%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL061-2 : 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 : 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 06:57:33 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 19 ( 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_q1_combinator,axiom,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) != apply(x,apply(z,y)),
file('theBenchmark.p',prove_q1_combinator) ).
cnf(c_3,plain,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) != apply(x,apply(z,y)),
inference(clausify,[status(thm)],[prove_q1_combinator]) ).
cnf(c_13,plain,
apply(apply(apply(apply(t,t),apply(apply(apply(b,b),b),x)),y),z) != apply(x,apply(z,y)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_4,plain,
apply(apply(apply(apply(t,t),apply(b,apply(b,x))),y),z) != apply(x,apply(z,y)),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_14,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_14]) ).
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_15,plain,
apply(apply(apply(b,x),apply(t,y)),z) != apply(x,apply(z,y)),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_11,plain,
apply(x,apply(apply(t,y),z)) != apply(x,apply(z,y)),
inference(paramod,[status(thm)],[c_1,c_15]) ).
cnf(c_12,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL061-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 23:12:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1027235 was started by sandbox2 on n015,
% 0.11/0.37 % Sat Sep 26 23:12:59 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 8.
% 0.11/0.39 % Level of proof is 3.
% 0.11/0.39 % Maximum clause weight is 19.000.
% 0.11/0.39 % Given clauses 2.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------