%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET015-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 90.06s 12.70s
% Output : CNFRefutation 90.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 24 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 115 ( 39 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 7 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(membership_in_subsets,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ subset(VAR_1,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',membership_in_subsets) ).
cnf(c_2,plain,
( member(A,C)
| ~ subset(B,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[membership_in_subsets]) ).
fof(subsets_axiom1,axiom,
! [VAR_0,VAR_1] :
( member(member_of_1_not_of_2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subsets_axiom1) ).
cnf(c_3,plain,
( member(member_of_1_not_of_2(A,B),A)
| subset(A,B) ),
inference(clausify,[status(thm)],[subsets_axiom1]) ).
fof(subsets_axiom2,axiom,
! [VAR_0,VAR_1] :
( subset(VAR_0,VAR_1)
| ~ member(member_of_1_not_of_2(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',subsets_axiom2) ).
cnf(c_4,plain,
( subset(A,B)
| ~ member(member_of_1_not_of_2(A,B),B) ),
inference(clausify,[status(thm)],[subsets_axiom2]) ).
fof(member_of_set1_is_member_of_union,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,union(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',member_of_set1_is_member_of_union) ).
cnf(c_7,plain,
( member(A,union(B,C))
| ~ member(A,B) ),
inference(clausify,[status(thm)],[member_of_set1_is_member_of_union]) ).
fof(member_of_set2_is_member_of_union,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,union(VAR_2,VAR_1))
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',member_of_set2_is_member_of_union) ).
cnf(c_8,plain,
( member(A,union(C,B))
| ~ member(A,B) ),
inference(clausify,[status(thm)],[member_of_set2_is_member_of_union]) ).
fof(member_of_union_is_member_of_one_set,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| member(VAR_0,VAR_1)
| ~ member(VAR_0,union(VAR_1,VAR_2)) ),
file('theBenchmark.p',member_of_union_is_member_of_one_set) ).
cnf(c_9,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[member_of_union_is_member_of_one_set]) ).
fof(set_equal_sets_are_subsets1,axiom,
! [VAR_0,VAR_1] :
( subset(VAR_0,VAR_1)
| ~ equal_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_equal_sets_are_subsets1) ).
cnf(c_13,plain,
( subset(A,B)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[set_equal_sets_are_subsets1]) ).
fof(set_equal_sets_are_subsets2,axiom,
! [VAR_0,VAR_1] :
( subset(VAR_1,VAR_0)
| ~ equal_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_equal_sets_are_subsets2) ).
cnf(c_14,plain,
( subset(B,A)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[set_equal_sets_are_subsets2]) ).
fof(subsets_are_set_equal_sets,axiom,
! [VAR_0,VAR_1] :
( equal_sets(VAR_1,VAR_0)
| ~ subset(VAR_1,VAR_0)
| ~ subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subsets_are_set_equal_sets) ).
cnf(c_15,plain,
( equal_sets(B,A)
| ~ subset(B,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subsets_are_set_equal_sets]) ).
fof(symmetry_for_set_equal,axiom,
! [VAR_0,VAR_1] :
( equal_sets(VAR_1,VAR_0)
| ~ equal_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_for_set_equal) ).
cnf(c_17,plain,
( equal_sets(B,A)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[symmetry_for_set_equal]) ).
fof(a_union_b_is_c,axiom,
equal_sets(union(as,bs),cs),
file('theBenchmark.p',a_union_b_is_c) ).
cnf(c_22,plain,
equal_sets(union(as,bs),cs),
inference(clausify,[status(thm)],[a_union_b_is_c]) ).
fof(b_union_a_is_d,axiom,
equal_sets(union(bs,as),ds),
file('theBenchmark.p',b_union_a_is_d) ).
cnf(c_23,plain,
equal_sets(union(bs,as),ds),
inference(clausify,[status(thm)],[b_union_a_is_d]) ).
fof(prove_c_equals_d,axiom,
~ equal_sets(cs,ds),
file('theBenchmark.p',prove_c_equals_d) ).
cnf(c_24,plain,
~ equal_sets(cs,ds),
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_27,plain,
( member(C,B)
| ~ member(C,A)
| member(member_of_1_not_of_2(A,B),A) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_39,plain,
( member(member_of_1_not_of_2(B,A),B)
| equal_sets(A,B)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_40,plain,
( member(member_of_1_not_of_2(B,A),B)
| equal_sets(B,A)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_45,plain,
subset(cs,union(as,bs)),
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_46,plain,
subset(union(as,bs),cs),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_50,plain,
subset(ds,union(bs,as)),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_51,plain,
subset(union(bs,as),ds),
inference(resolve,[status(thm)],[c_23,c_13]) ).
cnf(c_53,plain,
~ equal_sets(ds,cs),
inference(resolve,[status(thm)],[c_17,c_24]) ).
cnf(c_82,plain,
( member(A,union(as,bs))
| ~ member(A,cs) ),
inference(resolve,[status(thm)],[c_45,c_2]) ).
cnf(c_83,plain,
( member(A,cs)
| ~ member(A,union(as,bs)) ),
inference(resolve,[status(thm)],[c_46,c_2]) ).
cnf(c_87,plain,
( member(A,union(bs,as))
| ~ member(A,ds) ),
inference(resolve,[status(thm)],[c_50,c_2]) ).
cnf(c_90,plain,
( member(A,ds)
| ~ member(A,union(bs,as)) ),
inference(resolve,[status(thm)],[c_51,c_2]) ).
cnf(c_273,plain,
( member(member_of_1_not_of_2(A,B),A)
| member(member_of_1_not_of_2(B,A),B)
| equal_sets(A,B) ),
inference(resolve,[status(thm)],[c_39,c_3]) ).
cnf(c_295,plain,
( member(member_of_1_not_of_2(ds,cs),ds)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_273,c_53]) ).
cnf(c_302,plain,
( member(member_of_1_not_of_2(ds,cs),union(bs,as))
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_295,c_87]) ).
cnf(c_315,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(ds,cs),bs)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_302,c_9]) ).
cnf(c_910,plain,
( member(member_of_1_not_of_2(ds,cs),union(A,bs))
| member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_315,c_8]) ).
cnf(c_6267,plain,
( member(member_of_1_not_of_2(ds,cs),cs)
| member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_910,c_83]) ).
cnf(c_6296,plain,
( subset(ds,cs)
| member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_6267,c_4]) ).
cnf(c_27435,plain,
( member(member_of_1_not_of_2(cs,ds),cs)
| equal_sets(cs,ds)
| member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_6296,c_40]) ).
cnf(c_27436,plain,
( equal_sets(cs,ds)
| member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(copy,[status(thm)],[c_27435]) ).
cnf(c_6305,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_24,c_27436]) ).
cnf(c_6318,plain,
( member(member_of_1_not_of_2(ds,cs),union(as,A))
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_6305,c_7]) ).
cnf(c_6394,plain,
( member(member_of_1_not_of_2(ds,cs),cs)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_6318,c_83]) ).
cnf(c_6419,plain,
( subset(ds,cs)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_6394,c_4]) ).
cnf(c_27437,plain,
( member(member_of_1_not_of_2(cs,ds),cs)
| equal_sets(cs,ds)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_6419,c_40]) ).
cnf(c_27438,plain,
( equal_sets(cs,ds)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(copy,[status(thm)],[c_27437]) ).
cnf(c_6424,plain,
member(member_of_1_not_of_2(cs,ds),cs),
inference(resolve,[status(thm)],[c_24,c_27438]) ).
cnf(c_6428,plain,
member(member_of_1_not_of_2(cs,ds),union(as,bs)),
inference(resolve,[status(thm)],[c_6424,c_82]) ).
cnf(c_6431,plain,
( member(member_of_1_not_of_2(cs,ds),A)
| member(member_of_1_not_of_2(cs,A),cs) ),
inference(resolve,[status(thm)],[c_6424,c_27]) ).
cnf(c_6546,plain,
( member(member_of_1_not_of_2(cs,ds),bs)
| member(member_of_1_not_of_2(cs,ds),as) ),
inference(resolve,[status(thm)],[c_6428,c_9]) ).
cnf(c_7016,plain,
( member(member_of_1_not_of_2(cs,ds),union(bs,A))
| member(member_of_1_not_of_2(cs,ds),as) ),
inference(resolve,[status(thm)],[c_6546,c_7]) ).
cnf(c_8402,plain,
( member(member_of_1_not_of_2(cs,ds),ds)
| member(member_of_1_not_of_2(cs,ds),as) ),
inference(resolve,[status(thm)],[c_7016,c_90]) ).
cnf(c_8431,plain,
( subset(cs,ds)
| member(member_of_1_not_of_2(cs,ds),as) ),
inference(resolve,[status(thm)],[c_8402,c_4]) ).
cnf(c_8440,plain,
( member(A,ds)
| ~ member(A,cs)
| member(member_of_1_not_of_2(cs,ds),as) ),
inference(resolve,[status(thm)],[c_8431,c_2]) ).
cnf(c_8566,plain,
( member(member_of_1_not_of_2(cs,ds),A)
| member(member_of_1_not_of_2(cs,A),ds)
| member(member_of_1_not_of_2(cs,ds),as) ),
inference(resolve,[status(thm)],[c_8440,c_6431]) ).
cnf(c_24535,plain,
( member(member_of_1_not_of_2(cs,ds),union(B,as))
| member(member_of_1_not_of_2(cs,ds),A)
| member(member_of_1_not_of_2(cs,A),ds) ),
inference(resolve,[status(thm)],[c_8566,c_8]) ).
cnf(c_24558,plain,
( member(member_of_1_not_of_2(cs,ds),union(A,as))
| member(member_of_1_not_of_2(cs,ds),ds) ),
inference(factor,[status(thm)],[c_24535]) ).
cnf(c_27439,plain,
( member(member_of_1_not_of_2(cs,ds),ds)
| member(member_of_1_not_of_2(cs,ds),ds) ),
inference(resolve,[status(thm)],[c_24558,c_90]) ).
cnf(c_24739,plain,
member(member_of_1_not_of_2(cs,ds),ds),
inference(copy,[status(thm)],[c_27439]) ).
cnf(c_24755,plain,
subset(cs,ds),
inference(resolve,[status(thm)],[c_24739,c_4]) ).
cnf(c_27440,plain,
( member(member_of_1_not_of_2(ds,cs),ds)
| equal_sets(ds,cs) ),
inference(resolve,[status(thm)],[c_24755,c_40]) ).
cnf(c_24820,plain,
member(member_of_1_not_of_2(ds,cs),ds),
inference(resolve,[status(thm)],[c_53,c_27440]) ).
cnf(c_27441,plain,
( equal_sets(cs,ds)
| ~ subset(ds,cs) ),
inference(resolve,[status(thm)],[c_24755,c_15]) ).
cnf(c_24821,plain,
~ subset(ds,cs),
inference(resolve,[status(thm)],[c_24,c_27441]) ).
cnf(c_24829,plain,
~ member(member_of_1_not_of_2(ds,cs),cs),
inference(resolve,[status(thm)],[c_4,c_24821]) ).
cnf(c_24921,plain,
member(member_of_1_not_of_2(ds,cs),union(bs,as)),
inference(resolve,[status(thm)],[c_24820,c_87]) ).
cnf(c_25250,plain,
~ member(member_of_1_not_of_2(ds,cs),union(as,bs)),
inference(resolve,[status(thm)],[c_83,c_24829]) ).
cnf(c_25669,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(ds,cs),bs) ),
inference(resolve,[status(thm)],[c_24921,c_9]) ).
cnf(c_27432,plain,
~ member(member_of_1_not_of_2(ds,cs),bs),
inference(resolve,[status(thm)],[c_8,c_25250]) ).
cnf(c_27433,plain,
~ member(member_of_1_not_of_2(ds,cs),as),
inference(resolve,[status(thm)],[c_7,c_25250]) ).
cnf(c_27442,plain,
member(member_of_1_not_of_2(ds,cs),as),
inference(resolve,[status(thm)],[c_27432,c_25669]) ).
cnf(c_27434,plain,
$false,
inference(resolve,[status(thm)],[c_27433,c_27442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET015-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 06:48:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3034723 was started by sandbox on n007,
% 0.09/0.36 % Sat Sep 26 06:48:24 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 90.06/12.70
% 90.06/12.70 % given #500 (F,wt=25): 2082 -equal_sets(union(intersection(empty_set,A),intersection(empty_set,B)),complement(empty_set)). [ur(301,a,64,a,b,544,a,d,887,a)].
% 90.06/12.70
% 90.06/12.70 % given #1000 (F,wt=21): 9340 -equal_sets(cs,complement(intersection(cs,cs))). [ur(13,b,9094,a)].
% 90.06/12.70
% 90.06/12.70 % given #1500 (F,wt=23): 15883 -equal_sets(complement(cs),intersection(cs,union(A,cs))). [ur(14,b,14999,a)].
% 90.06/12.70
% 90.06/12.70 % given #2000 (F,wt=23): 19541 -equal_sets(intersection(complement(empty_set),union(A,cs)),empty_set). [ur(13,b,19416,a)].
% 90.06/12.70
% 90.06/12.70 % given #2500 (F,wt=25): 12207 -equal_sets(union(complement(cs),empty_set),intersection(complement(empty_set),complement(empty_set))). [ur(702,b,12201,a)].
% 90.06/12.70
% 90.06/12.70 % given #3000 (F,wt=15): 25713 -subset(union(ds,A),cs). [ur(2,a,24929,a,c,24829,a)].
% 90.06/12.70
% 90.06/12.70 % SZS status Unsatisfiable for theBenchmark
% 90.06/12.70
% 90.06/12.70 % Proof 1 at 3.00 (+ 1.28) seconds.
% 90.06/12.70 % Length of proof is 58.
% 90.06/12.70 % Level of proof is 29.
% 90.06/12.70 % Maximum clause weight is 27.000.
% 90.06/12.70 % Given clauses 3169.
% 90.06/12.70
% 90.06/12.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------