%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU077+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:55:19 PM UTC 2026
% Result : Theorem 1.10s 1.78s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 77 ( 17 unt; 0 def)
% Number of atoms : 335 ( 50 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 430 ( 172 ~; 172 |; 65 &)
% ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 160 ( 0 sgn 140 !; 20 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f28,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( subset(X0,relation_rng(X2))
& subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) )
=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( subset(X0,relation_rng(X2))
& subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) )
=> subset(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f39,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& subset(X0,relation_rng(X2))
& subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f40,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& subset(X0,relation_rng(X2))
& subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& ~ subset(X0,X1) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f41]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f63,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f62]) ).
fof(f65,plain,
( function(sK2)
& relation(sK2)
& subset(sK0,relation_rng(sK2))
& subset(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1))
& ~ subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
fof(f66,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f67,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| ( in(apply(X0,sK3(X0,X1,X2)),X1)
& in(sK3(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ~ in(apply(X0,sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f68]) ).
fof(f75,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,[],[f48]) ).
fof(f76,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,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK8(X0,X1),X0)
& ~ in(sK8(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f79,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK11(X0,X5)) = X5
& in(sK11(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK9(X0,X1),X1)
| ( sK9(X0,X1) = apply(X0,sK10(X0,X1))
& in(sK10(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK9(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK9(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X2,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X7,sK11(X0,X5))],[f79]) ).
fof(f86,plain,
function(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
relation(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f88,plain,
subset(sK0,relation_rng(sK2)),
inference(cnf_transformation,[],[f65]) ).
fof(f89,plain,
subset(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
~ subset(sK0,sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f91,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f93,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f114,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f115,plain,
! [X0,X1] :
( in(sK8(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f116,plain,
! [X0,X1] :
( ~ in(sK8(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f128,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| apply(X0,sK11(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f80]) ).
fof(f129,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(sK11(X0,X5),relation_dom(X0)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f145,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f93]) ).
fof(f147,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f91]) ).
fof(f150,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK11(X0,X5),relation_dom(X0)) ),
inference(equality_resolution,[],[f129]) ).
fof(f151,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| apply(X0,sK11(X0,X5)) = X5 ),
inference(equality_resolution,[],[f128]) ).
tcf(c_49,negated_conjecture,
~ subset(sK0,sK1),
inference(cnf_transformation,[],[f90]) ).
tcf(c_50,negated_conjecture,
subset(relation_inverse_image(sK2,sK0),relation_inverse_image(sK2,sK1)),
inference(cnf_transformation,[],[f89]) ).
tcf(c_51,negated_conjecture,
subset(sK0,relation_rng(sK2)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_52,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f87]) ).
tcf(c_53,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f86]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( in(sK11(X1,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK11(X1,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( ~ in(sK8(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_168]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( in(sK8(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_78]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_170]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i] :
( in(sK8(X0,X1),X0)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_171]) ).
tcf(c_1032,plain,
in(sK8(sK0,sK1),sK0),
inference(unflattening,[status(thm)],[c_1031]) ).
tcf(c_1036,plain,
! [X0: $i,X1: $i] :
( ~ in(sK8(X0,X1),X1)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_169]) ).
tcf(c_1037,plain,
~ in(sK8(sK0,sK1),sK1),
inference(unflattening,[status(thm)],[c_1036]) ).
tcf(c_9164,plain,
! [X0: $i] :
( in(X0,relation_inverse_image(sK2,sK1))
| ~ in(X0,relation_inverse_image(sK2,sK0)) ),
inference(superposition,[status(thm)],[c_50,c_79]) ).
tcf(c_9165,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ~ in(X0,sK0) ),
inference(superposition,[status(thm)],[c_51,c_79]) ).
tcf(c_9472,plain,
! [X0: $i] :
( ( apply(sK2,sK11(sK2,X0)) = X0 )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(X0,sK0) ),
inference(superposition,[status(thm)],[c_9165,c_96]) ).
tcf(c_9477,plain,
! [X0: $i] :
( ( apply(sK2,sK11(sK2,X0)) = X0 )
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9472,c_53,c_52]) ).
tcf(c_9562,plain,
! [X0: $i] :
( subset(sK0,X0)
| ( apply(sK2,sK11(sK2,sK8(sK0,X0))) = sK8(sK0,X0) ) ),
inference(superposition,[status(thm)],[c_78,c_9477]) ).
tcf(c_9642,plain,
apply(sK2,sK11(sK2,sK8(sK0,sK1))) = sK8(sK0,sK1),
inference(superposition,[status(thm)],[c_9562,c_49]) ).
tcf(c_10245,plain,
! [X0: $i] :
( in(sK11(sK2,sK8(sK0,sK1)),relation_inverse_image(sK2,X0))
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK8(sK0,sK1),X0)
| ~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9642,c_57]) ).
tcf(c_10250,plain,
! [X0: $i] :
( in(sK11(sK2,sK8(sK0,sK1)),relation_inverse_image(sK2,X0))
| ~ in(sK8(sK0,sK1),X0)
| ~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10245,c_53,c_52]) ).
tcf(c_10271,plain,
( in(sK11(sK2,sK8(sK0,sK1)),relation_inverse_image(sK2,sK1))
| ~ in(sK8(sK0,sK1),sK0)
| ~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10250,c_9164]) ).
tcf(c_11309,plain,
( in(sK11(sK2,sK8(sK0,sK1)),relation_inverse_image(sK2,sK1))
| ~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_10271,c_1032,c_10271]) ).
tcf(c_11315,plain,
( in(apply(sK2,sK11(sK2,sK8(sK0,sK1))),sK1)
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11309,c_59]) ).
tcf(c_11324,plain,
( in(sK8(sK0,sK1),sK1)
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_11315,c_9642]) ).
tcf(c_11325,plain,
( in(sK8(sK0,sK1),sK1)
| ~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11324,c_53,c_52]) ).
tcf(c_11342,plain,
~ in(sK11(sK2,sK8(sK0,sK1)),relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_11325,c_1037,c_11325]) ).
tcf(c_11344,plain,
( ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK8(sK0,sK1),relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_95,c_11342]) ).
tcf(c_11345,plain,
~ in(sK8(sK0,sK1),relation_rng(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_11344,c_53,c_52]) ).
tcf(c_11346,plain,
~ in(sK8(sK0,sK1),sK0),
inference(superposition,[status(thm)],[c_9165,c_11345]) ).
tcf(c_11347,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11346,c_1032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU077+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:48:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.44 % Proving...
% 1.10/1.78 % SZS status Started for theBenchmark.p
% 1.10/1.78 % SZS status Theorem for theBenchmark.p
% 1.10/1.78
% 1.10/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.10/1.78
% 1.10/1.78 % ------ iProver source info
% 1.10/1.78
% 1.10/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 1.10/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.10/1.78 % git: non_committed_changes: false
% 1.10/1.78
% 1.10/1.78 % ------ Parsing...
% 1.10/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.10/1.78
% 1.10/1.78 % ------ 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 %
% 1.10/1.78
% 1.10/1.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.10/1.78
% 1.10/1.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.10/1.78 % ------ Proving...
% 1.10/1.78 % ------ Problem Properties
% 1.10/1.78
% 1.10/1.78 %
% 1.10/1.78 % clauses 58
% 1.10/1.78 % conjectures 5
% 1.10/1.78 % EPR 28
% 1.10/1.78 % Horn 51
% 1.10/1.78 % unary 23
% 1.10/1.78 % binary 16
% 1.10/1.78 % lits 133
% 1.10/1.78 % lits eq 11
% 1.10/1.78 % fd_pure 0
% 1.10/1.78 % fd_pseudo 0
% 1.10/1.78 % fd_cond 1
% 1.10/1.78 % fd_pseudo_cond 7
% 1.10/1.78 % AC symbols 0
% 1.10/1.78
% 1.10/1.78 % ------ Schedule dynamic 5 is on
% 1.10/1.78
% 1.10/1.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.10/1.78
% 1.10/1.78
% 1.10/1.78 % ------
% 1.10/1.78 % Current options:
% 1.10/1.78 % ------
% 1.10/1.78
% 1.10/1.78
% 1.10/1.78 %
% 1.10/1.78
% 1.10/1.78 % ------ Proving...
% 1.10/1.78 %
% 1.10/1.78
% 1.10/1.78 % SZS status Theorem for theBenchmark.p
% 1.10/1.78
% 1.10/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.10/1.78
% 1.10/1.78
%------------------------------------------------------------------------------