%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP467-1 : 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 : n001.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 0.11s 5.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(divide(VAR_0,VAR_0),divide(VAR_1,divide(divide(VAR_2,divide(VAR_3,VAR_1)),inverse(VAR_3)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = C,
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_30,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_30]) ).
cnf(c_6,plain,
divide(divide(A,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,inverse(D)))) = divide(E,E),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_11,plain,
divide(divide(A,A),divide(B,divide(divide(C,C),inverse(D)))) = divide(D,B),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_12,plain,
divide(divide(A,A),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_23,plain,
divide(A,divide(divide(B,B),inverse(A))) = divide(C,C),
inference(paramod,[status(thm)],[c_11,c_9]) ).
cnf(c_31,plain,
divide(divide(A,A),divide(inverse(B),divide(divide(C,C),inverse(divide(D,D))))) = B,
inference(paramod,[status(thm)],[c_23,c_1]) ).
cnf(c_28,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_11,c_31]) ).
cnf(c_29,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP467-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n001.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 15:01:15 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 3607310 was started by sandbox2 on n001,
% 0.11/5.38 % Fri Sep 25 15:01:15 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.38
% 0.11/5.38 % From the command line: assign(max_seconds, 300).
% 0.11/5.39
% 0.11/5.39 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.11/5.39
% 0.11/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/5.39
% 0.11/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/5.39 % Length of proof is 11.
% 0.11/5.39 % Level of proof is 6.
% 0.11/5.39 % Maximum clause weight is 81.000.
% 0.11/5.39 % Given clauses 8.
% 0.11/5.39
% 0.11/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------