%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:35:18 AM UTC 2026
% Result : Unsatisfiable 18.14s 7.77s
% Output : CNFRefutation 18.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 77 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 34 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| ~ little_set(VAR_0)
| member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement2) ).
cnf(c_1,plain,
( member(A,B)
| ~ little_set(A)
| member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(a2,axiom,
! [VAR_0,VAR_1] :
( little_set(VAR_0)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',a2) ).
cnf(c_3,plain,
( little_set(A)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[a2]) ).
cnf(c_7,plain,
( ~ member(A,C)
| member(A,B)
| member(A,complement(B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(prove_a_union_b_subset_of_c,axiom,
~ subset(union(as,bs),cs),
file('theBenchmark.p',prove_a_union_b_subset_of_c) ).
cnf(c_9,plain,
~ subset(union(as,bs),cs),
inference(clausify,[status(thm)],[prove_a_union_b_subset_of_c]) ).
fof(b_subset_of_c,axiom,
subset(bs,cs),
file('theBenchmark.p',b_subset_of_c) ).
cnf(c_10,plain,
subset(bs,cs),
inference(clausify,[status(thm)],[b_subset_of_c]) ).
fof(a_subset_of_c,axiom,
subset(as,cs),
file('theBenchmark.p',a_subset_of_c) ).
cnf(c_11,plain,
subset(as,cs),
inference(clausify,[status(thm)],[a_subset_of_c]) ).
fof(subset3,axiom,
! [VAR_0,VAR_1] :
( ~ member(f17(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subset3) ).
cnf(c_12,plain,
( ~ member(f17(A,B),B)
| subset(A,B) ),
inference(clausify,[status(thm)],[subset3]) ).
fof(subset2,axiom,
! [VAR_0,VAR_1] :
( member(f17(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subset2) ).
cnf(c_13,plain,
( member(f17(A,B),A)
| subset(A,B) ),
inference(clausify,[status(thm)],[subset2]) ).
fof(subset1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subset1) ).
cnf(c_14,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset1]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : union(VAR_0,VAR_1) = complement(intersection(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',union) ).
cnf(c_16,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(clausify,[status(thm)],[union]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_17,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1)
| member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection3) ).
cnf(c_18,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection3]) ).
cnf(c_24,plain,
~ member(f17(union(as,bs),cs),cs),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_27,plain,
( member(f17(A,B),C)
| member(f17(A,B),complement(C))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_13,c_7]) ).
cnf(c_31,plain,
( member(A,cs)
| ~ member(A,bs) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_34,plain,
~ subset(complement(intersection(complement(as),complement(bs))),cs),
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_35,plain,
( subset(complement(A),B)
| ~ member(f17(complement(A),B),A) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_11005,plain,
( member(A,cs)
| ~ member(A,as) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_87,plain,
~ member(f17(union(as,bs),cs),as),
inference(resolve,[status(thm)],[c_11005,c_24]) ).
cnf(c_89,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),cs),
inference(paramod,[status(thm)],[c_16,c_24]) ).
cnf(c_137,plain,
( ~ member(f17(A,B),D)
| member(f17(A,B),intersection(complement(C),D))
| member(f17(A,B),C)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_27,c_18]) ).
cnf(c_141,plain,
( member(f17(A,B),cs)
| member(f17(A,B),complement(bs))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_27,c_31]) ).
cnf(c_180,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),as),
inference(paramod,[status(thm)],[c_16,c_87]) ).
cnf(c_224,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),intersection(complement(as),complement(bs))),
inference(resolve,[status(thm)],[c_35,c_34]) ).
cnf(c_11006,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),cs)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)) ),
inference(resolve,[status(thm)],[c_141,c_34]) ).
cnf(c_5153,plain,
member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)),
inference(resolve,[status(thm)],[c_89,c_11006]) ).
cnf(c_11007,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),B)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),intersection(complement(A),B))
| member(f17(complement(intersection(complement(as),complement(bs))),cs),A) ),
inference(resolve,[status(thm)],[c_137,c_34]) ).
cnf(c_11008,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),A)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),intersection(complement(as),A)) ),
inference(resolve,[status(thm)],[c_11007,c_180]) ).
cnf(c_11009,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)),
inference(resolve,[status(thm)],[c_11008,c_224]) ).
cnf(c_11004,plain,
$false,
inference(resolve,[status(thm)],[c_5153,c_11009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.41 % Computer : n002.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 06:52:56 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.41 % Process 1054513 was started by sandbox on n002,
% 0.14/5.41 % Sat Sep 26 06:52:56 2026
% 0.14/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.41
% 0.14/5.41 % From the command line: assign(max_seconds, 300).
% 18.14/7.77
% 18.14/7.77 % given #500 (W,wt=19): 9025 empty_set = A | member(f17(A,empty_set),complement(empty_set)). [resolve(8948,a,717,a)].
% 18.14/7.77
% 18.14/7.77 % SZS status Unsatisfiable for theBenchmark
% 18.14/7.77
% 18.14/7.77 % Proof 1 at 1.76 (+ 0.58) seconds.
% 18.14/7.77 % Length of proof is 25.
% 18.14/7.77 % Level of proof is 5.
% 18.14/7.77 % Maximum clause weight is 39.000.
% 18.14/7.77 % Given clauses 631.
% 18.14/7.77
% 18.14/7.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------