%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 06:57:19 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 23 ( 0 sgn 8 !; 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(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_2,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(i_definition,axiom,
! [VAR_0] : apply(i,VAR_0) = VAR_0,
file('theBenchmark.p',i_definition) ).
cnf(c_4,plain,
apply(i,A) = A,
inference(clausify,[status(thm)],[i_definition]) ).
fof(prove_fixed_point,axiom,
! [VAR_0] : VAR_0 != apply(fixed_pt,VAR_0),
file('theBenchmark.p',prove_fixed_point) ).
cnf(c_5,plain,
A != apply(fixed_pt,A),
inference(clausify,[status(thm)],[prove_fixed_point]) ).
cnf(c_6,plain,
apply(fixed_pt,A) != A,
inference(copy,[status(thm)],[c_5]) ).
cnf(c_24,plain,
apply(apply(apply(s,i),A),B) = apply(B,apply(A,B)),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_51,plain,
apply(apply(apply(s,i),i),A) = apply(A,A),
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_72,plain,
apply(apply(apply(s,i),i),apply(apply(b,A),B)) = apply(A,apply(B,apply(apply(b,A),B))),
inference(paramod,[status(thm)],[c_51,c_2]) ).
cnf(c_74,plain,
A != apply(fixed_pt,A),
inference(copy,[status(thm)],[c_6]) ).
cnf(c_73,plain,
$false,
inference(resolve,[status(thm)],[c_72,c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 23:02:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1357172 was started by sandbox2 on n009,
% 0.09/0.37 % Sat Sep 26 23:02:29 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.41
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.41
% 0.09/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.41 % Length of proof is 9.
% 0.09/0.41 % Level of proof is 4.
% 0.09/0.41 % Maximum clause weight is 81.000.
% 0.09/0.41 % Given clauses 9.
% 0.09/0.41
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------