%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:37:25 AM UTC 2026
% Result : Theorem 0.22s 0.72s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 84 ( 38 unt; 0 def)
% Number of atoms : 219 ( 88 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 235 ( 100 ~; 87 |; 34 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 7 sgn 43 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(s3_funct_1__e4_14__funct_1,axiom,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = n0 )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(s3_funct_1__e7_14__funct_1,axiom,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = n1 )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t16_funct_1,conjecture,
! [A] :
( ! [B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_dom(C) = A
& relation_dom(B) = A )
=> B = C ) ) )
=> A = empty_set ),
file('theBenchmark.p',t16_funct_1) ).
fof(t16_funct_1_neg,negated_conjecture,
~ ! [A] :
( ! [B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_dom(C) = A
& relation_dom(B) = A )
=> B = C ) ) )
=> A = empty_set ),
inference(assume_negation,[status(cth)],[t16_funct_1]) ).
cnf(c_31,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_32,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_33,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_32,c_31]) ).
fof(nnf_4,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : element(sK0(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_4]) ).
cnf(c_37,plain,
element(sK0(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_38,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc12_relat_1]) ).
cnf(c_40,plain,
~ empty(powerset(A)),
inference(clausify,[status(thm)],[fc1_subset_1]) ).
fof(nnf_19,plain,
! [A] :
? [B] :
( ! [C] :
( apply(B,C) = n0
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[s3_funct_1__e4_14__funct_1]) ).
fof(sk_s3_funct_1__e4_14__funct_1,plain,
! [A] :
( ! [C] :
( apply(sK1(A),C) = n0
| ~ in(C,A) )
& relation_dom(sK1(A)) = A
& function(sK1(A))
& relation(sK1(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(B,sK1(A))],[nnf_19]) ).
cnf(c_57,plain,
relation(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e4_14__funct_1]) ).
cnf(c_58,plain,
function(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e4_14__funct_1]) ).
cnf(c_59,plain,
relation_dom(sK1(A)) = A,
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e4_14__funct_1]) ).
cnf(c_60,plain,
( apply(sK1(B),A) = n0
| ~ in(A,B) ),
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e4_14__funct_1]) ).
fof(nnf_20,plain,
! [A] :
? [B] :
( ! [C] :
( apply(B,C) = n1
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[s3_funct_1__e7_14__funct_1]) ).
fof(sk_s3_funct_1__e7_14__funct_1,plain,
! [A] :
( ! [C] :
( apply(sK2(A),C) = n1
| ~ in(C,A) )
& relation_dom(sK2(A)) = A
& function(sK2(A))
& relation(sK2(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(B,sK2(A))],[nnf_20]) ).
cnf(c_61,plain,
relation(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e7_14__funct_1]) ).
cnf(c_62,plain,
function(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e7_14__funct_1]) ).
cnf(c_63,plain,
relation_dom(sK2(A)) = A,
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e7_14__funct_1]) ).
cnf(c_64,plain,
( apply(sK2(B),A) = n1
| ~ in(A,B) ),
inference(split_conjunct,[status(thm)],[sk_s3_funct_1__e7_14__funct_1]) ).
fof(spc0_boole,axiom,
empty(n0),
file('theBenchmark.p',spc0_boole) ).
cnf(c_65,plain,
empty(n0),
inference(clausify,[status(thm)],[spc0_boole]) ).
fof(spc1_boole,axiom,
~ empty(n1),
file('theBenchmark.p',spc1_boole) ).
cnf(c_66,plain,
~ empty(n1),
inference(clausify,[status(thm)],[spc1_boole]) ).
cnf(c_68,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_69,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_70,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_71,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
cnf(c_73,plain,
( ~ empty(B)
| B = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t8_boole]) ).
fof(nnf_29,plain,
? [A] :
( empty_set != A
& ! [B] :
( ! [C] :
( C = B
| relation_dom(C) != A
| relation_dom(B) != A
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ) ),
inference(fof_nnf,[status(thm)],[t16_funct_1_neg]) ).
fof(sk_t16_funct_1_neg_sk,plain,
( empty_set != sK3
& ! [B] :
( ! [C] :
( C = B
| relation_dom(C) != sK3
| relation_dom(B) != sK3
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(A,sK3)],[nnf_29]) ).
fof(sk_t16_funct_1_neg,plain,
( empty_set != sK3
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| relation_dom(VAR_1) != sK3
| relation_dom(VAR_0) != sK3
| ~ function(VAR_1)
| ~ relation(VAR_1)
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t16_funct_1_neg_sk]) ).
cnf(c_74,negated_conjecture,
( B = A
| relation_dom(B) != sK3
| relation_dom(A) != sK3
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_t16_funct_1_neg]) ).
cnf(c_75,negated_conjecture,
empty_set != sK3,
inference(split_conjunct,[status(thm)],[sk_t16_funct_1_neg]) ).
cnf(c_76,negated_conjecture,
sK3 != empty_set,
inference(copy,[status(thm)],[c_75]) ).
cnf(c_107,plain,
( in(sK0(A),A)
| empty(A) ),
inference(resolve,[status(thm)],[c_68,c_37]) ).
cnf(c_379,plain,
( in(A,powerset(A))
| empty(powerset(A)) ),
inference(resolve,[status(thm)],[c_68,c_33]) ).
cnf(c_108,plain,
in(A,powerset(A)),
inference(resolve,[status(thm)],[c_40,c_379]) ).
cnf(c_380,plain,
empty_set = n0,
inference(resolve,[status(thm)],[c_71,c_65]) ).
cnf(c_124,plain,
n0 = empty_set,
inference(copy,[status(thm)],[c_380]) ).
cnf(c_128,plain,
( apply(sK1(B),A) = empty_set
| ~ in(A,B) ),
inference(paramod,[status(thm)],[c_124,c_60]) ).
cnf(c_381,negated_conjecture,
( B = sK2(A)
| relation_dom(B) != sK3
| relation_dom(sK2(A)) != sK3
| ~ function(B)
| ~ relation(B)
| ~ relation(sK2(A)) ),
inference(resolve,[status(thm)],[c_74,c_62]) ).
cnf(c_382,negated_conjecture,
( B = sK2(A)
| relation_dom(B) != sK3
| A != sK3
| ~ function(B)
| ~ relation(B)
| ~ relation(sK2(A)) ),
inference(paramod,[status(thm)],[c_63,c_381]) ).
cnf(c_383,negated_conjecture,
( B = sK2(A)
| relation_dom(B) != sK3
| sK3 != A
| ~ function(B)
| ~ relation(B)
| ~ relation(sK2(A)) ),
inference(copy,[status(thm)],[c_382]) ).
cnf(c_384,negated_conjecture,
( sK2(A) = B
| relation_dom(B) != sK3
| sK3 != A
| ~ function(B)
| ~ relation(B)
| ~ relation(sK2(A)) ),
inference(copy,[status(thm)],[c_383]) ).
cnf(c_131,negated_conjecture,
( sK2(B) = A
| relation_dom(A) != sK3
| sK3 != B
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_61,c_384]) ).
cnf(c_385,plain,
( ~ empty(A)
| A = empty_set ),
inference(resolve,[status(thm)],[c_73,c_38]) ).
cnf(c_134,negated_conjecture,
~ empty(sK3),
inference(resolve,[status(thm)],[c_385,c_76]) ).
cnf(c_199,plain,
( ~ empty(B)
| ~ element(A,powerset(B))
| empty(A) ),
inference(resolve,[status(thm)],[c_107,c_70]) ).
cnf(c_201,plain,
( apply(sK2(A),sK0(A)) = n1
| empty(A) ),
inference(resolve,[status(thm)],[c_107,c_64]) ).
cnf(c_251,plain,
( empty(A)
| apply(sK1(A),sK0(A)) = empty_set ),
inference(resolve,[status(thm)],[c_128,c_107]) ).
cnf(c_386,plain,
( ~ empty(A)
| ~ element(n1,powerset(A)) ),
inference(resolve,[status(thm)],[c_199,c_66]) ).
cnf(c_269,plain,
~ element(n1,powerset(empty_set)),
inference(resolve,[status(thm)],[c_386,c_38]) ).
cnf(c_387,plain,
( sK2(B) = sK1(A)
| relation_dom(sK1(A)) != sK3
| sK3 != B
| ~ relation(sK1(A)) ),
inference(resolve,[status(thm)],[c_131,c_58]) ).
cnf(c_388,plain,
( sK2(B) = sK1(A)
| A != sK3
| sK3 != B
| ~ relation(sK1(A)) ),
inference(paramod,[status(thm)],[c_59,c_387]) ).
cnf(c_389,plain,
( sK2(B) = sK1(A)
| sK3 != A
| sK3 != B
| ~ relation(sK1(A)) ),
inference(copy,[status(thm)],[c_388]) ).
cnf(c_273,plain,
( sK2(A) = sK1(B)
| sK3 != B
| sK3 != A ),
inference(resolve,[status(thm)],[c_57,c_389]) ).
cnf(c_275,plain,
( sK2(A) = sK1(A)
| sK3 != A ),
inference(factor,[status(thm)],[c_273]) ).
cnf(c_390,plain,
( element(A,B)
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_69,c_33]) ).
cnf(c_281,plain,
~ in(n1,powerset(empty_set)),
inference(resolve,[status(thm)],[c_390,c_269]) ).
cnf(c_391,plain,
A = relation_dom(sK2(A)),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_392,plain,
sK2(relation_dom(sK2(sK3))) = sK1(relation_dom(sK2(sK3))),
inference(resolve,[status(thm)],[c_275,c_391]) ).
cnf(c_393,plain,
sK2(sK3) = sK1(relation_dom(sK2(sK3))),
inference(paramod,[status(thm)],[c_63,c_392]) ).
cnf(c_288,plain,
sK2(sK3) = sK1(sK3),
inference(paramod,[status(thm)],[c_63,c_393]) ).
cnf(c_394,plain,
apply(sK2(sK3),sK0(sK3)) = n1,
inference(resolve,[status(thm)],[c_201,c_134]) ).
cnf(c_296,plain,
apply(sK1(sK3),sK0(sK3)) = n1,
inference(paramod,[status(thm)],[c_288,c_394]) ).
cnf(c_395,plain,
apply(sK1(sK3),sK0(sK3)) = empty_set,
inference(resolve,[status(thm)],[c_251,c_134]) ).
cnf(c_327,plain,
n1 = empty_set,
inference(paramod,[status(thm)],[c_296,c_395]) ).
cnf(c_396,plain,
~ in(empty_set,powerset(empty_set)),
inference(paramod,[status(thm)],[c_327,c_281]) ).
cnf(c_378,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n015.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.63 % WCLimit : 300
% 0.16/0.63 % DateTime : Sat Sep 26 08:32:59 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.64 % Process 3581278 was started by sandbox2 on n015,
% 0.16/0.64 % Sat Sep 26 08:32:59 2026
% 0.16/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.65
% 0.22/0.65 % From the command line: assign(max_seconds, 300).
% 0.22/0.72
% 0.22/0.72 % SZS status Theorem for theBenchmark
% 0.22/0.72
% 0.22/0.72 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.22/0.72 % Length of proof is 54.
% 0.22/0.72 % Level of proof is 8.
% 0.22/0.72 % Maximum clause weight is 19.000.
% 0.22/0.72 % Given clauses 125.
% 0.22/0.72
% 0.22/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------