%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET022-3 : 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 : 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 08:35:22 AM UTC 2026
% Result : Unsatisfiable 19.26s 3.18s
% Output : CNFRefutation 19.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 67 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_first_component_is_small,axiom,
~ little_set(first(a)),
file('theBenchmark.p',prove_first_component_is_small) ).
cnf(c_64,plain,
~ little_set(first(a)),
inference(clausify,[status(thm)],[prove_first_component_is_small]) ).
fof(an_ordered_pair_predicate,axiom,
ordered_pair_predicate(a),
file('theBenchmark.p',an_ordered_pair_predicate) ).
cnf(c_65,plain,
ordered_pair_predicate(a),
inference(clausify,[status(thm)],[an_ordered_pair_predicate]) ).
fof(property_of_second,axiom,
! [VAR_0,VAR_1] :
( second(ordered_pair(VAR_0,VAR_1)) = VAR_1
| ~ little_set(VAR_1)
| ~ little_set(VAR_0) ),
file('theBenchmark.p',property_of_second) ).
cnf(c_66,plain,
( second(ordered_pair(A,B)) = B
| ~ little_set(B)
| ~ little_set(A) ),
inference(clausify,[status(thm)],[property_of_second]) ).
fof(property_of_first,axiom,
! [VAR_0,VAR_1] :
( first(ordered_pair(VAR_0,VAR_1)) = VAR_0
| ~ little_set(VAR_1)
| ~ little_set(VAR_0) ),
file('theBenchmark.p',property_of_first) ).
cnf(c_67,plain,
( first(ordered_pair(A,B)) = A
| ~ little_set(B)
| ~ little_set(A) ),
inference(clausify,[status(thm)],[property_of_first]) ).
fof(ordered_pair_predicate3,axiom,
! [VAR_0] :
( VAR_0 = ordered_pair(f2(VAR_0),f3(VAR_0))
| ~ ordered_pair_predicate(VAR_0) ),
file('theBenchmark.p',ordered_pair_predicate3) ).
cnf(c_186,plain,
( A = ordered_pair(f2(A),f3(A))
| ~ ordered_pair_predicate(A) ),
inference(clausify,[status(thm)],[ordered_pair_predicate3]) ).
cnf(c_187,plain,
( ordered_pair(f2(A),f3(A)) = A
| ~ ordered_pair_predicate(A) ),
inference(copy,[status(thm)],[c_186]) ).
fof(ordered_pair_predicate2,axiom,
! [VAR_0] :
( little_set(f3(VAR_0))
| ~ ordered_pair_predicate(VAR_0) ),
file('theBenchmark.p',ordered_pair_predicate2) ).
cnf(c_188,plain,
( little_set(f3(A))
| ~ ordered_pair_predicate(A) ),
inference(clausify,[status(thm)],[ordered_pair_predicate2]) ).
fof(ordered_pair_predicate1,axiom,
! [VAR_0] :
( little_set(f2(VAR_0))
| ~ ordered_pair_predicate(VAR_0) ),
file('theBenchmark.p',ordered_pair_predicate1) ).
cnf(c_189,plain,
( little_set(f2(A))
| ~ ordered_pair_predicate(A) ),
inference(clausify,[status(thm)],[ordered_pair_predicate1]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : ordered_pair(VAR_0,VAR_1) = non_ordered_pair(singleton_set(VAR_0),non_ordered_pair(VAR_0,VAR_1)),
file('theBenchmark.p',ordered_pair) ).
cnf(c_190,plain,
ordered_pair(A,B) = non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),
inference(clausify,[status(thm)],[ordered_pair]) ).
fof(singleton_set,axiom,
! [VAR_0] : singleton_set(VAR_0) = non_ordered_pair(VAR_0,VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_191,plain,
singleton_set(A) = non_ordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_1709,plain,
( non_ordered_pair(singleton_set(f2(A)),non_ordered_pair(f2(A),f3(A))) = A
| ~ ordered_pair_predicate(A) ),
inference(paramod,[status(thm)],[c_190,c_187]) ).
cnf(c_314,plain,
( non_ordered_pair(non_ordered_pair(f2(A),f2(A)),non_ordered_pair(f2(A),f3(A))) = A
| ~ ordered_pair_predicate(A) ),
inference(paramod,[status(thm)],[c_191,c_1709]) ).
cnf(c_1710,plain,
( first(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B))) = A
| ~ little_set(B)
| ~ little_set(A) ),
inference(paramod,[status(thm)],[c_190,c_67]) ).
cnf(c_336,plain,
( first(non_ordered_pair(non_ordered_pair(A,A),non_ordered_pair(A,B))) = A
| ~ little_set(B)
| ~ little_set(A) ),
inference(paramod,[status(thm)],[c_191,c_1710]) ).
cnf(c_1711,plain,
( second(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B))) = B
| ~ little_set(B)
| ~ little_set(A) ),
inference(paramod,[status(thm)],[c_190,c_66]) ).
cnf(c_337,plain,
( second(non_ordered_pair(non_ordered_pair(A,A),non_ordered_pair(A,B))) = B
| ~ little_set(B)
| ~ little_set(A) ),
inference(paramod,[status(thm)],[c_191,c_1711]) ).
cnf(c_460,plain,
little_set(f3(a)),
inference(resolve,[status(thm)],[c_188,c_65]) ).
cnf(c_461,plain,
little_set(f2(a)),
inference(resolve,[status(thm)],[c_189,c_65]) ).
cnf(c_805,plain,
non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f3(a))) = a,
inference(resolve,[status(thm)],[c_314,c_65]) ).
cnf(c_1712,plain,
( second(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),A))) = A
| ~ little_set(A) ),
inference(resolve,[status(thm)],[c_337,c_461]) ).
cnf(c_1713,plain,
second(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f3(a)))) = f3(a),
inference(resolve,[status(thm)],[c_1712,c_460]) ).
cnf(c_1714,plain,
second(a) = f3(a),
inference(paramod,[status(thm)],[c_805,c_1713]) ).
cnf(c_1434,plain,
f3(a) = second(a),
inference(copy,[status(thm)],[c_1714]) ).
cnf(c_1715,plain,
( first(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),A))) = f2(a)
| ~ little_set(A) ),
inference(resolve,[status(thm)],[c_336,c_461]) ).
cnf(c_1716,plain,
first(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f3(a)))) = f2(a),
inference(resolve,[status(thm)],[c_1715,c_460]) ).
cnf(c_1448,plain,
first(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),second(a)))) = f2(a),
inference(paramod,[status(thm)],[c_1434,c_1716]) ).
cnf(c_1594,plain,
non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),second(a))) = a,
inference(paramod,[status(thm)],[c_1434,c_805]) ).
cnf(c_1717,plain,
first(a) = f2(a),
inference(paramod,[status(thm)],[c_1594,c_1448]) ).
cnf(c_1602,plain,
f2(a) = first(a),
inference(copy,[status(thm)],[c_1717]) ).
cnf(c_1718,plain,
little_set(first(a)),
inference(paramod,[status(thm)],[c_1602,c_461]) ).
cnf(c_1708,plain,
$false,
inference(resolve,[status(thm)],[c_64,c_1718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 06:52:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1049236 was started by sandbox on n004,
% 0.13/0.36 % Sat Sep 26 06:52:51 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 19.26/3.18
% 19.26/3.18 % SZS status Unsatisfiable for theBenchmark
% 19.26/3.18
% 19.26/3.18 % Proof 1 at 2.65 (+ 0.08) seconds.
% 19.26/3.18 % Length of proof is 21.
% 19.26/3.18 % Level of proof is 7.
% 19.26/3.18 % Maximum clause weight is 50.000.
% 19.26/3.18 % Given clauses 259.
% 19.26/3.18
% 19.26/3.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------