%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL009-1 : 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 : n012.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 06:57:23 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 6 !; 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(l2_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(l2,VAR_0),VAR_1) = apply(VAR_1,apply(VAR_0,VAR_0)),
file('theBenchmark.p',l2_definition) ).
cnf(c_2,plain,
apply(apply(l2,A),B) = apply(B,apply(A,A)),
inference(clausify,[status(thm)],[l2_definition]) ).
fof(prove_fixed_point,axiom,
! [VAR_0] : VAR_0 != apply(combinator,VAR_0),
file('theBenchmark.p',prove_fixed_point) ).
cnf(c_3,plain,
A != apply(combinator,A),
inference(clausify,[status(thm)],[prove_fixed_point]) ).
cnf(c_4,plain,
apply(combinator,A) != A,
inference(copy,[status(thm)],[c_3]) ).
cnf(c_47,plain,
apply(apply(apply(b,A),apply(l2,B)),C) = apply(A,apply(C,apply(B,B))),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_5,plain,
apply(A,apply(apply(l2,B),C)) = apply(A,apply(C,apply(B,B))),
inference(paramod,[status(thm)],[c_1,c_47]) ).
cnf(c_7,plain,
apply(apply(l2,A),apply(apply(b,B),C)) = apply(B,apply(C,apply(A,A))),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_27,plain,
apply(combinator,apply(apply(l2,A),B)) != apply(B,apply(A,A)),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_45,plain,
apply(combinator,apply(apply(l2,apply(apply(b,A),B)),C)) != apply(C,apply(A,apply(B,apply(apply(b,A),B)))),
inference(paramod,[status(thm)],[c_1,c_27]) ).
cnf(c_48,plain,
apply(B,apply(C,apply(A,A))) = apply(apply(l2,A),apply(apply(b,B),C)),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_46,plain,
$false,
inference(resolve,[status(thm)],[c_45,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 23:05:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1719099 was started by sandbox2 on n012,
% 0.08/0.35 % Sat Sep 26 23:05:19 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 9.
% 0.12/0.36 % Level of proof is 4.
% 0.12/0.36 % Maximum clause weight is 23.000.
% 0.12/0.36 % Given clauses 6.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------