%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET632+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 : n012.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 08:36:41 AM UTC 2026
% Result : Theorem 0.03s 0.52s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 105 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 106 ( 44 ~; 33 |; 21 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 3 sgn 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(prove_th114,conjecture,
! [B,C,D] :
( ( disjoint(C,D)
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
file('theBenchmark.p',prove_th114) ).
fof(prove_th114_neg,negated_conjecture,
~ ! [B,C,D] :
( ( disjoint(C,D)
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
inference(assume_negation,[status(cth)],[prove_th114]) ).
cnf(c_11,plain,
( ~ intersect(A,B)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
fof(nnf_9,plain,
? [B,C,D] :
( empty_set != B
& disjoint(C,D)
& subset(B,D)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th114_neg]) ).
fof(sk_prove_th114_neg,plain,
( empty_set != sK4
& disjoint(sK0,sK1)
& subset(sK4,sK1)
& subset(sK4,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK0,sK1]),skolemize(B,sK4),skolemize(C,sK0),skolemize(D,sK1)],[nnf_9]) ).
cnf(c_12,negated_conjecture,
disjoint(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th114_neg]) ).
fof(nnf_8,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [X0] : ~ member(X0,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(sk_empty_defn_sk,plain,
! [B] :
( ( member(sK2(B),B)
| empty(B) )
& ( ! [X0] : ~ member(X0,B)
| ~ empty(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(B))],[nnf_8]) ).
fof(sk_empty_defn,plain,
( ! [VAR_0] :
( member(sK2(VAR_0),VAR_0)
| empty(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ member(VAR_1,VAR_0)
| ~ empty(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_empty_defn_sk]) ).
cnf(c_13,plain,
( ~ member(B,A)
| ~ empty(A) ),
inference(split_conjunct,[status(thm)],[sk_empty_defn]) ).
cnf(c_14,plain,
( member(sK2(A),A)
| empty(A) ),
inference(split_conjunct,[status(thm)],[sk_empty_defn]) ).
cnf(c_15,plain,
( member(sK2(B),B)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
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(sK3(B,C),C)
& member(sK3(B,C),B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(D,sK3(B,C))],[nnf_1]) ).
fof(sk_subset_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(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_16,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_17,plain,
( member(sK3(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_21,plain,
( ~ member(C,B)
| ~ member(C,A)
| intersect(A,B) ),
inference(clausify,[status(thm)],[intersect_defn]) ).
cnf(c_22,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
cnf(c_25,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_28,negated_conjecture,
subset(sK4,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_th114_neg]) ).
cnf(c_29,negated_conjecture,
subset(sK4,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th114_neg]) ).
cnf(c_30,negated_conjecture,
empty_set != sK4,
inference(split_conjunct,[status(thm)],[sk_prove_th114_neg]) ).
cnf(c_31,negated_conjecture,
sK4 != empty_set,
inference(copy,[status(thm)],[c_30]) ).
cnf(c_32,negated_conjecture,
~ intersect(sK0,sK1),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_37,plain,
( member(sK3(B,A),B)
| ~ subset(A,B)
| A = B ),
inference(resolve,[status(thm)],[c_25,c_17]) ).
cnf(c_40,plain,
( member(A,sK0)
| ~ member(A,sK4) ),
inference(resolve,[status(thm)],[c_28,c_16]) ).
cnf(c_42,plain,
( member(A,sK1)
| ~ member(A,sK4) ),
inference(resolve,[status(thm)],[c_29,c_16]) ).
cnf(c_68,negated_conjecture,
( member(sK3(empty_set,sK4),empty_set)
| ~ subset(sK4,empty_set) ),
inference(resolve,[status(thm)],[c_37,c_31]) ).
cnf(c_47,negated_conjecture,
~ subset(sK4,empty_set),
inference(resolve,[status(thm)],[c_68,c_22]) ).
cnf(c_48,plain,
member(sK3(sK4,empty_set),sK4),
inference(resolve,[status(thm)],[c_47,c_17]) ).
cnf(c_55,plain,
member(sK2(sK4),sK4),
inference(resolve,[status(thm)],[c_48,c_15]) ).
cnf(c_57,plain,
member(sK2(sK4),sK1),
inference(resolve,[status(thm)],[c_55,c_42]) ).
cnf(c_58,plain,
member(sK2(sK4),sK0),
inference(resolve,[status(thm)],[c_55,c_40]) ).
cnf(c_69,negated_conjecture,
( ~ member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_21,c_32]) ).
cnf(c_70,negated_conjecture,
~ member(sK2(sK4),sK0),
inference(resolve,[status(thm)],[c_69,c_57]) ).
cnf(c_67,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_58,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET632+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.50 % Computer : n012.cluster.edu
% 0.03/0.50 % Model : x86_64 x86_64
% 0.03/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.50 % Memory : 8046.5625MB
% 0.03/0.50 % OS : Linux 6.8.0-71-generic
% 0.03/0.50 % CPULimit : 300
% 0.03/0.50 % WCLimit : 300
% 0.03/0.50 % DateTime : Sat Sep 26 08:01:36 UTC 2026
% 0.03/0.50 % CPUTime :
% 0.03/0.50 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.50 % Process 81319 was started by sandbox2 on n012,
% 0.03/0.50 % Sat Sep 26 08:01:36 2026
% 0.03/0.50 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.51
% 0.03/0.51 % From the command line: assign(max_seconds, 300).
% 0.03/0.52
% 0.03/0.52 % SZS status Theorem for theBenchmark
% 0.03/0.52
% 0.03/0.52 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.52 % Length of proof is 31.
% 0.03/0.52 % Level of proof is 7.
% 0.03/0.52 % Maximum clause weight is 11.000.
% 0.03/0.52 % Given clauses 32.
% 0.03/0.52
% 0.03/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------