%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:35:14 AM UTC 2026
% Result : Unsatisfiable 0.15s 15.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 24 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,plain,
( equal_sets(B,A)
| ~ subset(B,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subsets_are_set_equal_sets]) ).
fof(prove_a_equals_aUa,axiom,
~ equal_sets(aUa,a),
file('theBenchmark.p',prove_a_equals_aUa) ).
cnf(c_4,plain,
~ equal_sets(aUa,a),
inference(clausify,[status(thm)],[prove_a_equals_aUa]) ).
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_5,plain,
( member(D,C)
| ~ member(D,B)
| ~ union(A,B,C) ),
inference(clausify,[status(thm)],[member_of_set2_is_member_of_union]) ).
fof(a_union_a_is_aUa,axiom,
union(a,a,aUa),
file('theBenchmark.p',a_union_a_is_aUa) ).
cnf(c_9,plain,
union(a,a,aUa),
inference(clausify,[status(thm)],[a_union_a_is_aUa]) ).
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_11,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]) ).
cnf(c_12,plain,
( member(A,a)
| member(A,a)
| ~ member(A,aUa) ),
inference(resolve,[status(thm)],[c_11,c_9]) ).
cnf(c_13,plain,
( member(A,a)
| ~ member(A,aUa) ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_20,plain,
( member(A,aUa)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_5,c_9]) ).
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_25,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_26,plain,
( subset(A,B)
| ~ member(member_of_1_not_of_2(A,B),B) ),
inference(clausify,[status(thm)],[subsets_axiom2]) ).
cnf(c_27,plain,
( ~ subset(aUa,a)
| ~ subset(a,aUa) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_40,plain,
( member(member_of_1_not_of_2(a,A),aUa)
| subset(a,A) ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
cnf(c_55,plain,
( member(member_of_1_not_of_2(aUa,a),aUa)
| ~ subset(a,aUa) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_100,plain,
( subset(a,aUa)
| subset(a,aUa) ),
inference(resolve,[status(thm)],[c_40,c_26]) ).
cnf(c_69,plain,
subset(a,aUa),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_79,plain,
member(member_of_1_not_of_2(aUa,a),aUa),
inference(resolve,[status(thm)],[c_69,c_55]) ).
cnf(c_80,plain,
~ subset(aUa,a),
inference(resolve,[status(thm)],[c_69,c_27]) ).
cnf(c_98,plain,
member(member_of_1_not_of_2(aUa,a),a),
inference(resolve,[status(thm)],[c_79,c_13]) ).
cnf(c_101,plain,
~ member(member_of_1_not_of_2(aUa,a),a),
inference(resolve,[status(thm)],[c_26,c_80]) ).
cnf(c_99,plain,
$false,
inference(resolve,[status(thm)],[c_98,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n013.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Sat Sep 26 06:46:59 UTC 2026
% 0.15/15.40 % CPUTime :
% 0.15/15.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/15.40 % Process 2143457 was started by sandbox2 on n013,
% 0.15/15.40 % Sat Sep 26 06:46:59 2026
% 0.15/15.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/15.40
% 0.15/15.40 % From the command line: assign(max_seconds, 300).
% 0.15/15.42
% 0.15/15.42 % SZS status Unsatisfiable for theBenchmark
% 0.15/15.42
% 0.15/15.42 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/15.42 % Length of proof is 18.
% 0.15/15.42 % Level of proof is 6.
% 0.15/15.42 % Maximum clause weight is 12.000.
% 0.15/15.42 % Given clauses 29.
% 0.15/15.42
% 0.15/15.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------