%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS144+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 01:54:16 PM UTC 2026
% Result : Theorem 0.41s 1.29s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 117 ( 16 unt; 3 def)
% Number of atoms : 514 ( 125 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 608 ( 221 ~; 277 |; 90 &)
% ( 4 <=>; 13 =>; 0 <=; 3 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 187 ( 0 sgn 138 !; 49 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f9,axiom,
! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f10,axiom,
! [X0] :
( cc(X0)
=> ( ! [X1,X2,X3] :
( ( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) )
& ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f11,conjecture,
( ! [X0] :
( cc(X0)
=> ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) )
& ! [X0] :
( cc(X0)
=> ! [X1,X2,X3] :
( ( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) ) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(f12,negated_conjecture,
~ ( ! [X0] :
( cc(X0)
=> ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) )
& ! [X0] :
( cc(X0)
=> ! [X1,X2,X3] :
( ( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) ) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0] :
( cc(X0)
=> ( ! [X3,X4,X5] :
( ( rp(X0,X5)
& rp(X0,X4)
& rp(X0,X3) )
=> ( X4 = X5
| X3 = X5
| X3 = X4 ) )
& ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) ) ),
inference(rectify,[],[f10]) ).
fof(f14,plain,
~ ( ! [X6] :
( cc(X6)
=> ? [X7,X8] :
( X7 != X8
& rp(X6,X8)
& rp(X6,X7) ) )
& ! [X2] :
( cc(X2)
=> ! [X3,X4,X5] :
( ( rp(X2,X5)
& rp(X2,X4)
& rp(X2,X3) )
=> ( X4 = X5
| X3 = X5
| X3 = X4 ) ) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f29,plain,
! [X0] :
( ~ cc(X0)
| ( ! [X3,X4,X5] :
( ~ rp(X0,X5)
| ~ rp(X0,X4)
| ~ rp(X0,X3)
| X4 = X5
| X3 = X5
| X3 = X4 )
& ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0] :
( ~ cc(X0)
| ( ! [X3,X4,X5] :
( ~ rp(X0,X5)
| ~ rp(X0,X4)
| ~ rp(X0,X3)
| X4 = X5
| X3 = X5
| X3 = X4 )
& ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
( ? [X6] :
( cc(X6)
& ! [X7,X8] :
( X7 = X8
| ~ rp(X6,X8)
| ~ rp(X6,X7) ) )
| ? [X2] :
( cc(X2)
& ? [X3,X4,X5] :
( rp(X2,X5)
& rp(X2,X4)
& rp(X2,X3)
& X4 != X5
& X3 != X5
& X3 != X4 ) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f32,plain,
( ? [X6] :
( cc(X6)
& ! [X7,X8] :
( X7 = X8
| ~ rp(X6,X8)
| ~ rp(X6,X7) ) )
| ? [X2] :
( cc(X2)
& ? [X3,X4,X5] :
( rp(X2,X5)
& rp(X2,X4)
& rp(X2,X3)
& X4 != X5
& X3 != X5
& X3 != X4 ) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
! [X0] :
( ( ~ xsd_string(X0)
| ~ xsd_integer(X0) )
& ( xsd_integer(X0)
| xsd_string(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0] :
( ~ cc(X0)
| ( ! [X3,X4,X5] :
( ~ rp(X0,X5)
| ~ rp(X0,X4)
| ~ rp(X0,X3)
| X4 = X5
| X3 = X5
| X3 = X4 )
& sK1(X0) != sK2(X0)
& rp(X0,sK2(X0))
& rp(X0,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f30]) ).
fof(f40,plain,
( ? [X6] :
( cc(X6)
& ! [X7,X8] :
( X7 = X8
| ~ rp(X6,X8)
| ~ rp(X6,X7) ) )
| sP0
| ? [X1] :
( ( xsd_string(X1)
| ~ xsd_integer(X1) )
& ( ~ xsd_string(X1)
| xsd_integer(X1) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f41,plain,
( ? [X2] :
( cc(X2)
& ! [X3,X4] :
( X3 = X4
| ~ rp(X2,X4)
| ~ rp(X2,X3) ) )
| sP0
| ? [X1] :
( ( xsd_string(X1)
| ~ xsd_integer(X1) )
& ( ~ xsd_string(X1)
| xsd_integer(X1) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
( ( cc(sK9)
& ! [X3,X4] :
( X3 = X4
| ~ rp(sK9,X4)
| ~ rp(sK9,X3) ) )
| sP0
| ( ( xsd_string(sK8)
| ~ xsd_integer(sK8) )
& ( ~ xsd_string(sK8)
| xsd_integer(sK8) ) )
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f41]) ).
fof(f50,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f52,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X3,X0,X4,X5] :
( ~ cc(X0)
| ~ rp(X0,X5)
| ~ rp(X0,X4)
| ~ rp(X0,X3)
| X4 = X5
| X3 = X5
| X3 = X4 ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0] :
( ~ cc(X0)
| sK1(X0) != sK2(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0] :
( ~ cc(X0)
| rp(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0] :
( ~ cc(X0)
| rp(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f65,plain,
( cc(sK9)
| sP0
| xsd_string(sK8)
| ~ xsd_integer(sK8)
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
! [X3,X4] :
( X3 = X4
| ~ rp(sK9,X4)
| ~ rp(sK9,X3)
| sP0
| xsd_string(sK8)
| ~ xsd_integer(sK8)
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f42]) ).
fof(f67,plain,
( cc(sK9)
| sP0
| ~ xsd_string(sK8)
| xsd_integer(sK8)
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X3,X4] :
( X3 = X4
| ~ rp(sK9,X4)
| ~ rp(sK9,X3)
| sP0
| ~ xsd_string(sK8)
| xsd_integer(sK8)
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_49,plain,
! [X0: $i] : cowlThing(X0),
inference(cnf_transformation,[],[f51]) ).
tcf(c_50,plain,
! [X0: $i] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f50]) ).
tcf(c_51,plain,
! [X0: $i] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_52,plain,
! [X0: $i] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_53,plain,
! [X0: $i] :
( rp(X0,sK1(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_54,plain,
! [X0: $i] :
( rp(X0,sK2(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_55,plain,
! [X0: $i] :
( ~ cc(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ cc(X0)
| ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0
| xsd_integer(sK8)
| cowlNothing(sK7)
| ( X0 = X1 )
| ~ xsd_string(sK8)
| ~ cowlThing(sK7)
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_65,negated_conjecture,
( sP0
| cc(sK9)
| xsd_integer(sK8)
| cowlNothing(sK7)
| ~ xsd_string(sK8)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0
| xsd_string(sK8)
| cowlNothing(sK7)
| ( X0 = X1 )
| ~ xsd_integer(sK8)
| ~ cowlThing(sK7)
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_67,negated_conjecture,
( sP0
| cc(sK9)
| xsd_string(sK8)
| cowlNothing(sK7)
| ~ xsd_integer(sK8)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_68,plain,
cowlThing(sK7),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_69,plain,
~ cowlNothing(sK7),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_78,negated_conjecture,
( sP0
| cc(sK9)
| xsd_string(sK8)
| ~ xsd_integer(sK8) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_68,c_69,c_67]) ).
tcf(c_80,negated_conjecture,
( sP0
| cc(sK9)
| xsd_integer(sK8)
| ~ xsd_string(sK8) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_68,c_69,c_65]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( sP0
| xsd_string(sK8)
| ~ rp(sK9,X1)
| ~ rp(sK9,X0)
| ~ xsd_integer(sK8)
| ( X0 = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_66,c_68,c_69,c_66]) ).
tcf(c_83,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0
| xsd_string(sK8)
| ( X0 = X1 )
| ~ xsd_integer(sK8)
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(renaming,[status(thm)],[c_82]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( sP0
| xsd_integer(sK8)
| ~ rp(sK9,X1)
| ~ rp(sK9,X0)
| ~ xsd_string(sK8)
| ( X0 = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_68,c_69,c_64]) ).
tcf(c_86,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0
| xsd_integer(sK8)
| ( X0 = X1 )
| ~ xsd_string(sK8)
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(renaming,[status(thm)],[c_85]) ).
tcf(c_88,plain,
! [X0: $i] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_89,plain,
! [X0: $i] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(renaming,[status(thm)],[c_88]) ).
tcf(c_90,plain,
! [X0: $i] :
( xsd_string(X0)
| xsd_integer(X0) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_91,plain,
! [X0: $i] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(renaming,[status(thm)],[c_90]) ).
tcf(c_92,plain,
! [X0: $i] :
( rp(X0,sK1(X0))
| ~ cc(X0) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
tcf(c_94,plain,
! [X0: $i] :
( rp(X0,sK2(X0))
| ~ cc(X0) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_96,plain,
! [X0: $i] :
( ( sK1(X0) != sK2(X0) )
| ~ cc(X0) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_97,plain,
! [X0: $i] :
( ~ cc(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(renaming,[status(thm)],[c_96]) ).
tcf(c_174,plain,
( sP0
| cc(sK9)
| xsd_integer(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_80,c_91]) ).
tcf(c_177,plain,
( sP0
| cc(sK9)
| xsd_string(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_78,c_91]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( sP0
| xsd_string(sK8)
| ( X0 = X1 )
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_91]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0
| ( X1 = X2 )
| ~ xsd_integer(X0)
| ~ rp(sK9,X2)
| ~ rp(sK9,X1)
| ( X0 != sK8 ) ),
inference(resolution_lifted,[status(thm)],[c_89,c_178]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i] :
( sP0
| ( X0 = X1 )
| ~ xsd_integer(sK8)
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(unflattening,[status(thm)],[c_372]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] :
( sP0
| ( X0 = X1 )
| ~ rp(sK9,X0)
| ~ rp(sK9,X1) ),
inference(global_subsumption_just,[status(thm)],[c_373,c_86,c_178,c_373]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( sP0
| ( X0 = X1 )
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(renaming,[status(thm)],[c_375]) ).
tcf(c_390,plain,
! [X0: $i] :
( sP0
| cc(sK9)
| ~ xsd_integer(X0)
| ( X0 != sK8 ) ),
inference(resolution_lifted,[status(thm)],[c_89,c_177]) ).
tcf(c_391,plain,
( sP0
| cc(sK9)
| ~ xsd_integer(sK8) ),
inference(unflattening,[status(thm)],[c_390]) ).
tcf(c_392,plain,
( sP0
| cc(sK9) ),
inference(global_subsumption_just,[status(thm)],[c_391,c_174,c_391]) ).
tcf(c_458,plain,
! [X0: $i] :
( sP0
| ( X0 != sK9 )
| ( sK1(X0) != sK2(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_392]) ).
tcf(c_459,plain,
( sP0
| ( sK1(sK9) != sK2(sK9) ) ),
inference(unflattening,[status(thm)],[c_458]) ).
tcf(c_466,plain,
! [X0: $i] :
( sP0
| rp(X0,sK2(X0))
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_392]) ).
tcf(c_467,plain,
( sP0
| rp(sK9,sK2(sK9)) ),
inference(unflattening,[status(thm)],[c_466]) ).
tcf(c_474,plain,
! [X0: $i] :
( sP0
| rp(X0,sK1(X0))
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_92,c_392]) ).
tcf(c_475,plain,
( sP0
| rp(sK9,sK1(sK9)) ),
inference(unflattening,[status(thm)],[c_474]) ).
tcf(c_1698,definition,
iPr_def_10 = sK1(sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1699,definition,
iPr_def_11 = sK2(sK9),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1700,plain,
( sP0
| rp(sK9,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_475,c_1698]) ).
tcf(c_1701,plain,
( sP0
| rp(sK9,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_467,c_1699]) ).
tcf(c_1702,plain,
( sP0
| ( iPr_def_10 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_459]) ).
tcf(c_1703,plain,
! [X0: $i,X1: $i] :
( sP0
| ( X0 = X1 )
| ~ rp(sK9,X1)
| ~ rp(sK9,X0) ),
inference(demodulation,[status(thm)],[c_376]) ).
tcf(c_1920,plain,
! [X0: $i] :
( sP0
| ( X0 = iPr_def_10 )
| ~ rp(sK9,X0) ),
inference(superposition,[status(thm)],[c_1700,c_1703]) ).
tcf(c_1929,plain,
! [X0: $i] :
( sP0
| ( X0 = iPr_def_11 )
| ~ rp(sK9,X0) ),
inference(superposition,[status(thm)],[c_1701,c_1703]) ).
tcf(c_1945,plain,
( sP0
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1701,c_1920]) ).
tcf(c_1948,plain,
sP0,
inference(global_subsumption_just,[status(thm)],[c_1929,c_1702,c_1945]) ).
fof(f33,definition,
( ~ sP0
| ? [X2] :
( cc(X2)
& ? [X3,X4,X5] :
( rp(X2,X5)
& rp(X2,X4)
& rp(X2,X3)
& X4 != X5
& X3 != X5
& X3 != X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f34,plain,
( ? [X6] :
( cc(X6)
& ! [X7,X8] :
( X7 = X8
| ~ rp(X6,X8)
| ~ rp(X6,X7) ) )
| sP0
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(definition_folding,[],[f32,f33]) ).
fof(f37,plain,
( ~ sP0
| ? [X2] :
( cc(X2)
& ? [X3,X4,X5] :
( rp(X2,X5)
& rp(X2,X4)
& rp(X2,X3)
& X4 != X5
& X3 != X5
& X3 != X4 ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f38,plain,
( ~ sP0
| ? [X0] :
( cc(X0)
& ? [X1,X2,X3] :
( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1)
& X2 != X3
& X1 != X3
& X1 != X2 ) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
( ~ sP0
| ( cc(sK3)
& rp(sK3,sK6)
& rp(sK3,sK5)
& rp(sK3,sK4)
& sK5 != sK6
& sK4 != sK6
& sK4 != sK5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f38]) ).
fof(f58,plain,
( ~ sP0
| cc(sK3) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
( ~ sP0
| rp(sK3,sK6) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
( ~ sP0
| rp(sK3,sK5) ),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
( ~ sP0
| rp(sK3,sK4) ),
inference(cnf_transformation,[],[f39]) ).
fof(f62,plain,
( ~ sP0
| sK5 != sK6 ),
inference(cnf_transformation,[],[f39]) ).
fof(f63,plain,
( ~ sP0
| sK4 != sK6 ),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
( ~ sP0
| sK4 != sK5 ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,plain,
( ~ sP0
| ( sK4 != sK5 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_58,plain,
( ~ sP0
| ( sK4 != sK6 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_59,plain,
( ~ sP0
| ( sK5 != sK6 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_60,plain,
( rp(sK3,sK4)
| ~ sP0 ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_61,plain,
( rp(sK3,sK5)
| ~ sP0 ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_62,plain,
( rp(sK3,sK6)
| ~ sP0 ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_63,plain,
( cc(sK3)
| ~ sP0 ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_114,plain,
( cc(sK3)
| ~ sP0 ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ sP0
| ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_114]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ sP0
| ~ rp(sK3,X2)
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(unflattening,[status(thm)],[c_406]) ).
tcf(c_1952,plain,
rp(sK3,sK4),
inference(global_subsumption_just,[status(thm)],[c_60,c_60,c_1702,c_1945]) ).
tcf(c_1954,plain,
rp(sK3,sK5),
inference(global_subsumption_just,[status(thm)],[c_61,c_61,c_1948]) ).
tcf(c_1956,plain,
rp(sK3,sK6),
inference(global_subsumption_just,[status(thm)],[c_62,c_62,c_1702,c_1945]) ).
tcf(c_1958,plain,
sK4 != sK5,
inference(global_subsumption_just,[status(thm)],[c_57,c_57,c_1702,c_1945]) ).
tcf(c_1964,plain,
sK4 != sK6,
inference(global_subsumption_just,[status(thm)],[c_58,c_58,c_1702,c_1945]) ).
tcf(c_1966,plain,
sK5 != sK6,
inference(global_subsumption_just,[status(thm)],[c_59,c_59,c_1702,c_1945]) ).
tcf(c_1970,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ rp(sK3,X0)
| ~ rp(sK3,X1)
| ~ rp(sK3,X2) ),
inference(global_subsumption_just,[status(thm)],[c_407,c_407,c_1702,c_1945]) ).
tcf(c_1971,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ rp(sK3,X2)
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(renaming,[status(thm)],[c_1970]) ).
tcf(c_1978,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK4 )
| ( X0 = sK4 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_1952,c_1971]) ).
tcf(c_2020,plain,
! [X0: $i] :
( ( sK4 = sK6 )
| ( X0 = sK6 )
| ( X0 = sK4 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_1956,c_1978]) ).
tcf(c_2023,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ( X0 = sK4 )
| ~ rp(sK3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2020,c_1964]) ).
tcf(c_2050,plain,
( ( sK5 = sK6 )
| ( sK4 = sK5 ) ),
inference(superposition,[status(thm)],[c_1954,c_2023]) ).
tcf(c_2054,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2050,c_1966,c_1958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS144+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n004.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 : Wed Sep 23 19:30:38 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.41/1.29 % SZS status Started for theBenchmark.p
% 0.41/1.29 % SZS status Theorem for theBenchmark.p
% 0.41/1.29
% 0.41/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.41/1.29
% 0.41/1.29 % ------ iProver source info
% 0.41/1.29
% 0.41/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.41/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.41/1.29 % git: non_committed_changes: false
% 0.41/1.29
% 0.41/1.29 % ------ Parsing...
% 0.41/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.41/1.29
% 0.41/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 0.41/1.29
% 0.41/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.41/1.29
% 0.41/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.41/1.29 % ------ Proving...
% 0.41/1.29 % ------ Problem Properties
% 0.41/1.29
% 0.41/1.29 %
% 0.41/1.29 % clauses 16
% 0.41/1.29 % conjectures 0
% 0.41/1.29 % EPR 11
% 0.41/1.29 % Horn 12
% 0.41/1.29 % unary 2
% 0.41/1.29 % binary 12
% 0.41/1.29 % lits 37
% 0.41/1.29 % lits eq 11
% 0.41/1.29 % fd_pure 0
% 0.41/1.29 % fd_pseudo 0
% 0.41/1.29 % fd_cond 0
% 0.41/1.29 % fd_pseudo_cond 2
% 0.41/1.29 % AC symbols 0
% 0.41/1.29
% 0.41/1.29 % ------ Schedule dynamic 5 is on
% 0.41/1.29
% 0.41/1.29 % ------ no conjectures: strip conj schedule
% 0.41/1.29
% 0.41/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.41/1.29
% 0.41/1.29
% 0.41/1.29 % ------
% 0.41/1.29 % Current options:
% 0.41/1.29 % ------
% 0.41/1.29
% 0.41/1.29
% 0.41/1.29 %
% 0.41/1.29
% 0.41/1.29 % ------ Proving...
% 0.41/1.29 %
% 0.41/1.29
% 0.41/1.29 % SZS status Theorem for theBenchmark.p
% 0.41/1.29
% 0.41/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.98/1.30
% 1.98/1.30
%------------------------------------------------------------------------------