%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:36:33 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 69 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 63 ( 27 ~; 21 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 5 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(prove_th53,conjecture,
! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
file('theBenchmark.p',prove_th53) ).
fof(prove_th53_neg,negated_conjecture,
~ ! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
inference(assume_negation,[status(cth)],[prove_th53]) ).
fof(nnf_1,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_1]) ).
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_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,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_14,plain,
( ~ member(A,B)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_15,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_17,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_22,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
fof(nnf_9,plain,
? [B,C,D] :
( ~ subset(B,union(C,D))
& union(intersection(B,C),intersection(B,D)) = B ),
inference(fof_nnf,[status(thm)],[prove_th53_neg]) ).
fof(sk_prove_th53_neg,plain,
( ~ subset(sK1,union(sK2,sK3))
& union(intersection(sK1,sK2),intersection(sK1,sK3)) = sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_9]) ).
cnf(c_29,negated_conjecture,
union(intersection(sK1,sK2),intersection(sK1,sK3)) = sK1,
inference(split_conjunct,[status(thm)],[sk_prove_th53_neg]) ).
cnf(c_30,negated_conjecture,
~ subset(sK1,union(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_prove_th53_neg]) ).
cnf(c_80,plain,
( member(A,intersection(sK1,sK3))
| member(A,intersection(sK1,sK2))
| ~ member(A,sK1) ),
inference(paramod,[status(thm)],[c_29,c_13]) ).
cnf(c_86,negated_conjecture,
~ member(sK0(sK1,union(sK2,sK3)),union(sK2,sK3)),
inference(resolve,[status(thm)],[c_12,c_30]) ).
cnf(c_87,plain,
~ subset(sK1,union(sK3,sK2)),
inference(paramod,[status(thm)],[c_22,c_30]) ).
cnf(c_98,plain,
member(sK0(sK1,union(sK3,sK2)),sK1),
inference(resolve,[status(thm)],[c_87,c_11]) ).
cnf(c_104,plain,
~ member(sK0(sK1,union(sK2,sK3)),sK3),
inference(resolve,[status(thm)],[c_15,c_86]) ).
cnf(c_105,plain,
~ member(sK0(sK1,union(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_14,c_86]) ).
cnf(c_123,plain,
~ member(sK0(sK1,union(sK3,sK2)),sK3),
inference(paramod,[status(thm)],[c_22,c_104]) ).
cnf(c_129,plain,
~ member(sK0(sK1,union(sK3,sK2)),sK2),
inference(paramod,[status(thm)],[c_22,c_105]) ).
cnf(c_131,plain,
~ member(sK0(sK1,union(sK3,sK2)),intersection(A,sK3)),
inference(resolve,[status(thm)],[c_17,c_123]) ).
cnf(c_134,plain,
~ member(sK0(sK1,union(sK3,sK2)),intersection(A,sK2)),
inference(resolve,[status(thm)],[c_17,c_129]) ).
cnf(c_155,plain,
( member(sK0(sK1,union(sK3,sK2)),intersection(sK1,sK3))
| member(sK0(sK1,union(sK3,sK2)),intersection(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_80,c_98]) ).
cnf(c_156,plain,
member(sK0(sK1,union(sK3,sK2)),intersection(sK1,sK3)),
inference(resolve,[status(thm)],[c_134,c_155]) ).
cnf(c_154,plain,
$false,
inference(resolve,[status(thm)],[c_131,c_156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 07:59:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1025188 was started by sandbox on n020,
% 0.08/0.36 % Sat Sep 26 07:59:04 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.39 % Length of proof is 25.
% 0.08/0.39 % Level of proof is 6.
% 0.08/0.39 % Maximum clause weight is 24.000.
% 0.08/0.39 % Given clauses 46.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------