%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL049-1 : 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 : n002.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 06:57:31 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 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 : 31 ( 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(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(m_definition,axiom,
! [VAR_0] : apply(m,VAR_0) = apply(VAR_0,VAR_0),
file('theBenchmark.p',m_definition) ).
cnf(c_3,plain,
apply(m,A) = apply(A,A),
inference(clausify,[status(thm)],[m_definition]) ).
fof(prove_strong_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_strong_fixed_point) ).
cnf(c_4,plain,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
inference(clausify,[status(thm)],[prove_strong_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_226,plain,
apply(apply(apply(b,A),B),B) = apply(A,apply(m,B)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_15,plain,
apply(apply(w,apply(b,A)),B) = apply(A,apply(m,B)),
inference(paramod,[status(thm)],[c_2,c_226]) ).
cnf(c_227,plain,
apply(f(apply(apply(b,A),B)),apply(A,apply(B,f(apply(apply(b,A),B))))) != apply(apply(apply(b,A),B),f(apply(apply(b,A),B))),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_19,plain,
apply(f(apply(apply(b,A),B)),apply(A,apply(B,f(apply(apply(b,A),B))))) != apply(A,apply(B,f(apply(apply(b,A),B)))),
inference(paramod,[status(thm)],[c_1,c_227]) ).
cnf(c_228,plain,
apply(f(apply(apply(b,apply(apply(b,A),B)),C)),apply(A,apply(B,apply(C,f(apply(apply(b,apply(apply(b,A),B)),C)))))) != apply(apply(apply(b,A),B),apply(C,f(apply(apply(b,apply(apply(b,A),B)),C)))),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_46,plain,
apply(f(apply(apply(b,apply(apply(b,A),B)),C)),apply(A,apply(B,apply(C,f(apply(apply(b,apply(apply(b,A),B)),C)))))) != apply(A,apply(B,apply(C,f(apply(apply(b,apply(apply(b,A),B)),C))))),
inference(paramod,[status(thm)],[c_1,c_228]) ).
cnf(c_229,plain,
apply(m,apply(w,apply(b,A))) = apply(A,apply(m,apply(w,apply(b,A)))),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_224,plain,
apply(A,apply(m,apply(w,apply(b,A)))) = apply(m,apply(w,apply(b,A))),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_225,plain,
$false,
inference(resolve,[status(thm)],[c_224,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL049-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 23:11:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2919144 was started by sandbox on n002,
% 0.12/0.36 % Sat Sep 26 23:11:36 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.44
% 0.12/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.44
% 0.12/0.44 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.12/0.44 % Length of proof is 10.
% 0.12/0.44 % Level of proof is 4.
% 0.12/0.44 % Maximum clause weight is 44.000.
% 0.12/0.44 % Given clauses 22.
% 0.12/0.44
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------