%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.07s 20.65s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 21 ( 0 sgn 8 !; 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(i_definition,axiom,
! [VAR_0] : apply(i,VAR_0) = VAR_0,
file('theBenchmark.p',i_definition) ).
cnf(c_4,plain,
apply(i,A) = A,
inference(clausify,[status(thm)],[i_definition]) ).
fof(weak_fixed_point,axiom,
! [VAR_0] : weak_fixed_point(VAR_0) = apply(apply(apply(s,apply(b,VAR_0)),i),apply(apply(s,apply(b,VAR_0)),i)),
file('theBenchmark.p',weak_fixed_point) ).
cnf(c_5,plain,
weak_fixed_point(A) = apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)),
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_43,plain,
apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_44,plain,
apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) != apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))),
inference(paramod,[status(thm)],[c_5,c_43]) ).
cnf(c_7,plain,
apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_45,plain,
weak_fixed_point(A) = apply(apply(apply(b,A),apply(apply(s,apply(b,A)),i)),apply(i,apply(apply(s,apply(b,A)),i))),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_46,plain,
apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)) = apply(apply(apply(b,A),apply(apply(s,apply(b,A)),i)),apply(i,apply(apply(s,apply(b,A)),i))),
inference(paramod,[status(thm)],[c_5,c_45]) ).
cnf(c_47,plain,
apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)) = apply(apply(apply(b,A),apply(apply(s,apply(b,A)),i)),apply(apply(s,apply(b,A)),i)),
inference(paramod,[status(thm)],[c_4,c_46]) ).
cnf(c_48,plain,
apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)) = apply(A,apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i))),
inference(paramod,[status(thm)],[c_2,c_47]) ).
cnf(c_41,plain,
apply(A,apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i))) = apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_42,plain,
$false,
inference(resolve,[status(thm)],[c_41,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.07/20.63 % CPULimit : 300
% 0.07/20.63 % WCLimit : 300
% 0.07/20.63 % DateTime : Sat Sep 26 23:02:48 UTC 2026
% 0.07/20.63 % CPUTime :
% 0.07/20.63 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/20.63 % Process 3760524 was started by sandbox on n013,
% 0.07/20.63 % Sat Sep 26 23:02:48 2026
% 0.07/20.63 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/20.63
% 0.07/20.63 % From the command line: assign(max_seconds, 300).
% 0.07/20.65
% 0.07/20.65 % SZS status Unsatisfiable for theBenchmark
% 0.07/20.65
% 0.07/20.65 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/20.65 % Length of proof is 8.
% 0.07/20.65 % Level of proof is 2.
% 0.07/20.65 % Maximum clause weight is 33.000.
% 0.07/20.65 % Given clauses 5.
% 0.07/20.65
% 0.07/20.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------