%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET592+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:36:33 AM UTC 2026
% Result : Theorem 0.17s 5.42s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 43 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 15 ~; 6 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 10 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_empty_set_is_empty_set,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('theBenchmark.p',subset_of_empty_set_is_empty_set) ).
fof(intersection_of_subsets,axiom,
! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
file('theBenchmark.p',intersection_of_subsets) ).
fof(prove_th51,conjecture,
! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
file('theBenchmark.p',prove_th51) ).
fof(prove_th51_neg,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
inference(assume_negation,[status(cth)],[prove_th51]) ).
fof(nnf_11,plain,
? [B,C,D] :
( empty_set != B
& intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th51_neg]) ).
fof(sk_prove_th51_neg,plain,
( empty_set != sK0
& intersection(sK1,sK2) = empty_set
& subset(sK0,sK2)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2)],[nnf_11]) ).
cnf(c_15,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_prove_th51_neg]) ).
cnf(c_16,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,negated_conjecture,
intersection(sK1,sK2) = empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th51_neg]) ).
cnf(c_18,negated_conjecture,
empty_set = intersection(sK1,sK2),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_19,negated_conjecture,
subset(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th51_neg]) ).
cnf(c_20,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th51_neg]) ).
cnf(c_38,plain,
( subset(A,intersection(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[intersection_of_subsets]) ).
cnf(c_39,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[subset_of_empty_set_is_empty_set]) ).
cnf(c_140,plain,
( empty_set = A
| ~ subset(A,intersection(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_18,c_39]) ).
cnf(c_40,plain,
( intersection(sK1,sK2) = A
| ~ subset(A,intersection(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_18,c_140]) ).
cnf(c_141,negated_conjecture,
sK0 != intersection(sK1,sK2),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_41,negated_conjecture,
intersection(sK1,sK2) != sK0,
inference(copy,[status(thm)],[c_141]) ).
cnf(c_94,negated_conjecture,
~ subset(sK0,intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_40,c_41]) ).
cnf(c_142,negated_conjecture,
( subset(sK0,intersection(A,sK2))
| ~ subset(sK0,A) ),
inference(resolve,[status(thm)],[c_38,c_19]) ).
cnf(c_143,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_142,c_94]) ).
cnf(c_139,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_20,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET592+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.39 % Computer : n008.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Sat Sep 26 07:59:00 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.40 % Process 3141077 was started by sandbox on n008,
% 0.13/5.40 % Sat Sep 26 07:59:00 2026
% 0.13/5.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.41
% 0.17/5.41 % From the command line: assign(max_seconds, 300).
% 0.17/5.42
% 0.17/5.42 % SZS status Theorem for theBenchmark
% 0.17/5.42
% 0.17/5.42 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/5.42 % Length of proof is 15.
% 0.17/5.42 % Level of proof is 5.
% 0.17/5.42 % Maximum clause weight is 21.000.
% 0.17/5.42 % Given clauses 29.
% 0.17/5.42
% 0.17/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------