%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 06:57:38 AM UTC 2026
% Result : Unsatisfiable 1.14s 0.63s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 17 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(k_definition,axiom,
! [VAR_0,VAR_1] : apply(k(VAR_0),VAR_1) = VAR_0,
file('theBenchmark.p',k_definition) ).
cnf(c_1,plain,
apply(k(A),B) = A,
inference(clausify,[status(thm)],[k_definition]) ).
fof(abstraction,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(abstraction,VAR_0),VAR_1),VAR_2) = apply(apply(VAR_0,k(VAR_2)),apply(VAR_1,VAR_2)),
file('theBenchmark.p',abstraction) ).
cnf(c_2,plain,
apply(apply(apply(abstraction,A),B),C) = apply(apply(A,k(C)),apply(B,C)),
inference(clausify,[status(thm)],[abstraction]) ).
fof(extensionality2,axiom,
! [VAR_0,VAR_1] :
( apply(VAR_0,n(VAR_0,VAR_1)) != apply(VAR_1,n(VAR_0,VAR_1))
| VAR_0 = VAR_1 ),
file('theBenchmark.p',extensionality2) ).
cnf(c_3,plain,
( apply(A,n(A,B)) != apply(B,n(A,B))
| A = B ),
inference(clausify,[status(thm)],[extensionality2]) ).
cnf(c_4,plain,
( apply(B,n(A,B)) != apply(A,n(A,B))
| A = B ),
inference(copy,[status(thm)],[c_3]) ).
fof(prove_TRC2a,axiom,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
file('theBenchmark.p',prove_TRC2a) ).
cnf(c_5,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(clausify,[status(thm)],[prove_TRC2a]) ).
cnf(c_577,plain,
apply(apply(apply(abstraction,apply(abstraction,A)),B),C) = apply(apply(A,k(apply(B,C))),apply(k(C),apply(B,C))),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_10,plain,
apply(apply(apply(abstraction,apply(abstraction,A)),B),C) = apply(apply(A,k(apply(B,C))),C),
inference(paramod,[status(thm)],[c_1,c_577]) ).
cnf(c_578,plain,
apply(abstraction,b) != apply(abstraction,apply(abstraction,apply(abstraction,b))),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_14,plain,
apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))) != apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),
inference(resolve,[status(thm)],[c_4,c_578]) ).
cnf(c_579,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,A))),B),C) = apply(apply(A,k(apply(k(C),apply(B,C)))),apply(B,C)),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_28,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,A))),B),C) = apply(apply(A,k(C)),apply(B,C)),
inference(paramod,[status(thm)],[c_1,c_579]) ).
cnf(c_580,plain,
apply(apply(apply(abstraction,A),B),C) = apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,A))),B),C),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_559,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,A))),B),C) = apply(apply(apply(abstraction,A),B),C),
inference(copy,[status(thm)],[c_580]) ).
cnf(c_581,plain,
apply(apply(abstraction,A),B) = apply(apply(abstraction,apply(abstraction,apply(abstraction,A))),B),
inference(resolve,[status(thm)],[c_4,c_559]) ).
cnf(c_575,plain,
apply(apply(abstraction,apply(abstraction,apply(abstraction,A))),B) = apply(apply(abstraction,A),B),
inference(copy,[status(thm)],[c_581]) ).
cnf(c_576,plain,
$false,
inference(resolve,[status(thm)],[c_575,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 23:13:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2761518 was started by sandbox on n020,
% 0.10/0.37 % Sat Sep 26 23:13:07 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 1.14/0.63
% 1.14/0.63 % Assigning unary symbol k kb_weight 0 and highest precedence (6).
% 1.14/0.63
% 1.14/0.63 % SZS status Unsatisfiable for theBenchmark
% 1.14/0.63
% 1.14/0.63 % Proof 1 at 0.17 (+ 0.06) seconds.
% 1.14/0.63 % Length of proof is 11.
% 1.14/0.63 % Level of proof is 5.
% 1.14/0.63 % Maximum clause weight is 81.000.
% 1.14/0.63 % Given clauses 33.
% 1.14/0.63
% 1.14/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------