%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL003-20 : 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 : n006.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 06:57:21 AM UTC 2026
% Result : Unsatisfiable 34.50s 5.50s
% Output : CNFRefutation 34.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 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 : 24 ( 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(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,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_11997,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,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_11998,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),fixed_pt)) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_11997]) ).
cnf(c_11999,plain,
apply(apply(w,w),apply(apply(b,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_11998]) ).
cnf(c_12000,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_11999]) ).
cnf(c_12001,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_12000]) ).
cnf(c_12002,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_12001]) ).
cnf(c_12003,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_12002]) ).
cnf(c_12004,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_12003]) ).
cnf(c_5,plain,
apply(fixed_pt,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_12004]) ).
cnf(c_9,plain,
apply(apply(w,apply(apply(b,A),B)),C) = apply(apply(A,apply(B,C)),C),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_11,plain,
apply(apply(w,w),A) = apply(apply(A,A),A),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_12005,plain,
apply(apply(w,w),apply(apply(b,A),B)) = apply(apply(A,apply(B,apply(apply(b,A),B))),apply(apply(b,A),B)),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_27,plain,
apply(apply(A,apply(B,apply(apply(b,A),B))),apply(apply(b,A),B)) = apply(apply(w,w),apply(apply(b,A),B)),
inference(copy,[status(thm)],[c_12005]) ).
cnf(c_144,plain,
apply(apply(w,apply(apply(b,apply(b,A)),B)),C) = apply(A,apply(apply(B,C),C)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_12006,plain,
apply(A,apply(apply(apply(apply(b,w),apply(b,apply(b,A))),apply(apply(b,w),apply(b,apply(b,A)))),apply(apply(b,w),apply(b,apply(b,A))))) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A)))),
inference(paramod,[status(thm)],[c_144,c_27]) ).
cnf(c_12007,plain,
apply(A,apply(apply(w,apply(apply(b,apply(b,A)),apply(apply(b,w),apply(b,apply(b,A))))),apply(apply(b,w),apply(b,apply(b,A))))) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A)))),
inference(paramod,[status(thm)],[c_1,c_12006]) ).
cnf(c_11995,plain,
apply(A,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A))))) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A)))),
inference(paramod,[status(thm)],[c_27,c_12007]) ).
cnf(c_11996,plain,
$false,
inference(resolve,[status(thm)],[c_11995,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-20 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 23:03:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2336717 was started by sandbox on n006,
% 0.10/0.38 % Sat Sep 26 23:03:55 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 34.50/5.50
% 34.50/5.50 % SZS status Unsatisfiable for theBenchmark
% 34.50/5.50
% 34.50/5.50 % Proof 1 at 4.35 (+ 0.74) seconds.
% 34.50/5.50 % Length of proof is 11.
% 34.50/5.50 % Level of proof is 4.
% 34.50/5.50 % Maximum clause weight is 81.000.
% 34.50/5.50 % Given clauses 152.
% 34.50/5.50
% 34.50/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------