%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET637+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 : n002.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 08:36:42 AM UTC 2026
% Result : Theorem 10.73s 1.92s
% Output : CNFRefutation 10.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 11 unt; 0 def)
% Number of atoms : 151 ( 35 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 151 ( 53 ~; 72 |; 19 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 3 sgn 46 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_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(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(not_equal_defn,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('theBenchmark.p',not_equal_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th119,conjecture,
! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
file('theBenchmark.p',prove_th119) ).
fof(prove_th119_neg,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
inference(assume_negation,[status(cth)],[prove_th119]) ).
fof(nnf_9,plain,
? [B,C] :
( ( ~ not_equal(intersection(B,C),empty_set)
| ~ intersect(B,C) )
& ( not_equal(intersection(B,C),empty_set)
| intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[prove_th119_neg]) ).
fof(sk_prove_th119_neg,plain,
( ( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) )
& ( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_9]) ).
cnf(c_13,negated_conjecture,
( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th119_neg]) ).
cnf(c_14,negated_conjecture,
( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th119_neg]) ).
cnf(c_16,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_17,plain,
( B = A
| not_equal(A,B) ),
inference(clausify,[status(thm)],[not_equal_defn]) ).
cnf(c_18,plain,
( B != A
| ~ not_equal(A,B) ),
inference(clausify,[status(thm)],[not_equal_defn]) ).
fof(nnf_4,plain,
! [B,C] :
( ( ? [D] :
( ( ~ member(D,C)
| ~ member(D,B) )
& ( member(D,C)
| member(D,B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(fof_nnf,[status(thm)],[equal_member_defn]) ).
fof(sk_equal_member_defn_sk,plain,
! [B,C] :
( ( ( ( ~ member(sK2(B,C),C)
| ~ member(sK2(B,C),B) )
& ( member(sK2(B,C),C)
| member(sK2(B,C),B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(D,sK2(B,C))],[nnf_4]) ).
fof(sk_equal_member_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(VAR_1,VAR_0),VAR_0)
| ~ member(sK2(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_1,VAR_0),VAR_0)
| member(sK2(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_0)
| member(VAR_2,VAR_1)
| VAR_0 != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_0)
| ~ member(VAR_2,VAR_1)
| VAR_0 != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_equal_member_defn_sk]) ).
cnf(c_20,plain,
( member(sK2(B,A),A)
| member(sK2(B,A),B)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_equal_member_defn]) ).
cnf(c_23,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
fof(nnf_2,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [X0] :
( member(X0,C)
& member(X0,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(sk_intersect_defn_sk,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ( member(sK3(B,C),C)
& member(sK3(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3(B,C))],[nnf_2]) ).
fof(sk_intersect_defn,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(VAR_0,VAR_1),VAR_1)
| ~ intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(VAR_0,VAR_1),VAR_0)
| ~ intersect(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_intersect_defn_sk]) ).
cnf(c_24,plain,
( ~ member(C,B)
| ~ member(C,A)
| intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_25,plain,
( member(sK3(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_26,plain,
( member(sK3(A,B),A)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_27,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_28,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_29,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_1575,negated_conjecture,
( ~ intersect(sK0,sK1)
| empty_set = intersection(sK0,sK1) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_32,negated_conjecture,
( ~ intersect(sK0,sK1)
| intersection(sK0,sK1) = empty_set ),
inference(copy,[status(thm)],[c_1575]) ).
cnf(c_1576,negated_conjecture,
( intersect(sK0,sK1)
| empty_set != intersection(sK0,sK1) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_33,negated_conjecture,
( intersect(sK0,sK1)
| intersection(sK0,sK1) != empty_set ),
inference(copy,[status(thm)],[c_1576]) ).
cnf(c_46,plain,
( member(sK2(A,empty_set),A)
| empty_set = A ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_1577,plain,
( member(sK2(intersection(A,B),C),C)
| C = intersection(A,B)
| member(sK2(intersection(A,B),C),B) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_69,plain,
( member(sK2(intersection(A,B),C),C)
| intersection(A,B) = C
| member(sK2(intersection(A,B),C),B) ),
inference(copy,[status(thm)],[c_1577]) ).
cnf(c_1578,plain,
( member(sK2(intersection(A,B),empty_set),A)
| empty_set = intersection(A,B) ),
inference(resolve,[status(thm)],[c_46,c_29]) ).
cnf(c_87,plain,
( member(sK2(intersection(A,B),empty_set),A)
| intersection(A,B) = empty_set ),
inference(copy,[status(thm)],[c_1578]) ).
cnf(c_1579,plain,
( member(sK2(intersection(C,A),D),D)
| intersection(C,A) = D
| ~ member(sK2(intersection(C,A),D),B)
| intersect(A,B) ),
inference(resolve,[status(thm)],[c_24,c_69]) ).
cnf(c_1580,plain,
( intersection(B,A) = empty_set
| member(sK2(intersection(B,A),empty_set),empty_set)
| intersection(B,A) = empty_set
| intersect(A,B) ),
inference(resolve,[status(thm)],[c_1579,c_87]) ).
cnf(c_1581,plain,
( member(sK2(intersection(B,A),empty_set),empty_set)
| intersection(B,A) = empty_set
| intersect(A,B) ),
inference(copy,[status(thm)],[c_1580]) ).
cnf(c_1520,plain,
( intersection(B,A) = empty_set
| intersect(A,B) ),
inference(resolve,[status(thm)],[c_23,c_1581]) ).
cnf(c_1582,plain,
( intersection(sK0,sK1) = empty_set
| intersection(sK1,sK0) = empty_set ),
inference(resolve,[status(thm)],[c_1520,c_32]) ).
cnf(c_1583,plain,
( intersection(sK0,sK1) = empty_set
| intersection(sK0,sK1) = empty_set ),
inference(paramod,[status(thm)],[c_16,c_1582]) ).
cnf(c_1525,plain,
intersection(sK0,sK1) = empty_set,
inference(copy,[status(thm)],[c_1583]) ).
cnf(c_1584,negated_conjecture,
( intersect(sK0,sK1)
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_1525,c_33]) ).
cnf(c_1528,negated_conjecture,
intersect(sK0,sK1),
inference(copy,[status(thm)],[c_1584]) ).
cnf(c_1529,plain,
member(sK3(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_1528,c_26]) ).
cnf(c_1530,plain,
member(sK3(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_1528,c_25]) ).
cnf(c_1585,plain,
( ~ member(sK3(sK0,sK1),A)
| member(sK3(sK0,sK1),intersection(sK0,A)) ),
inference(resolve,[status(thm)],[c_27,c_1529]) ).
cnf(c_1586,plain,
member(sK3(sK0,sK1),intersection(sK0,sK1)),
inference(resolve,[status(thm)],[c_1585,c_1530]) ).
cnf(c_1587,plain,
member(sK3(sK0,sK1),empty_set),
inference(paramod,[status(thm)],[c_1525,c_1586]) ).
cnf(c_1574,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_1587]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.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 08:04:51 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.37 % Process 1209506 was started by sandbox2 on n002,
% 0.02/0.37 % Sat Sep 26 08:04:51 2026
% 0.02/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.38
% 0.02/0.38 % From the command line: assign(max_seconds, 300).
% 10.73/1.92
% 10.73/1.92 % Assigning unary symbol f3 kb_weight 0 and highest precedence (11).
% 10.73/1.92
% 10.73/1.92 % SZS status Theorem for theBenchmark
% 10.73/1.92
% 10.73/1.92 % Proof 1 at 0.96 (+ 0.36) seconds.
% 10.73/1.92 % Length of proof is 31.
% 10.73/1.92 % Level of proof is 8.
% 10.73/1.92 % Maximum clause weight is 34.000.
% 10.73/1.92 % Given clauses 260.
% 10.73/1.92
% 10.73/1.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------