%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET673+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 15.85s 8.32s
% Output : CNFRefutation 15.85s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f157ERROR: Could not build tree for root c_20343ERROR: 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(X0,X3))
<=> ( member(ordered_pair(X1,X2),X3)
& member(X2,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,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_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,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> 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,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> 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(X0,X1))
=> ( subset(X1,X2)
=> restrict4(X0,X1,X2,X3) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_36) ).
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(X0,X1))
=> ( subset(X1,X2)
=> restrict4(X0,X1,X2,X3) = 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(X0,X3))
<=> ( member(ordered_pair(X1,X2),X3)
& member(X2,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,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_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,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| 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,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| 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(X0,X1))
& subset(X1,X2)
& restrict4(X0,X1,X2,X3) != 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(X0,X1))
& subset(X1,X2)
& restrict4(X0,X1,X2,X3) != 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(X0,X3))
| ( member(ordered_pair(X1,X2),X3)
& member(X2,X0) ) )
& ( ~ member(ordered_pair(X1,X2),X3)
| ~ member(X2,X0)
| member(ordered_pair(X1,X2),restrict(X0,X3)) ) ) ) ) ) ),
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(X0,X3))
| ( member(ordered_pair(X1,X2),X3)
& member(X2,X0) ) )
& ( ~ member(ordered_pair(X1,X2),X3)
| ~ member(X2,X0)
| member(ordered_pair(X1,X2),restrict(X0,X3)) ) ) ) ) ) ),
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(sK12,sK13))
& subset(sK13,sK14)
& sK15 != restrict4(sK12,sK13,sK14,sK15) ),
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(X0,X3))
| 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(X2,X0)
| member(ordered_pair(X1,X2),restrict(X0,X3)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f101,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(X3,X1) ),
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,set_type)
| ~ ilf_type(X1,binary_relation_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,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| 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,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| 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(sK12,sK13)),
inference(cnf_transformation,[],[f91]) ).
fof(f150,plain,
subset(sK13,sK14),
inference(cnf_transformation,[],[f91]) ).
fof(f151,plain,
sK15 != restrict4(sK12,sK13,sK14,sK15),
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(X3,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X1,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),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_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_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X1,X4)
| ~ 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,[],[f101]) ).
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,binary_relation_type)
| ~ ilf_type(X0,set_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,X3,X0) = restrict(X3,X0) )
| ~ 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,X3,X0),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(sK12,sK13,sK14,sK15) != 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(sK12,sK13)),
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_182,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X0,X1),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_100,c_69]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X1,X0),binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(renaming,[status(thm)],[c_182]) ).
tcf(c_195,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_241,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_242,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_241]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_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_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X1,X4)
| ~ 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_59,c_100,c_59]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X1,X4)
| ~ 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_249]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X3,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),X2)
| ~ member(X1,X3) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_100,c_55]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X3,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X3)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_253]) ).
tcf(c_257,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_176]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X1,X0),binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_100,c_70,c_183]) ).
tcf(c_390,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_257]) ).
tcf(c_391,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_257]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_247,c_100]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X3,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,X3)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_254,c_100]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( restrict4(X1,X2,X3,X0) = restrict(X3,X0) )
| ~ 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_406,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_195,c_100]) ).
tcf(c_408,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_242,c_100]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X1,X4)
| ~ 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_250,c_100]) ).
tcf(c_415,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_417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(restrict4(X1,X2,X3,X0),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_418,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_510,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_418,c_100]) ).
tcf(c_538,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_415,c_100]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_408,c_100]) ).
tcf(c_604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_402,c_100]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(restrict4(X1,X2,X3,X0),relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_417,c_100,c_100]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( restrict4(X1,X2,X3,X0) = restrict(X3,X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_405,c_100,c_100]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X1,X4)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_412,c_100,c_100]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X1),restrict(X3,X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,X3)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_403,c_100]) ).
tcf(c_1381,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_100,c_70]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_510,c_538]) ).
tcf(c_1393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( restrict4(X1,X2,X3,X0) = restrict(X3,X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_631]) ).
tcf(c_1395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(restrict4(X1,X2,X3,X0),relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_619]) ).
tcf(c_1405,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_406]) ).
tcf(c_1407,plain,
! [X0: $i,X1: $i] :
( ilf_type(restrict(X1,X0),binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_263]) ).
tcf(c_1525,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_391,c_1381]) ).
tcf(c_2006,definition,
iPr_def_10 = relation_type(sK12,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2007,definition,
iPr_def_11 = restrict4(sK12,sK13,sK14,sK15),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2008,negated_conjecture,
ilf_type(sK15,iPr_def_10),
inference(demodulation,[status(thm)],[c_103,c_2006]) ).
tcf(c_2009,negated_conjecture,
subset(sK13,sK14),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_2010,negated_conjecture,
iPr_def_11 != sK15,
inference(demodulation,[status(thm)],[c_101,c_2007]) ).
tcf(c_2011,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2887,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2006,c_1391]) ).
tcf(c_2919,plain,
relation_like(sK15),
inference(superposition,[status(thm)],[c_2008,c_2887]) ).
tcf(c_3173,plain,
! [X0: $i,X1: $i] :
( ( restrict4(sK12,sK13,X1,X0) = restrict(X1,X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2006,c_1393]) ).
tcf(c_3194,plain,
( ilf_type(iPr_def_11,relation_type(sK12,sK13))
| ~ ilf_type(sK15,relation_type(sK12,sK13)) ),
inference(superposition,[status(thm)],[c_2007,c_1395]) ).
tcf(c_3198,plain,
( ilf_type(iPr_def_11,iPr_def_10)
| ~ ilf_type(sK15,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_3194,c_2006]) ).
tcf(c_3199,plain,
ilf_type(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3198,c_2008]) ).
tcf(c_3220,plain,
relation_like(iPr_def_11),
inference(superposition,[status(thm)],[c_3199,c_2887]) ).
tcf(c_3253,plain,
! [X0: $i] :
( ( iPr_def_11 = sK15 )
| ( iPr_def_11 != X0 )
| ( sK15 != X0 ) ),
inference(instantiation,[status(thm)],[c_2013]) ).
tcf(c_3634,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_390]) ).
tcf(c_3651,plain,
( ilf_type(sK15,binary_relation_type)
| ~ relation_like(sK15) ),
inference(instantiation,[status(thm)],[c_1381]) ).
tcf(c_4077,plain,
! [X0: $i] : restrict4(sK12,sK13,X0,sK15) = restrict(X0,sK15),
inference(superposition,[status(thm)],[c_2008,c_3173]) ).
tcf(c_4092,plain,
restrict(sK14,sK15) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2007,c_4077]) ).
tcf(c_4145,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_4092,c_604]) ).
tcf(c_4148,plain,
( ilf_type(iPr_def_11,binary_relation_type)
| ~ relation_like(sK15) ),
inference(superposition,[status(thm)],[c_4092,c_1407]) ).
tcf(c_4149,plain,
ilf_type(iPr_def_11,binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[c_4148,c_2919]) ).
tcf(c_4419,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_4145,c_2919,c_3651,c_4145]) ).
tcf(c_4763,plain,
( ( iPr_def_11 = sK15 )
| ( iPr_def_11 != iPr_def_11 )
| ( sK15 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_3253]) ).
tcf(c_4764,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_2011]) ).
tcf(c_7182,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_3634]) ).
tcf(c_8676,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),iPr_def_11)
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(X1,sK14)
| ~ member(ordered_pair(X0,X1),sK15) ),
inference(superposition,[status(thm)],[c_4092,c_675]) ).
tcf(c_8683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,X3)
| ~ empty(restrict(X3,X2))
| ~ member(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_675,c_1405]) ).
tcf(c_9382,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),iPr_def_11)
| ~ member(ordered_pair(X0,X1),sK15)
| ~ member(X1,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_8676,c_2919,c_3651,c_8676]) ).
tcf(c_9383,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),iPr_def_11)
| ~ member(X1,sK14)
| ~ member(ordered_pair(X0,X1),sK15) ),
inference(renaming,[status(thm)],[c_9382]) ).
tcf(c_17856,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(sK1(sK15,X0),sK14) ),
inference(superposition,[status(thm)],[c_1525,c_9383]) ).
tcf(c_17871,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_1525,c_4419]) ).
tcf(c_17906,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_17871,c_3220]) ).
tcf(c_17970,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(sK1(sK15,X0),sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17856,c_2919]) ).
tcf(c_18726,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(sK1(sK15,iPr_def_11),sK14) ),
inference(equality_factoring,[status(thm)],[c_17970]) ).
tcf(c_18728,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),iPr_def_11)
| ( sK15 = iPr_def_11 )
| ~ member(sK1(sK15,iPr_def_11),sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18726,c_3220]) ).
tcf(c_19035,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),iPr_def_11)
| ~ member(sK1(sK15,iPr_def_11),sK14) ),
inference(global_subsumption_just,[status(thm)],[c_18728,c_2010,c_4763,c_4764,c_18728]) ).
tcf(c_19041,plain,
! [X0: $i] :
( ~ ilf_type(iPr_def_11,binary_relation_type)
| ~ empty(restrict(X0,iPr_def_11))
| ~ member(sK1(sK15,iPr_def_11),sK14)
| ~ member(sK1(sK15,iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_19035,c_8683]) ).
tcf(c_19047,plain,
( member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),sK15)
| ~ member(sK1(sK15,iPr_def_11),sK14) ),
inference(superposition,[status(thm)],[c_19035,c_4419]) ).
tcf(c_19062,plain,
! [X0: $i] :
( ~ empty(restrict(X0,iPr_def_11))
| ~ member(sK1(sK15,iPr_def_11),sK14)
| ~ member(sK1(sK15,iPr_def_11),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19041,c_4149]) ).
tcf(c_19073,plain,
~ member(sK1(sK15,iPr_def_11),sK14),
inference(global_subsumption_just,[status(thm)],[c_19062,c_2010,c_2919,c_4149,c_4763,c_4764,c_7182,c_19035,c_19047]) ).
tcf(c_19538,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_17906]) ).
tcf(c_19540,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_19538,c_2919]) ).
tcf(c_19680,plain,
member(ordered_pair(sK0(sK15,iPr_def_11),sK1(sK15,iPr_def_11)),sK15),
inference(global_subsumption_just,[status(thm)],[c_19540,c_2010,c_4763,c_4764,c_19540]) ).
tcf(c_19683,plain,
! [X0: $i,X1: $i] :
( member(sK1(sK15,iPr_def_11),X1)
| ~ ilf_type(sK15,relation_type(X0,X1)) ),
inference(superposition,[status(thm)],[c_19680,c_660]) ).
tcf(c_20312,plain,
( member(sK1(sK15,iPr_def_11),sK13)
| ~ ilf_type(sK15,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2006,c_19683]) ).
tcf(c_20313,plain,
member(sK1(sK15,iPr_def_11),sK13),
inference(forward_subsumption_resolution,[status(thm)],[c_20312,c_2008]) ).
tcf(c_20314,plain,
! [X0: $i] :
( member(sK1(sK15,iPr_def_11),X0)
| ~ subset(sK13,X0) ),
inference(superposition,[status(thm)],[c_20313,c_561]) ).
tcf(c_20342,plain,
~ subset(sK13,sK14),
inference(superposition,[status(thm)],[c_20314,c_19073]) ).
tcf(c_20343,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_20342,c_2009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET673+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 % Computer : n016.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Thu Sep 24 11:42:34 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.46 Running first-order theorem proving
% 0.13/5.46 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
% 0.13/5.48
% 0.13/5.48 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.48
% 0.13/5.48 % Detected problem language: tptp
% 0.13/5.49 % Proving...
% 15.85/8.32 % SZS status Started for theBenchmark.p
% 15.85/8.32 % SZS status Theorem for theBenchmark.p
% 15.85/8.32
% 15.85/8.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.85/8.32
% 15.85/8.32 % ------ iProver source info
% 15.85/8.32
% 15.85/8.32 % git: date: 2026-07-19 20:42:38 +0200
% 15.85/8.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.85/8.32 % git: non_committed_changes: false
% 15.85/8.32
% 15.85/8.32 % ------ Parsing...
% 15.85/8.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.85/8.32
% 15.85/8.32 % ------ 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 %
% 15.85/8.32
% 15.85/8.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.85/8.32
% 15.85/8.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.85/8.32 % ------ Proving...
% 15.85/8.32 % ------ Problem Properties
% 15.85/8.32
% 15.85/8.32 %
% 15.85/8.32 % clauses 43
% 15.85/8.32 % conjectures 3
% 15.85/8.32 % EPR 11
% 15.85/8.32 % Horn 36
% 15.85/8.32 % unary 11
% 15.85/8.32 % binary 21
% 15.85/8.32 % lits 91
% 15.85/8.32 % lits eq 8
% 15.85/8.32 % fd_pure 0
% 15.85/8.32 % fd_pseudo 0
% 15.85/8.32 % fd_cond 0
% 15.85/8.32 % fd_pseudo_cond 2
% 15.85/8.32 % AC symbols 0
% 15.85/8.32
% 15.85/8.32 % ------ Schedule dynamic 5 is on
% 15.85/8.32
% 15.85/8.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.85/8.32
% 15.85/8.32
% 15.85/8.32 % ------
% 15.85/8.32 % Current options:
% 15.85/8.32 % ------
% 15.85/8.32
% 15.85/8.32
% 15.85/8.32 %
% 15.85/8.32
% 15.85/8.32 % ------ Proving...
% 15.85/8.32 %
% 15.85/8.32
% 15.85/8.32 % SZS status Theorem for theBenchmark.p
% 15.85/8.32
% 15.85/8.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.85/8.32
%------------------------------------------------------------------------------