%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL062-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 06:57:34 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.63s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 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 : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 5 !; 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(t_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(t,VAR_0),VAR_1) = apply(VAR_1,VAR_0),
file('theBenchmark.p',t_definition) ).
cnf(c_2,plain,
apply(apply(t,A),B) = apply(B,A),
inference(clausify,[status(thm)],[t_definition]) ).
fof(prove_c_combinator,axiom,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),x),y),z) != apply(apply(x,z),y),
file('theBenchmark.p',prove_c_combinator) ).
cnf(c_3,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),x),y),z) != apply(apply(x,z),y),
inference(clausify,[status(thm)],[prove_c_combinator]) ).
cnf(c_13,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),x)),y),z) != apply(apply(x,z),y),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_4,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,x))),y),z) != apply(apply(x,z),y),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_7,plain,
apply(apply(apply(t,A),apply(b,B)),C) = apply(B,apply(A,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_14,plain,
apply(apply(apply(t,x),apply(apply(apply(b,b),t),y)),z) != apply(apply(x,z),y),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_15,plain,
apply(apply(apply(t,x),apply(b,apply(t,y))),z) != apply(apply(x,z),y),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_16,plain,
apply(apply(t,y),apply(x,z)) != apply(apply(x,z),y),
inference(paramod,[status(thm)],[c_7,c_15]) ).
cnf(c_11,plain,
apply(apply(x,z),y) != apply(apply(t,y),apply(x,z)),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_17,plain,
apply(B,A) = apply(apply(t,A),B),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_12,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL062-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.60 % Computer : n001.cluster.edu
% 0.14/0.60 % Model : x86_64 x86_64
% 0.14/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.60 % Memory : 8046.5625MB
% 0.14/0.60 % OS : Linux 6.8.0-71-generic
% 0.14/0.60 % CPULimit : 300
% 0.14/0.60 % WCLimit : 300
% 0.14/0.60 % DateTime : Sat Sep 26 23:16:01 UTC 2026
% 0.18/0.61 % CPUTime :
% 0.18/0.61 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.61 % Process 2908643 was started by sandbox2 on n001,
% 0.18/0.61 % Sat Sep 26 23:16:01 2026
% 0.18/0.61 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.61
% 0.18/0.61 % From the command line: assign(max_seconds, 300).
% 0.18/0.63
% 0.18/0.63 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.63
% 0.18/0.63 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.63 % Length of proof is 7.
% 0.18/0.63 % Level of proof is 3.
% 0.18/0.63 % Maximum clause weight is 23.000.
% 0.18/0.63 % Given clauses 2.
% 0.18/0.63
% 0.18/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------