%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET641+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:47:40 PM UTC 2026
% Result : Theorem 2.08s 1.08s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 15 unt; 2 def)
% Number of atoms : 366 ( 2 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 445 ( 182 ~; 183 |; 41 &)
% ( 13 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 175 !; 12 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(f18,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f19,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X0,cross_product(X1,X2))
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_3) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X0,cross_product(X1,X2))
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(flattening,[],[f25]) ).
fof(f28,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f31,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(flattening,[],[f31]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f35,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f34]) ).
fof(f38,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f44,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& subset(X0,cross_product(X1,X2))
& ~ ilf_type(X0,relation_type(X1,X2)) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& subset(X0,cross_product(X1,X2))
& ~ ilf_type(X0,relation_type(X1,X2)) ) ) ),
inference(flattening,[],[f44]) ).
fof(f50,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f51,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK3(X0,X1),set_type)
& member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) )
& ( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ) ) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f55,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK5(X0,X1),set_type)
& member(sK5(X0,X1),X0)
& ~ member(sK5(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ( ~ ilf_type(X0,member_type(X1))
| member(X0,X1) )
& ( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK7(X0),set_type)
& member(sK7(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f61]) ).
fof(f66,plain,
( ilf_type(sK11,set_type)
& ilf_type(sK12,set_type)
& ilf_type(sK13,set_type)
& subset(sK11,cross_product(sK12,sK13))
& ~ ilf_type(sK11,relation_type(sK12,sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f45]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f77,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f83,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f88,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f89,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK5(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f93,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f95,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f106,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f18]) ).
fof(f110,plain,
subset(sK11,cross_product(sK12,sK13)),
inference(cnf_transformation,[],[f66]) ).
fof(f111,plain,
~ ilf_type(sK11,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f66]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_88,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f106]) ).
tcf(c_89,negated_conjecture,
~ ilf_type(sK11,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f111]) ).
tcf(c_90,negated_conjecture,
subset(sK11,cross_product(sK12,sK13)),
inference(cnf_transformation,[],[f110]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_88,c_79]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_88,c_69]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK5(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_189]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK5(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_190,c_88,c_190]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_191]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_88,c_74,c_169]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_198]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ member(sK5(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_88,c_68]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_88,c_64]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ~ subset(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_88,c_62]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_215]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_199,c_88]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_201,c_88]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_205,c_88]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_216,c_88]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_88]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_248,c_88]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_242,c_88]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_378]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(renaming,[status(thm)],[c_754]) ).
tcf(c_758,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_239]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(renaming,[status(thm)],[c_758]) ).
tcf(c_772,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_236]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_237]) ).
tcf(c_780,plain,
! [X0: $i,X1: $i] :
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_192]) ).
tcf(c_781,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_780]) ).
tcf(c_1286,definition,
iPr_def_10 = cross_product(sK12,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1287,definition,
iPr_def_11 = relation_type(sK12,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1288,negated_conjecture,
subset(sK11,iPr_def_10),
inference(demodulation,[status(thm)],[c_90,c_1286]) ).
tcf(c_1289,negated_conjecture,
~ ilf_type(sK11,iPr_def_11),
inference(demodulation,[status(thm)],[c_89,c_1287]) ).
tcf(c_2067,plain,
! [X0: $i] :
( ilf_type(X0,relation_type(sK12,sK13))
| ~ ilf_type(X0,subset_type(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1286,c_755]) ).
tcf(c_2068,plain,
! [X0: $i] :
( ilf_type(X0,iPr_def_11)
| ~ ilf_type(X0,subset_type(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_2067,c_1287]) ).
tcf(c_2163,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(superposition,[status(thm)],[c_772,c_759]) ).
tcf(c_3093,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK11) ),
inference(superposition,[status(thm)],[c_1288,c_412]) ).
tcf(c_3112,plain,
! [X0: $i] :
( member(sK11,power_set(X0))
| member(sK5(sK11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_781,c_3093]) ).
tcf(c_3247,plain,
member(sK11,power_set(iPr_def_10)),
inference(superposition,[status(thm)],[c_3112,c_776]) ).
tcf(c_3274,plain,
ilf_type(sK11,subset_type(iPr_def_10)),
inference(superposition,[status(thm)],[c_3247,c_2163]) ).
tcf(c_3278,plain,
ilf_type(sK11,iPr_def_11),
inference(superposition,[status(thm)],[c_3274,c_2068]) ).
tcf(c_3279,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3278,c_1289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET641+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.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 11:32:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 2.08/1.08 % SZS status Started for theBenchmark.p
% 2.08/1.08 % SZS status Theorem for theBenchmark.p
% 2.08/1.08
% 2.08/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.08/1.08
% 2.08/1.08 % ------ iProver source info
% 2.08/1.08
% 2.08/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 2.08/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.08/1.08 % git: non_committed_changes: false
% 2.08/1.08
% 2.08/1.08 % ------ Parsing...
% 2.08/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.08/1.08
% 2.08/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.08/1.08
% 2.08/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.08/1.08
% 2.08/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.08/1.08 % ------ Proving...
% 2.08/1.08 % ------ Problem Properties
% 2.08/1.08
% 2.08/1.08 %
% 2.08/1.08 % clauses 33
% 2.08/1.08 % conjectures 2
% 2.08/1.08 % EPR 7
% 2.08/1.08 % Horn 27
% 2.08/1.08 % unary 9
% 2.08/1.08 % binary 19
% 2.08/1.08 % lits 62
% 2.08/1.08 % lits eq 5
% 2.08/1.08 % fd_pure 0
% 2.08/1.08 % fd_pseudo 0
% 2.08/1.08 % fd_cond 0
% 2.08/1.08 % fd_pseudo_cond 0
% 2.08/1.08 % AC symbols 0
% 2.08/1.08
% 2.08/1.08 % ------ Schedule dynamic 5 is on
% 2.08/1.08
% 2.08/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.08/1.08
% 2.08/1.08
% 2.08/1.08 % ------
% 2.08/1.08 % Current options:
% 2.08/1.08 % ------
% 2.08/1.08
% 2.08/1.08
% 2.08/1.08 %
% 2.08/1.08
% 2.08/1.08 % ------ Proving...
% 2.08/1.08 %
% 2.08/1.08
% 2.08/1.08 % SZS status Theorem for theBenchmark.p
% 2.08/1.08
% 2.08/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.09
% 2.08/1.09
%------------------------------------------------------------------------------