%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET699+4 : 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 : n026.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 02:47:49 PM UTC 2026
% Result : Theorem 10.71s 7.29s
% Output : CNFRefutation 10.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of formulae : 95 ( 11 unt; 0 def)
% Number of atoms : 268 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 275 ( 102 ~; 131 |; 31 &)
% ( 6 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 197 ( 0 sgn 183 !; 14 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI33) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
<~> subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
<~> subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
| subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) )
& ( ~ subset(X0,X1)
| ~ subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
| subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) )
& ( ~ subset(X0,X1)
| ~ subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( subset(sK1,sK2)
& subset(sK0,sK2)
& ( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)) )
& ( ~ subset(sK0,sK1)
| ~ subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( 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))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f25]) ).
fof(f28,plain,
subset(sK0,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
( ~ subset(sK0,sK1)
| ~ subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,negated_conjecture,
( ~ subset(sK0,sK1)
| ~ subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,negated_conjecture,
( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_51,negated_conjecture,
subset(sK0,sK2),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_174,plain,
( subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0))
| member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),intersection(sK0,difference(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_184,plain,
( member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),difference(sK2,sK1))
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),intersection(sK0,difference(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_185,plain,
( member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),sK0)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),intersection(sK0,difference(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_211,plain,
! [X0: $i] :
( member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),X1)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_54,c_57]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK3(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK3(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_485,plain,
( ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),sK1)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),difference(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X0,X1),X2)
| member(sK3(difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_54,c_60]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X0,X1),X2)
| ~ member(sK3(difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_54,c_61]) ).
tcf(c_573,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,difference(X1,X2))
| member(sK3(X0,difference(X1,X2)),X2)
| ~ member(sK3(X0,difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_59,c_53]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,difference(X1,X2))
| member(sK3(X0,difference(X1,X2)),X2)
| ~ member(sK3(X0,difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_59,c_53]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ~ member(sK3(X0,X3),X2)
| ~ subset(X0,difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_459,c_61]) ).
tcf(c_777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| member(sK3(X0,X3),X1)
| ~ subset(X0,difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_459,c_60]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| member(sK3(X0,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_469,c_55]) ).
tcf(c_874,plain,
( member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i] : subset(difference(X0,X0),X1),
inference(superposition,[status(thm)],[c_513,c_546]) ).
tcf(c_1364,plain,
! [X0: $i,X1: $i] :
( subset(X0,difference(X0,X1))
| member(sK3(X0,difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_54,c_590]) ).
tcf(c_1499,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,difference(X2,X0))
| member(sK3(X2,difference(X2,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1364,c_55]) ).
tcf(c_1665,plain,
! [X0: $i] :
( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK2,sK1)),X0)
| member(sK3(intersection(sK0,difference(sK2,sK1)),X0),sK2) ),
inference(superposition,[status(thm)],[c_50,c_777]) ).
tcf(c_1695,plain,
! [X0: $i] :
( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK2,sK1)),X0)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),X0),sK0) ),
inference(superposition,[status(thm)],[c_50,c_776]) ).
tcf(c_1803,plain,
! [X0: $i] :
( member(sK3(intersection(sK0,difference(sK2,sK1)),X0),sK2)
| subset(intersection(sK0,difference(sK2,sK1)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_1665,c_49,c_174,c_185,c_184,c_485,c_874,c_1665]) ).
tcf(c_1804,plain,
! [X0: $i] :
( subset(intersection(sK0,difference(sK2,sK1)),X0)
| member(sK3(intersection(sK0,difference(sK2,sK1)),X0),sK2) ),
inference(renaming,[status(thm)],[c_1803]) ).
tcf(c_1812,plain,
! [X0: $i] :
( subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,X0))
| member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,X0)),X0) ),
inference(superposition,[status(thm)],[c_1804,c_573]) ).
tcf(c_1818,plain,
( subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0))
| member(sK3(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_1812]) ).
tcf(c_1918,plain,
! [X0: $i] :
( ~ member(sK3(intersection(sK0,difference(sK2,sK1)),X0),sK0)
| subset(intersection(sK0,difference(sK2,sK1)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_1695,c_49,c_174,c_184,c_485,c_874,c_1695,c_1818]) ).
tcf(c_1919,plain,
! [X0: $i] :
( subset(intersection(sK0,difference(sK2,sK1)),X0)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),X0),sK0) ),
inference(renaming,[status(thm)],[c_1918]) ).
tcf(c_1923,plain,
! [X0: $i] : subset(intersection(sK0,difference(sK2,sK1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_1919,c_410]) ).
tcf(c_1924,plain,
~ subset(sK0,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_1923]) ).
tcf(c_3333,plain,
! [X0: $i,X1: $i] :
( subset(sK0,X1)
| member(sK3(sK0,X1),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_51,c_801]) ).
tcf(c_3490,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK0,X2)
| member(sK3(sK0,X2),X0)
| ~ subset(sK2,difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_3333,c_60]) ).
tcf(c_6514,negated_conjecture,
subset(intersection(sK0,difference(sK2,sK1)),difference(sK2,sK0)),
inference(global_subsumption_just,[status(thm)],[c_50,c_50,c_1924]) ).
tcf(c_6516,negated_conjecture,
~ subset(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_174,c_185,c_184,c_485,c_874]) ).
tcf(c_6529,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_54,c_57]) ).
tcf(c_6570,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK3(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_6674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| member(sK3(X0,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6570,c_55]) ).
tcf(c_6677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ~ member(sK3(X0,X3),X2)
| ~ subset(X0,difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6570,c_61]) ).
tcf(c_6730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| ~ subset(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_6936,plain,
! [X0: $i] :
( subset(intersection(sK0,difference(sK2,sK1)),X0)
| ~ member(sK3(intersection(sK0,difference(sK2,sK1)),X0),sK0) ),
inference(superposition,[status(thm)],[c_6514,c_6677]) ).
tcf(c_6952,plain,
! [X0: $i] : subset(intersection(sK0,difference(sK2,sK1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_6936,c_6529]) ).
tcf(c_7697,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,sK0)
| ~ member(X0,difference(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_6952,c_6730]) ).
tcf(c_9275,plain,
! [X0: $i,X1: $i] :
( member(X0,sK1)
| member(X0,X1)
| ~ member(X0,sK2)
| ~ member(X0,sK0) ),
inference(superposition,[status(thm)],[c_59,c_7697]) ).
tcf(c_9741,plain,
! [X0: $i,X1: $i] :
( subset(sK0,X0)
| member(sK3(sK0,X0),sK1)
| member(sK3(sK0,X0),X1)
| ~ member(sK3(sK0,X0),sK2) ),
inference(superposition,[status(thm)],[c_54,c_9275]) ).
tcf(c_12253,plain,
! [X0: $i,X1: $i] :
( subset(X1,difference(X1,X0))
| ~ subset(X0,difference(X1,X0)) ),
inference(superposition,[status(thm)],[c_1499,c_53]) ).
tcf(c_12806,plain,
! [X0: $i,X1: $i] : subset(X0,difference(X0,difference(X1,X1))),
inference(superposition,[status(thm)],[c_1221,c_12253]) ).
tcf(c_13318,plain,
! [X0: $i] :
( subset(sK0,X0)
| member(sK3(sK0,X0),sK2) ),
inference(superposition,[status(thm)],[c_12806,c_3490]) ).
tcf(c_16368,plain,
! [X0: $i,X1: $i] :
( subset(sK0,X1)
| member(sK3(sK0,X1),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_51,c_6674]) ).
tcf(c_16462,plain,
! [X0: $i,X1: $i] :
( subset(sK0,X0)
| member(sK3(sK0,X0),sK1)
| member(sK3(sK0,X0),X1)
| ~ subset(sK2,sK0)
| ~ member(sK3(sK0,X0),sK2) ),
inference(superposition,[status(thm)],[c_16368,c_9275]) ).
tcf(c_23666,plain,
! [X0: $i,X1: $i] :
( subset(sK0,X0)
| member(sK3(sK0,X0),sK1)
| member(sK3(sK0,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_16462,c_9741,c_13318]) ).
tcf(c_23690,plain,
! [X0: $i] :
( subset(sK0,X0)
| member(sK3(sK0,X0),sK1) ),
inference(equality_factoring,[status(thm)],[c_23666]) ).
tcf(c_27780,plain,
subset(sK0,sK1),
inference(superposition,[status(thm)],[c_23690,c_53]) ).
tcf(c_27785,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_27780,c_6516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET699+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n026.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 11:44:45 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 10.71/7.29 % SZS status Started for theBenchmark.p
% 10.71/7.29 % SZS status Theorem for theBenchmark.p
% 10.71/7.29
% 10.71/7.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.71/7.29
% 10.71/7.29 % ------ iProver source info
% 10.71/7.29
% 10.71/7.29 % git: date: 2026-07-19 20:42:38 +0200
% 10.71/7.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.71/7.29 % git: non_committed_changes: false
% 10.71/7.29
% 10.71/7.29 % ------ Parsing...
% 10.71/7.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.71/7.29
% 10.71/7.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.71/7.29
% 10.71/7.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.71/7.29 % ------ Proving...
% 10.71/7.29 % ------ Problem Properties
% 10.71/7.29
% 10.71/7.29 %
% 10.71/7.29 % clauses 13
% 10.71/7.29 % conjectures 4
% 10.71/7.29 % EPR 3
% 10.71/7.29 % Horn 10
% 10.71/7.29 % unary 2
% 10.71/7.29 % binary 8
% 10.71/7.29 % lits 27
% 10.71/7.29 % lits eq 0
% 10.71/7.29 % fd_pure 0
% 10.71/7.29 % fd_pseudo 0
% 10.71/7.29 % fd_cond 0
% 10.71/7.29 % fd_pseudo_cond 0
% 10.71/7.29 % AC symbols 0
% 10.71/7.29
% 10.71/7.29 % ------ Schedule dynamic 5 is on
% 10.71/7.29
% 10.71/7.29 % ------ no equalities: superposition off
% 10.71/7.29
% 10.71/7.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.71/7.29
% 10.71/7.29
% 10.71/7.29 % ------
% 10.71/7.29 % Current options:
% 10.71/7.29 % ------
% 10.71/7.29
% 10.71/7.29
% 10.71/7.29 %
% 10.71/7.29
% 10.71/7.29 % ------ Proving...
% 10.71/7.29 %
% 10.71/7.29
% 10.71/7.29 % SZS status Theorem for theBenchmark.p
% 10.71/7.29
% 10.71/7.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.71/7.29
% 10.71/7.29
%------------------------------------------------------------------------------