%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU283+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:56:28 PM UTC 2026
% Result : Theorem 53.93s 8.43s
% Output : CNFRefutation 53.93s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f160ERROR: Could not build tree for root c_104058ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ! [X1] :
~ ( ! [X2] : X2 != singleton(X1)
& in(X1,X0) )
& ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 ) )
=> ? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ! [X1] :
~ ( ! [X2] : X2 != singleton(X1)
& in(X1,X0) )
& ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 ) )
=> ? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 )
=> ? [X1] :
( ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X3 = singleton(X2)
& in(X2,X0)
& in(X2,X0) ) )
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
fof(f11,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f12,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f13,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f14,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f35,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f39,plain,
~ ! [X0] :
( ( ! [X4] :
~ ( ! [X5] : singleton(X4) != X5
& in(X4,X0) )
& ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 ) )
=> ? [X6] :
( ! [X7] :
( in(X7,X0)
=> apply(X6,X7) = singleton(X7) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) ) ),
inference(rectify,[],[f2]) ).
fof(f40,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 )
=> ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
inference(rectify,[],[f8]) ).
fof(f43,plain,
? [X0] :
( ! [X4] :
( ? [X5] : singleton(X4) = X5
| ~ in(X4,X0) )
& ! [X1,X2,X3] :
( singleton(X1) != X3
| singleton(X1) != X2
| ~ in(X1,X0)
| X2 = X3 )
& ! [X6] :
( ? [X7] :
( in(X7,X0)
& apply(X6,X7) != singleton(X7) )
| relation_dom(X6) != X0
| ~ function(X6)
| ~ relation(X6) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f44,plain,
? [X0] :
( ! [X4] :
( ? [X5] : singleton(X4) = X5
| ~ in(X4,X0) )
& ! [X1,X2,X3] :
( singleton(X1) != X3
| singleton(X1) != X2
| ~ in(X1,X0)
| X2 = X3 )
& ! [X6] :
( ? [X7] :
( in(X7,X0)
& apply(X6,X7) != singleton(X7) )
| relation_dom(X6) != X0
| ~ function(X6)
| ~ relation(X6) ) ),
inference(flattening,[],[f43]) ).
fof(f46,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f47,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f51,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f65,plain,
? [X0] :
( ! [X6] :
( ? [X7] : singleton(X6) = X7
| ~ in(X6,X0) )
& ! [X3,X4,X5] :
( singleton(X3) != X5
| singleton(X3) != X4
| ~ in(X3,X0)
| X4 = X5 )
& ! [X1] :
( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != singleton(X2) )
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ) ),
inference(rectify,[],[f44]) ).
fof(f66,plain,
( ! [X6] :
( singleton(X6) = sK3(X6)
| ~ in(X6,sK1) )
& ! [X3,X4,X5] :
( singleton(X3) != X5
| singleton(X3) != X4
| ~ in(X3,sK1)
| X4 = X5 )
& ! [X1] :
( ( in(sK2(X1),sK1)
& apply(X1,sK2(X1)) != singleton(sK2(X1)) )
| relation_dom(X1) != sK1
| ~ function(X1)
| ~ relation(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X2,sK2(X1)),skolemize(X7,sK3(X6))],[f65]) ).
fof(f72,plain,
! [X0] :
( ( sK8(X0) = singleton(sK6(X0))
& in(sK6(X0),X0)
& sK7(X0) = singleton(sK6(X0))
& in(sK6(X0),X0)
& sK7(X0) != sK8(X0) )
| sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0)),skolemize(X3,sK8(X0))],[f64]) ).
fof(f73,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK11(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK9(X0,X1),X1)
| in(ordered_pair(sK9(X0,X1),sK10(X0,X1)),X0) )
& ( ~ in(sK9(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK9(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X2,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X7,sK11(X0,X5))],[f75]) ).
fof(f83,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f59]) ).
fof(f84,plain,
! [X0,X1] :
( ( ( in(sK18(X0,X1),X0)
| in(sK18(X0,X1),X1) )
& ( ~ in(sK18(X0,X1),X0)
| ~ in(sK18(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X2,sK18(X0,X1))],[f83]) ).
fof(f87,plain,
! [X1] :
( in(sK2(X1),sK1)
| relation_dom(X1) != sK1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f88,plain,
! [X1] :
( apply(X1,sK2(X1)) != singleton(sK2(X1))
| relation_dom(X1) != sK1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f98,plain,
! [X0] :
( sK8(X0) = singleton(sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f100,plain,
! [X0] :
( sK7(X0) = singleton(sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
! [X0] :
( sK7(X0) != sK8(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f105,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2 ),
inference(cnf_transformation,[],[f73]) ).
fof(f111,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f114,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f136,plain,
! [X0,X1] :
( in(sK18(X0,X1),X0)
| in(sK18(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f84]) ).
fof(f137,plain,
! [X0,X1] :
( ~ in(sK18(X0,X1),X0)
| ~ in(sK18(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f84]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2 ),
inference(definition_unfolding,[],[f109,f114]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0) ),
inference(definition_unfolding,[],[f108,f114]) ).
fof(f149,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f111,f114]) ).
fof(f155,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0) ),
inference(equality_resolution,[],[f146]) ).
fof(f158,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f149]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ function(X0)
| ~ relation(X0)
| ( relation_dom(X0) != sK1 )
| ( apply(X0,sK2(X0)) != singleton(sK2(X0)) ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(sK2(X0),sK1)
| ~ function(X0)
| ~ relation(X0)
| ( relation_dom(X0) != sK1 ) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,singleton(X0)),singleton(X0)),sK5(X1))
| ~ sP0(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_61,plain,
! [X0: $i] :
( sP0(X0)
| ( sK7(X0) != sK8(X0) ) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_63,plain,
! [X0: $i] :
( sP0(X0)
| ( singleton(sK6(X0)) = sK7(X0) ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_65,plain,
! [X0: $i] :
( sP0(X0)
| ( singleton(sK6(X0)) = sK8(X0) ) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f105]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,apply(X1,X0)),singleton(X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK18(X0,X1),X1)
| ~ in(sK18(X0,X1),X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( in(sK18(X0,X1),X1)
| in(sK18(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_75,c_69]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_75,c_68]) ).
tcf(c_468,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,singleton(X0))),sK5(X1))
| ~ sP0(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_57,c_68]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_135,c_68]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_70,c_68]) ).
tcf(c_3860,negated_conjecture,
! [X0: $i] :
( in(sK2(X0),sK1)
| ~ function(X0)
| ~ relation(X0)
| ( relation_dom(X0) != sK1 ) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_3861,negated_conjecture,
! [X0: $i] :
( ~ function(X0)
| ~ relation(X0)
| ( relation_dom(X0) != sK1 )
| ( apply(X0,sK2(X0)) != singleton(sK2(X0)) ) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_3862,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3864,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4911,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ~ in(sK18(relation_dom(X0),sK1),sK1)
| ~ in(sK18(relation_dom(X0),sK1),relation_dom(X0)) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_4917,plain,
! [X0: $i] :
( in(sK18(relation_dom(X0),sK1),sK1)
| in(sK18(relation_dom(X0),sK1),relation_dom(X0))
| ( relation_dom(X0) = sK1 ) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_5210,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK2(X0)),unordered_pair(sK2(X0),singleton(sK2(X0)))),sK5(sK1))
| ~ sP0(sK1)
| ~ in(sK2(X0),sK1) ),
inference(instantiation,[status(thm)],[c_468]) ).
tcf(c_5256,plain,
! [X0: $i] :
( ( apply(X0,sK2(X0)) = singleton(sK2(X0)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK2(X0)),unordered_pair(sK2(X0),singleton(sK2(X0)))),X0) ),
inference(instantiation,[status(thm)],[c_498]) ).
tcf(c_5987,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK18(relation_dom(X0),sK1)),unordered_pair(sK18(relation_dom(X0),sK1),apply(X0,sK18(relation_dom(X0),sK1)))),X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(relation_dom(X0),sK1),relation_dom(X0)) ),
inference(instantiation,[status(thm)],[c_511]) ).
tcf(c_6080,plain,
( sP0(sK1)
| ( singleton(sK6(sK1)) = sK8(sK1) ) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_6082,plain,
( sP0(sK1)
| ( singleton(sK6(sK1)) = sK7(sK1) ) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_6083,plain,
( sP0(sK1)
| ( sK7(sK1) != sK8(sK1) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_8323,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = singleton(X0) )
| ( X2 != X1 )
| ( singleton(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_3864]) ).
tcf(c_9758,plain,
! [X0: $i] :
( ( sK7(sK1) = sK8(sK1) )
| ( sK8(sK1) != X0 )
| ( sK7(sK1) != X0 ) ),
inference(instantiation,[status(thm)],[c_3864]) ).
tcf(c_9768,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK18(relation_dom(X0),sK1)),unordered_pair(sK18(relation_dom(X0),sK1),singleton(sK18(relation_dom(X0),sK1)))),sK5(sK1))
| ~ sP0(sK1)
| ~ in(sK18(relation_dom(X0),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_468]) ).
tcf(c_14105,plain,
! [X0: $i] :
( ( X0 = singleton(sK6(sK1)) )
| ( X0 != sK8(sK1) )
| ( singleton(sK6(sK1)) != sK8(sK1) ) ),
inference(instantiation,[status(thm)],[c_8323]) ).
tcf(c_14107,plain,
! [X0: $i] :
( ( X0 = singleton(sK6(sK1)) )
| ( X0 != sK7(sK1) )
| ( singleton(sK6(sK1)) != sK7(sK1) ) ),
inference(instantiation,[status(thm)],[c_8323]) ).
tcf(c_21152,plain,
sK7(sK1) = sK7(sK1),
inference(instantiation,[status(thm)],[c_3862]) ).
tcf(c_21456,plain,
( ( sK8(sK1) = singleton(sK6(sK1)) )
| ( sK8(sK1) != sK8(sK1) )
| ( singleton(sK6(sK1)) != sK8(sK1) ) ),
inference(instantiation,[status(thm)],[c_14105]) ).
tcf(c_21457,plain,
sK8(sK1) = sK8(sK1),
inference(instantiation,[status(thm)],[c_3862]) ).
tcf(c_42205,plain,
( in(unordered_pair(singleton(sK2(sK5(sK1))),unordered_pair(sK2(sK5(sK1)),singleton(sK2(sK5(sK1))))),sK5(sK1))
| ~ sP0(sK1)
| ~ in(sK2(sK5(sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_5210]) ).
tcf(c_42206,plain,
( ( apply(sK5(sK1),sK2(sK5(sK1))) = singleton(sK2(sK5(sK1))) )
| ~ function(sK5(sK1))
| ~ relation(sK5(sK1))
| ~ in(unordered_pair(singleton(sK2(sK5(sK1))),unordered_pair(sK2(sK5(sK1)),singleton(sK2(sK5(sK1))))),sK5(sK1)) ),
inference(instantiation,[status(thm)],[c_5256]) ).
tcf(c_42220,plain,
! [X0: $i] :
( in(sK18(relation_dom(X0),sK1),relation_dom(sK5(sK1)))
| ~ relation(sK5(sK1))
| ~ in(unordered_pair(singleton(sK18(relation_dom(X0),sK1)),unordered_pair(sK18(relation_dom(X0),sK1),singleton(sK18(relation_dom(X0),sK1)))),sK5(sK1)) ),
inference(instantiation,[status(thm)],[c_432]) ).
tcf(c_52408,plain,
( ( sK7(sK1) = sK8(sK1) )
| ( sK8(sK1) != singleton(sK6(sK1)) )
| ( sK7(sK1) != singleton(sK6(sK1)) ) ),
inference(instantiation,[status(thm)],[c_9758]) ).
tcf(c_63328,plain,
! [X0: $i] :
( in(sK2(sK5(X0)),sK1)
| ~ function(sK5(X0))
| ~ relation(sK5(X0))
| ( relation_dom(sK5(X0)) != sK1 ) ),
inference(instantiation,[status(thm)],[c_3860]) ).
tcf(c_65142,plain,
( ( sK7(sK1) = singleton(sK6(sK1)) )
| ( sK7(sK1) != sK7(sK1) )
| ( singleton(sK6(sK1)) != sK7(sK1) ) ),
inference(instantiation,[status(thm)],[c_14107]) ).
tcf(c_81299,plain,
( in(sK18(relation_dom(sK5(sK1)),sK1),relation_dom(sK5(sK1)))
| ~ relation(sK5(sK1))
| ~ in(unordered_pair(singleton(sK18(relation_dom(sK5(sK1)),sK1)),unordered_pair(sK18(relation_dom(sK5(sK1)),sK1),singleton(sK18(relation_dom(sK5(sK1)),sK1)))),sK5(sK1)) ),
inference(instantiation,[status(thm)],[c_42220]) ).
tcf(c_81300,plain,
( in(unordered_pair(singleton(sK18(relation_dom(sK5(sK1)),sK1)),unordered_pair(sK18(relation_dom(sK5(sK1)),sK1),apply(sK5(sK1),sK18(relation_dom(sK5(sK1)),sK1)))),sK5(sK1))
| ~ function(sK5(sK1))
| ~ relation(sK5(sK1))
| ~ in(sK18(relation_dom(sK5(sK1)),sK1),relation_dom(sK5(sK1))) ),
inference(instantiation,[status(thm)],[c_5987]) ).
tcf(c_81304,plain,
( ( relation_dom(sK5(sK1)) = sK1 )
| ~ in(sK18(relation_dom(sK5(sK1)),sK1),sK1)
| ~ in(sK18(relation_dom(sK5(sK1)),sK1),relation_dom(sK5(sK1))) ),
inference(instantiation,[status(thm)],[c_4911]) ).
tcf(c_81911,plain,
( in(sK2(sK5(sK1)),sK1)
| ~ function(sK5(sK1))
| ~ relation(sK5(sK1))
| ( relation_dom(sK5(sK1)) != sK1 ) ),
inference(instantiation,[status(thm)],[c_63328]) ).
tcf(c_82048,plain,
( ~ function(sK5(sK1))
| ~ relation(sK5(sK1))
| ( relation_dom(sK5(sK1)) != sK1 )
| ( apply(sK5(sK1),sK2(sK5(sK1))) != singleton(sK2(sK5(sK1))) ) ),
inference(instantiation,[status(thm)],[c_3861]) ).
tcf(c_95852,plain,
( in(unordered_pair(singleton(sK18(relation_dom(sK5(sK1)),sK1)),unordered_pair(sK18(relation_dom(sK5(sK1)),sK1),singleton(sK18(relation_dom(sK5(sK1)),sK1)))),sK5(sK1))
| ~ sP0(sK1)
| ~ in(sK18(relation_dom(sK5(sK1)),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_9768]) ).
tcf(c_98502,plain,
( in(sK18(relation_dom(sK5(sK1)),sK1),sK1)
| in(sK18(relation_dom(sK5(sK1)),sK1),relation_dom(sK5(sK1)))
| ( relation_dom(sK5(sK1)) = sK1 ) ),
inference(instantiation,[status(thm)],[c_4917]) ).
fof(f63,definition,
! [X0] :
( ~ sP0(X0)
| ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f64,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| sP0(X0) ),
inference(definition_folding,[],[f47,f63]) ).
fof(f68,plain,
! [X0] :
( ~ sP0(X0)
| ? [X4] :
( ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X4)
| ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& ( singleton(X5) != X6
| ~ in(X5,X0)
| ~ in(X5,X0)
| in(ordered_pair(X5,X6),X4) ) )
& function(X4)
& relation(X4) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f69,plain,
! [X0] :
( ~ sP0(X0)
| ? [X4] :
( ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X4)
| ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& ( singleton(X5) != X6
| ~ in(X5,X0)
| ~ in(X5,X0)
| in(ordered_pair(X5,X6),X4) ) )
& function(X4)
& relation(X4) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ sP0(X0)
| ? [X1] :
( ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) ) )
& ( singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) )
& function(X1)
& relation(X1) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ sP0(X0)
| ( ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),sK5(X0))
| ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) ) )
& ( singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),sK5(X0)) ) )
& function(sK5(X0))
& relation(sK5(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f70]) ).
fof(f94,plain,
! [X2,X3,X0] :
( ~ sP0(X0)
| ~ in(ordered_pair(X2,X3),sK5(X0))
| in(X2,X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f96,plain,
! [X0] :
( ~ sP0(X0)
| function(sK5(X0)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X0] :
( ~ sP0(X0)
| relation(sK5(X0)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f142,plain,
! [X2,X3,X0] :
( ~ sP0(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK5(X0))
| in(X2,X0) ),
inference(definition_unfolding,[],[f94,f114]) ).
tcf(c_55,plain,
! [X0: $i] :
( relation(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_56,plain,
! [X0: $i] :
( function(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ sP0(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK5(X2)) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ sP0(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2)) ),
inference(demodulation,[status(thm)],[c_58,c_68]) ).
tcf(c_62321,plain,
( relation(sK5(sK1))
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_92078,plain,
( function(sK5(sK1))
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_104057,plain,
( in(sK18(relation_dom(sK5(sK1)),sK1),sK1)
| ~ sP0(sK1)
| ~ in(unordered_pair(singleton(sK18(relation_dom(sK5(sK1)),sK1)),unordered_pair(sK18(relation_dom(sK5(sK1)),sK1),apply(sK5(sK1),sK18(relation_dom(sK5(sK1)),sK1)))),sK5(sK1)) ),
inference(instantiation,[status(thm)],[c_450]) ).
tcf(c_104058,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_104057,c_98502,c_95852,c_92078,c_82048,c_81911,c_81300,c_81304,c_81299,c_65142,c_62321,c_52408,c_42206,c_42205,c_21457,c_21456,c_21152,c_6080,c_6082,c_6083]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU283+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 13:34:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 53.93/8.43 % SZS status Started for theBenchmark.p
% 53.93/8.43 % SZS status Theorem for theBenchmark.p
% 53.93/8.43
% 53.93/8.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 53.93/8.43
% 53.93/8.43 % ------ iProver source info
% 53.93/8.43
% 53.93/8.43 % git: date: 2026-07-19 20:42:38 +0200
% 53.93/8.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 53.93/8.43 % git: non_committed_changes: false
% 53.93/8.43
% 53.93/8.43 % ------ Parsing...
% 53.93/8.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 53.93/8.43
% 53.93/8.43 % ------ Preprocessing... sup_sim: 9 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 53.93/8.43
% 53.93/8.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 53.93/8.43
% 53.93/8.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 53.93/8.43 % ------ Proving...
% 53.93/8.43 % ------ Problem Properties
% 53.93/8.43
% 53.93/8.43 %
% 53.93/8.43 % clauses 45
% 53.93/8.43 % conjectures 3
% 53.93/8.43 % EPR 17
% 53.93/8.43 % Horn 38
% 53.93/8.43 % unary 14
% 53.93/8.43 % binary 15
% 53.93/8.43 % lits 99
% 53.93/8.43 % lits eq 17
% 53.93/8.43 % fd_pure 0
% 53.93/8.43 % fd_pseudo 0
% 53.93/8.43 % fd_cond 1
% 53.93/8.43 % fd_pseudo_cond 7
% 53.93/8.43 % AC symbols 0
% 53.93/8.43
% 53.93/8.43 % ------ Schedule dynamic 5 is on
% 53.93/8.43
% 53.93/8.43 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 53.93/8.43
% 53.93/8.43
% 53.93/8.43 % ------
% 53.93/8.43 % Current options:
% 53.93/8.43 % ------
% 53.93/8.43
% 53.93/8.43
% 53.93/8.43 %
% 53.93/8.43
% 53.93/8.43 % ------ Proving...
% 53.93/8.43 %
% 53.93/8.43
% 53.93/8.43 % SZS status Theorem for theBenchmark.p
% 53.93/8.43
% 53.93/8.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 53.93/8.43
% 53.93/8.43
%------------------------------------------------------------------------------