%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET579+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 : n011.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 08:36:30 AM UTC 2026
% Result : Theorem 1.05s 0.53s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 8 unt; 0 def)
% Number of atoms : 122 ( 10 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 127 ( 48 ~; 52 |; 19 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 75 ( 2 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_th20,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
file('theBenchmark.p',prove_th20) ).
fof(prove_th20_neg,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
inference(assume_negation,[status(cth)],[prove_th20]) ).
cnf(c_6,plain,
( member(A,B)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_7,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_8,plain,
( member(A,C)
| ~ member(A,B)
| member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_11,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
fof(nnf_3,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_3]) ).
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_13,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_14,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
fof(nnf_5,plain,
? [B,C,D] :
( difference(C,D) != B
& ! [E] :
( ( member(E,D)
| ~ member(E,C)
| member(E,B) )
& ( ( ~ member(E,D)
& member(E,C) )
| ~ member(E,B) ) ) ),
inference(fof_nnf,[status(thm)],[prove_th20_neg]) ).
fof(sk_prove_th20_neg_sk,plain,
( difference(sK2,sK3) != sK1
& ! [E] :
( ( member(E,sK3)
| ~ member(E,sK2)
| member(E,sK1) )
& ( ( ~ member(E,sK3)
& member(E,sK2) )
| ~ member(E,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_5]) ).
fof(sk_prove_th20_neg,plain,
( difference(sK2,sK3) != sK1
& ! [VAR_0] :
( member(VAR_0,sK3)
| ~ member(VAR_0,sK2)
| member(VAR_0,sK1) )
& ! [VAR_0] :
( ~ member(VAR_0,sK3)
| ~ member(VAR_0,sK1) )
& ! [VAR_0] :
( member(VAR_0,sK2)
| ~ member(VAR_0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_th20_neg_sk]) ).
cnf(c_16,negated_conjecture,
( member(A,sK2)
| ~ member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th20_neg]) ).
cnf(c_17,negated_conjecture,
( ~ member(A,sK3)
| ~ member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th20_neg]) ).
cnf(c_18,negated_conjecture,
( member(A,sK3)
| ~ member(A,sK2)
| member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th20_neg]) ).
cnf(c_19,negated_conjecture,
difference(sK2,sK3) != sK1,
inference(split_conjunct,[status(thm)],[sk_prove_th20_neg]) ).
cnf(c_23,plain,
( member(sK0(A,B),C)
| member(sK0(A,B),difference(A,C))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_24,plain,
( ~ member(sK0(difference(A,B),C),B)
| subset(difference(A,B),C) ),
inference(resolve,[status(thm)],[c_13,c_7]) ).
cnf(c_25,plain,
( member(sK0(difference(A,B),C),A)
| subset(difference(A,B),C) ),
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_26,plain,
( subset(sK1,A)
| member(sK0(sK1,A),sK2) ),
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_33,plain,
( member(sK0(sK1,A),B)
| member(sK0(sK1,A),difference(sK2,B))
| subset(sK1,A) ),
inference(resolve,[status(thm)],[c_26,c_8]) ).
cnf(c_55,plain,
( ~ member(sK0(A,B),sK1)
| member(sK0(A,B),difference(A,sK3))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_23,c_17]) ).
cnf(c_1928,plain,
( subset(sK1,A)
| member(sK0(sK1,A),difference(sK1,sK3))
| subset(sK1,A) ),
inference(resolve,[status(thm)],[c_55,c_13]) ).
cnf(c_1128,plain,
( member(sK0(sK1,A),difference(sK1,sK3))
| subset(sK1,A) ),
inference(copy,[status(thm)],[c_1928]) ).
cnf(c_1268,plain,
( ~ member(sK0(sK1,A),sK3)
| subset(sK1,A) ),
inference(resolve,[status(thm)],[c_1128,c_7]) ).
cnf(c_1929,plain,
( member(sK0(sK1,A),difference(sK2,sK3))
| subset(sK1,A)
| subset(sK1,A) ),
inference(resolve,[status(thm)],[c_1268,c_33]) ).
cnf(c_1455,plain,
( member(sK0(sK1,A),difference(sK2,sK3))
| subset(sK1,A) ),
inference(copy,[status(thm)],[c_1929]) ).
cnf(c_1930,plain,
( subset(sK1,difference(sK2,sK3))
| subset(sK1,difference(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_1455,c_14]) ).
cnf(c_1692,plain,
subset(sK1,difference(sK2,sK3)),
inference(copy,[status(thm)],[c_1930]) ).
cnf(c_1931,plain,
( ~ subset(difference(sK2,sK3),sK1)
| sK1 = difference(sK2,sK3) ),
inference(resolve,[status(thm)],[c_1692,c_11]) ).
cnf(c_1932,plain,
( ~ subset(difference(sK2,sK3),sK1)
| difference(sK2,sK3) = sK1 ),
inference(copy,[status(thm)],[c_1931]) ).
cnf(c_1698,negated_conjecture,
~ subset(difference(sK2,sK3),sK1),
inference(resolve,[status(thm)],[c_19,c_1932]) ).
cnf(c_1751,plain,
member(sK0(difference(sK2,sK3),sK1),sK2),
inference(resolve,[status(thm)],[c_1698,c_25]) ).
cnf(c_1752,plain,
~ member(sK0(difference(sK2,sK3),sK1),sK3),
inference(resolve,[status(thm)],[c_24,c_1698]) ).
cnf(c_1753,plain,
~ member(sK0(difference(sK2,sK3),sK1),sK1),
inference(resolve,[status(thm)],[c_14,c_1698]) ).
cnf(c_1933,negated_conjecture,
( member(sK0(difference(sK2,sK3),sK1),sK3)
| ~ member(sK0(difference(sK2,sK3),sK1),sK2) ),
inference(resolve,[status(thm)],[c_18,c_1753]) ).
cnf(c_1934,negated_conjecture,
~ member(sK0(difference(sK2,sK3),sK1),sK2),
inference(resolve,[status(thm)],[c_1933,c_1752]) ).
cnf(c_1927,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1751,c_1934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.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 07:57:14 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 4159715 was started by sandbox2 on n011,
% 0.09/0.35 % Sat Sep 26 07:57:14 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 1.05/0.53
% 1.05/0.53 % SZS status Theorem for theBenchmark
% 1.05/0.53
% 1.05/0.53 % Proof 1 at 0.13 (+ 0.03) seconds.
% 1.05/0.53 % Length of proof is 29.
% 1.05/0.53 % Level of proof is 10.
% 1.05/0.53 % Maximum clause weight is 27.000.
% 1.05/0.53 % Given clauses 136.
% 1.05/0.53
% 1.05/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------