%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL066-3 : 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 : 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 06:57:37 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 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; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 8 !; 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(q_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(q,VAR_0),VAR_1),VAR_2) = apply(VAR_1,apply(VAR_0,VAR_2)),
file('theBenchmark.p',q_definition) ).
cnf(c_2,plain,
apply(apply(apply(q,A),B),C) = apply(B,apply(A,C)),
inference(clausify,[status(thm)],[q_definition]) ).
fof(w_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(w,VAR_0),VAR_1) = apply(apply(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',w_definition) ).
cnf(c_3,plain,
apply(apply(w,A),B) = apply(apply(A,B),B),
inference(clausify,[status(thm)],[w_definition]) ).
fof(prove_p_combinator,axiom,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('theBenchmark.p',prove_p_combinator) ).
cnf(c_4,plain,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(clausify,[status(thm)],[prove_p_combinator]) ).
cnf(c_280,plain,
apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_3,c_280]) ).
cnf(c_7,plain,
apply(apply(apply(w,b),A),B) = apply(A,apply(A,B)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_10,plain,
apply(apply(apply(w,q),A),B) = apply(A,apply(A,B)),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_11,plain,
apply(apply(w,apply(q,A)),B) = apply(B,apply(A,B)),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_281,plain,
apply(apply(apply(w,b),A),B) = apply(apply(apply(w,q),A),B),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_124,plain,
apply(apply(apply(w,q),A),B) = apply(apply(apply(w,b),A),B),
inference(copy,[status(thm)],[c_281]) ).
cnf(c_144,plain,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_282,plain,
apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_3,c_144]) ).
cnf(c_283,plain,
apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_2,c_282]) ).
cnf(c_284,plain,
apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_2,c_283]) ).
cnf(c_285,plain,
apply(apply(apply(q,apply(x,y)),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_2,c_284]) ).
cnf(c_286,plain,
apply(apply(apply(w,q),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_3,c_285]) ).
cnf(c_287,plain,
apply(apply(apply(w,b),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(paramod,[status(thm)],[c_124,c_286]) ).
cnf(c_279,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL066-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n026.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 23:13:56 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 2192360 was started by sandbox2 on n026,
% 0.15/0.42 % Sat Sep 26 23:13:56 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.48
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48
% 0.15/0.48 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.48 % Length of proof is 11.
% 0.15/0.48 % Level of proof is 3.
% 0.15/0.48 % Maximum clause weight is 87.000.
% 0.15/0.48 % Given clauses 13.
% 0.15/0.48
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------