%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL042-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 06:57:28 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 23 unt; 0 def)
% Number of atoms : 29 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 20 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(w1_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(w1,VAR_0),VAR_1) = apply(apply(VAR_1,VAR_0),VAR_0),
file('theBenchmark.p',w1_definition) ).
cnf(c_2,plain,
apply(apply(w1,A),B) = apply(apply(B,A),A),
inference(clausify,[status(thm)],[w1_definition]) ).
fof(strong_fixed_point,axiom,
! [VAR_0] :
( fixed_point(VAR_0)
| apply(VAR_0,fixed_pt) != apply(fixed_pt,apply(VAR_0,fixed_pt)) ),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
( fixed_point(A)
| apply(A,fixed_pt) != apply(fixed_pt,apply(A,fixed_pt)) ),
inference(clausify,[status(thm)],[strong_fixed_point]) ).
cnf(c_4,plain,
( fixed_point(A)
| apply(fixed_pt,apply(A,fixed_pt)) != apply(A,fixed_pt) ),
inference(copy,[status(thm)],[c_3]) ).
fof(prove_strong_fixed_point,axiom,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b))),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_5,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b))),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_10,plain,
apply(apply(w1,A),w1) = apply(apply(A,A),A),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_51,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt)) != apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_52,plain,
apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(apply(apply(b,b),b),fixed_pt))) != apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_51]) ).
cnf(c_53,plain,
apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_52]) ).
cnf(c_54,plain,
apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_53]) ).
cnf(c_55,plain,
apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(apply(apply(b,b),b),fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_54]) ).
cnf(c_56,plain,
apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_16,plain,
apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))) != apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_56]) ).
cnf(c_57,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1)) != apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_2,c_16]) ).
cnf(c_35,plain,
apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_57]) ).
cnf(c_58,plain,
apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1),
inference(paramod,[status(thm)],[c_2,c_35]) ).
cnf(c_37,plain,
apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1),
inference(paramod,[status(thm)],[c_1,c_58]) ).
cnf(c_59,plain,
apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(apply(apply(apply(b,apply(b,fixed_pt)),w1),apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)),
inference(paramod,[status(thm)],[c_10,c_37]) ).
cnf(c_60,plain,
apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(apply(apply(b,fixed_pt),apply(w1,apply(apply(b,apply(b,fixed_pt)),w1))),apply(apply(b,apply(b,fixed_pt)),w1)),
inference(paramod,[status(thm)],[c_1,c_59]) ).
cnf(c_61,plain,
apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))),
inference(paramod,[status(thm)],[c_1,c_60]) ).
cnf(c_62,plain,
apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)),
inference(paramod,[status(thm)],[c_2,c_61]) ).
cnf(c_50,plain,
$false,
inference(copy,[status(thm)],[c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL042-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 23:07:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 134428 was started by sandbox on n014,
% 0.09/0.36 % Sat Sep 26 23:07:17 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 10.
% 0.09/0.38 % Level of proof is 5.
% 0.09/0.38 % Maximum clause weight is 29.000.
% 0.09/0.38 % Given clauses 10.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------