%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 02:55:45 PM UTC 2026
% Result : Theorem 3.34s 1.17s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 20 unt; 0 def)
% Number of atoms : 283 ( 44 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 345 ( 159 ~; 141 |; 30 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 171 ( 0 sgn 163 !; 8 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f6,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f7,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f11,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f12,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f20,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f22,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f25,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f26,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f27,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f28,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f29,plain,
? [X0,X1] :
( element(X1,powerset(powerset(X0)))
& complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ),
inference(ennf_transformation,[],[f23]) ).
fof(f30,plain,
? [X0,X1] :
( element(X1,powerset(powerset(X0)))
& complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f38,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ~ element(X3,powerset(X0))
| ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f26]) ).
fof(f40,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f41,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f42,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f12]) ).
fof(f46,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
( element(sK1,powerset(powerset(sK0)))
& empty_set = complements_of_subsets(sK0,sK1)
& empty_set != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f30]) ).
fof(f50,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f51,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ( element(sK4(X0,X1,X2),powerset(X0))
& ( in(sK4(X0,X1,X2),X2)
| in(subset_complement(X0,sK4(X0,X1,X2)),X1) )
& ( ~ in(sK4(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK4(X0,X1,X2)),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f52]) ).
fof(f54,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f9]) ).
fof(f57,plain,
element(sK1,powerset(powerset(sK0))),
inference(cnf_transformation,[],[f47]) ).
fof(f58,plain,
empty_set = complements_of_subsets(sK0,sK1),
inference(cnf_transformation,[],[f47]) ).
fof(f59,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f47]) ).
fof(f60,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f69,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f37]) ).
fof(f70,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f71,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f75,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f54]) ).
fof(f76,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f77,plain,
empty(empty_set),
inference(cnf_transformation,[],[f11]) ).
fof(f78,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f84,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f45]) ).
fof(f85,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f86,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,complements_of_subsets(X0,X1)) ),
inference(equality_resolution,[],[f71]) ).
fof(f87,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(X4,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X4),X1) ),
inference(equality_resolution,[],[f70]) ).
tcf(c_49,negated_conjecture,
empty_set != sK1,
inference(cnf_transformation,[],[f59]) ).
tcf(c_50,negated_conjecture,
complements_of_subsets(sK0,sK1) = empty_set,
inference(cnf_transformation,[],[f58]) ).
tcf(c_51,negated_conjecture,
element(sK1,powerset(powerset(sK0))),
inference(cnf_transformation,[],[f57]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,complements_of_subsets(X0,X1))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X2),X1)
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X0,X2),X1)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X2,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_67,plain,
! [X0: $i] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f75]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_69,plain,
empty(empty_set),
inference(cnf_transformation,[],[f77]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,complements_of_subsets(X0,X2))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_61]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_61]) ).
tcf(c_756,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(X0),X0) ),
inference(superposition,[status(thm)],[c_67,c_71]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK5(powerset(X1))) ),
inference(superposition,[status(thm)],[c_67,c_54]) ).
tcf(c_815,plain,
! [X0: $i] :
( element(X0,powerset(sK0))
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_51,c_55]) ).
tcf(c_960,plain,
( ( empty_set = sK1 )
| ~ empty(sK1)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_970,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_55]) ).
tcf(c_995,plain,
! [X0: $i] :
( ( subset_complement(sK0,subset_complement(sK0,X0)) = X0 )
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_815,c_76]) ).
tcf(c_1026,plain,
! [X0: $i] :
( in(X0,complements_of_subsets(sK0,sK1))
| ~ element(X0,powerset(sK0))
| ~ in(subset_complement(sK0,X0),sK1) ),
inference(superposition,[status(thm)],[c_51,c_147]) ).
tcf(c_1035,plain,
! [X0: $i] :
( in(X0,empty_set)
| ~ element(X0,powerset(sK0))
| ~ in(subset_complement(sK0,X0),sK1) ),
inference(light_normalisation,[status(thm)],[c_1026,c_50]) ).
tcf(c_1067,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ in(X0,complements_of_subsets(X1,X2))
| ~ element(X2,powerset(powerset(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_148,c_148,c_970]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(renaming,[status(thm)],[c_1067]) ).
tcf(c_1076,plain,
! [X0: $i] :
( in(subset_complement(sK0,X0),sK1)
| ~ in(X0,complements_of_subsets(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_51,c_1068]) ).
tcf(c_1084,plain,
! [X0: $i] :
( in(subset_complement(sK0,X0),sK1)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_1076,c_50]) ).
tcf(c_1144,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_1084,c_70]) ).
tcf(c_1198,plain,
~ empty(sK1),
inference(global_subsumption_just,[status(thm)],[c_1144,c_69,c_49,c_960]) ).
tcf(c_1509,plain,
! [X0: $i] :
( empty(sK5(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_756,c_797]) ).
tcf(c_1530,plain,
! [X0: $i] :
( ( sK5(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1509,c_68]) ).
tcf(c_1640,plain,
( empty(sK1)
| ( subset_complement(sK0,subset_complement(sK0,sK5(sK1))) = sK5(sK1) ) ),
inference(superposition,[status(thm)],[c_756,c_995]) ).
tcf(c_1642,plain,
subset_complement(sK0,subset_complement(sK0,sK5(sK1))) = sK5(sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_1640,c_1198]) ).
tcf(c_1802,plain,
sK5(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_69,c_1530]) ).
tcf(c_1815,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_1802,c_797]) ).
tcf(c_1818,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_1815,c_69]) ).
tcf(c_1822,plain,
! [X0: $i] :
( ~ element(X0,powerset(sK0))
| ~ in(subset_complement(sK0,X0),sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1035,c_1818]) ).
tcf(c_1851,plain,
( ~ in(sK5(sK1),sK1)
| ~ element(subset_complement(sK0,sK5(sK1)),powerset(sK0)) ),
inference(superposition,[status(thm)],[c_1642,c_1822]) ).
tcf(c_2119,plain,
( ~ in(sK5(sK1),sK1)
| ~ element(sK5(sK1),powerset(sK0)) ),
inference(superposition,[status(thm)],[c_77,c_1851]) ).
tcf(c_2138,plain,
~ in(sK5(sK1),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_2119,c_815]) ).
tcf(c_2139,plain,
empty(sK1),
inference(superposition,[status(thm)],[c_756,c_2138]) ).
tcf(c_2140,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2139,c_1198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 13:03:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 3.34/1.17 % SZS status Started for theBenchmark.p
% 3.34/1.17 % SZS status Theorem for theBenchmark.p
% 3.34/1.17
% 3.34/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.34/1.17
% 3.34/1.17 % ------ iProver source info
% 3.34/1.17
% 3.34/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.34/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.34/1.17 % git: non_committed_changes: false
% 3.34/1.17
% 3.34/1.17 % ------ Parsing...
% 3.34/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.34/1.17
% 3.34/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.34/1.17
% 3.34/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.34/1.17
% 3.34/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.34/1.17 % ------ Proving...
% 3.34/1.17 % ------ Problem Properties
% 3.34/1.17
% 3.34/1.17 %
% 3.34/1.17 % clauses 29
% 3.34/1.17 % conjectures 3
% 3.34/1.17 % EPR 10
% 3.34/1.17 % Horn 25
% 3.34/1.17 % unary 10
% 3.34/1.17 % binary 10
% 3.34/1.17 % lits 64
% 3.34/1.17 % lits eq 9
% 3.34/1.17 % fd_pure 0
% 3.34/1.17 % fd_pseudo 0
% 3.34/1.17 % fd_cond 1
% 3.34/1.17 % fd_pseudo_cond 4
% 3.34/1.17 % AC symbols 0
% 3.34/1.17
% 3.34/1.17 % ------ Schedule dynamic 5 is on
% 3.34/1.17
% 3.34/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.34/1.17
% 3.34/1.17
% 3.34/1.17 % ------
% 3.34/1.17 % Current options:
% 3.34/1.17 % ------
% 3.34/1.17
% 3.34/1.17
% 3.34/1.17 %
% 3.34/1.17
% 3.34/1.17 % ------ Proving...
% 3.34/1.17 %
% 3.34/1.17
% 3.34/1.17 % SZS status Theorem for theBenchmark.p
% 3.34/1.17
% 3.34/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.34/1.18
% 3.34/1.18
%------------------------------------------------------------------------------