%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 06:57:19 AM UTC 2026
% Result : Unsatisfiable 2.48s 0.73s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 13 unt; 0 def)
% Number of atoms : 19 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(s,VAR_0),VAR_1),VAR_2) = apply(apply(VAR_0,VAR_2),apply(VAR_1,VAR_2)),
file('theBenchmark.p',s_definition) ).
cnf(c_1,plain,
apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)),
inference(clausify,[status(thm)],[s_definition]) ).
fof(b_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(b,VAR_0),VAR_1),VAR_2) = apply(VAR_0,apply(VAR_1,VAR_2)),
file('theBenchmark.p',b_definition) ).
cnf(c_2,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(c_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(c,VAR_0),VAR_1),VAR_2) = apply(apply(VAR_0,VAR_2),VAR_1),
file('theBenchmark.p',c_definition) ).
cnf(c_3,plain,
apply(apply(apply(c,A),B),C) = apply(apply(A,C),B),
inference(clausify,[status(thm)],[c_definition]) ).
fof(weak_fixed_point,axiom,
! [VAR_0] :
( fixed_point(VAR_0)
| VAR_0 != apply(fixed_pt,VAR_0) ),
file('theBenchmark.p',weak_fixed_point) ).
cnf(c_5,plain,
( fixed_point(A)
| A != apply(fixed_pt,A) ),
inference(clausify,[status(thm)],[weak_fixed_point]) ).
cnf(c_6,plain,
( fixed_point(A)
| apply(fixed_pt,A) != A ),
inference(copy,[status(thm)],[c_5]) ).
fof(prove_weak_fixed_point,axiom,
! [VAR_0] : ~ fixed_point(apply(apply(apply(s,apply(c,apply(b,VAR_0))),apply(s,apply(c,apply(b,VAR_0)))),apply(s,apply(c,apply(b,VAR_0))))),
file('theBenchmark.p',prove_weak_fixed_point) ).
cnf(c_7,plain,
~ fixed_point(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A))))),
inference(clausify,[status(thm)],[prove_weak_fixed_point]) ).
cnf(c_32,plain,
apply(apply(apply(c,apply(b,A)),B),C) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_41,plain,
apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A))))) != apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_2032,plain,
apply(apply(apply(s,apply(c,apply(b,A))),B),C) = apply(A,apply(apply(B,C),C)),
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_2034,plain,
apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))) != apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A))))),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_2033,plain,
$false,
inference(resolve,[status(thm)],[c_2032,c_2034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 23:02:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1768006 was started by sandbox2 on n011,
% 0.08/0.36 % Sat Sep 26 23:02:44 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 2.48/0.73
% 2.48/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.48/0.73
% 2.48/0.73 % Proof 1 at 0.28 (+ 0.07) seconds.
% 2.48/0.73 % Length of proof is 10.
% 2.48/0.73 % Level of proof is 3.
% 2.48/0.73 % Maximum clause weight is 49.000.
% 2.48/0.73 % Given clauses 57.
% 2.48/0.73
% 2.48/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------