%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 14.95s 3.72s
% Output : CNFRefutation 14.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 86 ( 20 unt; 0 def)
% Number of atoms : 334 ( 102 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 414 ( 166 ~; 174 |; 51 &)
% ( 12 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 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 : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 114 !; 15 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f28,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f29,axiom,
! [X0,X1] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f30,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f34,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f39,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f50,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,[],[f5]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f52]) ).
fof(f61,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ relation(X1)
| ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f64,plain,
? [X0] :
( function(X0)
& relation(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& ~ one_to_one(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f65,plain,
? [X0] :
( function(X0)
& relation(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& ~ one_to_one(X0) ),
inference(flattening,[],[f64]) ).
fof(f73,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f39]) ).
fof(f76,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,[],[f51]) ).
fof(f77,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,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK2(X0,X5)) = X5
& in(sK2(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| ( sK0(X0,X1) = apply(X0,sK1(X0,X1))
& in(sK1(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK0(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK3(X0)) = apply(X0,sK4(X0))
& in(sK4(X0),relation_dom(X0))
& in(sK3(X0),relation_dom(X0))
& sK3(X0) != sK4(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f80]) ).
fof(f93,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( ~ in(X0,relation_rng(X1))
| relation_inverse_image(X1,singleton(X0)) != empty_set )
& ( empty_set = relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f94,plain,
( function(sK16)
& relation(sK16)
& ! [X1] : subset(relation_inverse_image(sK16,relation_image(sK16,X1)),X1)
& ~ one_to_one(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f65]) ).
fof(f95,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f96,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f95]) ).
fof(f106,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK3(X0)) = apply(X0,sK4(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f112,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK4(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f113,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK3(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f114,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK3(X0) != sK4(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f149,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f150,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| empty_set != relation_inverse_image(X1,singleton(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
function(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f153,plain,
relation(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f154,plain,
! [X1] : subset(relation_inverse_image(sK16,relation_image(sK16,X1)),X1),
inference(cnf_transformation,[],[f94]) ).
fof(f155,plain,
~ one_to_one(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f158,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f96]) ).
fof(f166,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f106]) ).
fof(f170,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f169]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_59,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( sK3(X0) != sK4(X0) ) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_60,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK3(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_61,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK4(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_62,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK3(X0)) = apply(X0,sK4(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ( singleton(apply(X1,X0)) = relation_image(X1,singleton(X0)) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(X1,relation_rng(X0))
| ( relation_inverse_image(X0,singleton(X1)) != empty_set ) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_101,negated_conjecture,
~ one_to_one(sK16),
inference(cnf_transformation,[],[f155]) ).
tcf(c_102,negated_conjecture,
! [X0: $i] : subset(relation_inverse_image(sK16,relation_image(sK16,X0)),X0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_103,negated_conjecture,
relation(sK16),
inference(cnf_transformation,[],[f153]) ).
tcf(c_104,negated_conjecture,
function(sK16),
inference(cnf_transformation,[],[f152]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_1282,plain,
! [X0: $i] :
( in(sK4(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_101]) ).
tcf(c_1283,plain,
( in(sK4(sK16),relation_dom(sK16))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(unflattening,[status(thm)],[c_1282]) ).
tcf(c_1296,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ function(X0)
| ( X0 != sK16 )
| ( sK3(X0) != sK4(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_101]) ).
tcf(c_1297,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ( sK3(sK16) != sK4(sK16) ) ),
inference(unflattening,[status(thm)],[c_1296]) ).
tcf(c_8926,negated_conjecture,
function(sK16),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_8927,negated_conjecture,
relation(sK16),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_8928,negated_conjecture,
! [X0: $i] : subset(relation_inverse_image(sK16,relation_image(sK16,X0)),X0),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_8929,negated_conjecture,
~ one_to_one(sK16),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_10817,plain,
( one_to_one(sK16)
| ( apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16)) )
| ~ relation(sK16) ),
inference(superposition,[status(thm)],[c_8926,c_62]) ).
tcf(c_10821,plain,
apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16)),
inference(forward_subsumption_resolution,[status(thm)],[c_10817,c_8929,c_8927]) ).
tcf(c_10894,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ relation(sK16)
| ~ function(sK16)
| ~ in(sK4(sK16),relation_dom(sK16)) ),
inference(superposition,[status(thm)],[c_10821,c_56]) ).
tcf(c_10895,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ in(sK4(sK16),relation_dom(sK16)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10894,c_8927,c_8926]) ).
tcf(c_11366,plain,
( ( sK3(sK16) = sK4(sK16) )
| ~ subset(singleton(sK3(sK16)),singleton(sK4(sK16))) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_13256,plain,
( ~ relation(sK16)
| ~ in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ( relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) != empty_set ) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_36941,plain,
! [X0: $i] :
( ( relation_inverse_image(sK16,relation_image(sK16,singleton(X0))) = empty_set )
| ( relation_inverse_image(sK16,relation_image(sK16,singleton(X0))) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_8928,c_109]) ).
tcf(c_37012,plain,
( one_to_one(sK16)
| ( apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16)) )
| ~ relation(sK16) ),
inference(superposition,[status(thm)],[c_8926,c_62]) ).
tcf(c_37016,plain,
apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16)),
inference(forward_subsumption_resolution,[status(thm)],[c_37012,c_8929,c_8927]) ).
tcf(c_37155,plain,
! [X0: $i] :
( one_to_one(X0)
| ( singleton(apply(X0,sK3(X0))) = relation_image(X0,singleton(sK3(X0))) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_60,c_98]) ).
tcf(c_37156,plain,
! [X0: $i] :
( one_to_one(X0)
| ( singleton(apply(X0,sK4(X0))) = relation_image(X0,singleton(sK4(X0))) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_61,c_98]) ).
tcf(c_42315,plain,
( one_to_one(sK16)
| ( singleton(apply(sK16,sK3(sK16))) = relation_image(sK16,singleton(sK3(sK16))) )
| ~ relation(sK16) ),
inference(superposition,[status(thm)],[c_8926,c_37155]) ).
tcf(c_42319,plain,
singleton(apply(sK16,sK3(sK16))) = relation_image(sK16,singleton(sK3(sK16))),
inference(forward_subsumption_resolution,[status(thm)],[c_42315,c_8929,c_8927]) ).
tcf(c_42363,plain,
( one_to_one(sK16)
| ( singleton(apply(sK16,sK4(sK16))) = relation_image(sK16,singleton(sK4(sK16))) )
| ~ relation(sK16) ),
inference(superposition,[status(thm)],[c_8926,c_37156]) ).
tcf(c_42367,plain,
( one_to_one(sK16)
| ( singleton(apply(sK16,sK3(sK16))) = relation_image(sK16,singleton(sK4(sK16))) )
| ~ relation(sK16) ),
inference(light_normalisation,[status(thm)],[c_42363,c_37016]) ).
tcf(c_42368,plain,
singleton(apply(sK16,sK3(sK16))) = relation_image(sK16,singleton(sK4(sK16))),
inference(forward_subsumption_resolution,[status(thm)],[c_42367,c_8929,c_8927]) ).
tcf(c_42388,plain,
( ( relation_inverse_image(sK16,relation_image(sK16,singleton(sK3(sK16)))) = empty_set )
| ( relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) = singleton(sK3(sK16)) ) ),
inference(superposition,[status(thm)],[c_42319,c_36941]) ).
tcf(c_42393,plain,
( ( relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) = empty_set )
| ( relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) = singleton(sK3(sK16)) ) ),
inference(light_normalisation,[status(thm)],[c_42388,c_42319]) ).
tcf(c_42427,plain,
subset(relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))),singleton(sK4(sK16))),
inference(superposition,[status(thm)],[c_42368,c_8928]) ).
tcf(c_42444,plain,
relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) = singleton(sK3(sK16)),
inference(global_subsumption_just,[status(thm)],[c_42393,c_104,c_103,c_1283,c_10895,c_13256,c_42393]) ).
tcf(c_42446,plain,
subset(singleton(sK3(sK16)),singleton(sK4(sK16))),
inference(demodulation,[status(thm)],[c_42427,c_42444]) ).
tcf(c_42448,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_42446,c_11366,c_1297,c_103,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:41:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 14.95/3.72 % SZS status Started for theBenchmark.p
% 14.95/3.72 % SZS status Theorem for theBenchmark.p
% 14.95/3.72
% 14.95/3.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.95/3.72
% 14.95/3.72 % ------ iProver source info
% 14.95/3.72
% 14.95/3.72 % git: date: 2026-07-19 20:42:38 +0200
% 14.95/3.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.95/3.72 % git: non_committed_changes: false
% 14.95/3.72
% 14.95/3.72 % ------ Parsing...
% 14.95/3.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.95/3.72
% 14.95/3.72 % ------ 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 %
% 14.95/3.72
% 14.95/3.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.95/3.72
% 14.95/3.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.95/3.72 % ------ Proving...
% 14.95/3.72 % ------ Problem Properties
% 14.95/3.72
% 14.95/3.72 %
% 14.95/3.72 % clauses 65
% 14.95/3.72 % conjectures 4
% 14.95/3.72 % EPR 32
% 14.95/3.72 % Horn 56
% 14.95/3.72 % unary 28
% 14.95/3.72 % binary 16
% 14.95/3.72 % lits 142
% 14.95/3.72 % lits eq 18
% 14.95/3.72 % fd_pure 0
% 14.95/3.72 % fd_pseudo 0
% 14.95/3.72 % fd_cond 1
% 14.95/3.72 % fd_pseudo_cond 7
% 14.95/3.72 % AC symbols 0
% 14.95/3.72
% 14.95/3.72 % ------ Schedule dynamic 5 is on
% 14.95/3.72
% 14.95/3.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.95/3.72
% 14.95/3.72
% 14.95/3.72 % ------
% 14.95/3.72 % Current options:
% 14.95/3.72 % ------
% 14.95/3.72
% 14.95/3.72
% 14.95/3.72 %
% 14.95/3.72
% 14.95/3.72 % ------ Proving...
% 14.95/3.72 %
% 14.95/3.72
% 14.95/3.72 % SZS status Theorem for theBenchmark.p
% 14.95/3.72
% 14.95/3.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.95/3.73
% 14.95/3.73
%------------------------------------------------------------------------------