%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL075-1 : 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 : 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 06:57:37 AM UTC 2026
% Result : Unsatisfiable 1.03s 0.59s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 25 ( 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_7,plain,
apply(apply(apply(abstraction,A),B),C) = apply(apply(A,apply(k,C)),apply(B,C)),
inference(clausify,[status(thm)],[abstraction]) ).
cnf(c_8,plain,
apply(apply(A,apply(k,B)),apply(C,B)) = apply(apply(apply(abstraction,A),C),B),
inference(copy,[status(thm)],[c_7]) ).
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_15,plain,
apply(apply(A,b(A)),c(A)) != apply(b(A),b(A)),
inference(clausify,[status(thm)],[prove_diagonal_combinator]) ).
cnf(c_516,plain,
apply(apply(A,apply(k,B)),C) = apply(apply(apply(abstraction,A),apply(k,C)),B),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_27,plain,
apply(apply(apply(abstraction,A),apply(k,B)),C) = apply(apply(A,apply(k,C)),B),
inference(copy,[status(thm)],[c_516]) ).
cnf(c_517,plain,
apply(apply(apply(apply(abstraction,abstraction),k),A),B) = apply(apply(apply(k,A),apply(k,B)),A),
inference(paramod,[status(thm)],[c_8,c_27]) ).
cnf(c_514,plain,
apply(apply(apply(apply(abstraction,abstraction),k),A),B) = apply(A,A),
inference(paramod,[status(thm)],[c_1,c_517]) ).
cnf(c_515,plain,
$false,
inference(resolve,[status(thm)],[c_514,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL075-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n001.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 23:17:29 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2910882 was started by sandbox on n001,
% 0.15/0.43 % Sat Sep 26 23:17:29 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 1.03/0.59
% 1.03/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.03/0.59
% 1.03/0.59 % Proof 1 at 0.11 (+ 0.04) seconds.
% 1.03/0.59 % Length of proof is 7.
% 1.03/0.59 % Level of proof is 4.
% 1.03/0.59 % Maximum clause weight is 47.000.
% 1.03/0.59 % Given clauses 67.
% 1.03/0.59
% 1.03/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------