%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 18 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 12 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 2 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 8 !; 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_7,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_10,plain,
( apply(A,n(A,B)) != apply(B,n(A,B))
| A = B ),
inference(clausify,[status(thm)],[extensionality2]) ).
cnf(c_11,plain,
( apply(B,n(A,B)) != apply(A,n(A,B))
| A = B ),
inference(copy,[status(thm)],[c_10]) ).
fof(identity_definition,axiom,
! [VAR_0] : apply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',identity_definition) ).
cnf(c_14,plain,
apply(identity,A) = A,
inference(clausify,[status(thm)],[identity_definition]) ).
fof(prove_TRC1a,axiom,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
file('theBenchmark.p',prove_TRC1a) ).
cnf(c_15,plain,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
inference(clausify,[status(thm)],[prove_TRC1a]) ).
cnf(c_91,plain,
apply(apply(apply(apply(abstraction,abstraction),A),B),C) = apply(apply(k(B),k(C)),apply(apply(A,B),C)),
inference(paramod,[status(thm)],[c_7,c_7]) ).
cnf(c_36,plain,
apply(apply(apply(apply(abstraction,abstraction),A),B),C) = apply(B,apply(apply(A,B),C)),
inference(paramod,[status(thm)],[c_1,c_91]) ).
cnf(c_38,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) != identity,
inference(paramod,[status(thm)],[c_36,c_15]) ).
cnf(c_92,plain,
apply(identity,n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)) != apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)),
inference(resolve,[status(thm)],[c_11,c_38]) ).
cnf(c_93,plain,
n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity) != apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)),
inference(paramod,[status(thm)],[c_14,c_92]) ).
cnf(c_84,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)) != n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
apply(apply(apply(apply(abstraction,abstraction),abstraction),k(n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity))),apply(abstraction,n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity))) != n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity),
inference(paramod,[status(thm)],[c_7,c_84]) ).
cnf(c_95,plain,
apply(k(n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)),apply(apply(abstraction,k(n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity))),apply(abstraction,n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)))) != n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity),
inference(paramod,[status(thm)],[c_36,c_94]) ).
cnf(c_96,plain,
n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity) != n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity),
inference(paramod,[status(thm)],[c_1,c_95]) ).
cnf(c_90,plain,
$false,
inference(copy,[status(thm)],[c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n026.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 23:14:12 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2192756 was started by sandbox2 on n026,
% 0.16/0.44 % Sat Sep 26 23:14:12 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.47 % Length of proof is 10.
% 0.16/0.47 % Level of proof is 4.
% 0.16/0.47 % Maximum clause weight is 33.000.
% 0.16/0.47 % Given clauses 16.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------