%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG173+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 06:49:38 AM UTC 2026
% Result : Theorem 0.43s 0.70s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 122 ( 121 equ)
% Maximal formula atoms : 50 ( 10 avg)
% Number of connectives : 174 ( 64 ~; 8 |; 102 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
( e3 != e4
& e2 != e4
& e2 != e3
& e1 != e4
& e1 != e3
& e1 != e2
& e0 != e4
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('theBenchmark.p',ax5) ).
fof(ax6,axiom,
( e4 = op(e3,op(e3,e3))
& e2 = op(e3,e3)
& e1 = op(e3,op(e3,op(e3,e3)))
& e0 = op(op(e3,op(e3,e3)),op(e3,op(e3,e3))) ),
file('theBenchmark.p',ax6) ).
fof(co1,conjecture,
~ ( op(e4,op(e4,e4)) = e4
& op(e4,op(e4,e3)) = e3
& op(e4,op(e4,e2)) = e2
& op(e4,op(e4,e1)) = e1
& op(e4,op(e4,e0)) = e0
& op(e3,op(e3,e4)) = e4
& op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e2)) = e2
& op(e3,op(e3,e1)) = e1
& op(e3,op(e3,e0)) = e0
& op(e2,op(e2,e4)) = e4
& op(e2,op(e2,e3)) = e3
& op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e1)) = e1
& op(e2,op(e2,e0)) = e0
& op(e1,op(e1,e4)) = e4
& op(e1,op(e1,e3)) = e3
& op(e1,op(e1,e2)) = e2
& op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e0)) = e0
& op(e0,op(e0,e4)) = e4
& op(e0,op(e0,e3)) = e3
& op(e0,op(e0,e2)) = e2
& op(e0,op(e0,e1)) = e1
& op(e0,op(e0,e0)) = e0
& ( ( op(e4,e4) != e4
& op(e4,e3) != e3
& op(e4,e2) != e2
& op(e4,e1) != e1
& op(e4,e0) != e0 )
| ( op(e3,e4) != e4
& op(e3,e3) != e3
& op(e3,e2) != e2
& op(e3,e1) != e1
& op(e3,e0) != e0 )
| ( op(e2,e4) != e4
& op(e2,e3) != e3
& op(e2,e2) != e2
& op(e2,e1) != e1
& op(e2,e0) != e0 )
| ( op(e1,e4) != e4
& op(e1,e3) != e3
& op(e1,e2) != e2
& op(e1,e1) != e1
& op(e1,e0) != e0 )
| ( op(e0,e4) != e4
& op(e0,e3) != e3
& op(e0,e2) != e2
& op(e0,e1) != e1
& op(e0,e0) != e0 ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ~ ( op(e4,op(e4,e4)) = e4
& op(e4,op(e4,e3)) = e3
& op(e4,op(e4,e2)) = e2
& op(e4,op(e4,e1)) = e1
& op(e4,op(e4,e0)) = e0
& op(e3,op(e3,e4)) = e4
& op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e2)) = e2
& op(e3,op(e3,e1)) = e1
& op(e3,op(e3,e0)) = e0
& op(e2,op(e2,e4)) = e4
& op(e2,op(e2,e3)) = e3
& op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e1)) = e1
& op(e2,op(e2,e0)) = e0
& op(e1,op(e1,e4)) = e4
& op(e1,op(e1,e3)) = e3
& op(e1,op(e1,e2)) = e2
& op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e0)) = e0
& op(e0,op(e0,e4)) = e4
& op(e0,op(e0,e3)) = e3
& op(e0,op(e0,e2)) = e2
& op(e0,op(e0,e1)) = e1
& op(e0,op(e0,e0)) = e0
& ( ( op(e4,e4) != e4
& op(e4,e3) != e3
& op(e4,e2) != e2
& op(e4,e1) != e1
& op(e4,e0) != e0 )
| ( op(e3,e4) != e4
& op(e3,e3) != e3
& op(e3,e2) != e2
& op(e3,e1) != e1
& op(e3,e0) != e0 )
| ( op(e2,e4) != e4
& op(e2,e3) != e3
& op(e2,e2) != e2
& op(e2,e1) != e1
& op(e2,e0) != e0 )
| ( op(e1,e4) != e4
& op(e1,e3) != e3
& op(e1,e2) != e2
& op(e1,e1) != e1
& op(e1,e0) != e0 )
| ( op(e0,e4) != e4
& op(e0,e3) != e3
& op(e0,e2) != e2
& op(e0,e1) != e1
& op(e0,e0) != e0 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_283,plain,
e4 != e3,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_286,plain,
op(e3,e3) = e2,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_287,plain,
op(e3,op(e3,e3)) = e4,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_288,plain,
op(e3,e2) = e4,
inference(paramod,[status(thm)],[c_286,c_287]) ).
cnf(c_933,negated_conjecture,
op(e3,op(e3,e3)) = e3,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_935,negated_conjecture,
op(e3,e2) = e3,
inference(paramod,[status(thm)],[c_286,c_933]) ).
cnf(c_936,negated_conjecture,
e4 = e3,
inference(paramod,[status(thm)],[c_288,c_935]) ).
cnf(c_934,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_283,c_936]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG173+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 21:22:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1173409 was started by sandbox on n009,
% 0.09/0.37 % Sat Sep 26 21:22:14 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.38/0.63
% 0.38/0.63 % From the command line: assign(max_seconds, 300).
% 0.43/0.70
% 0.43/0.70 % SZS status Theorem for theBenchmark
% 0.43/0.70
% 0.43/0.70 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.43/0.70 % Length of proof is 9.
% 0.43/0.70 % Level of proof is 3.
% 0.43/0.70 % Maximum clause weight is 5.000.
% 0.43/0.70 % Given clauses 0.
% 0.43/0.70
% 0.43/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------