%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP561-1 : 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 : n015.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 07:30:22 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 34 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,inverse(VAR_1)),VAR_2),divide(VAR_0,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,inverse(B)),C),divide(A,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_54,plain,
divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_55,plain,
divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)),
inference(paramod,[status(thm)],[c_2,c_54]) ).
cnf(c_4,plain,
divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_5,plain,
divide(A,divide(divide(B,inverse(A)),divide(B,inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(D)),divide(A,C)),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_56,plain,
divide(divide(A,divide(divide(divide(B,inverse(inverse(C))),D),divide(B,D))),A) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_16,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_1,c_56]) ).
cnf(c_19,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_28,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_19,c_16]) ).
cnf(c_57,plain,
divide(A,divide(A,divide(divide(B,B),inverse(C)))) = C,
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_31,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_28,c_57]) ).
cnf(c_52,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_19,c_31]) ).
cnf(c_53,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP561-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 15:03:12 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1674636 was started by sandbox2 on n015,
% 0.18/0.45 % Fri Sep 25 15:03:12 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.18/0.47 % Length of proof is 12.
% 0.18/0.47 % Level of proof is 7.
% 0.18/0.47 % Maximum clause weight is 17.000.
% 0.18/0.47 % Given clauses 10.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------