%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU210+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 7.34s 1.72s
% Output : CNFRefutation 7.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 110 ( 25 unt; 0 def)
% Number of atoms : 331 ( 43 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 396 ( 175 ~; 157 |; 47 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 224 ( 0 sgn 204 !; 20 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
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(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f21,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f23,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f26,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f31,axiom,
! [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(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> ~ ( relation_inverse_image(X1,X0) = empty_set
& subset(X0,relation_rng(X1))
& X0 != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ~ ( relation_inverse_image(X1,X0) = empty_set
& subset(X0,relation_rng(X1))
& X0 != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f44,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,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(f49,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f51,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,[],[f31]) ).
fof(f52,plain,
? [X0,X1] :
( relation(X1)
& relation_inverse_image(X1,X0) = empty_set
& subset(X0,relation_rng(X1))
& X0 != empty_set ),
inference(ennf_transformation,[],[f33]) ).
fof(f53,plain,
? [X0,X1] :
( relation(X1)
& relation_inverse_image(X1,X0) = empty_set
& subset(X0,relation_rng(X1))
& X0 != empty_set ),
inference(flattening,[],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f55]) ).
fof(f60,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f39]) ).
fof(f61,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f62,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f64,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f64]) ).
fof(f66,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,[],[f46]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK3(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK1(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f67]) ).
fof(f69,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f15]) ).
fof(f72,plain,
empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f26]) ).
fof(f76,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)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f77,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)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ( in(sK11(X0,X1,X2),X1)
& in(ordered_pair(X0,sK11(X0,X1,X2)),X2)
& in(sK11(X0,X1,X2),relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X2))],[f77]) ).
fof(f79,plain,
( relation(sK13)
& empty_set = relation_inverse_image(sK13,sK12)
& subset(sK12,relation_rng(sK13))
& empty_set != sK12 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f53]) ).
fof(f82,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f84,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK3(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f88,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f91,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f92,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f69]) ).
fof(f99,plain,
empty(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f102,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f107,plain,
empty(sK7),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(ordered_pair(X0,sK11(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ relation(X2)
| ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2))
| in(X0,relation_inverse_image(X2,X1)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
relation(sK13),
inference(cnf_transformation,[],[f79]) ).
fof(f119,plain,
empty_set = relation_inverse_image(sK13,sK12),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
empty_set != sK12,
inference(cnf_transformation,[],[f79]) ).
fof(f123,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f128,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f129,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f130,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f133,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,[],[f88,f91]) ).
fof(f134,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0) ),
inference(definition_unfolding,[],[f87,f91]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ relation(X2)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),X2)
| ~ in(X3,relation_rng(X2))
| in(X0,relation_inverse_image(X2,X1)) ),
inference(definition_unfolding,[],[f117,f91]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(unordered_pair(unordered_pair(X0,sK11(X0,X1,X2)),singleton(X0)),X2) ),
inference(definition_unfolding,[],[f115,f91]) ).
fof(f138,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f133]) ).
fof(f139,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0) ),
inference(equality_resolution,[],[f134]) ).
tcf(c_50,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_57,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,[],[f138]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK3(X1,X0),X0),singleton(sK3(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_59,plain,
! [X0: $i] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f92]) ).
tcf(c_65,plain,
empty(empty_set),
inference(cnf_transformation,[],[f99]) ).
tcf(c_68,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_74,plain,
empty(sK7),
inference(cnf_transformation,[],[f107]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK11(X0,X2,X1)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_85,negated_conjecture,
empty_set != sK12,
inference(cnf_transformation,[],[f121]) ).
tcf(c_86,negated_conjecture,
subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f120]) ).
tcf(c_87,negated_conjecture,
relation_inverse_image(sK13,sK12) = empty_set,
inference(cnf_transformation,[],[f119]) ).
tcf(c_88,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f118]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_95,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_121,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(global_subsumption_just,[status(thm)],[c_81,c_57,c_81]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_96]) ).
tcf(c_137,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_702,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ( X0 != sK12 )
| ( relation_rng(sK13) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_86]) ).
tcf(c_703,plain,
! [X0: $i] :
( in(X0,relation_rng(sK13))
| ~ in(X0,sK12) ),
inference(unflattening,[status(thm)],[c_702]) ).
tcf(c_777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,sK11(X2,X3,X0)),singleton(X2)),X0)
| ~ empty(X1)
| ~ in(X2,relation_inverse_image(X0,X3))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_137]) ).
tcf(c_778,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK11(X0,X2,X1)),singleton(X0)),X1)
| ~ empty(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(unflattening,[status(thm)],[c_777]) ).
tcf(c_786,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_778,c_129]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK3(X0,X2),X2),singleton(sK3(X0,X2))),X0)
| ~ empty(X1)
| ~ in(X2,relation_rng(X0))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_137]) ).
tcf(c_793,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK3(X1,X0),X0),singleton(sK3(X1,X0))),X1)
| ~ empty(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(unflattening,[status(thm)],[c_792]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_793,c_129]) ).
tcf(c_3270,plain,
( ( empty_set = sK12 )
| ~ empty(sK12)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_3367,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_68,c_95]) ).
tcf(c_5171,plain,
! [X0: $i] :
( empty(X0)
| in(sK4(X0),X0) ),
inference(superposition,[status(thm)],[c_59,c_90]) ).
tcf(c_5229,plain,
relation_rng(sK7) = empty_set,
inference(superposition,[status(thm)],[c_74,c_3367]) ).
tcf(c_5346,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_58,c_96]) ).
tcf(c_5353,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_83,c_96]) ).
tcf(c_5356,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X0),relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_58,c_121]) ).
tcf(c_5369,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_5346,c_801]) ).
tcf(c_5380,plain,
! [X0: $i] :
( ~ empty(sK7)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5229,c_5369]) ).
tcf(c_5389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_5353,c_786]) ).
tcf(c_5396,plain,
! [X0: $i] :
( ~ empty(sK13)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_87,c_5389]) ).
tcf(c_5415,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_5396,c_74,c_5380]) ).
tcf(c_5994,plain,
! [X0: $i] :
( in(sK3(sK13,X0),empty_set)
| ~ relation(sK13)
| ~ in(X0,sK12)
| ~ in(X0,relation_rng(sK13)) ),
inference(superposition,[status(thm)],[c_87,c_5356]) ).
tcf(c_6105,plain,
! [X0: $i] :
( in(sK3(sK13,X0),empty_set)
| ~ in(X0,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_5994,c_88,c_703,c_5994]) ).
tcf(c_6112,plain,
! [X0: $i] : ~ in(X0,sK12),
inference(superposition,[status(thm)],[c_6105,c_5415]) ).
tcf(c_6128,plain,
empty(sK12),
inference(superposition,[status(thm)],[c_5171,c_6112]) ).
tcf(c_6129,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6128,c_3270,c_85,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU210+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:11:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 7.34/1.72 % SZS status Started for theBenchmark.p
% 7.34/1.72 % SZS status Theorem for theBenchmark.p
% 7.34/1.72
% 7.34/1.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.34/1.72
% 7.34/1.72 % ------ iProver source info
% 7.34/1.72
% 7.34/1.72 % git: date: 2026-07-19 20:42:38 +0200
% 7.34/1.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.34/1.72 % git: non_committed_changes: false
% 7.34/1.72
% 7.34/1.72 % ------ Parsing...
% 7.34/1.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.34/1.72
% 7.34/1.72 % ------ 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 %
% 7.34/1.72
% 7.34/1.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.34/1.72
% 7.34/1.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.34/1.72 % ------ Proving...
% 7.34/1.72 % ------ Problem Properties
% 7.34/1.72
% 7.34/1.72 %
% 7.34/1.72 % clauses 47
% 7.34/1.72 % conjectures 4
% 7.34/1.72 % EPR 21
% 7.34/1.72 % Horn 43
% 7.34/1.72 % unary 20
% 7.34/1.72 % binary 13
% 7.34/1.72 % lits 91
% 7.34/1.72 % lits eq 7
% 7.34/1.72 % fd_pure 0
% 7.34/1.72 % fd_pseudo 0
% 7.34/1.72 % fd_cond 1
% 7.34/1.72 % fd_pseudo_cond 3
% 7.34/1.72 % AC symbols 0
% 7.34/1.72
% 7.34/1.72 % ------ Input Options Time Limit: Unbounded
% 7.34/1.72
% 7.34/1.72
% 7.34/1.72 % ------
% 7.34/1.72 % Current options:
% 7.34/1.72 % ------
% 7.34/1.72
% 7.34/1.72
% 7.34/1.72 %
% 7.34/1.72
% 7.34/1.72 % ------ Proving...
% 7.34/1.72 %
% 7.34/1.72
% 7.34/1.72 % SZS status Theorem for theBenchmark.p
% 7.34/1.72
% 7.34/1.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.34/1.72
% 7.34/1.72
%------------------------------------------------------------------------------