%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL065-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 06:57:36 AM UTC 2026
% Result : Unsatisfiable 245.19s 33.75s
% Output : CNFRefutation 245.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 6 !; 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_g_combinator,axiom,
! [VAR_0] : apply(apply(apply(apply(VAR_0,f(VAR_0)),g(VAR_0)),h(VAR_0)),i(VAR_0)) != apply(apply(f(VAR_0),i(VAR_0)),apply(g(VAR_0),h(VAR_0))),
file('theBenchmark.p',prove_g_combinator) ).
cnf(c_3,plain,
apply(apply(apply(apply(A,f(A)),g(A)),h(A)),i(A)) != apply(apply(f(A),i(A)),apply(g(A),h(A))),
inference(clausify,[status(thm)],[prove_g_combinator]) ).
cnf(c_4,plain,
apply(apply(f(A),i(A)),apply(g(A),h(A))) != apply(apply(apply(apply(A,f(A)),g(A)),h(A)),i(A)),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_7,plain,
apply(apply(apply(apply(apply(b,b),A),B),C),D) = apply(apply(A,B),apply(C,D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
apply(apply(apply(b,apply(t,A)),B),C) = apply(apply(B,C),A),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_13,plain,
apply(apply(f(apply(apply(b,A),B)),i(apply(apply(b,A),B))),apply(g(apply(apply(b,A),B)),h(apply(apply(b,A),B)))) != apply(apply(apply(apply(A,apply(B,f(apply(apply(b,A),B)))),g(apply(apply(b,A),B))),h(apply(apply(b,A),B))),i(apply(apply(b,A),B))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_99,plain,
apply(apply(apply(apply(apply(b,b),t),A),B),C) = apply(apply(B,C),A),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_149,plain,
apply(apply(apply(apply(b,apply(t,A)),b),apply(t,B)),C) = apply(apply(A,C),B),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_2727,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,A)),B),C) = apply(apply(A,C),B),
inference(paramod,[status(thm)],[c_149,c_99]) ).
cnf(c_3146,plain,
apply(apply(f(apply(apply(b,apply(apply(b,b),A)),B)),i(apply(apply(b,apply(apply(b,b),A)),B))),apply(g(apply(apply(b,apply(apply(b,b),A)),B)),h(apply(apply(b,apply(apply(b,b),A)),B)))) != apply(apply(apply(A,apply(B,f(apply(apply(b,apply(apply(b,b),A)),B)))),apply(g(apply(apply(b,apply(apply(b,b),A)),B)),h(apply(apply(b,apply(apply(b,b),A)),B)))),i(apply(apply(b,apply(apply(b,b),A)),B))),
inference(paramod,[status(thm)],[c_7,c_13]) ).
cnf(c_3148,plain,
apply(apply(A,C),B) = apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,A)),B),C),
inference(copy,[status(thm)],[c_2727]) ).
cnf(c_3147,plain,
$false,
inference(resolve,[status(thm)],[c_3146,c_3148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL065-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:13:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1028834 was started by sandbox on n015,
% 0.09/0.36 % Sat Sep 26 23:13:59 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 245.19/33.75
% 245.19/33.75 % SZS status Unsatisfiable for theBenchmark
% 245.19/33.75
% 245.19/33.75 % Proof 1 at 0.98 (+ 0.17) seconds.
% 245.19/33.75 % Length of proof is 12.
% 245.19/33.75 % Level of proof is 4.
% 245.19/33.75 % Maximum clause weight is 91.000.
% 245.19/33.75 % Given clauses 48.
% 245.19/33.75
% 245.19/33.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------