TSTP Solution File: SEU182+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 17:04:27 EDT 2023
% Result : Theorem 4.30s 1.16s
% Output : CNFRefutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 77 ( 14 unt; 0 def)
% Number of atoms : 317 ( 31 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 399 ( 159 ~; 156 |; 55 &)
% ( 10 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 2 con; 0-4 aty)
% Number of variables : 225 ( 2 sgn; 146 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f5,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(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f30,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f42]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ~ subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
& relation(X1) )
& relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f55,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,[],[f39]) ).
fof(f56,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,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f58,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])],[f56,f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK1(X0,X1),X3),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK1(X0,X1),X4),X0)
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK1(X0,X1),X4),X0)
=> in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK3(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK1(X0,X1),X3),X0)
| ~ in(sK1(X0,X1),X1) )
& ( in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK3(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f60,f63,f62,f61]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f41]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) ) )
& ( ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK5(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK4(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK5(X0,X1,X2)),X1)
& in(ordered_pair(sK4(X0,X1,X2),X6),X0) )
| in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK5(X0,X1,X2)),X1)
& in(ordered_pair(sK4(X0,X1,X2),X6),X0) )
=> ( in(ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)),X1)
& in(ordered_pair(sK4(X0,X1,X2),sK6(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) )
=> ( in(ordered_pair(sK7(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK7(X0,X1,X7,X8)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK5(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK4(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)),X1)
& in(ordered_pair(sK4(X0,X1,X2),sK6(X0,X1,X2)),X0) )
| in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) ) )
& ( ( in(ordered_pair(sK7(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK7(X0,X1,X7,X8)),X0) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f66,f69,f68,f67]) ).
fof(f84,plain,
( ? [X0] :
( ? [X1] :
( ~ subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
& relation(X1) )
& relation(X0) )
=> ( ? [X1] :
( ~ subset(relation_dom(relation_composition(sK14,X1)),relation_dom(sK14))
& relation(X1) )
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ? [X1] :
( ~ subset(relation_dom(relation_composition(sK14,X1)),relation_dom(sK14))
& relation(X1) )
=> ( ~ subset(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ~ subset(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))
& relation(sK15)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f48,f85,f84]) ).
fof(f88,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f90,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f91,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f92,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK3(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f93,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f96,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f97,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK7(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f103,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f123,plain,
relation(sK14),
inference(cnf_transformation,[],[f86]) ).
fof(f124,plain,
relation(sK15),
inference(cnf_transformation,[],[f86]) ).
fof(f125,plain,
~ subset(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),
inference(cnf_transformation,[],[f86]) ).
fof(f133,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f93,f96]) ).
fof(f134,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f92,f96]) ).
fof(f140,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK7(X0,X1,X7,X8)),singleton(X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f97,f96,f96]) ).
fof(f142,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f133]) ).
fof(f143,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f146,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK7(X0,X1,X7,X8)),singleton(X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f140]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f88]) ).
cnf(c_51,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_52,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_56,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_57,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK3(X1,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_63,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3))
| ~ relation(relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,sK7(X2,X3,X0,X1)),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_64,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_84,negated_conjecture,
~ subset(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),
inference(cnf_transformation,[],[f125]) ).
cnf(c_85,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f124]) ).
cnf(c_86,negated_conjecture,
relation(sK14),
inference(cnf_transformation,[],[f123]) ).
cnf(c_133,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
cnf(c_145,plain,
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
cnf(c_146,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_145]) ).
cnf(c_315,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,sK7(X2,X3,X0,X1)),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_64]) ).
cnf(c_437,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
cnf(c_438,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_57,c_50]) ).
cnf(c_441,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X0,X1))),X2) ),
inference(demodulation,[status(thm)],[c_315,c_50]) ).
cnf(c_715,plain,
( relation_dom(relation_composition(sK14,sK15)) != X0
| relation_dom(sK14) != X1
| in(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_146,c_84]) ).
cnf(c_716,plain,
in(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),relation_dom(relation_composition(sK14,sK15))),
inference(unflattening,[status(thm)],[c_715]) ).
cnf(c_720,plain,
( relation_dom(relation_composition(sK14,sK15)) != X0
| relation_dom(sK14) != X1
| ~ in(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_133,c_84]) ).
cnf(c_721,plain,
~ in(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),relation_dom(sK14)),
inference(unflattening,[status(thm)],[c_720]) ).
cnf(c_2184,plain,
( ~ relation(X0)
| ~ relation(sK15)
| relation(relation_composition(X0,sK15)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_2185,plain,
( ~ relation(sK14)
| ~ relation(sK15)
| relation(relation_composition(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_2184]) ).
cnf(c_2241,plain,
( ~ in(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),relation_dom(relation_composition(sK14,sK15)))
| ~ relation(relation_composition(sK14,sK15))
| in(unordered_pair(singleton(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))),unordered_pair(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),sK3(relation_composition(sK14,sK15),sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))))),relation_composition(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_438]) ).
cnf(c_2549,plain,
( ~ in(unordered_pair(singleton(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))),unordered_pair(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),sK3(relation_composition(sK14,sK15),sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))))),relation_composition(sK14,sK15))
| ~ relation(sK14)
| ~ relation(sK15)
| in(unordered_pair(singleton(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))),unordered_pair(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),sK7(sK14,sK15,sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),sK3(relation_composition(sK14,sK15),sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)))))),sK14) ),
inference(instantiation,[status(thm)],[c_441]) ).
cnf(c_3395,plain,
( ~ in(unordered_pair(singleton(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14))),unordered_pair(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),sK7(sK14,sK15,sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),sK3(relation_composition(sK14,sK15),sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)))))),sK14)
| ~ relation(sK14)
| in(sK0(relation_dom(relation_composition(sK14,sK15)),relation_dom(sK14)),relation_dom(sK14)) ),
inference(instantiation,[status(thm)],[c_437]) ).
cnf(c_3396,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3395,c_2549,c_2241,c_2185,c_721,c_716,c_85,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 15:29:20 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.30/1.16 % SZS status Started for theBenchmark.p
% 4.30/1.16 % SZS status Theorem for theBenchmark.p
% 4.30/1.16
% 4.30/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.30/1.16
% 4.30/1.16 ------ iProver source info
% 4.30/1.16
% 4.30/1.16 git: date: 2023-05-31 18:12:56 +0000
% 4.30/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.30/1.16 git: non_committed_changes: false
% 4.30/1.16 git: last_make_outside_of_git: false
% 4.30/1.16
% 4.30/1.16 ------ Parsing...
% 4.30/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.30/1.16
% 4.30/1.16 ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 4.30/1.16
% 4.30/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.30/1.16
% 4.30/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.30/1.16 ------ Proving...
% 4.30/1.16 ------ Problem Properties
% 4.30/1.16
% 4.30/1.16
% 4.30/1.16 clauses 42
% 4.30/1.16 conjectures 3
% 4.30/1.16 EPR 17
% 4.30/1.16 Horn 36
% 4.30/1.16 unary 16
% 4.30/1.16 binary 10
% 4.30/1.16 lits 100
% 4.30/1.16 lits eq 8
% 4.30/1.16 fd_pure 0
% 4.30/1.16 fd_pseudo 0
% 4.30/1.16 fd_cond 1
% 4.30/1.16 fd_pseudo_cond 6
% 4.30/1.16 AC symbols 0
% 4.30/1.16
% 4.30/1.16 ------ Input Options Time Limit: Unbounded
% 4.30/1.16
% 4.30/1.16
% 4.30/1.16 ------
% 4.30/1.16 Current options:
% 4.30/1.16 ------
% 4.30/1.16
% 4.30/1.16
% 4.30/1.16
% 4.30/1.16
% 4.30/1.16 ------ Proving...
% 4.30/1.16
% 4.30/1.16
% 4.30/1.16 % SZS status Theorem for theBenchmark.p
% 4.30/1.16
% 4.30/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.30/1.16
% 4.30/1.16
%------------------------------------------------------------------------------