%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP558-1 : 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 : n005.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 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% 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 : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 33 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,inverse(divide(divide(VAR_1,VAR_2),divide(VAR_0,VAR_2)))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,inverse(divide(divide(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_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_45,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_45]) ).
cnf(c_5,plain,
divide(A,inverse(divide(B,divide(A,inverse(divide(divide(B,C),divide(D,C))))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
divide(A,inverse(divide(B,divide(A,inverse(divide(C,divide(D,inverse(divide(divide(C,E),divide(B,E)))))))))) = D,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
divide(A,inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_46,plain,
divide(A,inverse(divide(B,divide(A,inverse(divide(C,C)))))) = B,
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_12,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_10,c_46]) ).
cnf(c_29,plain,
divide(inverse(divide(A,A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_47,plain,
divide(A,A) = inverse(divide(B,B)),
inference(paramod,[status(thm)],[c_29,c_10]) ).
cnf(c_40,plain,
inverse(divide(A,A)) = divide(B,B),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_48,plain,
divide(inverse(divide(A,A)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_40,c_4]) ).
cnf(c_49,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_29,c_48]) ).
cnf(c_44,plain,
$false,
inference(copy,[status(thm)],[c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP558-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 15:00:01 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3773131 was started by sandbox on n005,
% 0.16/0.44 % Fri Sep 25 15:00:01 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.16/0.46 % Length of proof is 11.
% 0.16/0.46 % Level of proof is 6.
% 0.16/0.46 % Maximum clause weight is 97.000.
% 0.16/0.46 % Given clauses 10.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------