%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:36:43 AM UTC 2026
% Result : Theorem 0.04s 0.33s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 198 ( 76 ~; 71 |; 18 &)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 109 ( 12 sgn 27 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(C,E)
& member(B,D) ) ) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('theBenchmark.p',p4) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('theBenchmark.p',p10) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p13) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p14) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('theBenchmark.p',p15) ).
fof(p21,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p21) ).
fof(prove_relset_1_7,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_7) ).
fof(prove_relset_1_7_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_7]) ).
fof(nnf_22,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ( ~ member(E,C)
| ~ member(D,B) )
& member(ordered_pair(D,E),F)
& ilf_type(F,relation_type(B,C)) )
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_7_neg]) ).
fof(sk_prove_relset_1_7_neg,plain,
( ( ~ member(sK2,sK3)
| ~ member(sK0,sK1) )
& member(ordered_pair(sK0,sK2),sK4)
& ilf_type(sK4,relation_type(sK1,sK3))
& ilf_type(sK2,set_type)
& ilf_type(sK0,set_type)
& ilf_type(sK3,set_type)
& ilf_type(sK1,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK3,sK0,sK2,sK4]),skolemize(B,sK1),skolemize(C,sK3),skolemize(D,sK0),skolemize(E,sK2),skolemize(F,sK4)],[nnf_22]) ).
cnf(c_38,negated_conjecture,
( ~ member(sK2,sK3)
| ~ member(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_7_neg]) ).
cnf(c_39,negated_conjecture,
member(ordered_pair(sK0,sK2),sK4),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_7_neg]) ).
cnf(c_40,negated_conjecture,
ilf_type(sK4,relation_type(sK1,sK3)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_7_neg]) ).
cnf(c_45,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p21]) ).
cnf(c_55,plain,
( member(A,B)
| ~ ilf_type(A,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p15]) ).
cnf(c_340,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_45,c_55]) ).
cnf(c_56,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_45,c_340]) ).
cnf(c_58,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p14]) ).
cnf(c_59,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_45,c_58]) ).
cnf(c_65,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p13]) ).
cnf(c_341,plain,
( member(C,A)
| ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_65]) ).
cnf(c_342,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_45,c_341]) ).
cnf(c_66,plain,
( member(C,B)
| ~ member(C,A)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_45,c_342]) ).
cnf(c_80,plain,
( ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,subset_type(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p10]) ).
cnf(c_343,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ ilf_type(A,subset_type(B))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_80]) ).
cnf(c_81,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_45,c_343]) ).
cnf(c_89,plain,
( ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p4]) ).
cnf(c_344,plain,
( ilf_type(B,subset_type(cross_product(C,A)))
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_89]) ).
cnf(c_90,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_45,c_344]) ).
cnf(c_100,plain,
( member(B,D)
| ~ member(ordered_pair(A,B),cross_product(C,D))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_345,plain,
( member(A,C)
| ~ member(ordered_pair(D,A),cross_product(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_100]) ).
cnf(c_346,plain,
( member(D,B)
| ~ member(ordered_pair(C,D),cross_product(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_345]) ).
cnf(c_347,plain,
( member(C,A)
| ~ member(ordered_pair(B,C),cross_product(D,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_346]) ).
cnf(c_101,plain,
( member(B,D)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(resolve,[status(thm)],[c_45,c_347]) ).
cnf(c_102,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_348,plain,
( member(D,B)
| ~ member(ordered_pair(D,A),cross_product(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_102]) ).
cnf(c_349,plain,
( member(C,A)
| ~ member(ordered_pair(C,D),cross_product(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_348]) ).
cnf(c_350,plain,
( member(B,D)
| ~ member(ordered_pair(B,C),cross_product(D,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_45,c_349]) ).
cnf(c_103,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(resolve,[status(thm)],[c_45,c_350]) ).
cnf(c_133,plain,
( member(ordered_pair(sK0,sK2),A)
| ~ member(sK4,power_set(A)) ),
inference(resolve,[status(thm)],[c_66,c_39]) ).
cnf(c_161,plain,
ilf_type(sK4,subset_type(cross_product(sK1,sK3))),
inference(resolve,[status(thm)],[c_90,c_40]) ).
cnf(c_244,plain,
ilf_type(sK4,member_type(power_set(cross_product(sK1,sK3)))),
inference(resolve,[status(thm)],[c_161,c_81]) ).
cnf(c_351,plain,
( member(sK4,power_set(cross_product(sK1,sK3)))
| empty(power_set(cross_product(sK1,sK3))) ),
inference(resolve,[status(thm)],[c_244,c_56]) ).
cnf(c_277,plain,
member(sK4,power_set(cross_product(sK1,sK3))),
inference(resolve,[status(thm)],[c_59,c_351]) ).
cnf(c_326,plain,
member(ordered_pair(sK0,sK2),cross_product(sK1,sK3)),
inference(resolve,[status(thm)],[c_133,c_277]) ).
cnf(c_332,plain,
member(sK0,sK1),
inference(resolve,[status(thm)],[c_326,c_103]) ).
cnf(c_333,plain,
member(sK2,sK3),
inference(resolve,[status(thm)],[c_326,c_101]) ).
cnf(c_352,negated_conjecture,
~ member(sK2,sK3),
inference(resolve,[status(thm)],[c_332,c_38]) ).
cnf(c_339,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_333,c_352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 26 08:02:20 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 83434 was started by sandbox on n012,
% 0.04/0.30 % Sat Sep 26 08:02:20 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 0.04/0.33
% 0.04/0.33 % SZS status Theorem for theBenchmark
% 0.04/0.33
% 0.04/0.33 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.04/0.33 % Length of proof is 34.
% 0.04/0.33 % Level of proof is 8.
% 0.04/0.33 % Maximum clause weight is 11.000.
% 0.04/0.33 % Given clauses 71.
% 0.04/0.33
% 0.04/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------