%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET014+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:35:17 AM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 65 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 20 |; 12 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(prove_union_subset,conjecture,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('theBenchmark.p',prove_union_subset) ).
fof(prove_union_subset_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
inference(assume_negation,[status(cth)],[prove_union_subset]) ).
cnf(c_7,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
fof(nnf_2,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(sk_subset_defn_sk,plain,
! [B,C] :
( ( ( ~ member(sK0(B,C),C)
& member(sK0(B,C),B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(B,C))],[nnf_2]) ).
fof(sk_subset_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subset_defn_sk]) ).
cnf(c_10,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_11,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_12,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_13,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
fof(nnf_6,plain,
? [B,C,D] :
( ~ subset(union(B,D),C)
& subset(D,C)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_union_subset_neg]) ).
fof(sk_prove_union_subset_neg,plain,
( ~ subset(union(sK1,sK3),sK2)
& subset(sK3,sK2)
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_6]) ).
cnf(c_19,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_union_subset_neg]) ).
cnf(c_20,negated_conjecture,
subset(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_union_subset_neg]) ).
cnf(c_21,negated_conjecture,
~ subset(union(sK1,sK3),sK2),
inference(split_conjunct,[status(thm)],[sk_prove_union_subset_neg]) ).
cnf(c_50,plain,
member(sK0(union(sK1,sK3),sK2),union(sK1,sK3)),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_51,negated_conjecture,
~ member(sK0(union(sK1,sK3),sK2),sK2),
inference(resolve,[status(thm)],[c_12,c_21]) ).
cnf(c_63,negated_conjecture,
( member(A,sK2)
| ~ member(A,sK3) ),
inference(resolve,[status(thm)],[c_10,c_20]) ).
cnf(c_57,negated_conjecture,
~ member(sK0(union(sK1,sK3),sK2),sK3),
inference(resolve,[status(thm)],[c_63,c_51]) ).
cnf(c_64,negated_conjecture,
( member(A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_10,c_19]) ).
cnf(c_58,negated_conjecture,
~ member(sK0(union(sK1,sK3),sK2),sK1),
inference(resolve,[status(thm)],[c_64,c_51]) ).
cnf(c_65,plain,
( member(sK0(union(sK1,sK3),sK2),A)
| ~ member(sK0(union(sK1,sK3),sK2),union(sK3,A)) ),
inference(resolve,[status(thm)],[c_7,c_57]) ).
cnf(c_66,plain,
~ member(sK0(union(sK1,sK3),sK2),union(sK3,sK1)),
inference(resolve,[status(thm)],[c_65,c_58]) ).
cnf(c_67,plain,
~ member(sK0(union(sK1,sK3),sK2),union(sK1,sK3)),
inference(paramod,[status(thm)],[c_13,c_66]) ).
cnf(c_62,plain,
$false,
inference(resolve,[status(thm)],[c_50,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 06:49:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1471123 was started by sandbox2 on n005,
% 0.10/0.37 % Sat Sep 26 06:49:47 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 17.
% 0.14/0.38 % Level of proof is 4.
% 0.14/0.38 % Maximum clause weight is 11.000.
% 0.14/0.38 % Given clauses 20.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------