%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET007-1 : 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 : n009.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 08:35:15 AM UTC 2026
% Result : Unsatisfiable 50.19s 6.88s
% Output : CNFRefutation 50.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 82 ( 19 unt; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 180 ( 73 ~; 107 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 100 ( 4 sgn 40 !; 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_4,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_5,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_6,plain,
( subset(A,B)
| ~ member(member_of_1_not_of_2(A,B),B) ),
inference(clausify,[status(thm)],[subsets_axiom2]) ).
fof(union_axiom1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(g(VAR_0,VAR_1,VAR_2),VAR_2)
| member(g(VAR_0,VAR_1,VAR_2),VAR_1)
| member(g(VAR_0,VAR_1,VAR_2),VAR_0)
| union(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',union_axiom1) ).
cnf(c_7,plain,
( member(g(A,B,C),C)
| member(g(A,B,C),B)
| member(g(A,B,C),A)
| union(A,B,C) ),
inference(clausify,[status(thm)],[union_axiom1]) ).
fof(member_of_set2_is_member_of_union,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_2)
| ~ member(VAR_3,VAR_1)
| ~ union(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_set2_is_member_of_union) ).
cnf(c_8,plain,
( member(D,C)
| ~ member(D,B)
| ~ union(A,B,C) ),
inference(clausify,[status(thm)],[member_of_set2_is_member_of_union]) ).
fof(member_of_set1_is_member_of_union,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_2)
| ~ member(VAR_3,VAR_0)
| ~ union(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_set1_is_member_of_union) ).
cnf(c_9,plain,
( member(D,C)
| ~ member(D,A)
| ~ union(A,B,C) ),
inference(clausify,[status(thm)],[member_of_set1_is_member_of_union]) ).
fof(member_of_union_is_member_of_one_set,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_1)
| member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ union(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_union_is_member_of_one_set) ).
cnf(c_10,plain,
( member(D,B)
| member(D,A)
| ~ member(D,C)
| ~ union(A,B,C) ),
inference(clausify,[status(thm)],[member_of_union_is_member_of_one_set]) ).
fof(union_axiom2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( union(VAR_0,VAR_1,VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_0) ),
file('theBenchmark.p',union_axiom2) ).
cnf(c_11,plain,
( union(A,B,C)
| ~ member(g(A,B,C),C)
| ~ member(g(A,B,C),A) ),
inference(clausify,[status(thm)],[union_axiom2]) ).
fof(union_axiom3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( union(VAR_0,VAR_1,VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_1) ),
file('theBenchmark.p',union_axiom3) ).
cnf(c_12,plain,
( union(A,B,C)
| ~ member(g(A,B,C),C)
| ~ member(g(A,B,C),B) ),
inference(clausify,[status(thm)],[union_axiom3]) ).
fof(b_union_c,axiom,
union(b,c,bUc),
file('theBenchmark.p',b_union_c) ).
cnf(c_13,plain,
union(b,c,bUc),
inference(clausify,[status(thm)],[b_union_c]) ).
fof(prove_aIb_union_aIc_is_aI_bUc,axiom,
~ union(aIb,aIc,aI_bUc),
file('theBenchmark.p',prove_aIb_union_aIc_is_aI_bUc) ).
cnf(c_14,plain,
~ union(aIb,aIc,aI_bUc),
inference(clausify,[status(thm)],[prove_aIb_union_aIc_is_aI_bUc]) ).
fof(member_of_both_is_member_of_intersection,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_2)
| ~ member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_1)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_both_is_member_of_intersection) ).
cnf(c_15,plain,
( member(D,C)
| ~ member(D,A)
| ~ member(D,B)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_both_is_member_of_intersection]) ).
fof(a_intersection_b,axiom,
intersection(a,b,aIb),
file('theBenchmark.p',a_intersection_b) ).
cnf(c_19,plain,
intersection(a,b,aIb),
inference(clausify,[status(thm)],[a_intersection_b]) ).
fof(a_intersection_c,axiom,
intersection(a,c,aIc),
file('theBenchmark.p',a_intersection_c) ).
cnf(c_20,plain,
intersection(a,c,aIc),
inference(clausify,[status(thm)],[a_intersection_c]) ).
fof(a_intersection_bUc,axiom,
intersection(a,bUc,aI_bUc),
file('theBenchmark.p',a_intersection_bUc) ).
cnf(c_21,plain,
intersection(a,bUc,aI_bUc),
inference(clausify,[status(thm)],[a_intersection_bUc]) ).
fof(member_of_intersection_is_member_of_set2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_1)
| ~ member(VAR_3,VAR_2)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set2) ).
cnf(c_22,plain,
( member(D,B)
| ~ member(D,C)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set2]) ).
fof(member_of_intersection_is_member_of_set1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set1) ).
cnf(c_23,plain,
( member(D,A)
| ~ member(D,C)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set1]) ).
cnf(c_24,plain,
( member(A,a)
| ~ member(A,aI_bUc) ),
inference(resolve,[status(thm)],[c_23,c_21]) ).
cnf(c_25,plain,
( member(A,a)
| ~ member(A,aIc) ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_26,plain,
( member(A,a)
| ~ member(A,aIb) ),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_30,plain,
( member(A,bUc)
| ~ member(A,aI_bUc) ),
inference(resolve,[status(thm)],[c_22,c_21]) ).
cnf(c_31,plain,
( member(A,c)
| ~ member(A,aIc) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_32,plain,
( member(A,b)
| ~ member(A,aIb) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_36,plain,
( member(A,aI_bUc)
| ~ member(A,a)
| ~ member(A,bUc) ),
inference(resolve,[status(thm)],[c_15,c_21]) ).
cnf(c_37,plain,
( member(A,aIc)
| ~ member(A,a)
| ~ member(A,c) ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_38,plain,
( member(A,aIb)
| ~ member(A,a)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_42,plain,
( ~ member(member_of_1_not_of_2(B,C),C)
| member(A,C)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_43,plain,
( member(member_of_1_not_of_2(B,C),B)
| member(A,C)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_53,plain,
( member(A,bUc)
| ~ member(A,c) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_54,plain,
( member(A,bUc)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_13,c_9]) ).
cnf(c_55,plain,
( member(A,c)
| member(A,b)
| ~ member(A,bUc) ),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_56,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[status(thm)],[c_14,c_12]) ).
cnf(c_57,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_58,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_75,plain,
( member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[status(thm)],[c_58,c_32]) ).
cnf(c_76,plain,
( member(g(aIb,aIc,aI_bUc),a)
| member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[status(thm)],[c_58,c_26]) ).
cnf(c_254,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[status(thm)],[c_75,c_30]) ).
cnf(c_22436,plain,
( member(g(aIb,aIc,aI_bUc),a)
| member(g(aIb,aIc,aI_bUc),a)
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(resolve,[status(thm)],[c_76,c_25]) ).
cnf(c_306,plain,
( member(g(aIb,aIc,aI_bUc),a)
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(copy,[status(thm)],[c_22436]) ).
cnf(c_22437,plain,
( member(g(aIb,aIc,aI_bUc),a)
| member(g(aIb,aIc,aI_bUc),a) ),
inference(resolve,[status(thm)],[c_306,c_24]) ).
cnf(c_360,plain,
member(g(aIb,aIc,aI_bUc),a),
inference(copy,[status(thm)],[c_22437]) ).
cnf(c_22438,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(resolve,[status(thm)],[c_306,c_36]) ).
cnf(c_382,plain,
( ~ member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(copy,[status(thm)],[c_22438]) ).
cnf(c_441,plain,
( member(g(aIb,aIc,aI_bUc),aIb)
| ~ member(g(aIb,aIc,aI_bUc),b) ),
inference(resolve,[status(thm)],[c_360,c_38]) ).
cnf(c_442,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| ~ member(g(aIb,aIc,aI_bUc),c) ),
inference(resolve,[status(thm)],[c_360,c_37]) ).
cnf(c_22439,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[status(thm)],[c_254,c_54]) ).
cnf(c_17976,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(copy,[status(thm)],[c_22439]) ).
cnf(c_22440,plain,
( member(g(aIb,aIc,aI_bUc),c)
| member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[status(thm)],[c_254,c_55]) ).
cnf(c_17977,plain,
( member(g(aIb,aIc,aI_bUc),c)
| member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(copy,[status(thm)],[c_22440]) ).
cnf(c_20295,plain,
( member(member_of_1_not_of_2(aIc,A),aIc)
| member(g(aIb,aIc,aI_bUc),A)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(resolve,[status(thm)],[c_17976,c_43]) ).
cnf(c_20296,plain,
( ~ member(member_of_1_not_of_2(aIc,A),A)
| member(g(aIb,aIc,aI_bUc),A)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(resolve,[status(thm)],[c_17976,c_42]) ).
cnf(c_20345,plain,
( member(member_of_1_not_of_2(aIc,bUc),aIc)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(factor,[status(thm)],[c_20295]) ).
cnf(c_20346,plain,
( ~ member(member_of_1_not_of_2(aIc,bUc),bUc)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(factor,[status(thm)],[c_20296]) ).
cnf(c_20497,plain,
( member(member_of_1_not_of_2(aIc,bUc),c)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(resolve,[status(thm)],[c_20345,c_31]) ).
cnf(c_20792,plain,
( member(member_of_1_not_of_2(aIc,bUc),bUc)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(resolve,[status(thm)],[c_20497,c_53]) ).
cnf(c_22441,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(resolve,[status(thm)],[c_20792,c_20346]) ).
cnf(c_22025,plain,
member(g(aIb,aIc,aI_bUc),bUc),
inference(copy,[status(thm)],[c_22441]) ).
cnf(c_22026,plain,
member(g(aIb,aIc,aI_bUc),aI_bUc),
inference(resolve,[status(thm)],[c_22025,c_382]) ).
cnf(c_22073,plain,
~ member(g(aIb,aIc,aI_bUc),aIb),
inference(resolve,[status(thm)],[c_22026,c_57]) ).
cnf(c_22074,plain,
~ member(g(aIb,aIc,aI_bUc),aIc),
inference(resolve,[status(thm)],[c_22026,c_56]) ).
cnf(c_22275,plain,
~ member(g(aIb,aIc,aI_bUc),b),
inference(resolve,[status(thm)],[c_22073,c_441]) ).
cnf(c_22442,plain,
( member(g(aIb,aIc,aI_bUc),c)
| member(g(aIb,aIc,aI_bUc),b) ),
inference(resolve,[status(thm)],[c_22074,c_17977]) ).
cnf(c_22403,plain,
member(g(aIb,aIc,aI_bUc),c),
inference(resolve,[status(thm)],[c_22275,c_22442]) ).
cnf(c_22443,plain,
member(g(aIb,aIc,aI_bUc),aIc),
inference(resolve,[status(thm)],[c_22403,c_442]) ).
cnf(c_22435,plain,
$false,
inference(resolve,[status(thm)],[c_22074,c_22443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:48:14 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 3589584 was started by sandbox on n009,
% 0.09/0.36 % Sat Sep 26 06:48:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 50.19/6.88
% 50.19/6.88 % given #500 (T,wt=16): 7671 member(h(a,aIc,a),a) | member(g(aIb,aIc,aI_bUc),c). [resolve(5691,b,436,b)].
% 50.19/6.88
% 50.19/6.88 % SZS status Unsatisfiable for theBenchmark
% 50.19/6.88
% 50.19/6.88 % Proof 1 at 4.77 (+ 1.47) seconds.
% 50.19/6.88 % Length of proof is 57.
% 50.19/6.88 % Level of proof is 14.
% 50.19/6.88 % Maximum clause weight is 22.000.
% 50.19/6.88 % Given clauses 733.
% 50.19/6.88
% 50.19/6.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------