%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU226+3 : 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 02:56:14 PM UTC 2026
% Result : Theorem 6.82s 11.78s
% Output : CNFRefutation 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 95 ( 17 unt; 2 def)
% Number of atoms : 454 ( 51 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 498 ( 204 ~; 206 |; 67 &)
% ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 198 ( 0 sgn 180 !; 18 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,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/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f26,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f34,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f46,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f46]) ).
fof(f48,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,[],[f6]) ).
fof(f49,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,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f55,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ~ subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f56,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ~ subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f58,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f59,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f58]) ).
fof(f64,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f66,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f67,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK2(X0,X1,X6)) = X6
& in(sK2(X0,X1,X6),X1)
& in(sK2(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
& in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f67]) ).
fof(f69,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,[],[f49]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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,[],[f70]) ).
fof(f72,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))],[f71]) ).
fof(f73,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,[],[f50]) ).
fof(f74,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,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK4(X0,X1),X0)
& ~ in(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f74]) ).
fof(f87,plain,
( function(sK17)
& relation(sK17)
& ~ subset(relation_image(sK17,relation_inverse_image(sK17,sK16)),sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f56]) ).
fof(f94,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK2(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f68]) ).
fof(f95,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f97,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f102,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,[],[f72]) ).
fof(f103,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f110,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f140,plain,
function(sK17),
inference(cnf_transformation,[],[f87]) ).
fof(f141,plain,
relation(sK17),
inference(cnf_transformation,[],[f87]) ).
fof(f142,plain,
~ subset(relation_image(sK17,relation_inverse_image(sK17,sK16)),sK16),
inference(cnf_transformation,[],[f87]) ).
fof(f143,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f144,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f150,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f152,plain,
! [X2,X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),X2) ),
inference(equality_resolution,[],[f97]) ).
fof(f153,plain,
! [X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),relation_image(X0,X1)) ),
inference(equality_resolution,[],[f152]) ).
fof(f155,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK2(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f95]) ).
fof(f156,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK2(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f94]) ).
fof(f158,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f103]) ).
fof(f159,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f102]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK2(X1,X2,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_98,negated_conjecture,
~ subset(relation_image(sK17,relation_inverse_image(sK17,sK16)),sK16),
inference(cnf_transformation,[],[f142]) ).
tcf(c_99,negated_conjecture,
relation(sK17),
inference(cnf_transformation,[],[f141]) ).
tcf(c_100,negated_conjecture,
function(sK17),
inference(cnf_transformation,[],[f140]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_9391,definition,
iPr_def_10 = relation_inverse_image(sK17,sK16),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9392,definition,
iPr_def_11 = relation_image(sK17,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_9393,negated_conjecture,
function(sK17),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_9394,negated_conjecture,
relation(sK17),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_9395,negated_conjecture,
~ subset(iPr_def_11,sK16),
inference(demodulation,[status(thm)],[c_98,c_9391,c_9392]) ).
tcf(c_10509,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_67,c_108]) ).
tcf(c_10525,plain,
~ empty(iPr_def_11),
inference(superposition,[status(thm)],[c_10509,c_9395]) ).
tcf(c_10735,plain,
! [X0: $i] :
( in(X0,relation_dom(sK17))
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9391,c_64]) ).
tcf(c_10736,plain,
! [X0: $i] :
( in(X0,relation_dom(sK17))
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10735,c_9394,c_9393]) ).
tcf(c_10760,plain,
! [X0: $i] :
( in(apply(sK17,X0),sK16)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9391,c_65]) ).
tcf(c_10761,plain,
! [X0: $i] :
( in(apply(sK17,X0),sK16)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10760,c_9394,c_9393]) ).
tcf(c_10874,plain,
! [X0: $i] :
( element(apply(sK17,X0),sK16)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_10761,c_101]) ).
tcf(c_10985,plain,
( subset(iPr_def_11,sK16)
| ~ in(sK4(iPr_def_11,sK16),sK16) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_10997,plain,
! [X0: $i] :
( ( apply(sK17,sK2(sK17,iPr_def_10,X0)) = X0 )
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_9392,c_59]) ).
tcf(c_10998,plain,
! [X0: $i] :
( ( apply(sK17,sK2(sK17,iPr_def_10,X0)) = X0 )
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10997,c_9394,c_9393]) ).
tcf(c_11019,plain,
( subset(iPr_def_11,sK16)
| in(sK4(iPr_def_11,sK16),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_11032,plain,
! [X0: $i] :
( in(apply(sK17,X0),iPr_def_11)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_9392,c_56]) ).
tcf(c_11043,plain,
! [X0: $i] :
( in(apply(sK17,X0),iPr_def_11)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11032,c_9394,c_9393]) ).
tcf(c_11143,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| ( apply(sK17,sK2(sK17,iPr_def_10,sK4(iPr_def_11,X0))) = sK4(iPr_def_11,X0) ) ),
inference(superposition,[status(thm)],[c_67,c_10998]) ).
tcf(c_11160,plain,
! [X0: $i] :
( in(apply(sK17,X0),iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_11043,c_10736,c_11043]) ).
tcf(c_11170,plain,
! [X0: $i] :
( element(apply(sK17,X0),iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_11160,c_101]) ).
tcf(c_11246,plain,
( element(sK4(iPr_def_11,sK16),iPr_def_11)
| ~ in(sK4(iPr_def_11,sK16),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_15219,plain,
apply(sK17,sK2(sK17,iPr_def_10,sK4(iPr_def_11,sK16))) = sK4(iPr_def_11,sK16),
inference(superposition,[status(thm)],[c_11143,c_9395]) ).
tcf(c_15261,plain,
( element(sK4(iPr_def_11,sK16),iPr_def_11)
| ~ in(sK2(sK17,iPr_def_10,sK4(iPr_def_11,sK16)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_15219,c_11170]) ).
tcf(c_15264,plain,
( element(sK4(iPr_def_11,sK16),sK16)
| ~ in(sK2(sK17,iPr_def_10,sK4(iPr_def_11,sK16)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_15219,c_10874]) ).
tcf(c_15265,plain,
( in(sK4(iPr_def_11,sK16),sK16)
| ~ in(sK2(sK17,iPr_def_10,sK4(iPr_def_11,sK16)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_15219,c_10761]) ).
tcf(c_16301,plain,
element(sK4(iPr_def_11,sK16),iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_15261,c_9395,c_11019,c_11246]) ).
tcf(c_16303,plain,
( empty(iPr_def_11)
| in(sK4(iPr_def_11,sK16),iPr_def_11) ),
inference(superposition,[status(thm)],[c_16301,c_102]) ).
tcf(c_16304,plain,
in(sK4(iPr_def_11,sK16),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_16303,c_10525]) ).
tcf(c_16328,plain,
~ in(sK2(sK17,iPr_def_10,sK4(iPr_def_11,sK16)),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_15264,c_9395,c_10985,c_15265]) ).
tcf(c_16330,plain,
( ~ relation(sK17)
| ~ function(sK17)
| ~ in(sK4(iPr_def_11,sK16),relation_image(sK17,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_58,c_16328]) ).
tcf(c_16331,plain,
( ~ relation(sK17)
| ~ function(sK17)
| ~ in(sK4(iPr_def_11,sK16),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_16330,c_9392]) ).
tcf(c_16332,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16331,c_9394,c_9393,c_16304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU226+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.38 % Computer : n014.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Thu Sep 24 13:17:28 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 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
% 0.15/10.43
% 0.15/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43
% 0.15/10.43 % Detected problem language: tptp
% 0.15/10.44 % Proving...
% 6.82/11.78 % SZS status Started for theBenchmark.p
% 6.82/11.78 % SZS status Theorem for theBenchmark.p
% 6.82/11.78
% 6.82/11.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.82/11.78
% 6.82/11.78 % ------ iProver source info
% 6.82/11.78
% 6.82/11.78 % git: date: 2026-07-19 20:42:38 +0200
% 6.82/11.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.82/11.78 % git: non_committed_changes: false
% 6.82/11.78
% 6.82/11.78 % ------ Parsing...
% 6.82/11.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.82/11.78
% 6.82/11.78 % ------ 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 %
% 6.82/11.78
% 6.82/11.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.82/11.78
% 6.82/11.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.82/11.78 % ------ Proving...
% 6.82/11.78 % ------ Problem Properties
% 6.82/11.78
% 6.82/11.78 %
% 6.82/11.78 % clauses 60
% 6.82/11.78 % conjectures 3
% 6.82/11.78 % EPR 31
% 6.82/11.78 % Horn 52
% 6.82/11.78 % unary 26
% 6.82/11.78 % binary 14
% 6.82/11.78 % lits 140
% 6.82/11.78 % lits eq 14
% 6.82/11.78 % fd_pure 0
% 6.82/11.78 % fd_pseudo 0
% 6.82/11.78 % fd_cond 1
% 6.82/11.78 % fd_pseudo_cond 8
% 6.82/11.78 % AC symbols 0
% 6.82/11.78
% 6.82/11.78 % ------ Schedule dynamic 5 is on
% 6.82/11.78
% 6.82/11.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.82/11.78
% 6.82/11.78
% 6.82/11.78 % ------
% 6.82/11.78 % Current options:
% 6.82/11.78 % ------
% 6.82/11.78
% 6.82/11.78
% 6.82/11.78 %
% 6.82/11.78
% 6.82/11.78 % ------ Proving...
% 6.82/11.78 %
% 6.82/11.78
% 6.82/11.78 % SZS status Theorem for theBenchmark.p
% 6.82/11.78
% 6.82/11.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.82/11.78
% 6.82/11.78
%------------------------------------------------------------------------------