%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET684+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 : n019.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 02:47:47 PM UTC 2026
% Result : Theorem 4.01s 6.38s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f161ERROR: Could not build tree for root c_7723ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) ) ) ) ) ) ),
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,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',p2) ).
fof(f5,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',p5) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f9,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',p9) ).
fof(f26,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',p26) ).
fof(f27,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))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f29,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f30,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_51) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ~ empty(X2)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X1))
& ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ilf_type(X6,member_type(X2))
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f33,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ~ empty(X2)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X1))
& ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ilf_type(X6,member_type(X2))
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f32]) ).
fof(f35,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f36,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,[],[f2]) ).
fof(f37,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,[],[f36]) ).
fof(f45,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f45]) ).
fof(f50,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))
| ! [X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ) ) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f54,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,[],[f26]) ).
fof(f57,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,[],[f5]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) ) ) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f64,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ~ empty(X2)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X1))
& ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ilf_type(X6,member_type(X2))
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) )
& ( ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f65,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ~ empty(X2)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X1))
& ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ilf_type(X6,member_type(X2))
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) )
& ( ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ~ empty(X2)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X1))
& ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ilf_type(X6,member_type(X2))
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(X1)) ) )
& ( ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
( ilf_type(sK0,set_type)
& ~ empty(sK0)
& ilf_type(sK1,set_type)
& ~ empty(sK1)
& ilf_type(sK2,set_type)
& ~ empty(sK2)
& ilf_type(sK3,relation_type(sK0,sK1))
& ilf_type(sK4,relation_type(sK1,sK2))
& ilf_type(sK5,member_type(sK0))
& ilf_type(sK6,member_type(sK2))
& ( member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| ( member(ordered_pair(sK7,sK6),sK4)
& member(ordered_pair(sK5,sK7),sK3)
& ilf_type(sK7,member_type(sK1)) ) )
& ( ~ member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| ! [X7] :
( ~ member(ordered_pair(X7,sK6),sK4)
| ~ member(ordered_pair(sK5,X7),sK3)
| ~ ilf_type(X7,member_type(sK1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X8,sK7)],[f66]) ).
fof(f72,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,[],[f35]) ).
fof(f73,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,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK9(X0),set_type)
& member(sK9(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f73]) ).
fof(f79,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ( ~ ilf_type(X0,member_type(X1))
| member(X0,X1) )
& ( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f88,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) ) )
& ( ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) )
| member(ordered_pair(X0,X1),compose(X2,X3)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f89,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ? [X5] :
( member(ordered_pair(X5,X1),X3)
& member(ordered_pair(X0,X5),X2)
& ilf_type(X5,set_type) ) )
& ( ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) )
| member(ordered_pair(X0,X1),compose(X2,X3)) ) ) ) ) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ( member(ordered_pair(sK17(X0,X1,X2,X3),X1),X3)
& member(ordered_pair(X0,sK17(X0,X1,X2,X3)),X2)
& ilf_type(sK17(X0,X1,X2,X3),set_type) ) )
& ( ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) )
| member(ordered_pair(X0,X1),compose(X2,X3)) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X5,sK17(X0,X1,X2,X3))],[f89]) ).
fof(f98,plain,
ilf_type(sK3,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f67]) ).
fof(f99,plain,
ilf_type(sK4,relation_type(sK1,sK2)),
inference(cnf_transformation,[],[f67]) ).
fof(f102,plain,
( member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| member(ordered_pair(sK7,sK6),sK4) ),
inference(cnf_transformation,[],[f67]) ).
fof(f103,plain,
( member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| member(ordered_pair(sK5,sK7),sK3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f104,plain,
( member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| ilf_type(sK7,member_type(sK1)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f105,plain,
! [X7] :
( ~ member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| ~ member(ordered_pair(X7,sK6),sK4)
| ~ member(ordered_pair(sK5,X7),sK3)
| ~ ilf_type(X7,member_type(sK1)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f106,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f29]) ).
fof(f112,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f115,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,[],[f37]) ).
fof(f127,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f132,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X4,relation_type(X1,X2))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f135,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,[],[f54]) ).
fof(f140,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,[],[f57]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| member(ordered_pair(sK17(X0,X1,X2,X3),X1),X3) ),
inference(cnf_transformation,[],[f90]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| member(ordered_pair(X0,sK17(X0,X1,X2,X3)),X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type)
| member(ordered_pair(X0,X1),compose(X2,X3)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK5,X0),sK3)
| ~ member(ordered_pair(X0,sK6),sK4)
| ~ member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_50,negated_conjecture,
( ilf_type(sK7,member_type(sK1))
| member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_51,negated_conjecture,
( member(ordered_pair(sK5,sK7),sK3)
| member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_52,negated_conjecture,
( member(ordered_pair(sK7,sK6),sK4)
| member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_55,negated_conjecture,
ilf_type(sK4,relation_type(sK1,sK2)),
inference(cnf_transformation,[],[f99]) ).
tcf(c_56,negated_conjecture,
ilf_type(sK3,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f98]) ).
tcf(c_63,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f106]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X4,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( compose5(X1,X2,X4,X0,X3) = compose(X0,X3) )
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X2,X4))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_91,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,[],[f135]) ).
tcf(c_92,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_96,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,[],[f140]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(ordered_pair(X0,X3),compose(X2,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X1,X3),X4)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,sK17(X0,X1,X2,X3)),X2)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(sK17(X0,X1,X2,X3),X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_168,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_92,c_63,c_92]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_63,c_71,c_83]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_226]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(sK17(X0,X1,X2,X3),X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_107,c_63,c_107]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,sK17(X0,X1,X2,X3)),X2)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_106,c_63,c_106]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(ordered_pair(X0,X3),compose(X2,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),X2)
| ~ member(ordered_pair(X1,X3),X4) ),
inference(global_subsumption_just,[status(thm)],[c_104,c_63,c_104]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(ordered_pair(X0,X3),compose(X2,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X3),X4)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_252]) ).
tcf(c_411,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_91,c_63]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(ordered_pair(X0,X3),compose(X2,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X1,X3),X4)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_253,c_63]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,sK17(X0,X1,X2,X3)),X2)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_250,c_63]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(sK17(X0,X1,X2,X3),X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_248,c_63]) ).
tcf(c_418,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_96,c_63]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( compose5(X1,X2,X4,X0,X3) = compose(X0,X3) )
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X2,X4))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_89,c_63]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X4,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_73,c_63]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_227,c_63]) ).
tcf(c_531,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_411,c_63]) ).
tcf(c_571,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_418,c_63]) ).
tcf(c_649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( compose5(X1,X2,X4,X0,X3) = compose(X0,X3) )
| ~ ilf_type(X3,relation_type(X2,X4))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421,c_63,c_63]) ).
tcf(c_666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X4,X2)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_422,c_63,c_63,c_63]) ).
tcf(c_699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(ordered_pair(X0,X3),compose(X2,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X1,X3),X4)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_413,c_63]) ).
tcf(c_1248,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_168]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_427]) ).
tcf(c_1268,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_531,c_571]) ).
tcf(c_2825,plain,
! [X0: $i] :
( member(ordered_pair(sK7,sK6),sK4)
| ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK5,X0),sK3)
| ~ member(ordered_pair(X0,sK6),sK4) ),
inference(superposition,[status(thm)],[c_52,c_49]) ).
tcf(c_2826,plain,
! [X0: $i] :
( member(ordered_pair(sK5,sK7),sK3)
| ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK5,X0),sK3)
| ~ member(ordered_pair(X0,sK6),sK4) ),
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_2827,plain,
! [X0: $i] :
( ilf_type(sK7,member_type(sK1))
| ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK5,X0),sK3)
| ~ member(ordered_pair(X0,sK6),sK4) ),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_2879,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK5,sK7),sK3)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(sK17(sK5,X0,sK3,X1),member_type(sK1))
| ~ member(ordered_pair(sK17(sK5,X0,sK3,X1),sK6),sK4) ),
inference(superposition,[status(thm)],[c_414,c_2826]) ).
tcf(c_2880,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK7,sK6),sK4)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(sK17(sK5,X0,sK3,X1),member_type(sK1))
| ~ member(ordered_pair(sK17(sK5,X0,sK3,X1),sK6),sK4) ),
inference(superposition,[status(thm)],[c_414,c_2825]) ).
tcf(c_2881,plain,
! [X0: $i,X1: $i] :
( ilf_type(sK7,member_type(sK1))
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(sK17(sK5,X0,sK3,X1),member_type(sK1))
| ~ member(ordered_pair(sK17(sK5,X0,sK3,X1),sK6),sK4) ),
inference(superposition,[status(thm)],[c_414,c_2827]) ).
tcf(c_2932,plain,
relation_like(sK4),
inference(superposition,[status(thm)],[c_55,c_1268]) ).
tcf(c_2933,plain,
relation_like(sK3),
inference(superposition,[status(thm)],[c_56,c_1268]) ).
tcf(c_3014,plain,
( member(ordered_pair(sK7,sK6),sK4)
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ ilf_type(sK17(sK5,sK6,sK3,sK4),member_type(sK1)) ),
inference(superposition,[status(thm)],[c_415,c_2880]) ).
tcf(c_3015,plain,
( member(ordered_pair(sK5,sK7),sK3)
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ ilf_type(sK17(sK5,sK6,sK3,sK4),member_type(sK1)) ),
inference(superposition,[status(thm)],[c_415,c_2879]) ).
tcf(c_3016,plain,
( ilf_type(sK7,member_type(sK1))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ ilf_type(sK17(sK5,sK6,sK3,sK4),member_type(sK1)) ),
inference(superposition,[status(thm)],[c_415,c_2881]) ).
tcf(c_3091,plain,
( ilf_type(sK7,member_type(sK1))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ member(sK17(sK5,sK6,sK3,sK4),sK1) ),
inference(superposition,[status(thm)],[c_1262,c_3016]) ).
tcf(c_3107,plain,
( member(ordered_pair(sK7,sK6),sK4)
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ member(sK17(sK5,sK6,sK3,sK4),sK1) ),
inference(superposition,[status(thm)],[c_1262,c_3014]) ).
tcf(c_3123,plain,
( member(ordered_pair(sK5,sK7),sK3)
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ member(sK17(sK5,sK6,sK3,sK4),sK1) ),
inference(superposition,[status(thm)],[c_1262,c_3015]) ).
tcf(c_3253,plain,
! [X0: $i,X1: $i] :
( member(X1,sK1)
| ~ member(ordered_pair(X0,X1),sK3) ),
inference(superposition,[status(thm)],[c_56,c_666]) ).
tcf(c_3304,plain,
! [X0: $i,X1: $i] :
( ( compose5(sK0,sK1,X1,sK3,X0) = compose(sK3,X0) )
| ~ ilf_type(X0,relation_type(sK1,X1)) ),
inference(superposition,[status(thm)],[c_56,c_649]) ).
tcf(c_3345,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK17(X0,X1,sK3,X2),sK1)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),compose(sK3,X2)) ),
inference(superposition,[status(thm)],[c_414,c_3253]) ).
tcf(c_3415,plain,
compose5(sK0,sK1,sK2,sK3,sK4) = compose(sK3,sK4),
inference(superposition,[status(thm)],[c_55,c_3304]) ).
tcf(c_3424,plain,
! [X0: $i] :
( ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK5,X0),sK3)
| ~ member(ordered_pair(X0,sK6),sK4)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_49,c_3415]) ).
tcf(c_3425,plain,
( member(ordered_pair(sK7,sK6),sK4)
| member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_52,c_3415]) ).
tcf(c_3426,plain,
( member(ordered_pair(sK5,sK7),sK3)
| member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_51,c_3415]) ).
tcf(c_3427,plain,
( ilf_type(sK7,member_type(sK1))
| member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_50,c_3415]) ).
tcf(c_3470,plain,
( ilf_type(sK7,member_type(sK1))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(sK17(sK5,sK6,sK3,sK4),sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3091,c_3427]) ).
tcf(c_3501,plain,
( member(ordered_pair(sK7,sK6),sK4)
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(sK17(sK5,sK6,sK3,sK4),sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3107,c_3425]) ).
tcf(c_3529,plain,
( member(ordered_pair(sK5,sK7),sK3)
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(sK17(sK5,sK6,sK3,sK4),sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3123,c_3426]) ).
tcf(c_4059,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(sK5,sK7),sK3)
| ~ member(ordered_pair(sK7,X0),X1) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_5861,plain,
( ilf_type(sK3,binary_relation_type)
| ~ relation_like(sK3) ),
inference(instantiation,[status(thm)],[c_1248]) ).
tcf(c_5862,plain,
( ilf_type(sK4,binary_relation_type)
| ~ relation_like(sK4) ),
inference(instantiation,[status(thm)],[c_1248]) ).
tcf(c_6220,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK17(X0,X1,sK3,X2),sK1)
| ~ member(ordered_pair(X0,X1),compose(sK3,X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_3345,c_2933,c_3345,c_5861]) ).
tcf(c_6221,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK17(X0,X1,sK3,X2),sK1)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),compose(sK3,X2)) ),
inference(renaming,[status(thm)],[c_6220]) ).
tcf(c_6231,plain,
( member(ordered_pair(sK5,sK7),sK3)
| member(sK17(sK5,sK6,sK3,sK4),sK1)
| ~ ilf_type(sK4,binary_relation_type) ),
inference(superposition,[status(thm)],[c_3426,c_6221]) ).
tcf(c_6232,plain,
( member(ordered_pair(sK7,sK6),sK4)
| member(sK17(sK5,sK6,sK3,sK4),sK1)
| ~ ilf_type(sK4,binary_relation_type) ),
inference(superposition,[status(thm)],[c_3425,c_6221]) ).
tcf(c_6233,plain,
( ilf_type(sK7,member_type(sK1))
| member(sK17(sK5,sK6,sK3,sK4),sK1)
| ~ ilf_type(sK4,binary_relation_type) ),
inference(superposition,[status(thm)],[c_3427,c_6221]) ).
tcf(c_6406,plain,
! [X0: $i,X1: $i] :
( ( compose5(sK0,sK1,X1,sK3,X0) = compose(sK3,X0) )
| ~ ilf_type(X0,relation_type(sK1,X1)) ),
inference(superposition,[status(thm)],[c_56,c_649]) ).
tcf(c_6829,plain,
compose5(sK0,sK1,sK2,sK3,sK4) = compose(sK3,sK4),
inference(superposition,[status(thm)],[c_55,c_6406]) ).
tcf(c_6838,plain,
! [X0: $i] :
( ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK5,X0),sK3)
| ~ member(ordered_pair(X0,sK6),sK4)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_49,c_6829]) ).
tcf(c_6839,plain,
( member(ordered_pair(sK7,sK6),sK4)
| member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_52,c_6829]) ).
tcf(c_6840,plain,
( member(ordered_pair(sK5,sK7),sK3)
| member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_51,c_6829]) ).
tcf(c_6841,plain,
( ilf_type(sK7,member_type(sK1))
| member(ordered_pair(sK5,sK6),compose(sK3,sK4)) ),
inference(demodulation,[status(thm)],[c_50,c_6829]) ).
tcf(c_6888,plain,
ilf_type(sK7,member_type(sK1)),
inference(global_subsumption_just,[status(thm)],[c_6233,c_2933,c_2932,c_3470,c_5861,c_5862,c_6233]) ).
tcf(c_6900,plain,
member(ordered_pair(sK5,sK7),sK3),
inference(global_subsumption_just,[status(thm)],[c_6231,c_2933,c_2932,c_3529,c_5861,c_5862,c_6231]) ).
tcf(c_7149,plain,
( member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK7,sK6),sK4)
| ~ member(ordered_pair(sK5,sK7),sK3) ),
inference(instantiation,[status(thm)],[c_4059]) ).
tcf(c_7176,plain,
ilf_type(sK7,member_type(sK1)),
inference(global_subsumption_just,[status(thm)],[c_6841,c_6888]) ).
tcf(c_7184,plain,
member(ordered_pair(sK7,sK6),sK4),
inference(global_subsumption_just,[status(thm)],[c_6839,c_2933,c_2932,c_3501,c_5861,c_5862,c_6232]) ).
tcf(c_7191,plain,
member(ordered_pair(sK5,sK7),sK3),
inference(global_subsumption_just,[status(thm)],[c_6840,c_6900]) ).
tcf(c_7712,plain,
! [X0: $i] :
( ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK5,X0),sK3)
| ~ member(ordered_pair(X0,sK6),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_6838,c_2933,c_2932,c_3424,c_3529,c_5861,c_5862,c_6231,c_7149,c_7184]) ).
tcf(c_7721,plain,
( ~ ilf_type(sK7,member_type(sK1))
| ~ member(ordered_pair(sK7,sK6),sK4) ),
inference(superposition,[status(thm)],[c_7191,c_7712]) ).
tcf(c_7723,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7721,c_7176,c_7184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET684+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.54 % Computer : n019.cluster.edu
% 0.09/5.54 % Model : x86_64 x86_64
% 0.09/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.54 % Memory : 8046.5625MB
% 0.09/5.54 % OS : Linux 6.8.0-71-generic
% 0.09/5.54 % CPULimit : 300
% 0.09/5.54 % WCLimit : 300
% 0.09/5.54 % DateTime : Thu Sep 24 11:39:57 UTC 2026
% 0.09/5.54 % CPUTime :
% 0.09/5.54 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.58 Running first-order theorem proving
% 0.09/5.58 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
% 0.09/5.59
% 0.09/5.59 % ======== iProver multi-core TPTP/SMT =========
% 0.09/5.59
% 0.09/5.59 % Detected problem language: tptp
% 0.14/5.60 % Proving...
% 4.01/6.38 % SZS status Started for theBenchmark.p
% 4.01/6.38 % SZS status Theorem for theBenchmark.p
% 4.01/6.38
% 4.01/6.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.01/6.38
% 4.01/6.38 % ------ iProver source info
% 4.01/6.38
% 4.01/6.38 % git: date: 2026-07-19 20:42:38 +0200
% 4.01/6.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.01/6.38 % git: non_committed_changes: false
% 4.01/6.38
% 4.01/6.38 % ------ Parsing...
% 4.01/6.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.01/6.38
% 4.01/6.38 % ------ 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 %
% 4.01/6.38
% 4.01/6.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.01/6.38
% 4.01/6.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.01/6.38 % ------ Proving...
% 4.01/6.38 % ------ Problem Properties
% 4.01/6.38
% 4.01/6.38 %
% 4.01/6.38 % clauses 45
% 4.01/6.38 % conjectures 11
% 4.01/6.38 % EPR 9
% 4.01/6.38 % Horn 36
% 4.01/6.38 % unary 12
% 4.01/6.38 % binary 19
% 4.01/6.38 % lits 97
% 4.01/6.38 % lits eq 5
% 4.01/6.38 % fd_pure 0
% 4.01/6.38 % fd_pseudo 0
% 4.01/6.38 % fd_cond 0
% 4.01/6.38 % fd_pseudo_cond 2
% 4.01/6.38 % AC symbols 0
% 4.01/6.38
% 4.01/6.38 % ------ Schedule dynamic 5 is on
% 4.01/6.38
% 4.01/6.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.01/6.38
% 4.01/6.38
% 4.01/6.38 % ------
% 4.01/6.38 % Current options:
% 4.01/6.38 % ------
% 4.01/6.38
% 4.01/6.38
% 4.01/6.38 %
% 4.01/6.38
% 4.01/6.38 % ------ Proving...
% 4.01/6.38 %
% 4.01/6.38
% 4.01/6.38 % SZS status Theorem for theBenchmark.p
% 4.01/6.38
% 4.01/6.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.01/6.39
% 4.01/6.39
%------------------------------------------------------------------------------