%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL031-1 : 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 : n016.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 06:57:26 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(l,VAR_0),VAR_1) = apply(VAR_0,apply(VAR_1,VAR_1)),
file('theBenchmark.p',l_definition) ).
cnf(c_1,plain,
apply(apply(l,A),B) = apply(A,apply(B,B)),
inference(clausify,[status(thm)],[l_definition]) ).
fof(o_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(o,VAR_0),VAR_1) = apply(VAR_1,apply(VAR_0,VAR_1)),
file('theBenchmark.p',o_definition) ).
cnf(c_2,plain,
apply(apply(o,A),B) = apply(B,apply(A,B)),
inference(clausify,[status(thm)],[o_definition]) ).
fof(prove_fixed_point,axiom,
! [VAR_0] : apply(VAR_0,f(VAR_0)) != apply(f(VAR_0),apply(VAR_0,f(VAR_0))),
file('theBenchmark.p',prove_fixed_point) ).
cnf(c_3,plain,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
inference(clausify,[status(thm)],[prove_fixed_point]) ).
cnf(c_14,plain,
apply(A,f(A)) != apply(apply(o,A),f(A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
apply(apply(o,A),f(A)) != apply(A,f(A)),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_15,plain,
apply(apply(apply(l,o),A),f(apply(A,A))) != apply(apply(A,A),f(apply(A,A))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_13,plain,
$false,
inference(copy,[status(thm)],[c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 23:11:31 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1965733 was started by sandbox on n016,
% 0.18/0.45 % Sat Sep 26 23:11:31 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.46
% 0.18/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.46 % Length of proof is 5.
% 0.18/0.46 % Level of proof is 2.
% 0.18/0.46 % Maximum clause weight is 11.000.
% 0.18/0.46 % Given clauses 3.
% 0.18/0.46
% 0.18/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------