%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP552-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.17s 5.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,VAR_0),divide(divide(divide(VAR_1,VAR_0),VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(identity,VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_5,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_4]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_6,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_59,plain,
divide(a,divide(identity,b)) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_60,plain,
divide(a,divide(identity,b)) != divide(b,divide(identity,a)),
inference(paramod,[status(thm)],[c_2,c_59]) ).
cnf(c_7,plain,
divide(b,divide(identity,a)) != divide(a,divide(identity,b)),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_61,plain,
divide(divide(identity,A),divide(B,identity)) = divide(divide(divide(C,A),B),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),divide(C,identity)),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_11,plain,
divide(divide(identity,A),divide(divide(identity,A),divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_62,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),divide(A,identity)),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_12,plain,
divide(divide(identity,A),divide(B,identity)) = divide(divide(identity,B),A),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_63,plain,
divide(identity,divide(divide(identity,identity),divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_16,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_63]) ).
cnf(c_64,plain,
divide(divide(A,B),identity) = divide(divide(identity,divide(identity,divide(A,identity))),divide(B,identity)),
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_19,plain,
divide(divide(A,B),identity) = divide(A,divide(B,identity)),
inference(paramod,[status(thm)],[c_16,c_64]) ).
cnf(c_65,plain,
divide(A,divide(divide(identity,divide(identity,divide(A,identity))),divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_21,plain,
divide(A,divide(A,divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_16,c_65]) ).
cnf(c_66,plain,
divide(divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_5,c_21]) ).
cnf(c_67,plain,
divide(A,divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_19,c_66]) ).
cnf(c_24,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_5,c_67]) ).
cnf(c_68,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(C,divide(A,identity))),divide(B,identity)),
inference(paramod,[status(thm)],[c_21,c_9]) ).
cnf(c_69,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(C,A)),divide(B,identity)),
inference(paramod,[status(thm)],[c_24,c_68]) ).
cnf(c_70,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(C,A)),B),
inference(paramod,[status(thm)],[c_24,c_69]) ).
cnf(c_25,plain,
divide(divide(identity,divide(A,B)),C) = divide(divide(B,C),A),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_34,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_24,c_12]) ).
cnf(c_71,plain,
divide(divide(A,identity),B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_25,c_24]) ).
cnf(c_72,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_24,c_71]) ).
cnf(c_40,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
divide(b,divide(identity,a)) != divide(identity,divide(divide(identity,b),a)),
inference(paramod,[status(thm)],[c_40,c_7]) ).
cnf(c_74,plain,
divide(b,divide(identity,a)) != divide(identity,divide(divide(identity,a),b)),
inference(paramod,[status(thm)],[c_34,c_73]) ).
cnf(c_57,plain,
divide(identity,divide(divide(identity,a),b)) != divide(b,divide(identity,a)),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_58,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP552-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n003.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Fri Sep 25 15:01:28 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.43 % Process 474544 was started by sandbox2 on n003,
% 0.17/5.43 % Fri Sep 25 15:01:28 2026
% 0.17/5.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.44
% 0.17/5.44 % From the command line: assign(max_seconds, 300).
% 0.17/5.45
% 0.17/5.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.45
% 0.17/5.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/5.45 % Length of proof is 18.
% 0.17/5.45 % Level of proof is 9.
% 0.17/5.45 % Maximum clause weight is 15.000.
% 0.17/5.45 % Given clauses 14.
% 0.17/5.45
% 0.17/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------