%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU225+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 02:56:11 PM UTC 2026
% Result : Theorem 2.29s 6.18s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 21 unt; 3 def)
% Number of atoms : 385 ( 96 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 405 ( 159 ~; 169 |; 51 &)
% ( 12 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 132 !; 9 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f16,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(f26,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,X0)
& in(X1,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(f43,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f45,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f46,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f57,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f60,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f60]) ).
fof(f64,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f65,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f64]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(flattening,[],[f69]) ).
fof(f74,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f75,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(flattening,[],[f74]) ).
fof(f77,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,X0)
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f78,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,X0)
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(flattening,[],[f77]) ).
fof(f81,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ( in(X1,X0)
& in(X1,relation_dom(X2)) ) )
& ( ~ in(X1,X0)
| ~ in(X1,relation_dom(X2))
| in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ( in(X1,X0)
& in(X1,relation_dom(X2)) ) )
& ( ~ in(X1,X0)
| ~ in(X1,relation_dom(X2))
| in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) ) ),
inference(flattening,[],[f83]) ).
fof(f93,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f94,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ( in(sK9(X1,X2),relation_dom(X1))
& apply(X1,sK9(X1,X2)) != apply(X2,sK9(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X1,X2))],[f95]) ).
fof(f97,plain,
( function(sK12)
& relation(sK12)
& in(sK11,sK10)
& apply(relation_dom_restriction(sK12,sK10),sK11) != apply(sK12,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f78]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f110,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f116,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f122,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| ~ in(X1,relation_dom(X2))
| in(X1,relation_dom(relation_dom_restriction(X2,X0))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f151,plain,
! [X2,X0,X1,X4] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom_restriction(X2,X0) != X1
| ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) ),
inference(cnf_transformation,[],[f96]) ).
fof(f156,plain,
function(sK12),
inference(cnf_transformation,[],[f97]) ).
fof(f157,plain,
relation(sK12),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
in(sK11,sK10),
inference(cnf_transformation,[],[f97]) ).
fof(f159,plain,
apply(relation_dom_restriction(sK12,sK10),sK11) != apply(sK12,sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f167,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(equality_resolution,[],[f105]) ).
fof(f169,plain,
! [X2,X0,X4] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4) ),
inference(equality_resolution,[],[f151]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_104,negated_conjecture,
apply(relation_dom_restriction(sK12,sK10),sK11) != apply(sK12,sK11),
inference(cnf_transformation,[],[f159]) ).
tcf(c_105,negated_conjecture,
in(sK11,sK10),
inference(cnf_transformation,[],[f158]) ).
tcf(c_106,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f157]) ).
tcf(c_107,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f156]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_58]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_141]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_236,c_71]) ).
tcf(c_947,definition,
iPr_def_10 = relation_dom_restriction(sK12,sK10),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_948,definition,
iPr_def_11 = apply(iPr_def_10,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_949,definition,
iPr_def_12 = apply(sK12,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_950,negated_conjecture,
function(sK12),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_951,negated_conjecture,
relation(sK12),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_952,negated_conjecture,
in(sK11,sK10),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_953,negated_conjecture,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_104,c_949,c_947,c_948]) ).
tcf(c_1560,plain,
( relation(iPr_def_10)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_947,c_58]) ).
tcf(c_1561,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1560,c_951]) ).
tcf(c_1658,plain,
( function(iPr_def_10)
| ~ relation(sK12)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_947,c_71]) ).
tcf(c_1659,plain,
function(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1658,c_951,c_950]) ).
tcf(c_1793,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(X0,sK10)
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_947,c_78]) ).
tcf(c_1798,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ~ in(X0,sK10)
| ~ in(X0,relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1793,c_951,c_950]) ).
tcf(c_1892,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ( apply(sK12,X0) = empty_set )
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(X0,sK10) ),
inference(superposition,[status(thm)],[c_57,c_1798]) ).
tcf(c_1897,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ( apply(sK12,X0) = empty_set )
| ~ in(X0,sK10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1892,c_951,c_950]) ).
tcf(c_2081,plain,
! [X0: $i] :
( ( apply(relation_dom_restriction(sK12,sK10),X0) = apply(sK12,X0) )
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_947,c_272]) ).
tcf(c_2088,plain,
! [X0: $i] :
( ( apply(sK12,X0) = apply(iPr_def_10,X0) )
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_2081,c_947]) ).
tcf(c_2089,plain,
! [X0: $i] :
( ( apply(sK12,X0) = apply(iPr_def_10,X0) )
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2088,c_951,c_950]) ).
tcf(c_2357,plain,
! [X0: $i] :
( ( apply(iPr_def_10,X0) = empty_set )
| ( apply(sK12,X0) = apply(iPr_def_10,X0) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_57,c_2089]) ).
tcf(c_2366,plain,
! [X0: $i] :
( ( apply(iPr_def_10,X0) = empty_set )
| ( apply(sK12,X0) = apply(iPr_def_10,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2357,c_1561,c_1659]) ).
tcf(c_3078,plain,
( ( apply(iPr_def_10,sK11) = iPr_def_12 )
| ( apply(iPr_def_10,sK11) = empty_set ) ),
inference(superposition,[status(thm)],[c_2366,c_949]) ).
tcf(c_3079,plain,
( ( iPr_def_11 = iPr_def_12 )
| ( empty_set = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_3078,c_948]) ).
tcf(c_3080,plain,
empty_set = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3079,c_953]) ).
tcf(c_3099,plain,
! [X0: $i] :
( ( apply(iPr_def_10,X0) = iPr_def_11 )
| ( apply(sK12,X0) = apply(iPr_def_10,X0) ) ),
inference(demodulation,[status(thm)],[c_2366,c_3080]) ).
tcf(c_3115,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ( apply(sK12,X0) = iPr_def_11 )
| ~ in(X0,sK10) ),
inference(demodulation,[status(thm)],[c_1897,c_3080]) ).
tcf(c_3916,plain,
( ( apply(iPr_def_10,sK11) = iPr_def_12 )
| ( apply(iPr_def_10,sK11) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_3099,c_949]) ).
tcf(c_3919,plain,
( ( iPr_def_11 = iPr_def_12 )
| ( apply(iPr_def_10,sK11) = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_3916,c_948]) ).
tcf(c_3920,plain,
apply(iPr_def_10,sK11) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3919,c_953]) ).
tcf(c_4176,plain,
! [X0: $i] :
( ( apply(sK12,X0) = iPr_def_11 )
| ( apply(sK12,X0) = apply(iPr_def_10,X0) )
| ~ in(X0,sK10) ),
inference(superposition,[status(thm)],[c_3115,c_2089]) ).
tcf(c_5541,plain,
( ( apply(sK12,sK11) = iPr_def_11 )
| ( apply(sK12,sK11) = apply(iPr_def_10,sK11) ) ),
inference(superposition,[status(thm)],[c_952,c_4176]) ).
tcf(c_5547,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_5541,c_949,c_3920]) ).
tcf(c_5548,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5547,c_953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n016.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Thu Sep 24 13:21:32 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.40 Running first-order theorem proving
% 0.09/5.40 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
% 0.13/5.41
% 0.13/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.41
% 0.13/5.41 % Detected problem language: tptp
% 0.13/5.42 % Proving...
% 2.29/6.18 % SZS status Started for theBenchmark.p
% 2.29/6.18 % SZS status Theorem for theBenchmark.p
% 2.29/6.18
% 2.29/6.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.29/6.18
% 2.29/6.18 % ------ iProver source info
% 2.29/6.18
% 2.29/6.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.29/6.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.29/6.18 % git: non_committed_changes: false
% 2.29/6.18
% 2.29/6.18 % ------ Parsing...
% 2.29/6.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.29/6.18
% 2.29/6.18 % ------ Preprocessing... sup_sim: 2 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.29/6.18
% 2.29/6.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.29/6.18
% 2.29/6.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.29/6.18 % ------ Proving...
% 2.29/6.18 % ------ Problem Properties
% 2.29/6.18
% 2.29/6.18 %
% 2.29/6.18 % clauses 52
% 2.29/6.18 % conjectures 4
% 2.29/6.18 % EPR 26
% 2.29/6.18 % Horn 49
% 2.29/6.18 % unary 29
% 2.29/6.18 % binary 9
% 2.29/6.18 % lits 106
% 2.29/6.18 % lits eq 19
% 2.29/6.18 % fd_pure 0
% 2.29/6.18 % fd_pseudo 0
% 2.29/6.18 % fd_cond 1
% 2.29/6.18 % fd_pseudo_cond 4
% 2.29/6.18 % AC symbols 0
% 2.29/6.18
% 2.29/6.18 % ------ Schedule dynamic 5 is on
% 2.29/6.18
% 2.29/6.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.29/6.18
% 2.29/6.18
% 2.29/6.18 % ------
% 2.29/6.18 % Current options:
% 2.29/6.18 % ------
% 2.29/6.18
% 2.29/6.18
% 2.29/6.18 %
% 2.29/6.18
% 2.29/6.18 % ------ Proving...
% 2.29/6.18 %
% 2.29/6.18
% 2.29/6.18 % SZS status Theorem for theBenchmark.p
% 2.29/6.18
% 2.29/6.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.29/6.18
% 2.29/6.18
%------------------------------------------------------------------------------