%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG199+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 06:49:43 AM UTC 2026
% Result : Theorem 0.34s 0.63s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 114 ( 113 equ)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 152 ( 60 ~; 51 |; 41 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
( e5 != e6
& e4 != e6
& e4 != e5
& e3 != e6
& e3 != e5
& e3 != e4
& e2 != e6
& e2 != e5
& e2 != e4
& e2 != e3
& e1 != e6
& e1 != e5
& e1 != e4
& e1 != e3
& e1 != e2
& e0 != e6
& e0 != e5
& e0 != e4
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('theBenchmark.p',ax5) ).
fof(ax6,axiom,
( e6 = op(op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5),op(e5,op(e5,e5)))
& e4 = op(e5,op(e5,e5))
& e3 = op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5)
& e2 = op(op(e5,op(e5,e5)),op(e5,op(e5,e5)))
& e1 = op(e5,e5)
& e0 = op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),op(e5,op(e5,e5))) ),
file('theBenchmark.p',ax6) ).
fof(co1,conjecture,
~ ( ( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3
| op(e2,e2) != e2
| op(e1,e1) != e1
| op(e0,e0) != e0 )
& ( op(e6,e6) = e6
| op(e5,e5) = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0 )
& op(e6,e6) != e6
& op(e5,e5) != e5
& op(e4,e4) != e4
& op(e3,e3) != e3
& op(e2,e2) != e2
& op(e1,e1) != e1
& op(e0,e0) != e0 ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ~ ( ( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3
| op(e2,e2) != e2
| op(e1,e1) != e1
| op(e0,e0) != e0 )
& ( op(e6,e6) = e6
| op(e5,e5) = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0 )
& op(e6,e6) != e6
& op(e5,e5) != e5
& op(e4,e4) != e4
& op(e3,e3) != e3
& op(e2,e2) != e2
& op(e1,e1) != e1
& op(e0,e0) != e0 ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_578,plain,
e5 != e1,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_579,plain,
e1 != e5,
inference(copy,[status(thm)],[c_578]) ).
cnf(c_595,plain,
op(e5,e5) = e1,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_604,negated_conjecture,
op(e0,e0) != e0,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_605,negated_conjecture,
op(e1,e1) != e1,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_606,negated_conjecture,
op(e2,e2) != e2,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_607,negated_conjecture,
op(e3,e3) != e3,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_608,negated_conjecture,
op(e4,e4) != e4,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_610,negated_conjecture,
op(e6,e6) != e6,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_611,negated_conjecture,
( op(e6,e6) = e6
| op(e5,e5) = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_613,negated_conjecture,
( op(e6,e6) = e6
| e1 = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0 ),
inference(paramod,[status(thm)],[c_595,c_611]) ).
cnf(c_614,negated_conjecture,
( op(e6,e6) = e6
| e1 = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1 ),
inference(resolve,[status(thm)],[c_604,c_613]) ).
cnf(c_615,negated_conjecture,
( op(e6,e6) = e6
| e1 = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2 ),
inference(resolve,[status(thm)],[c_605,c_614]) ).
cnf(c_616,negated_conjecture,
( op(e6,e6) = e6
| e1 = e5
| op(e4,e4) = e4
| op(e3,e3) = e3 ),
inference(resolve,[status(thm)],[c_606,c_615]) ).
cnf(c_617,negated_conjecture,
( op(e6,e6) = e6
| e1 = e5
| op(e4,e4) = e4 ),
inference(resolve,[status(thm)],[c_607,c_616]) ).
cnf(c_618,negated_conjecture,
( op(e6,e6) = e6
| e1 = e5 ),
inference(resolve,[status(thm)],[c_608,c_617]) ).
cnf(c_619,negated_conjecture,
op(e6,e6) = e6,
inference(resolve,[status(thm)],[c_579,c_618]) ).
cnf(c_612,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_610,c_619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG199+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 21:25:34 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 2532884 was started by sandbox2 on n020,
% 0.18/0.45 % Sat Sep 26 21:25:34 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.26/0.58
% 0.26/0.58 % From the command line: assign(max_seconds, 300).
% 0.34/0.63
% 0.34/0.63 % SZS status Theorem for theBenchmark
% 0.34/0.63
% 0.34/0.63 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.34/0.63 % Length of proof is 14.
% 0.34/0.63 % Level of proof is 3.
% 0.34/0.63 % Maximum clause weight is 15.000.
% 0.34/0.63 % Given clauses 0.
% 0.34/0.63
% 0.34/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------