%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 10 !; 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] : weak_fixed_point(VAR_0) = 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',weak_fixed_point) ).
cnf(c_5,plain,
weak_fixed_point(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(clausify,[status(thm)],[weak_fixed_point]) ).
fof(prove_weak_fixed_point,axiom,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('theBenchmark.p',prove_weak_fixed_point) ).
cnf(c_6,plain,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
inference(clausify,[status(thm)],[prove_weak_fixed_point]) ).
cnf(c_46,plain,
apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_47,plain,
apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_5,c_46]) ).
cnf(c_7,plain,
apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) != apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_47]) ).
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_44,plain,
apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) != apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_48,plain,
apply(A,apply(C,B)) = apply(apply(apply(c,apply(b,A)),B),C),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_45,plain,
$false,
inference(resolve,[status(thm)],[c_44,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n007.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 26 23:00:39 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 712320 was started by sandbox2 on n007,
% 0.07/0.34 % Sat Sep 26 23:00:39 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.34
% 0.07/0.34 % From the command line: assign(max_seconds, 300).
% 0.11/0.36
% 0.11/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.36
% 0.11/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.36 % Length of proof is 9.
% 0.11/0.36 % Level of proof is 3.
% 0.11/0.36 % Maximum clause weight is 55.000.
% 0.11/0.36 % Given clauses 6.
% 0.11/0.36
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------