%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL003-15 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 06:57:20 AM UTC 2026
% Result : Unsatisfiable 1.94s 0.65s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 5 !; 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(w_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(w,VAR_0),VAR_1) = apply(apply(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',w_definition) ).
cnf(c_2,plain,
apply(apply(w,A),B) = apply(apply(A,B),B),
inference(clausify,[status(thm)],[w_definition]) ).
fof(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),
inference(clausify,[status(thm)],[strong_fixed_point]) ).
fof(prove_strong_fixed_point,axiom,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_4,plain,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_355,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_356,plain,
apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),fixed_pt)) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_355]) ).
cnf(c_357,plain,
apply(apply(apply(b,apply(w,w)),w),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_356]) ).
cnf(c_358,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_357]) ).
cnf(c_359,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_358]) ).
cnf(c_360,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_359]) ).
cnf(c_361,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),w),apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_360]) ).
cnf(c_362,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_361]) ).
cnf(c_5,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_362]) ).
cnf(c_8,plain,
apply(apply(w,apply(b,A)),B) = apply(A,apply(B,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_11,plain,
apply(apply(w,w),A) = apply(apply(A,A),A),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_32,plain,
apply(apply(apply(w,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(B,B),C)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_363,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,A)))) = apply(A,apply(apply(apply(w,apply(b,apply(b,A))),apply(w,apply(b,apply(b,A)))),apply(w,apply(b,apply(b,A))))),
inference(paramod,[status(thm)],[c_32,c_11]) ).
cnf(c_364,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,A)))) = apply(A,apply(apply(w,w),apply(w,apply(b,apply(b,A))))),
inference(paramod,[status(thm)],[c_11,c_363]) ).
cnf(c_353,plain,
apply(A,apply(apply(w,w),apply(w,apply(b,apply(b,A))))) = apply(apply(w,w),apply(w,apply(b,apply(b,A)))),
inference(copy,[status(thm)],[c_364]) ).
cnf(c_354,plain,
$false,
inference(resolve,[status(thm)],[c_353,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-15 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 23:04:09 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 581297 was started by sandbox on n008,
% 0.09/0.36 % Sat Sep 26 23:04:09 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).
% 1.94/0.65
% 1.94/0.65 % SZS status Unsatisfiable for theBenchmark
% 1.94/0.65
% 1.94/0.65 % Proof 1 at 0.22 (+ 0.06) seconds.
% 1.94/0.65 % Length of proof is 10.
% 1.94/0.65 % Level of proof is 4.
% 1.94/0.65 % Maximum clause weight is 100.000.
% 1.94/0.65 % Given clauses 52.
% 1.94/0.65
% 1.94/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------