(A,inverse(B)) = divide(divide(A,inverse(D)),inverse(divide(B,D))),
inference(paramod,[status(thm)],[c_15,c_51]) ).
cnf(c_18,plain,
divide(divide(A,inverse(B)),inverse(divide(C,B))) = divide(A,inverse(C)),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_53,plain,
divide(divide(divide(C,inverse(B)),inverse(D)),C) = divide(divide(E,inverse(divide(F,divide(E,B)))),inverse(divide(D,F))),
inference(paramod,[status(thm)],[c_15,c_13]) ).
cnf(c_54,plain,
divide(divide(divide(C,inverse(B)),inverse(D)),C) = divide(divide(B,inverse(F)),inverse(divide(D,F))),
inference(paramod,[status(thm)],[c_15,c_53]) ).
cnf(c_20,plain,
divide(divide(divide(A,inverse(B)),inverse(C)),A) = divide(B,inverse(C)),
inference(paramod,[status(thm)],[c_18,c_54]) ).
cnf(c_55,plain,
divide(divide(divide(divide(divide(C,inverse(B)),inverse(divide(D,B))),inverse(divide(E,D))),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_15,c_11]) ).
cnf(c_56,plain,
divide(divide(divide(divide(C,inverse(D)),inverse(divide(E,D))),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_18,c_55]) ).
cnf(c_57,plain,
divide(divide(divide(C,inverse(E)),inverse(divide(F,E))),C) = F,
inference(paramod,[status(thm)],[c_18,c_56]) ).
cnf(c_21,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_18,c_57]) ).
cnf(c_32,plain,
divide(divide(A,inverse(B)),divide(inverse(C),inverse(A))) = divide(C,inverse(B)),
inference(paramod,[status(thm)],[c_21,c_20]) ).
cnf(c_35,plain,
divide(divide(A,inverse(B)),divide(inverse(C),inverse(A))) = divide(B,inverse(C)),
inference(paramod,[status(thm)],[c_20,c_20]) ).
cnf(c_37,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_35,c_32]) ).
cnf(c_38,plain,
divide(divide(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_37,c_21]) ).
cnf(c_58,plain,
divide(A,A) = divide(inverse(B),inverse(B)),
inference(paramod,[status(thm)],[c_38,c_20]) ).
cnf(c_46,plain,
divide(inverse(A),inverse(A)) = divide(B,B),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_47,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP553-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:01:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2248439 was started by sandbox2 on n018,
% 0.09/0.35 % Fri Sep 25 15:01:50 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.36
% 0.13/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.36
% 0.13/0.36 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.36 % Length of proof is 18.
% 0.13/0.36 % Level of proof is 10.
% 0.13/0.36 % Maximum clause weight is 27.000.
% 0.13/0.36 % Given clauses 11.
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------