%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET671+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 02:47:45 PM UTC 2026
% Result : Theorem 17.98s 3.75s
% Output : CNFRefutation 17.98s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f157ERROR: Could not build tree for root c_47922ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( X0 = X1
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X2,X3),X0)
<=> member(ordered_pair(X2,X3),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),restrict(X3,X0))
<=> ( member(ordered_pair(X1,X2),X3)
& member(X1,X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(restrict(X0,X1),binary_relation_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f25,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> restrict4(X0,X1,X2,X3) = restrict(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f26,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X0))
=> ( subset(X1,X2)
=> restrict4(X1,X0,X3,X2) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_34) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X0))
=> ( subset(X1,X2)
=> restrict4(X1,X0,X3,X2) = X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( X0 = X1
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( member(ordered_pair(X2,X3),X0)
<=> member(ordered_pair(X2,X3),X1) ) ) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( member(ordered_pair(X1,X2),restrict(X3,X0))
<=> ( member(ordered_pair(X1,X2),X3)
& member(X1,X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(flattening,[],[f36]) ).
fof(f40,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ilf_type(restrict(X0,X1),binary_relation_type) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f57,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| restrict4(X0,X1,X2,X3) = restrict(X2,X3) ) ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f63,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X1,X0))
& subset(X1,X2)
& restrict4(X1,X0,X3,X2) != X3 ) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f64,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X1,X0))
& subset(X1,X2)
& restrict4(X1,X0,X3,X2) != X3 ) ) ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( X0 != X1
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(ordered_pair(X2,X3),X0)
| member(ordered_pair(X2,X3),X1) )
& ( ~ member(ordered_pair(X2,X3),X1)
| member(ordered_pair(X2,X3),X0) ) ) ) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ( member(ordered_pair(X2,X3),X0)
| member(ordered_pair(X2,X3),X1) )
& ( ~ member(ordered_pair(X2,X3),X0)
| ~ member(ordered_pair(X2,X3),X1) ) ) )
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f66,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( X0 != X1
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(ordered_pair(X2,X3),X0)
| member(ordered_pair(X2,X3),X1) )
& ( ~ member(ordered_pair(X2,X3),X1)
| member(ordered_pair(X2,X3),X0) ) ) ) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ( member(ordered_pair(X2,X3),X0)
| member(ordered_pair(X2,X3),X1) )
& ( ~ member(ordered_pair(X2,X3),X0)
| ~ member(ordered_pair(X2,X3),X1) ) ) )
| X0 = X1 ) ) ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( X0 != X1
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(ordered_pair(X4,X5),X0)
| member(ordered_pair(X4,X5),X1) )
& ( ~ member(ordered_pair(X4,X5),X1)
| member(ordered_pair(X4,X5),X0) ) ) ) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ( member(ordered_pair(X2,X3),X0)
| member(ordered_pair(X2,X3),X1) )
& ( ~ member(ordered_pair(X2,X3),X0)
| ~ member(ordered_pair(X2,X3),X1) ) ) )
| X0 = X1 ) ) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( X0 != X1
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(ordered_pair(X4,X5),X0)
| member(ordered_pair(X4,X5),X1) )
& ( ~ member(ordered_pair(X4,X5),X1)
| member(ordered_pair(X4,X5),X0) ) ) ) ) )
& ( ( ilf_type(sK0(X0,X1),set_type)
& ilf_type(sK1(X0,X1),set_type)
& ( member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ) )
| X0 = X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f67]) ).
fof(f69,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(ordered_pair(X1,X2),restrict(X3,X0))
| ( member(ordered_pair(X1,X2),X3)
& member(X1,X0) ) )
& ( ~ member(ordered_pair(X1,X2),X3)
| ~ member(X1,X0)
| member(ordered_pair(X1,X2),restrict(X3,X0)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f70,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(ordered_pair(X1,X2),restrict(X3,X0))
| ( member(ordered_pair(X1,X2),X3)
& member(X1,X0) ) )
& ( ~ member(ordered_pair(X1,X2),X3)
| ~ member(X1,X0)
| member(ordered_pair(X1,X2),restrict(X3,X0)) ) ) ) ) ) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f73,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK3(X0,X1),set_type)
& member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f73]) ).
fof(f88,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f89,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK11(X0),set_type)
& member(sK11(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f89]) ).
fof(f91,plain,
( ilf_type(sK12,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK14,set_type)
& ilf_type(sK15,relation_type(sK13,sK12))
& subset(sK13,sK14)
& sK15 != restrict4(sK13,sK12,sK15,sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f64]) ).
fof(f96,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f97,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),restrict(X3,X0))
| member(ordered_pair(X1,X2),X3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ member(X1,X0)
| member(ordered_pair(X1,X2),restrict(X3,X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f103,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[],[f34]) ).
fof(f106,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f112,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ilf_type(restrict(X0,X1),binary_relation_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f139,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| restrict4(X0,X1,X2,X3) = restrict(X2,X3) ),
inference(cnf_transformation,[],[f61]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f145,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f149,plain,
ilf_type(sK15,relation_type(sK13,sK12)),
inference(cnf_transformation,[],[f91]) ).
fof(f150,plain,
subset(sK13,sK14),
inference(cnf_transformation,[],[f91]) ).
fof(f151,plain,
sK15 != restrict4(sK13,sK12,sK15,sK14),
inference(cnf_transformation,[],[f91]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ( X0 = X1 )
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X3)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X0,X1),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_70,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( restrict4(X1,X2,X0,X3) = restrict(X0,X3) )
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(restrict4(X1,X2,X0,X3),relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_100,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f145]) ).
tcf(c_101,negated_conjecture,
restrict4(sK13,sK12,sK15,sK14) != sK15,
inference(cnf_transformation,[],[f151]) ).
tcf(c_102,negated_conjecture,
subset(sK13,sK14),
inference(cnf_transformation,[],[f150]) ).
tcf(c_103,negated_conjecture,
ilf_type(sK15,relation_type(sK13,sK12)),
inference(cnf_transformation,[],[f149]) ).
tcf(c_176,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_70,c_100,c_70]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_96,c_100,c_96]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ~ subset(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_66,c_100,c_66]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_238]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_100,c_57]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4)) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_100,c_58]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_248]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),X2)
| ~ member(X0,X3) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_100,c_55]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X3)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_250]) ).
tcf(c_254,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_176]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation_like(X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) ),
inference(bin_hyper_res,[status(thm)],[c_49,c_254]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK0(X1,X0),sK1(X1,X0)),X1)
| member(ordered_pair(sK0(X1,X0),sK1(X1,X0)),X0)
| ( X1 = X0 )
| ~ relation_like(X1)
| ~ ilf_type(X0,binary_relation_type) ),
inference(bin_hyper_res,[status(thm)],[c_50,c_254]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X1,X0),binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X0,set_type) ),
inference(bin_hyper_res,[status(thm)],[c_69,c_254]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X1,X0),binary_relation_type)
| ~ relation_like(X1) ),
inference(global_subsumption_just,[status(thm)],[c_385,c_100,c_385]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X0,X1),binary_relation_type)
| ~ relation_like(X0) ),
inference(renaming,[status(thm)],[c_387]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_100]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_244,c_100]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X0,X3)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_251,c_100]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( restrict4(X1,X2,X0,X3) = restrict(X0,X3) )
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_98,c_100]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_192,c_100]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_239,c_100]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_249,c_100]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_100]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(restrict4(X1,X2,X0,X3),relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_99,c_100]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_394,c_100]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_412,c_100]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_405,c_100]) ).
tcf(c_599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_399,c_100]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(restrict4(X1,X2,X0,X3),relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_414,c_100,c_100]) ).
tcf(c_626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( restrict4(X1,X2,X0,X3) = restrict(X0,X3) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_402,c_100,c_100]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X3)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_408,c_100,c_100]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X2,X3))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X0,X3)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_400,c_100]) ).
tcf(c_1377,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_100,c_70]) ).
tcf(c_1387,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_505,c_533]) ).
tcf(c_1389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( restrict4(X1,X2,X0,X3) = restrict(X0,X3) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_626]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(restrict4(X1,X2,X0,X3),relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_614]) ).
tcf(c_1401,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_403]) ).
tcf(c_1403,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X0,X1),binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_388]) ).
tcf(c_1519,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK0(X1,X0),sK1(X1,X0)),X1)
| member(ordered_pair(sK0(X1,X0),sK1(X1,X0)),X0)
| ( X1 = X0 )
| ~ relation_like(X1)
| ~ relation_like(X0) ),
inference(bin_hyper_res,[status(thm)],[c_382,c_1377]) ).
tcf(c_2000,definition,
iPr_def_10 = relation_type(sK13,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2001,definition,
iPr_def_11 = restrict4(sK13,sK12,sK15,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2002,negated_conjecture,
ilf_type(sK15,iPr_def_10),
inference(demodulation,[status(thm)],[c_103,c_2000]) ).
tcf(c_2003,negated_conjecture,
subset(sK13,sK14),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_2004,negated_conjecture,
iPr_def_11 != sK15,
inference(demodulation,[status(thm)],[c_101,c_2001]) ).
tcf(c_2005,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2879,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2000,c_1387]) ).
tcf(c_2911,plain,
relation_like(sK15),
inference(superposition,[status(thm)],[c_2002,c_2879]) ).
tcf(c_3165,plain,
! [X0: $i,X1: $i] :
( ( restrict4(sK13,sK12,X0,X1) = restrict(X0,X1) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2000,c_1389]) ).
tcf(c_3186,plain,
( ilf_type(iPr_def_11,relation_type(sK13,sK12))
| ~ ilf_type(sK15,relation_type(sK13,sK12)) ),
inference(superposition,[status(thm)],[c_2001,c_1391]) ).
tcf(c_3190,plain,
( ilf_type(iPr_def_11,iPr_def_10)
| ~ ilf_type(sK15,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_3186,c_2000]) ).
tcf(c_3191,plain,
ilf_type(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3190,c_2002]) ).
tcf(c_3212,plain,
relation_like(iPr_def_11),
inference(superposition,[status(thm)],[c_3191,c_2879]) ).
tcf(c_3245,plain,
! [X0: $i] :
( ( iPr_def_11 = sK15 )
| ( iPr_def_11 != X0 )
| ( sK15 != X0 ) ),
inference(instantiation,[status(thm)],[c_2007]) ).
tcf(c_3626,plain,
! [X0: $i] :
( ( sK15 = X0 )
| ~ relation_like(sK15)
| ~ ilf_type(X0,binary_relation_type)
| ~ member(ordered_pair(sK0(sK15,X0),sK1(sK15,X0)),sK15)
| ~ member(ordered_pair(sK0(sK15,X0),sK1(sK15,X0)),X0) ),
inference(instantiation,[status(thm)],[c_381]) ).
tcf(c_3643,plain,
( ilf_type(sK15,binary_relation_type)
| ~ relation_like(sK15) ),
inference(instantiation,[status(thm)],[c_1377]) ).
tcf(c_4069,plain,
! [X0: $i] : restrict4(sK13,sK12,sK15,X0) = restrict(sK15,X0),
inference(superposition,[status(thm)],[c_2002,c_3165]) ).
tcf(c_4084,plain,
restrict(sK15,sK14) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2001,c_4069]) ).
tcf(c_4137,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),sK15)
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(ordered_pair(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4084,c_599]) ).
tcf(c_4140,plain,
( ilf_type(iPr_def_11,binary_relation_type)
| ~ relation_like(sK15) ),
inference(superposition,[status(thm)],[c_4084,c_1403]) ).
tcf(c_4141,plain,
ilf_type(iPr_def_11,binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[c_4140,c_2911]) ).
tcf(c_4411,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),sK15)
| ~ member(ordered_pair(X0,X1),iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_4137,c_2911,c_3643,c_4137]) ).
tcf(c_4755,plain,
( ( iPr_def_11 = sK15 )
| ( iPr_def_11 != iPr_def_11 )
| ( sK15 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_3245]) ).
tcf(c_4756,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_2005]) ).
tcf(c_7174,plain,
( ( sK15 = iPr_def_11 )
| ~ relation_like(sK15)
| ~ ilf_type(iPr_def_11,binary_relation_type)
| ~ member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),iPr_def_11)
| ~ member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),sK15) ),
inference(instantiation,[status(thm)],[c_3626]) ).
tcf(c_8668,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),iPr_def_11)
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(X0,sK14)
| ~ member(ordered_pair(X0,X1),sK15) ),
inference(superposition,[status(thm)],[c_4084,c_670]) ).
tcf(c_8675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X0,X3)
| ~ empty(restrict(X2,X3))
| ~ member(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_670,c_1401]) ).
tcf(c_9374,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),iPr_def_11)
| ~ member(ordered_pair(X0,X1),sK15)
| ~ member(X0,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_8668,c_2911,c_3643,c_8668]) ).
tcf(c_9375,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),iPr_def_11)
| ~ member(X0,sK14)
| ~ member(ordered_pair(X0,X1),sK15) ),
inference(renaming,[status(thm)],[c_9374]) ).
tcf(c_17012,plain,
! [X0: $i] :
( member(ordered_pair(sK0(sK15,X0),sK1(sK15,X0)),iPr_def_11)
| member(ordered_pair(sK0(sK15,X0),sK1(sK15,X0)),X0)
| ( X0 = sK15 )
| ~ relation_like(sK15)
| ~ relation_like(X0)
| ~ member(sK0(sK15,X0),sK14) ),
inference(superposition,[status(thm)],[c_1519,c_9375]) ).
tcf(c_17027,plain,
! [X0: $i] :
( member(ordered_pair(sK0(X0,iPr_def_11),sK1(X0,iPr_def_11)),sK15)
| member(ordered_pair(sK0(X0,iPr_def_11),sK1(X0,iPr_def_11)),X0)
| ( X0 = iPr_def_11 )
| ~ relation_like(iPr_def_11)
| ~ relation_like(X0) ),
inference(superposition,[status(thm)],[c_1519,c_4411]) ).
tcf(c_17062,plain,
! [X0: $i] :
( member(ordered_pair(sK0(X0,iPr_def_11),sK1(X0,iPr_def_11)),sK15)
| member(ordered_pair(sK0(X0,iPr_def_11),sK1(X0,iPr_def_11)),X0)
| ( X0 = iPr_def_11 )
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17027,c_3212]) ).
tcf(c_17126,plain,
! [X0: $i] :
( member(ordered_pair(sK0(sK15,X0),sK1(sK15,X0)),iPr_def_11)
| member(ordered_pair(sK0(sK15,X0),sK1(sK15,X0)),X0)
| ( X0 = sK15 )
| ~ relation_like(X0)
| ~ member(sK0(sK15,X0),sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17012,c_2911]) ).
tcf(c_17994,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),iPr_def_11)
| ( sK15 = iPr_def_11 )
| ~ relation_like(iPr_def_11)
| ~ member(sK0(sK15,iPr_def_11),sK14) ),
inference(equality_factoring,[status(thm)],[c_17126]) ).
tcf(c_17996,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),iPr_def_11)
| ( sK15 = iPr_def_11 )
| ~ member(sK0(sK15,iPr_def_11),sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17994,c_3212]) ).
tcf(c_24259,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),iPr_def_11)
| ~ member(sK0(sK15,iPr_def_11),sK14) ),
inference(global_subsumption_just,[status(thm)],[c_17996,c_2004,c_4755,c_4756,c_17996]) ).
tcf(c_24265,plain,
! [X0: $i] :
( ~ ilf_type(iPr_def_11,binary_relation_type)
| ~ empty(restrict(iPr_def_11,X0))
| ~ member(sK0(sK15,iPr_def_11),sK14)
| ~ member(sK0(sK15,iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_24259,c_8675]) ).
tcf(c_24271,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),sK15)
| ~ member(sK0(sK15,iPr_def_11),sK14) ),
inference(superposition,[status(thm)],[c_24259,c_4411]) ).
tcf(c_24286,plain,
! [X0: $i] :
( ~ empty(restrict(iPr_def_11,X0))
| ~ member(sK0(sK15,iPr_def_11),sK14)
| ~ member(sK0(sK15,iPr_def_11),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24265,c_4141]) ).
tcf(c_24297,plain,
~ member(sK0(sK15,iPr_def_11),sK14),
inference(global_subsumption_just,[status(thm)],[c_24286,c_2004,c_2911,c_4141,c_4755,c_4756,c_7174,c_24259,c_24271]) ).
tcf(c_46324,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),sK15)
| ( sK15 = iPr_def_11 )
| ~ relation_like(sK15) ),
inference(equality_factoring,[status(thm)],[c_17062]) ).
tcf(c_46326,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),sK15)
| ( sK15 = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46324,c_2911]) ).
tcf(c_46612,plain,
member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),sK15),
inference(global_subsumption_just,[status(thm)],[c_46326,c_2004,c_4755,c_4756,c_46326]) ).
tcf(c_46616,plain,
! [X0: $i,X1: $i] :
( member(sK0(sK15,iPr_def_11),X0)
| ~ ilf_type(sK15,relation_type(X0,X1)) ),
inference(superposition,[status(thm)],[c_46612,c_639]) ).
tcf(c_47877,plain,
( member(sK0(sK15,iPr_def_11),sK13)
| ~ ilf_type(sK15,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2000,c_46616]) ).
tcf(c_47878,plain,
member(sK0(sK15,iPr_def_11),sK13),
inference(forward_subsumption_resolution,[status(thm)],[c_47877,c_2002]) ).
tcf(c_47879,plain,
! [X0: $i] :
( member(sK0(sK15,iPr_def_11),X0)
| ~ subset(sK13,X0) ),
inference(superposition,[status(thm)],[c_47878,c_556]) ).
tcf(c_47921,plain,
~ subset(sK13,sK14),
inference(superposition,[status(thm)],[c_47879,c_24297]) ).
tcf(c_47922,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_47921,c_2003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET671+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:42:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 17.98/3.75 % SZS status Started for theBenchmark.p
% 17.98/3.75 % SZS status Theorem for theBenchmark.p
% 17.98/3.75
% 17.98/3.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.98/3.75
% 17.98/3.75 % ------ iProver source info
% 17.98/3.75
% 17.98/3.75 % git: date: 2026-07-19 20:42:38 +0200
% 17.98/3.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.98/3.75 % git: non_committed_changes: false
% 17.98/3.75
% 17.98/3.75 % ------ Parsing...
% 17.98/3.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.98/3.75
% 17.98/3.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 17.98/3.75
% 17.98/3.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.98/3.75
% 17.98/3.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.98/3.75 % ------ Proving...
% 17.98/3.75 % ------ Problem Properties
% 17.98/3.75
% 17.98/3.75 %
% 17.98/3.75 % clauses 43
% 17.98/3.75 % conjectures 3
% 17.98/3.75 % EPR 11
% 17.98/3.75 % Horn 36
% 17.98/3.75 % unary 11
% 17.98/3.75 % binary 21
% 17.98/3.75 % lits 91
% 17.98/3.75 % lits eq 8
% 17.98/3.75 % fd_pure 0
% 17.98/3.75 % fd_pseudo 0
% 17.98/3.75 % fd_cond 0
% 17.98/3.75 % fd_pseudo_cond 2
% 17.98/3.75 % AC symbols 0
% 17.98/3.75
% 17.98/3.75 % ------ Schedule dynamic 5 is on
% 17.98/3.75
% 17.98/3.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.98/3.75
% 17.98/3.75
% 17.98/3.75 % ------
% 17.98/3.75 % Current options:
% 17.98/3.75 % ------
% 17.98/3.75
% 17.98/3.75
% 17.98/3.75 %
% 17.98/3.75
% 17.98/3.75 % ------ Proving...
% 17.98/3.75 %
% 17.98/3.75
% 17.98/3.75 % SZS status Theorem for theBenchmark.p
% 17.98/3.75
% 17.98/3.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.98/3.75
% 17.98/3.75
%------------------------------------------------------------------------------