%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET002+4 : 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 : n019.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 : Theorem 0.14s 0.63s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 55 ( 19 ~; 25 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 3 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',equal_set) ).
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('theBenchmark.p',union) ).
fof(thI14,conjecture,
! [A] : equal_set(union(A,A),A),
file('theBenchmark.p',thI14) ).
fof(thI14_neg,negated_conjecture,
~ ! [A] : equal_set(union(A,A),A),
inference(assume_negation,[status(cth)],[thI14]) ).
fof(nnf_1,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(sk_subset_sk,plain,
! [A,B] :
( ( ( ~ member(sK0(A,B),B)
& member(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(A,B))],[nnf_1]) ).
fof(sk_subset,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_sk]) ).
cnf(c_14,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_15,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_18,plain,
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
cnf(c_24,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_25,plain,
( ~ member(A,B)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
fof(nnf_12,plain,
? [A] : ~ equal_set(union(A,A),A),
inference(fof_nnf,[status(thm)],[thI14_neg]) ).
fof(sk_thI14_neg,plain,
~ equal_set(union(sK1,sK1),sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_12]) ).
cnf(c_42,negated_conjecture,
~ equal_set(union(sK1,sK1),sK1),
inference(split_conjunct,[status(thm)],[sk_thI14_neg]) ).
cnf(c_60,plain,
( subset(union(A,B),C)
| member(sK0(union(A,B),C),B)
| member(sK0(union(A,B),C),A) ),
inference(resolve,[status(thm)],[c_24,c_14]) ).
cnf(c_61,plain,
( subset(union(A,A),B)
| member(sK0(union(A,A),B),A) ),
inference(factor,[status(thm)],[c_60]) ).
cnf(c_62,plain,
( subset(A,B)
| member(sK0(A,B),union(A,C)) ),
inference(resolve,[status(thm)],[c_25,c_14]) ).
cnf(c_787,plain,
( subset(union(A,A),A)
| subset(union(A,A),A) ),
inference(resolve,[status(thm)],[c_61,c_15]) ).
cnf(c_716,plain,
subset(union(A,A),A),
inference(copy,[status(thm)],[c_787]) ).
cnf(c_788,plain,
( subset(A,union(A,B))
| subset(A,union(A,B)) ),
inference(resolve,[status(thm)],[c_62,c_15]) ).
cnf(c_738,plain,
subset(A,union(A,B)),
inference(copy,[status(thm)],[c_788]) ).
cnf(c_789,plain,
( ~ subset(A,union(A,A))
| equal_set(union(A,A),A) ),
inference(resolve,[status(thm)],[c_716,c_18]) ).
cnf(c_785,plain,
equal_set(union(A,A),A),
inference(resolve,[status(thm)],[c_738,c_789]) ).
cnf(c_786,plain,
$false,
inference(resolve,[status(thm)],[c_785,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET002+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n019.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 26 06:47:38 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.57 % Process 636240 was started by sandbox2 on n019,
% 0.09/0.57 % Sat Sep 26 06:47:38 2026
% 0.09/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.58
% 0.14/0.58 % From the command line: assign(max_seconds, 300).
% 0.14/0.63
% 0.14/0.63 % SZS status Theorem for theBenchmark
% 0.14/0.63
% 0.14/0.63 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.63 % Length of proof is 17.
% 0.14/0.63 % Level of proof is 6.
% 0.14/0.63 % Maximum clause weight is 25.000.
% 0.14/0.63 % Given clauses 110.
% 0.14/0.63
% 0.14/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------