TSTP Solution File: SEU210+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:04:43 EDT 2023
% Result : Theorem 0.47s 1.17s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 118 ( 25 unt; 0 def)
% Number of atoms : 365 ( 47 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 430 ( 183 ~; 161 |; 61 &)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 249 ( 15 sgn; 144 !; 31 ?)
% 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] :
( relation_rng(X0) = X1
<=> ! [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)
=> ~ ( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ~ ( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0 ) ),
inference(negated_conjecture,[],[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)
=> empty_set = X0 ),
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] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f52,plain,
? [X0,X1] :
( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0
& relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f53,plain,
? [X0,X1] :
( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0
& relation(X1) ),
inference(flattening,[],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f60,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
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,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f64,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f64,f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK1(X0,X1)),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK1(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK1(X0,X1)),X0)
=> in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK3(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK1(X0,X1)),X0)
| ~ in(sK1(X0,X1),X1) )
& ( in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK3(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f68,f71,f70,f69]) ).
fof(f73,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f15,f73]) ).
fof(f79,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f26,f79]) ).
fof(f87,plain,
! [X0,X1,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)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f51]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
=> ( in(sK11(X0,X1,X2),X1)
& in(ordered_pair(X0,sK11(X0,X1,X2)),X2)
& in(sK11(X0,X1,X2),relation_rng(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ( in(sK11(X0,X1,X2),X1)
& in(ordered_pair(X0,sK11(X0,X1,X2)),X2)
& in(sK11(X0,X1,X2),relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f88,f89]) ).
fof(f91,plain,
( ? [X0,X1] :
( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0
& relation(X1) )
=> ( empty_set = relation_inverse_image(sK13,sK12)
& subset(sK12,relation_rng(sK13))
& empty_set != sK12
& relation(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
( empty_set = relation_inverse_image(sK13,sK12)
& subset(sK12,relation_rng(sK13))
& empty_set != sK12
& relation(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f53,f91]) ).
fof(f95,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f97,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f100,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK3(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f104,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f105,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f74]) ).
fof(f111,plain,
empty(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f114,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f120,plain,
empty(sK7),
inference(cnf_transformation,[],[f80]) ).
fof(f128,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK11(X0,X1,X2)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f131,plain,
relation(sK13),
inference(cnf_transformation,[],[f92]) ).
fof(f132,plain,
empty_set != sK12,
inference(cnf_transformation,[],[f92]) ).
fof(f133,plain,
subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f92]) ).
fof(f134,plain,
empty_set = relation_inverse_image(sK13,sK12),
inference(cnf_transformation,[],[f92]) ).
fof(f136,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f141,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f142,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f143,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f146,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f101,f104]) ).
fof(f147,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f100,f104]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f130,f104]) ).
fof(f150,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK11(X0,X1,X2)),singleton(X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f128,f104]) ).
fof(f151,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f146]) ).
fof(f152,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f147]) ).
cnf(c_50,plain,
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_54,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_57,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_58,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK3(X1,X0),X0),singleton(sK3(X1,X0))),X1) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_59,plain,
element(sK4(X0),X0),
inference(cnf_transformation,[],[f105]) ).
cnf(c_66,plain,
empty(empty_set),
inference(cnf_transformation,[],[f111]) ).
cnf(c_69,plain,
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_74,plain,
empty(sK7),
inference(cnf_transformation,[],[f120]) ).
cnf(c_81,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(X1,relation_rng(X2))
| ~ in(X1,X3)
| ~ relation(X2)
| in(X0,relation_inverse_image(X2,X3)) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_83,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK11(X0,X2,X1)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_85,negated_conjecture,
relation_inverse_image(sK13,sK12) = empty_set,
inference(cnf_transformation,[],[f134]) ).
cnf(c_86,negated_conjecture,
subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f133]) ).
cnf(c_87,negated_conjecture,
empty_set != sK12,
inference(cnf_transformation,[],[f132]) ).
cnf(c_88,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f131]) ).
cnf(c_90,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_95,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_96,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_97,plain,
( ~ empty(X0)
| ~ empty(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_121,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(X1,X3)
| ~ relation(X2)
| in(X0,relation_inverse_image(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_81,c_57,c_81]) ).
cnf(c_129,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(prop_impl_just,[status(thm)],[c_96]) ).
cnf(c_137,plain,
( ~ empty(X0)
| relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
cnf(c_702,plain,
( relation_rng(sK13) != X1
| X0 != sK12
| ~ in(X2,X0)
| in(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_54,c_86]) ).
cnf(c_703,plain,
( ~ in(X0,sK12)
| in(X0,relation_rng(sK13)) ),
inference(unflattening,[status(thm)],[c_702]) ).
cnf(c_777,plain,
( X0 != X1
| ~ in(X2,relation_inverse_image(X0,X3))
| ~ empty(X1)
| in(unordered_pair(unordered_pair(X2,sK11(X2,X3,X0)),singleton(X2)),X0) ),
inference(resolution_lifted,[status(thm)],[c_83,c_137]) ).
cnf(c_778,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ empty(X1)
| in(unordered_pair(unordered_pair(X0,sK11(X0,X2,X1)),singleton(X0)),X1) ),
inference(unflattening,[status(thm)],[c_777]) ).
cnf(c_786,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_778,c_129]) ).
cnf(c_792,plain,
( X0 != X1
| ~ in(X2,relation_rng(X0))
| ~ empty(X1)
| in(unordered_pair(unordered_pair(sK3(X0,X2),X2),singleton(sK3(X0,X2))),X0) ),
inference(resolution_lifted,[status(thm)],[c_58,c_137]) ).
cnf(c_793,plain,
( ~ in(X0,relation_rng(X1))
| ~ empty(X1)
| in(unordered_pair(unordered_pair(sK3(X1,X0),X0),singleton(sK3(X1,X0))),X1) ),
inference(unflattening,[status(thm)],[c_792]) ).
cnf(c_801,plain,
( ~ in(X0,relation_rng(X1))
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_793,c_129]) ).
cnf(c_3270,plain,
( ~ empty(empty_set)
| ~ empty(sK12)
| empty_set = sK12 ),
inference(instantiation,[status(thm)],[c_97]) ).
cnf(c_3367,plain,
( ~ empty(X0)
| relation_rng(X0) = empty_set ),
inference(superposition,[status(thm)],[c_69,c_95]) ).
cnf(c_5173,plain,
( in(sK4(X0),X0)
| empty(X0) ),
inference(superposition,[status(thm)],[c_59,c_90]) ).
cnf(c_5231,plain,
relation_rng(sK7) = empty_set,
inference(superposition,[status(thm)],[c_74,c_3367]) ).
cnf(c_5348,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) ),
inference(superposition,[status(thm)],[c_58,c_96]) ).
cnf(c_5355,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(X1) ),
inference(superposition,[status(thm)],[c_83,c_96]) ).
cnf(c_5358,plain,
( ~ in(X0,relation_rng(X1))
| ~ in(X0,X2)
| ~ relation(X1)
| in(sK3(X1,X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_121]) ).
cnf(c_5371,plain,
( ~ in(X0,relation_rng(X1))
| ~ empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_5348,c_801]) ).
cnf(c_5382,plain,
( ~ in(X0,empty_set)
| ~ empty(sK7) ),
inference(superposition,[status(thm)],[c_5231,c_5371]) ).
cnf(c_5391,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_5355,c_786]) ).
cnf(c_5398,plain,
( ~ in(X0,empty_set)
| ~ empty(sK13) ),
inference(superposition,[status(thm)],[c_85,c_5391]) ).
cnf(c_5417,plain,
~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_5398,c_74,c_5382]) ).
cnf(c_5996,plain,
( ~ in(X0,relation_rng(sK13))
| ~ in(X0,sK12)
| ~ relation(sK13)
| in(sK3(sK13,X0),empty_set) ),
inference(superposition,[status(thm)],[c_85,c_5358]) ).
cnf(c_6107,plain,
( ~ in(X0,sK12)
| in(sK3(sK13,X0),empty_set) ),
inference(global_subsumption_just,[status(thm)],[c_5996,c_88,c_703,c_5996]) ).
cnf(c_6114,plain,
~ in(X0,sK12),
inference(superposition,[status(thm)],[c_6107,c_5417]) ).
cnf(c_6130,plain,
empty(sK12),
inference(superposition,[status(thm)],[c_5173,c_6114]) ).
cnf(c_6131,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6130,c_3270,c_87,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 15:45:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.47/1.17 % SZS status Started for theBenchmark.p
% 0.47/1.17 % SZS status Theorem for theBenchmark.p
% 0.47/1.17
% 0.47/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.47/1.17
% 0.47/1.17 ------ iProver source info
% 0.47/1.17
% 0.47/1.17 git: date: 2023-05-31 18:12:56 +0000
% 0.47/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.47/1.17 git: non_committed_changes: false
% 0.47/1.17 git: last_make_outside_of_git: false
% 0.47/1.17
% 0.47/1.17 ------ Parsing...
% 0.47/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.47/1.17
% 0.47/1.17 ------ 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
% 0.47/1.17
% 0.47/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.47/1.17
% 0.47/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.47/1.17 ------ Proving...
% 0.47/1.17 ------ Problem Properties
% 0.47/1.17
% 0.47/1.17
% 0.47/1.17 clauses 47
% 0.47/1.17 conjectures 4
% 0.47/1.17 EPR 21
% 0.47/1.17 Horn 43
% 0.47/1.17 unary 20
% 0.47/1.17 binary 13
% 0.47/1.17 lits 91
% 0.47/1.17 lits eq 7
% 0.47/1.17 fd_pure 0
% 0.47/1.17 fd_pseudo 0
% 0.47/1.17 fd_cond 1
% 0.47/1.17 fd_pseudo_cond 3
% 0.47/1.17 AC symbols 0
% 0.47/1.17
% 0.47/1.17 ------ Input Options Time Limit: Unbounded
% 0.47/1.17
% 0.47/1.17
% 0.47/1.17 ------
% 0.47/1.17 Current options:
% 0.47/1.17 ------
% 0.47/1.17
% 0.47/1.17
% 0.47/1.17
% 0.47/1.17
% 0.47/1.17 ------ Proving...
% 0.47/1.17
% 0.47/1.17
% 0.47/1.17 % SZS status Theorem for theBenchmark.p
% 0.47/1.17
% 0.47/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.47/1.17
% 0.90/1.18
%------------------------------------------------------------------------------