%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL006-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 24 unt; 0 def)
% Number of atoms : 30 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 16 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 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 : 33 ( 2 sgn 6 !; 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,
! [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(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k))),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_5,plain,
~ fixed_point(apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k))),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_7,plain,
apply(apply(apply(s,A),apply(apply(s,B),C)),D) = apply(apply(A,D),apply(apply(B,D),apply(C,D))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
apply(apply(apply(apply(s,s),A),B),C) = apply(apply(B,C),apply(apply(A,B),C)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
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_531,plain,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k)))))),apply(apply(s,apply(k,s)),k))),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_19,plain,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k))),
inference(paramod,[status(thm)],[c_14,c_531]) ).
cnf(c_532,plain,
apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),fixed_pt)) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),fixed_pt),
inference(resolve,[status(thm)],[c_4,c_19]) ).
cnf(c_533,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(apply(apply(s,apply(k,s)),k),fixed_pt))) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),fixed_pt),
inference(paramod,[status(thm)],[c_12,c_532]) ).
cnf(c_534,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),fixed_pt),
inference(paramod,[status(thm)],[c_12,c_533]) ).
cnf(c_535,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(apply(apply(s,apply(k,s)),k),fixed_pt)),
inference(paramod,[status(thm)],[c_12,c_534]) ).
cnf(c_50,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))),
inference(paramod,[status(thm)],[c_12,c_535]) ).
cnf(c_54,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_50]) ).
cnf(c_536,plain,
apply(apply(apply(s,apply(k,A)),apply(apply(s,B),C)),D) = apply(A,apply(apply(B,D),apply(C,D))),
inference(paramod,[status(thm)],[c_2,c_7]) ).
cnf(c_89,plain,
apply(A,apply(apply(apply(s,B),C),D)) = apply(A,apply(apply(B,D),apply(C,D))),
inference(paramod,[status(thm)],[c_12,c_536]) ).
cnf(c_537,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),apply(apply(apply(s,k),apply(s,apply(k,fixed_pt))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))),
inference(paramod,[status(thm)],[c_9,c_54]) ).
cnf(c_538,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),
inference(paramod,[status(thm)],[c_14,c_537]) ).
cnf(c_529,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))),
inference(paramod,[status(thm)],[c_12,c_538]) ).
cnf(c_530,plain,
$false,
inference(resolve,[status(thm)],[c_529,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 23:04:46 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 131127 was started by sandbox on n014,
% 0.08/0.35 % Sat Sep 26 23:04:46 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.47
% 0.12/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.47
% 0.12/0.47 % Proof 1 at 0.10 (+ 0.02) seconds.
% 0.12/0.47 % Length of proof is 15.
% 0.12/0.47 % Level of proof is 6.
% 0.12/0.47 % Maximum clause weight is 55.000.
% 0.12/0.47 % Given clauses 32.
% 0.12/0.47
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------