%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 06:57:29 AM UTC 2026
% Result : Unsatisfiable 0.10s 10.59s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 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(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,
strong_fixed_point = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
strong_fixed_point = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),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_46,plain,
apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),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_47,plain,
apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt)) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_46]) ).
cnf(c_48,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_47]) ).
cnf(c_49,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_48]) ).
cnf(c_50,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_49]) ).
cnf(c_51,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_50]) ).
cnf(c_52,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_51]) ).
cnf(c_53,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_52]) ).
cnf(c_5,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(copy,[status(thm)],[c_53]) ).
cnf(c_10,plain,
apply(apply(w1,A),w1) = apply(apply(A,A),A),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_54,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_5]) ).
cnf(c_12,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_54]) ).
cnf(c_55,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_12]) ).
cnf(c_32,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_55]) ).
cnf(c_56,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_32]) ).
cnf(c_57,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_56]) ).
cnf(c_58,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_57]) ).
cnf(c_59,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_58]) ).
cnf(c_45,plain,
$false,
inference(copy,[status(thm)],[c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.57 % Computer : n002.cluster.edu
% 0.10/10.57 % Model : x86_64 x86_64
% 0.10/10.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.57 % Memory : 8046.5625MB
% 0.10/10.57 % OS : Linux 6.8.0-71-generic
% 0.10/10.57 % CPULimit : 300
% 0.10/10.57 % WCLimit : 300
% 0.10/10.57 % DateTime : Sat Sep 26 23:10:35 UTC 2026
% 0.10/10.57 % CPUTime :
% 0.10/10.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.57 % Process 2914282 was started by sandbox2 on n002,
% 0.10/10.57 % Sat Sep 26 23:10:35 2026
% 0.10/10.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/10.58
% 0.10/10.58 % From the command line: assign(max_seconds, 300).
% 0.10/10.59
% 0.10/10.59 % SZS status Unsatisfiable for theBenchmark
% 0.10/10.59
% 0.10/10.59 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/10.59 % Length of proof is 9.
% 0.10/10.59 % Level of proof is 4.
% 0.10/10.59 % Maximum clause weight is 29.000.
% 0.10/10.59 % Given clauses 9.
% 0.10/10.59
% 0.10/10.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------