%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET693+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 : n006.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 08:36:50 AM UTC 2026
% Result : Theorem 153.22s 21.23s
% Output : CNFRefutation 153.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 9 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 35 ~; 43 |; 9 &)
% ( 5 <=>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 5 sgn 25 !; 3 ?)
% 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(thI20,conjecture,
! [A,B] :
( equal_set(A,union(A,B))
<=> subset(B,A) ),
file('theBenchmark.p',thI20) ).
fof(thI20_neg,negated_conjecture,
~ ! [A,B] :
( equal_set(A,union(A,B))
<=> subset(B,A) ),
inference(assume_negation,[status(cth)],[thI20]) ).
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_13,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
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_17,plain,
( subset(B,A)
| ~ equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
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]) ).
cnf(c_26,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
fof(nnf_12,plain,
? [A,B] :
( ( ~ subset(B,A)
| ~ equal_set(A,union(A,B)) )
& ( subset(B,A)
| equal_set(A,union(A,B)) ) ),
inference(fof_nnf,[status(thm)],[thI20_neg]) ).
fof(sk_thI20_neg,plain,
( ( ~ subset(sK2,sK1)
| ~ equal_set(sK1,union(sK1,sK2)) )
& ( subset(sK2,sK1)
| equal_set(sK1,union(sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_12]) ).
cnf(c_42,negated_conjecture,
( subset(sK2,sK1)
| equal_set(sK1,union(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_thI20_neg]) ).
cnf(c_43,negated_conjecture,
( ~ subset(sK2,sK1)
| ~ equal_set(sK1,union(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_thI20_neg]) ).
cnf(c_62,plain,
( subset(A,B)
| member(sK0(A,B),union(A,C)) ),
inference(resolve,[status(thm)],[c_25,c_14]) ).
cnf(c_63,plain,
( subset(A,B)
| member(sK0(A,B),union(C,A)) ),
inference(resolve,[status(thm)],[c_26,c_14]) ).
cnf(c_118,plain,
( subset(union(sK1,sK2),sK1)
| subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_42,c_17]) ).
cnf(c_123,plain,
( member(A,sK1)
| ~ member(A,sK2)
| equal_set(sK1,union(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_42,c_13]) ).
cnf(c_593,plain,
( member(A,sK1)
| ~ member(A,union(sK1,sK2))
| subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_118,c_13]) ).
cnf(c_21123,plain,
( subset(A,union(A,B))
| subset(A,union(A,B)) ),
inference(resolve,[status(thm)],[c_62,c_15]) ).
cnf(c_859,plain,
subset(A,union(A,B)),
inference(copy,[status(thm)],[c_21123]) ).
cnf(c_884,plain,
( ~ subset(union(A,B),A)
| equal_set(A,union(A,B)) ),
inference(resolve,[status(thm)],[c_859,c_18]) ).
cnf(c_3618,plain,
( subset(sK2,A)
| member(sK0(sK2,A),sK1)
| subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_593,c_63]) ).
cnf(c_3622,plain,
( member(sK0(sK2,sK1),sK1)
| subset(sK2,sK1) ),
inference(factor,[status(thm)],[c_3618]) ).
cnf(c_21124,plain,
( subset(sK2,sK1)
| subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_3622,c_15]) ).
cnf(c_3640,plain,
subset(sK2,sK1),
inference(copy,[status(thm)],[c_21124]) ).
cnf(c_3642,negated_conjecture,
~ equal_set(sK1,union(sK1,sK2)),
inference(resolve,[status(thm)],[c_3640,c_43]) ).
cnf(c_3665,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_3642,c_123]) ).
cnf(c_3669,negated_conjecture,
~ subset(union(sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_884,c_3642]) ).
cnf(c_3673,plain,
member(sK0(union(sK1,sK2),sK1),union(sK1,sK2)),
inference(resolve,[status(thm)],[c_3669,c_14]) ).
cnf(c_3676,plain,
~ member(sK0(union(sK1,sK2),sK1),sK1),
inference(resolve,[status(thm)],[c_15,c_3669]) ).
cnf(c_13062,plain,
~ member(sK0(union(sK1,sK2),sK1),sK2),
inference(resolve,[status(thm)],[c_3665,c_3676]) ).
cnf(c_21125,plain,
( member(sK0(union(sK1,sK2),sK1),A)
| ~ member(sK0(union(sK1,sK2),sK1),union(sK1,A)) ),
inference(resolve,[status(thm)],[c_24,c_3676]) ).
cnf(c_21126,plain,
~ member(sK0(union(sK1,sK2),sK1),union(sK1,sK2)),
inference(resolve,[status(thm)],[c_21125,c_13062]) ).
cnf(c_21122,plain,
$false,
inference(resolve,[status(thm)],[c_3673,c_21126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET693+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:05:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 785101 was started by sandbox2 on n006,
% 0.09/0.35 % Sat Sep 26 08:05:55 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 153.22/21.23
% 153.22/21.23 % given #500 (T,wt=21): 2488 equal_set(product(power_set(A)),sum(empty_set)). [resolve(1091,a,319,b)].
% 153.22/21.23
% 153.22/21.23 % given #1000 (F,wt=22): 6902 -equal_set(power_set(A),union(empty_set,sum(empty_set))). [ur(16,b,341,a)].
% 153.22/21.23
% 153.22/21.23 % SZS status Theorem for theBenchmark
% 153.22/21.23
% 153.22/21.23 % Proof 1 at 3.08 (+ 1.51) seconds.
% 153.22/21.23 % Length of proof is 31.
% 153.22/21.23 % Level of proof is 11.
% 153.22/21.23 % Maximum clause weight is 24.000.
% 153.22/21.23 % Given clauses 1386.
% 153.22/21.23
% 153.22/21.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------