%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP522-1 : 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 : 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 07:30:17 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 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 : 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 : 74 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(VAR_1,divide(VAR_2,divide(VAR_0,VAR_1)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(B,divide(C,divide(A,B)))) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(divide(VAR_2,VAR_2),VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
inference(clausify,[status(thm)],[multiply]) ).
cnf(c_3,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(copy,[status(thm)],[c_2]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_4,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_5,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_78,plain,
divide(A,inverse(C)) = multiply(A,C),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_7,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_79,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_80,plain,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_7,c_79]) ).
cnf(c_8,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_5,c_80]) ).
cnf(c_9,plain,
divide(A,divide(divide(B,divide(C,divide(A,B))),divide(D,C))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_81,plain,
divide(divide(A,A),divide(B,divide(C,inverse(B)))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
inverse(divide(A,divide(B,inverse(A)))) = B,
inference(paramod,[status(thm)],[c_5,c_81]) ).
cnf(c_13,plain,
divide(A,inverse(divide(B,divide(A,divide(C,C))))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_14,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_25,plain,
divide(A,divide(A,divide(B,divide(C,divide(D,divide(D,C)))))) = B,
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_29,plain,
divide(inverse(inverse(divide(A,A))),B) = inverse(B),
inference(paramod,[status(thm)],[c_14,c_5]) ).
cnf(c_34,plain,
inverse(divide(A,inverse(inverse(A)))) = divide(B,B),
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_37,plain,
inverse(inverse(divide(A,inverse(inverse(divide(B,B)))))) = A,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_40,plain,
divide(A,divide(divide(B,inverse(divide(A,B))),divide(C,inverse(inverse(divide(D,D)))))) = C,
inference(paramod,[status(thm)],[c_29,c_9]) ).
cnf(c_47,plain,
divide(A,divide(A,divide(B,inverse(divide(C,inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_34,c_1]) ).
cnf(c_48,plain,
divide(A,divide(B,inverse(divide(C,inverse(inverse(C)))))) = divide(A,B),
inference(paramod,[status(thm)],[c_34,c_1]) ).
cnf(c_65,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_48,c_47]) ).
cnf(c_82,plain,
divide(A,divide(A,divide(B,divide(C,C)))) = B,
inference(paramod,[status(thm)],[c_65,c_25]) ).
cnf(c_66,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_65,c_82]) ).
cnf(c_71,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_66,c_13]) ).
cnf(c_83,plain,
divide(A,divide(A,divide(C,inverse(inverse(divide(D,D)))))) = C,
inference(paramod,[status(thm)],[c_71,c_40]) ).
cnf(c_73,plain,
divide(A,inverse(inverse(divide(B,B)))) = A,
inference(paramod,[status(thm)],[c_65,c_83]) ).
cnf(c_76,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_73,c_37]) ).
cnf(c_77,plain,
$false,
inference(resolve,[status(thm)],[c_76,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP522-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n018.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 15:00:06 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2244196 was started by sandbox on n018,
% 0.19/0.45 % Fri Sep 25 15:00:06 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 25.
% 0.19/0.48 % Level of proof is 10.
% 0.19/0.48 % Maximum clause weight is 75.000.
% 0.19/0.48 % Given clauses 9.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------