%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL044-1 : 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 : n008.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 06:57:29 AM UTC 2026
% Result : Unsatisfiable 0.13s 6.06s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 26 ( 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(n_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(n,VAR_0),VAR_1),VAR_2) = apply(apply(apply(VAR_0,VAR_2),VAR_1),VAR_2),
file('theBenchmark.p',n_definition) ).
cnf(c_2,plain,
apply(apply(apply(n,A),B),C) = apply(apply(apply(A,C),B),C),
inference(clausify,[status(thm)],[n_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_4,plain,
apply(f(A),apply(A,f(A))) != apply(A,f(A)),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_6,plain,
apply(apply(apply(n,b),A),B) = apply(B,apply(A,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_8,plain,
apply(apply(apply(n,apply(b,A)),B),C) = apply(apply(A,apply(C,B)),C),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_35,plain,
apply(apply(apply(n,b),A),f(A)) != apply(A,f(A)),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_76,plain,
apply(apply(apply(n,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(C,B),C)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_303,plain,
apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),A),B),f(apply(apply(B,A),B))) != apply(apply(apply(B,A),B),f(apply(apply(B,A),B))),
inference(paramod,[status(thm)],[c_76,c_35]) ).
cnf(c_302,plain,
$false,
inference(copy,[status(thm)],[c_303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.40 % Computer : n008.cluster.edu
% 0.10/5.40 % Model : x86_64 x86_64
% 0.10/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.40 % Memory : 8046.5625MB
% 0.10/5.40 % OS : Linux 6.8.0-71-generic
% 0.10/5.40 % CPULimit : 300
% 0.10/5.40 % WCLimit : 300
% 0.10/5.40 % DateTime : Sat Sep 26 23:08:46 UTC 2026
% 0.10/5.40 % CPUTime :
% 0.10/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.41 % Process 589272 was started by sandbox on n008,
% 0.10/5.41 % Sat Sep 26 23:08:46 2026
% 0.10/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.41
% 0.10/5.41 % From the command line: assign(max_seconds, 300).
% 0.13/6.06
% 0.13/6.06 % SZS status Unsatisfiable for theBenchmark
% 0.13/6.06
% 0.13/6.06 % Proof 1 at 0.24 (+ 0.06) seconds.
% 0.13/6.06 % Length of proof is 9.
% 0.13/6.06 % Level of proof is 3.
% 0.13/6.06 % Maximum clause weight is 79.000.
% 0.13/6.06 % Given clauses 42.
% 0.13/6.06
% 0.13/6.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------