%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL063-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 06:57:34 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(b,VAR_0),VAR_1),VAR_2) = apply(VAR_0,apply(VAR_1,VAR_2)),
file('theBenchmark.p',b_definition) ).
cnf(c_1,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(t_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(t,VAR_0),VAR_1) = apply(VAR_1,VAR_0),
file('theBenchmark.p',t_definition) ).
cnf(c_2,plain,
apply(apply(t,A),B) = apply(B,A),
inference(clausify,[status(thm)],[t_definition]) ).
fof(prove_f_combinator,axiom,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) != apply(apply(z,y),x),
file('theBenchmark.p',prove_f_combinator) ).
cnf(c_3,plain,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) != apply(apply(z,y),x),
inference(clausify,[status(thm)],[prove_f_combinator]) ).
cnf(c_21,plain,
apply(apply(apply(apply(t,t),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z) != apply(apply(z,y),x),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_22,plain,
apply(apply(apply(apply(t,t),apply(b,apply(apply(apply(b,b),t),x))),y),z) != apply(apply(z,y),x),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_4,plain,
apply(apply(apply(apply(t,t),apply(b,apply(b,apply(t,x)))),y),z) != apply(apply(z,y),x),
inference(paramod,[status(thm)],[c_1,c_22]) ).
cnf(c_23,plain,
apply(apply(apply(b,A),apply(t,B)),C) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_5,plain,
apply(A,apply(apply(t,B),C)) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_1,c_23]) ).
cnf(c_7,plain,
apply(apply(apply(t,A),apply(b,B)),C) = apply(B,apply(A,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_24,plain,
apply(apply(apply(b,apply(t,x)),apply(t,y)),z) != apply(apply(z,y),x),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_25,plain,
apply(apply(t,x),apply(apply(t,y),z)) != apply(apply(z,y),x),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_11,plain,
apply(apply(z,y),x) != apply(apply(t,x),apply(apply(t,y),z)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_19,plain,
apply(apply(t,A),apply(apply(t,B),C)) = apply(apply(C,B),A),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_26,plain,
apply(apply(t,x),apply(apply(t,y),z)) != apply(apply(z,y),x),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_20,plain,
$false,
inference(resolve,[status(thm)],[c_19,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL063-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 23:09:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2860582 was started by sandbox2 on n004,
% 0.09/0.35 % Sat Sep 26 23:09:51 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 9.
% 0.09/0.37 % Level of proof is 3.
% 0.09/0.37 % Maximum clause weight is 21.000.
% 0.09/0.37 % Given clauses 3.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------