%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 : Fri Sep 25 02:43:42 PM UTC 2026
% Result : Theorem 7.48s 1.61s
% Output : Proof 7.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 25 unt; 0 def)
% Number of atoms : 126 ( 18 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 134 ( 53 ~; 41 |; 17 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 66 ( 2 sgn 38 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_4) ).
fof(f19_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,relation_type(C,D))
=> ( subset(B,E)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(B,relation_type(C,D))
& subset(B,E)
& ilf_type(E,relation_type(C,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ~ ilf_type(sk9,relation_type(sk10,sk11))
& subset(sk9,sk12)
& ilf_type(sk12,relation_type(sk10,sk11))
& ilf_type(sk11,set_type)
& ilf_type(sk10,set_type)
& ilf_type(sk9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10,sk11,sk12])],[f19_nnf]) ).
cnf(c41,plain,
~ ilf_type(sk9,relation_type(sk10,sk11)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t66,plain,
ifeq(ilf_type(sk9,relation_type(sk10,sk11)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( subset(B,cross_product(C,D))
| ~ subset(B,E)
| ~ ilf_type(E,relation_type(C,D)) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D,E] :
( subset(B,cross_product(C,D))
| ~ subset(B,E)
| ~ ilf_type(E,relation_type(C,D))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X3,relation_type(X1,X2)),true,ifeq(subset(X0,X3),true,subset(X0,cross_product(X1,X2)),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c36,plain,
ilf_type(sk9,set_type),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi34,negated_conjecture,
ilf_type(sk9,set_type) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(c37,plain,
ilf_type(sk10,set_type),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi35,negated_conjecture,
ilf_type(sk10,set_type) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(c38,plain,
ilf_type(sk11,set_type),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi36,negated_conjecture,
ilf_type(sk11,set_type) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(c39,plain,
ilf_type(sk12,relation_type(sk10,sk11)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi37,negated_conjecture,
ilf_type(sk12,relation_type(sk10,sk11)) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(c40,plain,
subset(sk9,sk12),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi38,negated_conjecture,
subset(sk9,sk12) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h29,plain,
subset(sk9,cross_product(sk10,sk11)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi34,hi35,hi36,hi37,hi38]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(B,relation_type(C,D))
| ~ subset(B,cross_product(C,D))
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ilf_type(B,relation_type(C,D))
| ~ subset(B,cross_product(C,D))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(subset(X0,cross_product(X1,X2)),true,ilf_type(X0,relation_type(X1,X2)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t17,plain,
ilf_type(sk9,relation_type(sk10,sk11)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi34,hi35,hi36,h29]) ).
cnf(t112,plain,
ilf_type(sk9,relation_type(sk10,sk11)) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t290,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t66,t112]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t107,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t291,plain,
false = true,
inference(step,[status(thm)],[t290,t107]) ).
cnf(t176,plain,
false = true,
inference(orient,[status(thm)],[t291]) ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(f10_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c18,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f13_nnf,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [B,C] :
( ( ( ( member(sk5(B),B)
& ilf_type(sk5(B),set_type) )
| empty(B) )
& ( ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f13_nnf]) ).
cnf(c23,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c18,c23,c41]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t176]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:32:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.48/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.48/1.61 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------