%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU208+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 : n011.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 02:55:54 PM UTC 2026
% Result : Theorem 3.94s 1.52s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 14 unt; 4 def)
% Number of atoms : 314 ( 34 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 376 ( 156 ~; 156 |; 49 &)
% ( 10 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 190 ( 0 sgn 156 !; 34 ?; 46 :)
% 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] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_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(f26,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f35,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f40,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_inverse_image(X2,X1))
<~> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f48,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(X6,sK2(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK5(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f51]) ).
fof(f58,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_inverse_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
& ( ~ in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f59,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_inverse_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
& ( ~ in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_inverse_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) ) )
& ( ~ in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
( relation(sK13)
& ( in(sK11,relation_inverse_image(sK13,sK12))
| ( in(sK14,sK12)
& in(ordered_pair(sK11,sK14),sK13)
& in(sK14,relation_rng(sK13)) ) )
& ( ~ in(sK11,relation_inverse_image(sK13,sK12))
| ! [X3] :
( ~ in(X3,sK12)
| ~ in(ordered_pair(sK11,X3),sK13)
| ~ in(X3,relation_rng(sK13)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X4,sK14)],[f60]) ).
fof(f64,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f65,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f66,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK2(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f67,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f92,plain,
relation(sK13),
inference(cnf_transformation,[],[f61]) ).
fof(f93,plain,
( in(sK11,relation_inverse_image(sK13,sK12))
| in(sK14,sK12) ),
inference(cnf_transformation,[],[f61]) ).
fof(f94,plain,
( in(sK11,relation_inverse_image(sK13,sK12))
| in(ordered_pair(sK11,sK14),sK13) ),
inference(cnf_transformation,[],[f61]) ).
fof(f96,plain,
! [X3] :
( ~ in(sK11,relation_inverse_image(sK13,sK12))
| ~ in(X3,sK12)
| ~ in(ordered_pair(sK11,X3),sK13)
| ~ in(X3,relation_rng(sK13)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f67,f75]) ).
fof(f105,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0) ),
inference(definition_unfolding,[],[f66,f75]) ).
fof(f108,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f72,f75]) ).
fof(f111,plain,
! [X3] :
( ~ in(sK11,relation_inverse_image(sK13,sK12))
| ~ in(X3,sK12)
| ~ in(unordered_pair(unordered_pair(sK11,X3),singleton(sK11)),sK13)
| ~ in(X3,relation_rng(sK13)) ),
inference(definition_unfolding,[],[f96,f75]) ).
fof(f112,plain,
( in(sK11,relation_inverse_image(sK13,sK12))
| in(unordered_pair(unordered_pair(sK11,sK14),singleton(sK11)),sK13) ),
inference(definition_unfolding,[],[f94,f75]) ).
fof(f113,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f104]) ).
fof(f114,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f115,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK2(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f65]) ).
fof(f116,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f108]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f64]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK2(X1,X2,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_78,negated_conjecture,
! [X0: $i] :
( ~ in(X0,sK12)
| ~ in(X0,relation_rng(sK13))
| ~ in(sK11,relation_inverse_image(sK13,sK12))
| ~ in(unordered_pair(unordered_pair(sK11,X0),singleton(sK11)),sK13) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_80,negated_conjecture,
( in(sK11,relation_inverse_image(sK13,sK12))
| in(unordered_pair(unordered_pair(sK11,sK14),singleton(sK11)),sK13) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_81,negated_conjecture,
( in(sK14,sK12)
| in(sK11,relation_inverse_image(sK13,sK12)) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_82,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f92]) ).
tcf(c_329,plain,
( in(sK11,relation_inverse_image(sK13,sK12))
| in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK14)),sK13) ),
inference(demodulation,[status(thm)],[c_80,c_51]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_56,c_51]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_55,c_51]) ).
tcf(c_393,plain,
! [X0: $i] :
( ~ in(X0,sK12)
| ~ in(X0,relation_rng(sK13))
| ~ in(sK11,relation_inverse_image(sK13,sK12))
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK13) ),
inference(demodulation,[status(thm)],[c_78,c_51]) ).
tcf(c_1071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_inverse_image(X0,X3))
| ~ in(X2,X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_372,c_82]) ).
tcf(c_1072,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_inverse_image(sK13,X2))
| ~ in(X1,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK13) ),
inference(unflattening,[status(thm)],[c_1071]) ).
tcf(c_1082,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,relation_rng(X0))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_342,c_82]) ).
tcf(c_1083,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK13))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK13) ),
inference(unflattening,[status(thm)],[c_1082]) ).
tcf(c_1220,plain,
! [X0: $i] :
( ~ in(X0,sK12)
| ~ in(X0,relation_rng(sK13))
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_393,c_1072]) ).
tcf(c_1224,plain,
! [X0: $i] :
( ~ in(X0,sK12)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1220,c_1083]) ).
tcf(c_2196,definition,
iPr_def_10 = singleton(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2197,definition,
iPr_def_11 = unordered_pair(sK11,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2198,definition,
iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2199,definition,
iPr_def_13 = relation_inverse_image(sK13,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2201,plain,
! [X0: $i] :
( ~ in(X0,sK12)
| ~ in(unordered_pair(iPr_def_10,unordered_pair(sK11,X0)),sK13) ),
inference(demodulation,[status(thm)],[c_1224,c_2196]) ).
tcf(c_2202,plain,
( in(iPr_def_12,sK13)
| in(sK11,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_329,c_2199,c_2197,c_2198]) ).
tcf(c_2203,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_2204,negated_conjecture,
( in(sK14,sK12)
| in(sK11,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_2712,plain,
( ~ in(sK14,sK12)
| ~ in(unordered_pair(iPr_def_10,iPr_def_11),sK13) ),
inference(superposition,[status(thm)],[c_2197,c_2201]) ).
tcf(c_2713,plain,
( ~ in(iPr_def_12,sK13)
| ~ in(sK14,sK12) ),
inference(light_normalisation,[status(thm)],[c_2712,c_2198]) ).
tcf(c_2746,plain,
( in(sK11,iPr_def_13)
| ~ in(iPr_def_12,sK13) ),
inference(superposition,[status(thm)],[c_2204,c_2713]) ).
tcf(c_2749,plain,
in(sK11,iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_2746,c_2202,c_2746]) ).
tcf(c_2789,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(iPr_def_10,unordered_pair(sK11,sK2(X0,X1,sK11))),X0)
| ~ relation(X0)
| ~ in(sK11,relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_2196,c_362]) ).
tcf(c_4499,plain,
! [X0: $i] :
( ~ relation(sK13)
| ~ in(sK11,relation_inverse_image(sK13,X0))
| ~ in(sK2(sK13,X0,sK11),sK12) ),
inference(superposition,[status(thm)],[c_2789,c_2201]) ).
tcf(c_4516,plain,
! [X0: $i] :
( ~ in(sK11,relation_inverse_image(sK13,X0))
| ~ in(sK2(sK13,X0,sK11),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4499,c_2203]) ).
tcf(c_4661,plain,
( ~ relation(sK13)
| ~ in(sK11,relation_inverse_image(sK13,sK12)) ),
inference(superposition,[status(thm)],[c_57,c_4516]) ).
tcf(c_4662,plain,
( ~ relation(sK13)
| ~ in(sK11,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_4661,c_2199]) ).
tcf(c_4663,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4662,c_2203,c_2749]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU208+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n011.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 13:11:13 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.50 Running first-order theorem proving
% 0.23/0.50 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
% 0.23/0.52
% 0.23/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.52
% 0.23/0.52 % Detected problem language: tptp
% 0.23/0.54 % Proving...
% 3.94/1.52 % SZS status Started for theBenchmark.p
% 3.94/1.52 % SZS status Theorem for theBenchmark.p
% 3.94/1.52
% 3.94/1.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.94/1.52
% 3.94/1.52 % ------ iProver source info
% 3.94/1.52
% 3.94/1.52 % git: date: 2026-07-19 20:42:38 +0200
% 3.94/1.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.94/1.52 % git: non_committed_changes: false
% 3.94/1.52
% 3.94/1.52 % ------ Parsing...
% 3.94/1.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.94/1.52
% 3.94/1.52 % ------ Preprocessing... sup_sim: 10 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 %
% 3.94/1.52
% 3.94/1.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.94/1.52
% 3.94/1.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.94/1.52 % ------ Proving...
% 3.94/1.52 % ------ Problem Properties
% 3.94/1.52
% 3.94/1.52 %
% 3.94/1.52 % clauses 40
% 3.94/1.52 % conjectures 3
% 3.94/1.52 % EPR 17
% 3.94/1.52 % Horn 33
% 3.94/1.52 % unary 17
% 3.94/1.52 % binary 11
% 3.94/1.52 % lits 82
% 3.94/1.52 % lits eq 13
% 3.94/1.52 % fd_pure 0
% 3.94/1.52 % fd_pseudo 0
% 3.94/1.52 % fd_cond 1
% 3.94/1.52 % fd_pseudo_cond 6
% 3.94/1.52 % AC symbols 0
% 3.94/1.52
% 3.94/1.52 % ------ Schedule dynamic 5 is on
% 3.94/1.52
% 3.94/1.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.94/1.52
% 3.94/1.52
% 3.94/1.52 % ------
% 3.94/1.52 % Current options:
% 3.94/1.52 % ------
% 3.94/1.52
% 3.94/1.52
% 3.94/1.52 %
% 3.94/1.52
% 3.94/1.52 % ------ Proving...
% 3.94/1.52 %
% 3.94/1.52
% 3.94/1.52 % SZS status Theorem for theBenchmark.p
% 3.94/1.52
% 3.94/1.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/1.52
% 3.94/1.52
%------------------------------------------------------------------------------