%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET194+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 08:36:00 AM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 14 |; 6 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn 23 !; 3 ?)
% 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(prove_subset_of_union,conjecture,
! [B,C] : subset(B,union(B,C)),
file('theBenchmark.p',prove_subset_of_union) ).
fof(prove_subset_of_union_neg,negated_conjecture,
~ ! [B,C] : subset(B,union(B,C)),
inference(assume_negation,[status(cth)],[prove_subset_of_union]) ).
cnf(c_8,plain,
( ~ 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_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]) ).
fof(nnf_6,plain,
? [B,C] : ~ subset(B,union(B,C)),
inference(fof_nnf,[status(thm)],[prove_subset_of_union_neg]) ).
fof(sk_prove_subset_of_union_neg,plain,
~ subset(sK1,union(sK1,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1),skolemize(C,sK2)],[nnf_6]) ).
cnf(c_19,negated_conjecture,
~ subset(sK1,union(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_subset_of_union_neg]) ).
cnf(c_46,plain,
member(sK0(sK1,union(sK1,sK2)),sK1),
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_47,negated_conjecture,
~ member(sK0(sK1,union(sK1,sK2)),union(sK1,sK2)),
inference(resolve,[status(thm)],[c_12,c_19]) ).
cnf(c_55,plain,
~ member(sK0(sK1,union(sK1,sK2)),sK1),
inference(resolve,[status(thm)],[c_8,c_47]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET194+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.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 07:18:16 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 1539190 was started by sandbox2 on n005,
% 0.08/0.36 % Sat Sep 26 07:18:16 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 10.
% 0.08/0.38 % Level of proof is 3.
% 0.08/0.38 % Maximum clause weight is 9.000.
% 0.08/0.38 % Given clauses 16.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------