%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET156+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 : 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 02:46:47 PM UTC 2026
% Result : Theorem 29.71s 11.36s
% Output : CNFRefutation 29.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 5 unt; 0 def)
% Number of atoms : 246 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 270 ( 113 ~; 117 |; 30 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 185 ( 0 sgn 177 !; 8 ?; 85 :)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
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(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
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) )
=> equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI25) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1))) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ~ equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1))) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ~ equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1))) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( subset(sK1,sK2)
& subset(sK0,sK2)
& ~ equal_set(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f21,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,[],[f17]) ).
fof(f22,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,[],[f21]) ).
fof(f23,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))],[f22]) ).
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(nnf_transformation,[],[f4]) ).
fof(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f26]) ).
fof(f28,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(f29,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,[],[f28]) ).
fof(f32,plain,
~ equal_set(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_49,negated_conjecture,
~ equal_set(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),
inference(cnf_transformation,[],[f32]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_142,plain,
( ~ subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
| ~ subset(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))) ),
inference(resolution,[status(thm)],[c_49,c_61]) ).
tcf(c_216,plain,
( subset(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1)))
| member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),union(difference(sK2,sK0),difference(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_217,plain,
( subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
| member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,intersection(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_218,plain,
( subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),union(difference(sK2,sK0),difference(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_246,plain,
( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK1))
| member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK0))
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),union(difference(sK2,sK0),difference(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_248,plain,
! [X0: $i] :
( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),X0)
| member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,X0))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] :
( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),intersection(X0,X1))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),X1)
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] :
( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),union(X0,X1))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),X1)
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),X1)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),X0)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_370,plain,
! [X0: $i] : subset(X0,X0),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_371,plain,
subset(sK2,sK2),
inference(instantiation,[status(thm)],[c_370]) ).
tcf(c_599,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,union(X1,X2))
| ~ member(sK3(X0,union(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_59,c_52]) ).
tcf(c_623,plain,
( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK2)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_350]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X0,X1),X2)
| member(sK3(difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_53,c_63]) ).
tcf(c_762,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_62,c_52]) ).
tcf(c_1272,plain,
( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK2)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_350]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(difference(X0,X2),X3)
| member(sK3(difference(X0,X2),X3),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_656,c_54]) ).
tcf(c_1778,plain,
( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),intersection(sK0,sK1))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,intersection(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_291]) ).
tcf(c_2065,plain,
( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),union(difference(sK2,sK0),difference(sK2,sK1)))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_2170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,union(X1,difference(X2,X3)))
| member(sK3(X0,union(X1,difference(X2,X3))),X3)
| ~ member(sK3(X0,union(X1,difference(X2,X3))),X2) ),
inference(superposition,[status(thm)],[c_62,c_599]) ).
tcf(c_5283,plain,
( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),intersection(sK0,sK1))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK1)
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK0) ),
inference(instantiation,[status(thm)],[c_288]) ).
tcf(c_9894,plain,
( ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK0)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_20232,plain,
( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK0)
| member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK0))
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2) ),
inference(instantiation,[status(thm)],[c_248]) ).
tcf(c_61277,plain,
! [X0: $i] :
( subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
| member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),X0)
| ~ subset(sK2,X0) ),
inference(instantiation,[status(thm)],[c_1536]) ).
tcf(c_61278,plain,
( subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
| member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2)
| ~ subset(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_61277]) ).
tcf(c_61286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,difference(X1,intersection(X2,X3)))
| member(sK3(X0,difference(X1,intersection(X2,X3))),intersection(X2,X3))
| ~ member(sK3(X0,difference(X1,intersection(X2,X3))),X1) ),
inference(instantiation,[status(thm)],[c_762]) ).
tcf(c_61287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,difference(X1,intersection(X2,X3))),X3)
| ~ member(sK3(X0,difference(X1,intersection(X2,X3))),intersection(X2,X3)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_61288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,difference(X1,intersection(X2,X3))),X2)
| ~ member(sK3(X0,difference(X1,intersection(X2,X3))),intersection(X2,X3)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_62031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ member(sK3(X0,difference(X1,X2)),X4)
| ~ member(sK3(X0,difference(X1,X2)),difference(X3,X4)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_63931,plain,
( subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
| member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK1)
| ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2) ),
inference(instantiation,[status(thm)],[c_2170]) ).
tcf(c_68523,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),X1)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_62031]) ).
tcf(c_74939,plain,
( subset(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1)))
| member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),intersection(sK0,sK1))
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK2) ),
inference(instantiation,[status(thm)],[c_61286]) ).
tcf(c_81142,plain,
( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK0)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_61288]) ).
tcf(c_81370,plain,
( ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK1)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_68523]) ).
tcf(c_87789,plain,
( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK1)
| ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_61287]) ).
tcf(c_87790,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_87789,c_81370,c_81142,c_74939,c_63931,c_61278,c_20232,c_9894,c_5283,c_2065,c_1778,c_1272,c_623,c_371,c_246,c_217,c_218,c_216,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET156+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.37 % Computer : n009.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Thu Sep 24 10:03:48 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.41 Running first-order theorem proving
% 0.16/5.41 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
% 0.16/5.42
% 0.16/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.42
% 0.16/5.42 % Detected problem language: tptp
% 0.16/5.43 % Proving...
% 29.71/11.36 % SZS status Started for theBenchmark.p
% 29.71/11.36 % SZS status Theorem for theBenchmark.p
% 29.71/11.36
% 29.71/11.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.71/11.36
% 29.71/11.36 % ------ iProver source info
% 29.71/11.36
% 29.71/11.36 % git: date: 2026-07-19 20:42:38 +0200
% 29.71/11.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.71/11.36 % git: non_committed_changes: false
% 29.71/11.36
% 29.71/11.36 % ------ Parsing...
% 29.71/11.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.71/11.36
% 29.71/11.36 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 29.71/11.36
% 29.71/11.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 29.71/11.36 % ------ Proving...
% 29.71/11.36 % ------ Problem Properties
% 29.71/11.36
% 29.71/11.36 %
% 29.71/11.36 % clauses 15
% 29.71/11.36 % conjectures 2
% 29.71/11.36 % EPR 3
% 29.71/11.36 % Horn 12
% 29.71/11.36 % unary 2
% 29.71/11.36 % binary 9
% 29.71/11.36 % lits 32
% 29.71/11.36 % lits eq 0
% 29.71/11.36 % fd_pure 0
% 29.71/11.36 % fd_pseudo 0
% 29.71/11.36 % fd_cond 0
% 29.71/11.36 % fd_pseudo_cond 0
% 29.71/11.36 % AC symbols 0
% 29.71/11.36
% 29.71/11.36 % ------ Schedule dynamic 5 is on
% 29.71/11.36
% 29.71/11.36 % ------ no equalities: superposition off
% 29.71/11.36
% 29.71/11.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 29.71/11.36
% 29.71/11.36
% 29.71/11.36 % ------
% 29.71/11.36 % Current options:
% 29.71/11.36 % ------
% 29.71/11.36
% 29.71/11.36
% 29.71/11.36 %
% 29.71/11.36
% 29.71/11.36 % ------ Proving...
% 29.71/11.36 %
% 29.71/11.36
% 29.71/11.36 % SZS status Theorem for theBenchmark.p
% 29.71/11.36
% 29.71/11.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.71/11.36
% 29.71/11.36
%------------------------------------------------------------------------------