%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL035-1 : 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 : n005.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 06:57:27 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.61s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 8 !; 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(w_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(w,VAR_0),VAR_1) = apply(apply(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',w_definition) ).
cnf(c_2,plain,
apply(apply(w,A),B) = apply(apply(A,B),B),
inference(clausify,[status(thm)],[w_definition]) ).
fof(q_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(q,VAR_0),VAR_1),VAR_2) = apply(VAR_1,apply(VAR_0,VAR_2)),
file('theBenchmark.p',q_definition) ).
cnf(c_3,plain,
apply(apply(apply(q,A),B),C) = apply(B,apply(A,C)),
inference(clausify,[status(thm)],[q_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_4,plain,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
inference(clausify,[status(thm)],[prove_fixed_point]) ).
cnf(c_5,plain,
apply(f(A),apply(A,f(A))) != apply(A,f(A)),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_21,plain,
apply(apply(w,apply(q,A)),B) = apply(B,apply(A,B)),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_119,plain,
apply(apply(w,apply(q,A)),f(A)) != apply(A,f(A)),
inference(paramod,[status(thm)],[c_21,c_5]) ).
cnf(c_232,plain,
apply(apply(w,apply(apply(l,q),A)),f(apply(A,A))) != apply(apply(A,A),f(apply(A,A))),
inference(paramod,[status(thm)],[c_1,c_119]) ).
cnf(c_243,plain,
apply(apply(w,apply(apply(l,q),apply(apply(q,A),B))),f(apply(B,apply(A,apply(apply(q,A),B))))) != apply(apply(apply(apply(q,A),B),apply(apply(q,A),B)),f(apply(apply(apply(q,A),B),apply(apply(q,A),B)))),
inference(paramod,[status(thm)],[c_3,c_232]) ).
cnf(c_244,plain,
apply(apply(w,apply(apply(l,q),apply(apply(q,A),B))),f(apply(B,apply(A,apply(apply(q,A),B))))) != apply(apply(B,apply(A,apply(apply(q,A),B))),f(apply(apply(apply(q,A),B),apply(apply(q,A),B)))),
inference(paramod,[status(thm)],[c_3,c_243]) ).
cnf(c_245,plain,
apply(apply(w,apply(apply(l,q),apply(apply(q,A),B))),f(apply(B,apply(A,apply(apply(q,A),B))))) != apply(apply(B,apply(A,apply(apply(q,A),B))),f(apply(B,apply(A,apply(apply(q,A),B))))),
inference(paramod,[status(thm)],[c_3,c_244]) ).
cnf(c_242,plain,
$false,
inference(copy,[status(thm)],[c_245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL035-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n005.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sat Sep 26 23:06:48 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.56 % Process 3322159 was started by sandbox2 on n005,
% 0.09/0.56 % Sat Sep 26 23:06:48 2026
% 0.09/0.56 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.56
% 0.09/0.56 % From the command line: assign(max_seconds, 300).
% 0.13/0.61
% 0.13/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.61
% 0.13/0.61 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.61 % Length of proof is 9.
% 0.13/0.61 % Level of proof is 4.
% 0.13/0.61 % Maximum clause weight is 21.000.
% 0.13/0.61 % Given clauses 16.
% 0.13/0.61
% 0.13/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------