%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 08:35:27 AM UTC 2026
% Result : Unsatisfiable 0.18s 5.56s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 31 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_apply_for_composition3,axiom,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('theBenchmark.p',prove_apply_for_composition3) ).
cnf(c_34,plain,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
inference(clausify,[status(thm)],[prove_apply_for_composition3]) ).
cnf(c_35,plain,
apply(compose(another_function,a_function),a) != apply(another_function,apply(a_function,a)),
inference(copy,[status(thm)],[c_34]) ).
fof(member_of_domain,axiom,
member(a,domain_of(a_function)),
file('theBenchmark.p',member_of_domain) ).
cnf(c_36,plain,
member(a,domain_of(a_function)),
inference(clausify,[status(thm)],[member_of_domain]) ).
fof(a_function,axiom,
function(a_function),
file('theBenchmark.p',a_function) ).
cnf(c_37,plain,
function(a_function),
inference(clausify,[status(thm)],[a_function]) ).
fof(apply_for_composition2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subset(apply(compose(VAR_1,VAR_0),VAR_2),apply(VAR_1,apply(VAR_0,VAR_2)))
| ~ function(VAR_0) ),
file('theBenchmark.p',apply_for_composition2) ).
cnf(c_38,plain,
( subset(apply(compose(B,A),C),apply(B,apply(A,C)))
| ~ function(A) ),
inference(clausify,[status(thm)],[apply_for_composition2]) ).
fof(apply_for_composition1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subset(apply(VAR_2,apply(VAR_0,VAR_1)),apply(compose(VAR_2,VAR_0),VAR_1))
| ~ member(VAR_1,domain_of(VAR_0))
| ~ function(VAR_0) ),
file('theBenchmark.p',apply_for_composition1) ).
cnf(c_39,plain,
( subset(apply(C,apply(A,B)),apply(compose(C,A),B))
| ~ member(B,domain_of(A))
| ~ function(A) ),
inference(clausify,[status(thm)],[apply_for_composition1]) ).
fof(two_sets_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subset(VAR_1,VAR_0)
| ~ subset(VAR_0,VAR_1) ),
file('theBenchmark.p',two_sets_equal) ).
cnf(c_59,plain,
( A = B
| ~ subset(B,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[two_sets_equal]) ).
cnf(c_293,plain,
subset(apply(compose(A,a_function),B),apply(A,apply(a_function,B))),
inference(resolve,[status(thm)],[c_38,c_37]) ).
cnf(c_1485,plain,
( subset(apply(A,apply(a_function,a)),apply(compose(A,a_function),a))
| ~ function(a_function) ),
inference(resolve,[status(thm)],[c_39,c_36]) ).
cnf(c_294,plain,
subset(apply(A,apply(a_function,a)),apply(compose(A,a_function),a)),
inference(resolve,[status(thm)],[c_37,c_1485]) ).
cnf(c_1486,plain,
( apply(compose(A,a_function),a) = apply(A,apply(a_function,a))
| ~ subset(apply(compose(A,a_function),a),apply(A,apply(a_function,a))) ),
inference(resolve,[status(thm)],[c_294,c_59]) ).
cnf(c_1483,plain,
apply(compose(A,a_function),a) = apply(A,apply(a_function,a)),
inference(resolve,[status(thm)],[c_293,c_1486]) ).
cnf(c_1484,plain,
$false,
inference(resolve,[status(thm)],[c_1483,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n010.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Sat Sep 26 06:58:36 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.42 % Process 2735438 was started by sandbox2 on n010,
% 0.15/5.42 % Sat Sep 26 06:58:36 2026
% 0.15/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.43
% 0.15/5.43 % From the command line: assign(max_seconds, 300).
% 0.18/5.56
% 0.18/5.56 % SZS status Unsatisfiable for theBenchmark
% 0.18/5.56
% 0.18/5.56 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.18/5.56 % Length of proof is 11.
% 0.18/5.56 % Level of proof is 3.
% 0.18/5.56 % Maximum clause weight is 32.000.
% 0.18/5.56 % Given clauses 255.
% 0.18/5.56
% 0.18/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------