%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.09s 0.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 41 unt; 0 def)
% Number of atoms : 47 ( 41 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 36 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 3 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 : 24 ( 0 sgn 7 !; 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(h_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(h,VAR_0),VAR_1),VAR_2) = apply(apply(apply(VAR_0,VAR_1),VAR_2),VAR_1),
file('theBenchmark.p',h_definition) ).
cnf(c_2,plain,
apply(apply(apply(h,A),B),C) = apply(apply(apply(A,B),C),B),
inference(clausify,[status(thm)],[h_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(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b)),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_5,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b)),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_9,plain,
apply(apply(apply(h,apply(b,A)),B),C) = apply(apply(A,apply(B,C)),B),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_441,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt)) != apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_442,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt))) != apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_441]) ).
cnf(c_443,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_442]) ).
cnf(c_444,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_443]) ).
cnf(c_20,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_444]) ).
cnf(c_445,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b)))),h),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_2,c_20]) ).
cnf(c_446,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_445]) ).
cnf(c_46,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_446]) ).
cnf(c_447,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b)))),h),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_2,c_46]) ).
cnf(c_448,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_447]) ).
cnf(c_49,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_448]) ).
cnf(c_449,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_2,c_49]) ).
cnf(c_450,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_449]) ).
cnf(c_451,plain,
apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_450]) ).
cnf(c_50,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_451]) ).
cnf(c_452,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(apply(apply(b,h),apply(b,b)),h),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_50]) ).
cnf(c_53,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_452]) ).
cnf(c_453,plain,
apply(apply(apply(apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_53]) ).
cnf(c_454,plain,
apply(apply(apply(b,apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_453]) ).
cnf(c_202,plain,
apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_454]) ).
cnf(c_455,plain,
apply(apply(apply(apply(apply(apply(b,h),apply(b,b)),h),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_202]) ).
cnf(c_456,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_455]) ).
cnf(c_204,plain,
apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_456]) ).
cnf(c_285,plain,
apply(apply(apply(h,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(B,C),B)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_457,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(apply(b,b),h),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_2,c_204]) ).
cnf(c_458,plain,
apply(fixed_pt,apply(apply(apply(apply(b,apply(h,apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_457]) ).
cnf(c_459,plain,
apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_458]) ).
cnf(c_436,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_459]) ).
cnf(c_460,plain,
apply(apply(apply(apply(apply(apply(b,b),h),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_436]) ).
cnf(c_461,plain,
apply(apply(apply(apply(b,apply(h,apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_460]) ).
cnf(c_462,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_461]) ).
cnf(c_439,plain,
apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_462]) ).
cnf(c_463,plain,
apply(A,apply(apply(B,C),B)) = apply(apply(apply(h,apply(b,apply(b,A))),B),C),
inference(copy,[status(thm)],[c_285]) ).
cnf(c_440,plain,
$false,
inference(resolve,[status(thm)],[c_439,c_463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 23:10:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 2184708 was started by sandbox on n026,
% 0.09/0.38 % Sat Sep 26 23:10:26 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.47
% 0.09/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.47
% 0.09/0.47 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.09/0.47 % Length of proof is 17.
% 0.09/0.47 % Level of proof is 11.
% 0.09/0.47 % Maximum clause weight is 61.000.
% 0.09/0.47 % Given clauses 25.
% 0.09/0.47
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------