%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU195+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 02:55:50 PM UTC 2026
% Result : Theorem 1.45s 1.19s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 98 ( 16 unt; 0 def)
% Number of atoms : 406 ( 57 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 545 ( 237 ~; 249 |; 40 &)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 265 ( 0 sgn 253 !; 12 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f12,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f30,axiom,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f33,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f37,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f40,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f53,plain,
? [X0,X1] :
( relation(X1)
& relation_dom_restriction(X1,X0) != relation_composition(identity_relation(X0),X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
& in(sK0(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| ~ in(sK0(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ( ( in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1) )
& ( ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1) ) )
| X0 = X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f59]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
( relation(sK10)
& relation_dom_restriction(sK10,sK9) != relation_composition(identity_relation(sK9),sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f53]) ).
fof(f71,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f72,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f73,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X5,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f74,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f80,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f81,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f83,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f85,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| in(ordered_pair(X0,X1),X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
relation(sK10),
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
relation_dom_restriction(sK10,sK9) != relation_composition(identity_relation(sK9),sK10),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2) ),
inference(definition_unfolding,[],[f74,f82,f82]) ).
fof(f117,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(X5,X1) ),
inference(definition_unfolding,[],[f73,f82]) ).
fof(f118,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f72,f82,f82]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f81,f82,f82]) ).
fof(f120,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f80,f82,f82]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3)) ),
inference(definition_unfolding,[],[f108,f82,f82]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f107,f82]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3) ),
inference(definition_unfolding,[],[f106,f82,f82]) ).
fof(f127,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1)) ),
inference(equality_resolution,[],[f116]) ).
fof(f128,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(X5,X1) ),
inference(equality_resolution,[],[f117]) ).
fof(f129,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0) ),
inference(equality_resolution,[],[f118]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f71]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK2(X1,X0),sK3(X1,X0)),singleton(sK2(X1,X0))),X1)
| in(unordered_pair(unordered_pair(sK2(X1,X0),sK3(X1,X0)),singleton(sK2(X1,X0))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_63,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f84]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X3),X2))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_90,negated_conjecture,
relation_composition(identity_relation(sK9),sK10) != relation_dom_restriction(sK10,sK9),
inference(cnf_transformation,[],[f112]) ).
tcf(c_91,negated_conjecture,
relation(sK10),
inference(cnf_transformation,[],[f111]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_64]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_64]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_64]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_153,c_51]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X2),X3)) ),
inference(demodulation,[status(thm)],[c_86,c_51]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_154,c_51]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X2),X3)) ),
inference(demodulation,[status(thm)],[c_87,c_51]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_155,c_51]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X3),X2))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_85,c_51]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK2(X1,X0)),unordered_pair(sK2(X1,X0),sK3(X1,X0))),X1)
| in(unordered_pair(singleton(sK2(X1,X0)),unordered_pair(sK2(X1,X0),sK3(X1,X0))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_59,c_51]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X1)
| ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_58,c_51]) ).
tcf(c_543,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_545,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1040,plain,
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9))
| in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10))
| ( relation_composition(identity_relation(sK9),sK10) = relation_dom_restriction(sK10,sK9) )
| ~ relation(relation_dom_restriction(sK10,sK9))
| ~ relation(relation_composition(identity_relation(sK9),sK10)) ),
inference(instantiation,[status(thm)],[c_315]) ).
tcf(c_1041,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(sK9),sK10) = relation_dom_restriction(sK10,sK9) )
| ( relation_dom_restriction(sK10,sK9) != X0 )
| ( relation_composition(identity_relation(sK9),sK10) != X0 ) ),
inference(instantiation,[status(thm)],[c_545]) ).
tcf(c_1093,plain,
( ( relation_composition(identity_relation(sK9),sK10) = relation_dom_restriction(sK10,sK9) )
| ( relation_dom_restriction(sK10,sK9) != relation_composition(identity_relation(sK9),sK10) )
| ( relation_composition(identity_relation(sK9),sK10) != relation_composition(identity_relation(sK9),sK10) ) ),
inference(instantiation,[status(thm)],[c_1041]) ).
tcf(c_1119,plain,
( relation(relation_dom_restriction(sK10,sK9))
| ~ relation(sK10) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1210,plain,
( relation(relation_composition(identity_relation(sK9),sK10))
| ~ relation(sK10)
| ~ relation(identity_relation(sK9)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1279,plain,
! [X0: $i] :
( ( relation_dom_restriction(sK10,sK9) = X0 )
| ~ relation(X0)
| ~ relation(relation_dom_restriction(sK10,sK9))
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),X0)),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),X0),sK3(relation_dom_restriction(sK10,sK9),X0))),X0)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),X0)),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),X0),sK3(relation_dom_restriction(sK10,sK9),X0))),relation_dom_restriction(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_1301,plain,
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10)
| ~ relation(sK10)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10)) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_1302,plain,
( in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ relation(sK10)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10)) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_1370,plain,
relation_composition(identity_relation(sK9),sK10) = relation_composition(identity_relation(sK9),sK10),
inference(instantiation,[status(thm)],[c_543]) ).
tcf(c_2359,plain,
relation(identity_relation(sK9)),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2637,plain,
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10)
| ~ relation(sK10)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_2638,plain,
( in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ relation(sK10)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_308]) ).
tcf(c_2640,plain,
( ( relation_dom_restriction(sK10,sK9) = relation_composition(identity_relation(sK9),sK10) )
| ~ relation(relation_dom_restriction(sK10,sK9))
| ~ relation(relation_composition(identity_relation(sK9),sK10))
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9))
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10)) ),
inference(instantiation,[status(thm)],[c_1279]) ).
tcf(c_3076,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),X0)),relation_composition(identity_relation(sK9),X1))
| ~ relation(X1)
| ~ in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),X0)),X1) ),
inference(instantiation,[status(thm)],[c_313]) ).
tcf(c_3077,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),X0)),relation_dom_restriction(X1,sK9))
| ~ relation(X1)
| ~ in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),X0)),X1) ),
inference(instantiation,[status(thm)],[c_312]) ).
tcf(c_3469,plain,
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10))
| ~ relation(sK10)
| ~ in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10) ),
inference(instantiation,[status(thm)],[c_3076]) ).
tcf(c_3473,plain,
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9))
| ~ relation(sK10)
| ~ in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10) ),
inference(instantiation,[status(thm)],[c_3077]) ).
tcf(c_3506,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3473,c_3469,c_2640,c_2637,c_2638,c_2359,c_1370,c_1301,c_1302,c_1210,c_1119,c_1093,c_1040,c_90,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU195+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 13:07:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.45/1.19 % SZS status Started for theBenchmark.p
% 1.45/1.19 % SZS status Theorem for theBenchmark.p
% 1.45/1.19
% 1.45/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.45/1.19
% 1.45/1.19 % ------ iProver source info
% 1.45/1.19
% 1.45/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 1.45/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.45/1.19 % git: non_committed_changes: false
% 1.45/1.19
% 1.45/1.19 % ------ Parsing...
% 1.45/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.45/1.19
% 1.45/1.19 % ------ Preprocessing... sup_sim: 11 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.45/1.19
% 1.45/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.45/1.19
% 1.45/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.45/1.19 % ------ Proving...
% 1.45/1.19 % ------ Problem Properties
% 1.45/1.19
% 1.45/1.19 %
% 1.45/1.19 % clauses 37
% 1.45/1.19 % conjectures 2
% 1.45/1.19 % EPR 14
% 1.45/1.19 % Horn 33
% 1.45/1.19 % unary 14
% 1.45/1.19 % binary 6
% 1.45/1.19 % lits 90
% 1.45/1.19 % lits eq 9
% 1.45/1.19 % fd_pure 0
% 1.45/1.19 % fd_pseudo 0
% 1.45/1.19 % fd_cond 1
% 1.45/1.19 % fd_pseudo_cond 6
% 1.45/1.19 % AC symbols 0
% 1.45/1.19
% 1.45/1.19 % ------ Input Options Time Limit: Unbounded
% 1.45/1.19
% 1.45/1.19
% 1.45/1.19 % ------
% 1.45/1.19 % Current options:
% 1.45/1.19 % ------
% 1.45/1.19
% 1.45/1.19
% 1.45/1.19 %
% 1.45/1.19
% 1.45/1.19 % ------ Proving...
% 1.45/1.19 %
% 1.45/1.19
% 1.45/1.19 % SZS status Theorem for theBenchmark.p
% 1.45/1.19
% 1.45/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.45/1.19
% 1.45/1.19
%------------------------------------------------------------------------------