%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL006-6 : 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 : n010.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 06:57:23 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 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 : 10 ( 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 : 15 ( 2 sgn 5 !; 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(k_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(k,VAR_0),VAR_1) = VAR_0,
file('theBenchmark.p',k_definition) ).
cnf(c_2,plain,
apply(apply(k,A),B) = A,
inference(clausify,[status(thm)],[k_definition]) ).
fof(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
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_55,plain,
apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_56,plain,
apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt) != apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_55]) ).
cnf(c_5,plain,
apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt)) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_12,plain,
apply(apply(apply(s,apply(k,A)),B),C) = apply(A,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_14,plain,
apply(apply(apply(s,k),A),B) = B,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_57,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt),
inference(paramod,[status(thm)],[c_12,c_5]) ).
cnf(c_15,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)),
inference(paramod,[status(thm)],[c_12,c_57]) ).
cnf(c_58,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt)))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_15]) ).
cnf(c_59,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt)))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)),
inference(paramod,[status(thm)],[c_12,c_58]) ).
cnf(c_60,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)),
inference(paramod,[status(thm)],[c_2,c_59]) ).
cnf(c_46,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_61,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramod,[status(thm)],[c_1,c_46]) ).
cnf(c_62,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramod,[status(thm)],[c_12,c_61]) ).
cnf(c_63,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramod,[status(thm)],[c_2,c_62]) ).
cnf(c_50,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_64,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramod,[status(thm)],[c_1,c_50]) ).
cnf(c_65,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramod,[status(thm)],[c_14,c_64]) ).
cnf(c_66,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(paramod,[status(thm)],[c_14,c_65]) ).
cnf(c_67,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramod,[status(thm)],[c_12,c_66]) ).
cnf(c_54,plain,
$false,
inference(copy,[status(thm)],[c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43 % Computer : n010.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8046.5625MB
% 0.09/0.43 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Sat Sep 26 23:05:30 UTC 2026
% 0.09/0.44 % CPUTime :
% 0.09/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.44 % Process 260570 was started by sandbox on n010,
% 0.09/0.44 % Sat Sep 26 23:05:30 2026
% 0.09/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.45
% 0.09/0.45 % From the command line: assign(max_seconds, 300).
% 0.15/0.52
% 0.15/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.52
% 0.15/0.52 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.52 % Length of proof is 11.
% 0.15/0.52 % Level of proof is 5.
% 0.15/0.52 % Maximum clause weight is 93.000.
% 0.15/0.52 % Given clauses 7.
% 0.15/0.52
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------