%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL075-2 : 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 : 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 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 20 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(k_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(k,VAR_0),VAR_1) = VAR_0,
file('theBenchmark.p',k_definition) ).
cnf(c_1,plain,
apply(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,apply(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,apply(k,C)),apply(B,C)),
inference(clausify,[status(thm)],[abstraction]) ).
fof(prove_diagonal_combinator,axiom,
! [VAR_0] : apply(apply(VAR_0,b(VAR_0)),c(VAR_0)) != apply(b(VAR_0),b(VAR_0)),
file('theBenchmark.p',prove_diagonal_combinator) ).
cnf(c_3,plain,
apply(apply(A,b(A)),c(A)) != apply(b(A),b(A)),
inference(clausify,[status(thm)],[prove_diagonal_combinator]) ).
cnf(c_5,plain,
apply(apply(apply(abstraction,apply(k,A)),B),C) = apply(A,apply(B,C)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_15,plain,
apply(apply(apply(A,apply(k,b(apply(apply(abstraction,A),B)))),apply(B,b(apply(apply(abstraction,A),B)))),c(apply(apply(abstraction,A),B))) != apply(b(apply(apply(abstraction,A),B)),b(apply(apply(abstraction,A),B))),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_22,plain,
apply(apply(apply(abstraction,apply(k,A)),apply(k,B)),C) = apply(A,B),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_23,plain,
$false,
inference(resolve,[status(thm)],[c_22,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 23:14:26 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2193518 was started by sandbox on n026,
% 0.07/0.35 % Sat Sep 26 23:14:26 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 7.
% 0.12/0.37 % Level of proof is 3.
% 0.12/0.37 % Maximum clause weight is 80.000.
% 0.12/0.37 % Given clauses 5.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------