%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL079-1 : 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 : 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 06:57:38 AM UTC 2026
% Result : Unsatisfiable 8.67s 1.47s
% Output : CNFRefutation 8.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 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 : 31 ( 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_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(prove_TRC2a,axiom,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
file('theBenchmark.p',prove_TRC2a) ).
cnf(c_14,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(clausify,[status(thm)],[prove_TRC2a]) ).
cnf(c_25,plain,
apply(apply(apply(abstraction,A),k(B)),C) = apply(apply(A,k(C)),B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_5458,plain,
( apply(apply(B,k(n(A,apply(apply(abstraction,B),C)))),apply(C,n(A,apply(apply(abstraction,B),C)))) != apply(A,n(A,apply(apply(abstraction,B),C)))
| A = apply(apply(abstraction,B),C) ),
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_47,plain,
( apply(apply(A,k(n(C,apply(apply(abstraction,A),B)))),apply(B,n(C,apply(apply(abstraction,A),B)))) != apply(C,n(C,apply(apply(abstraction,A),B)))
| apply(apply(abstraction,A),B) = C ),
inference(copy,[status(thm)],[c_5458]) ).
cnf(c_5459,plain,
apply(abstraction,b) != apply(abstraction,apply(abstraction,apply(abstraction,b))),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_52,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_11,c_5459]) ).
cnf(c_5460,plain,
apply(apply(apply(abstraction,apply(abstraction,A)),k(B)),C) = apply(apply(A,k(B)),apply(k(C),B)),
inference(paramod,[status(thm)],[c_25,c_7]) ).
cnf(c_865,plain,
apply(apply(apply(abstraction,apply(abstraction,A)),k(B)),C) = apply(apply(A,k(B)),C),
inference(paramod,[status(thm)],[c_1,c_5460]) ).
cnf(c_5461,plain,
apply(apply(apply(abstraction,apply(abstraction,b)),k(n(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b)))))))),apply(n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b)))),n(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b)))))))) != apply(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),n(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))))),
inference(resolve,[status(thm)],[c_47,c_52]) ).
cnf(c_5462,plain,
apply(apply(b,k(n(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b)))))))),apply(n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b)))),n(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b)))))))) != apply(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),n(apply(apply(abstraction,b),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,b),apply(abstraction,apply(abstraction,apply(abstraction,b))))))),
inference(paramod,[status(thm)],[c_865,c_5461]) ).
cnf(c_5457,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_5462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL079-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 26 23:12:06 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 1737674 was started by sandbox on n012,
% 0.04/0.30 % Sat Sep 26 23:12:06 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 8.67/1.47
% 8.67/1.47 % SZS status Unsatisfiable for theBenchmark
% 8.67/1.47
% 8.67/1.47 % Proof 1 at 1.02 (+ 0.11) seconds.
% 8.67/1.47 % Length of proof is 10.
% 8.67/1.47 % Level of proof is 3.
% 8.67/1.47 % Maximum clause weight is 37.000.
% 8.67/1.47 % Given clauses 125.
% 8.67/1.47
% 8.67/1.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------