%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW102+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 03:29:11 PM UTC 2026
% Result : Theorem 8.35s 6.80s
% Output : CNFRefutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 22
% Syntax : Number of formulae : 153 ( 63 unt; 2 def)
% Number of atoms : 307 ( 183 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 218 ( 78 ~; 104 |; 27 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 91 !; 4 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( bool(X0)
<=> ( X0 = true
| X0 = false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_bool) ).
fof(f2,axiom,
( false != err
& true != err
& true != false ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',distinct_false_true_err) ).
fof(f3,axiom,
( d(err)
& d(false)
& d(true) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).
fof(f4,axiom,
! [X0,X1] :
( forallprefers(X0,X1)
<=> ( ( X1 = true
& X0 = false )
| ( bool(X1)
& ~ bool(X0)
& d(X1)
& d(X0) )
| ( d(X1)
& ~ d(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).
fof(f6,axiom,
! [X0] :
( ( phi(X0) = err
& ~ d(X0) )
| ( phi(X0) = X0
& d(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).
fof(f7,axiom,
! [X0] :
( prop(X0) = true
<=> bool(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_true) ).
fof(f8,axiom,
! [X0] :
( prop(X0) = false
<=> ~ bool(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_false) ).
fof(f9,axiom,
! [X0,X1] :
( ~ bool(X0)
=> impl(X0,X1) = phi(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom1) ).
fof(f11,axiom,
! [X0] :
( bool(X0)
=> impl(false,X0) = true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom3) ).
fof(f12,axiom,
! [X0] :
( bool(X0)
=> impl(true,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom4) ).
fof(f14,axiom,
! [X0] : lazy_impl(false,X0) = true,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).
fof(f15,axiom,
! [X0] : lazy_impl(true,X0) = phi(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).
fof(f38,axiom,
false1 = false,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false1) ).
fof(f39,axiom,
! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f7) ).
fof(f40,axiom,
? [X0] :
( ~ ? [X1] : forallprefers(f7(X1),f7(X0))
& false2 = phi(f7(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false2) ).
fof(f41,axiom,
! [X0] :
( ~ bool(X0)
=> not1(X0) = phi(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',not1_axiom1) ).
fof(f42,axiom,
not1(false) = true,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',not1_axiom2) ).
fof(f43,axiom,
not1(true) = false,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',not1_axiom3) ).
fof(f44,axiom,
! [X0] : not2(X0) = impl(X0,false2),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_not2) ).
fof(f45,conjecture,
! [X0] : not1(X0) = not2(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_not2) ).
fof(f46,negated_conjecture,
~ ! [X0] : not1(X0) = not2(X0),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f48,plain,
! [X0,X1] :
( ( ( X1 = true
& X0 = false )
| ( bool(X1)
& ~ bool(X0)
& d(X1)
& d(X0) )
| ( d(X1)
& ~ d(X0) ) )
=> forallprefers(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f49,plain,
! [X0,X1] :
( ( ( true != X1
| false != X0 )
& ( ~ bool(X1)
| bool(X0)
| ~ d(X1)
| ~ d(X0) )
& ( ~ d(X1)
| d(X0) ) )
| forallprefers(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( bool(X0)
| impl(X0,X1) = phi(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0] :
( ~ bool(X0)
| impl(false,X0) = true ),
inference(ennf_transformation,[],[f11]) ).
fof(f55,plain,
! [X0] :
( ~ bool(X0)
| impl(true,X0) = X0 ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
? [X0] :
( ! [X1] : ~ forallprefers(f7(X1),f7(X0))
& false2 = phi(f7(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f75,plain,
! [X0] :
( bool(X0)
| not1(X0) = phi(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f76,plain,
? [X0] : not1(X0) != not2(X0),
inference(ennf_transformation,[],[f46]) ).
fof(f77,plain,
! [X0] :
( ( ~ bool(X0)
| X0 = true
| X0 = false )
& ( ( true != X0
& false != X0 )
| bool(X0) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f78,plain,
! [X0] :
( ( ~ bool(X0)
| X0 = true
| X0 = false )
& ( ( true != X0
& false != X0 )
| bool(X0) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( true != prop(X0)
| bool(X0) )
& ( ~ bool(X0)
| prop(X0) = true ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f80,plain,
! [X0] :
( ( false != prop(X0)
| ~ bool(X0) )
& ( bool(X0)
| prop(X0) = false ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f87,plain,
( ! [X1] : ~ forallprefers(f7(X1),f7(sK6))
& false2 = phi(f7(sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f74]) ).
fof(f88,plain,
not1(sK7) != not2(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f76]) ).
fof(f89,plain,
! [X0] :
( ~ bool(X0)
| true = X0
| false = X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f91,plain,
! [X0] :
( false != X0
| bool(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f92,plain,
false != err,
inference(cnf_transformation,[],[f2]) ).
fof(f96,plain,
d(false),
inference(cnf_transformation,[],[f3]) ).
fof(f97,plain,
d(true),
inference(cnf_transformation,[],[f3]) ).
fof(f98,plain,
! [X0,X1] :
( true != X1
| false != X0
| forallprefers(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f100,plain,
! [X0,X1] :
( ~ d(X1)
| d(X0)
| forallprefers(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f104,plain,
! [X0] :
( err = phi(X0)
| phi(X0) = X0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f105,plain,
! [X0] :
( ~ d(X0)
| phi(X0) = X0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f108,plain,
! [X0] :
( true != prop(X0)
| bool(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f109,plain,
! [X0] :
( ~ bool(X0)
| true = prop(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f111,plain,
! [X0] :
( bool(X0)
| false = prop(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
! [X0,X1] :
( bool(X0)
| phi(X0) = impl(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f114,plain,
! [X0] :
( ~ bool(X0)
| true = impl(false,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f115,plain,
! [X0] :
( ~ bool(X0)
| impl(true,X0) = X0 ),
inference(cnf_transformation,[],[f55]) ).
fof(f117,plain,
! [X0] : true = lazy_impl(false,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f118,plain,
! [X0] : phi(X0) = lazy_impl(true,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f147,plain,
false = false1,
inference(cnf_transformation,[],[f38]) ).
fof(f148,plain,
! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
inference(cnf_transformation,[],[f39]) ).
fof(f149,plain,
! [X1] : ~ forallprefers(f7(X1),f7(sK6)),
inference(cnf_transformation,[],[f87]) ).
fof(f150,plain,
false2 = phi(f7(sK6)),
inference(cnf_transformation,[],[f87]) ).
fof(f151,plain,
! [X0] :
( bool(X0)
| phi(X0) = not1(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f152,plain,
true = not1(false),
inference(cnf_transformation,[],[f42]) ).
fof(f153,plain,
false = not1(true),
inference(cnf_transformation,[],[f43]) ).
fof(f154,plain,
! [X0] : not2(X0) = impl(X0,false2),
inference(cnf_transformation,[],[f44]) ).
fof(f155,plain,
not1(sK7) != not2(sK7),
inference(cnf_transformation,[],[f88]) ).
fof(f163,plain,
! [X0] :
( false1 != X0
| bool(X0) ),
inference(definition_unfolding,[],[f91,f147]) ).
fof(f164,plain,
! [X0] :
( ~ bool(X0)
| true = X0
| false1 = X0 ),
inference(definition_unfolding,[],[f89,f147]) ).
fof(f166,plain,
err != false1,
inference(definition_unfolding,[],[f92,f147]) ).
fof(f167,plain,
d(false1),
inference(definition_unfolding,[],[f96,f147]) ).
fof(f168,plain,
! [X0,X1] :
( true != X1
| false1 != X0
| forallprefers(X0,X1) ),
inference(definition_unfolding,[],[f98,f147]) ).
fof(f171,plain,
! [X0] :
( ~ d(X0)
| lazy_impl(true,X0) = X0 ),
inference(definition_unfolding,[],[f105,f118]) ).
fof(f172,plain,
! [X0] :
( err = lazy_impl(true,X0)
| lazy_impl(true,X0) = X0 ),
inference(definition_unfolding,[],[f104,f118,f118]) ).
fof(f173,plain,
! [X0] :
( bool(X0)
| prop(X0) = false1 ),
inference(definition_unfolding,[],[f111,f147]) ).
fof(f175,plain,
! [X0,X1] :
( bool(X0)
| impl(X0,X1) = lazy_impl(true,X0) ),
inference(definition_unfolding,[],[f112,f118]) ).
fof(f177,plain,
! [X0] :
( ~ bool(X0)
| true = impl(false1,X0) ),
inference(definition_unfolding,[],[f114,f147]) ).
fof(f179,plain,
! [X0] : true = lazy_impl(false1,X0),
inference(definition_unfolding,[],[f117,f147]) ).
fof(f194,plain,
false2 = lazy_impl(true,lazy_impl(prop(sK6),sK6)),
inference(definition_unfolding,[],[f150,f118,f148]) ).
fof(f195,plain,
! [X1] : ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(sK6),sK6)),
inference(definition_unfolding,[],[f149,f148,f148]) ).
fof(f196,plain,
! [X0] :
( bool(X0)
| lazy_impl(true,X0) = not1(X0) ),
inference(definition_unfolding,[],[f151,f118]) ).
fof(f197,plain,
true = not1(false1),
inference(definition_unfolding,[],[f152,f147]) ).
fof(f198,plain,
false1 = not1(true),
inference(definition_unfolding,[],[f153,f147]) ).
fof(f199,plain,
not1(sK7) != impl(sK7,false2),
inference(definition_unfolding,[],[f155,f154]) ).
fof(f200,plain,
bool(false1),
inference(equality_resolution,[],[f163]) ).
fof(f202,plain,
! [X1] :
( true != X1
| forallprefers(false1,X1) ),
inference(equality_resolution,[],[f168]) ).
fof(f203,plain,
forallprefers(false1,true),
inference(equality_resolution,[],[f202]) ).
tcf(c_49,plain,
bool(false1),
inference(cnf_transformation,[],[f200]) ).
tcf(c_51,plain,
! [X0: $i] :
( ( X0 = true )
| ( X0 = false1 )
| ~ bool(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_54,plain,
false1 != err,
inference(cnf_transformation,[],[f166]) ).
tcf(c_55,plain,
d(true),
inference(cnf_transformation,[],[f97]) ).
tcf(c_56,plain,
d(false1),
inference(cnf_transformation,[],[f167]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( d(X1)
| forallprefers(X1,X0)
| ~ d(X0) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_60,plain,
forallprefers(false1,true),
inference(cnf_transformation,[],[f203]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( lazy_impl(true,X0) = X0 )
| ~ d(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_66,plain,
! [X0: $i] :
( ( lazy_impl(true,X0) = err )
| ( lazy_impl(true,X0) = X0 ) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_67,plain,
! [X0: $i] :
( ( prop(X0) = true )
| ~ bool(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_68,plain,
! [X0: $i] :
( bool(X0)
| ( prop(X0) != true ) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_69,plain,
! [X0: $i] :
( bool(X0)
| ( prop(X0) = false1 ) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( bool(X0)
| ( impl(X0,X1) = lazy_impl(true,X0) ) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_73,plain,
! [X0: $i] :
( ( impl(false1,X0) = true )
| ~ bool(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_74,plain,
! [X0: $i] :
( ( impl(true,X0) = X0 )
| ~ bool(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_76,plain,
! [X0: $i] : lazy_impl(false1,X0) = true,
inference(cnf_transformation,[],[f179]) ).
tcf(c_94,plain,
lazy_impl(true,lazy_impl(prop(sK6),sK6)) = false2,
inference(cnf_transformation,[],[f194]) ).
tcf(c_95,plain,
! [X0: $i] : ~ forallprefers(lazy_impl(prop(X0),X0),lazy_impl(prop(sK6),sK6)),
inference(cnf_transformation,[],[f195]) ).
tcf(c_96,plain,
! [X0: $i] :
( bool(X0)
| ( lazy_impl(true,X0) = not1(X0) ) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_97,plain,
not1(false1) = true,
inference(cnf_transformation,[],[f197]) ).
tcf(c_98,plain,
not1(true) = false1,
inference(cnf_transformation,[],[f198]) ).
tcf(c_99,negated_conjecture,
impl(sK7,false2) != not1(sK7),
inference(cnf_transformation,[],[f199]) ).
tcf(c_822,definition,
iPr_def_10 = impl(sK7,false2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_823,definition,
iPr_def_11 = not1(sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_824,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_99,c_823,c_822]) ).
tcf(c_1743,plain,
prop(false1) = true,
inference(superposition,[status(thm)],[c_49,c_67]) ).
tcf(c_1745,plain,
! [X0: $i] :
( ( prop(X0) = true )
| ( prop(X0) = false1 ) ),
inference(superposition,[status(thm)],[c_69,c_67]) ).
tcf(c_1767,plain,
lazy_impl(true,true) = true,
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_1768,plain,
lazy_impl(true,false1) = false1,
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_1852,plain,
! [X0: $i] :
( ( prop(X0) = true )
| ( lazy_impl(true,X0) = not1(X0) ) ),
inference(superposition,[status(thm)],[c_96,c_67]) ).
tcf(c_1877,plain,
! [X0: $i,X1: $i] :
( ( prop(X0) = true )
| ( impl(X0,X1) = lazy_impl(true,X0) ) ),
inference(superposition,[status(thm)],[c_71,c_67]) ).
tcf(c_2007,plain,
~ forallprefers(lazy_impl(true,false1),lazy_impl(prop(sK6),sK6)),
inference(superposition,[status(thm)],[c_1743,c_95]) ).
tcf(c_2009,plain,
~ forallprefers(false1,lazy_impl(prop(sK6),sK6)),
inference(light_normalisation,[status(thm)],[c_2007,c_1768]) ).
tcf(c_2078,plain,
( ( lazy_impl(prop(sK6),sK6) = false2 )
| ( lazy_impl(true,lazy_impl(prop(sK6),sK6)) = err ) ),
inference(superposition,[status(thm)],[c_66,c_94]) ).
tcf(c_2085,plain,
( ( err = false2 )
| ( lazy_impl(prop(sK6),sK6) = false2 ) ),
inference(light_normalisation,[status(thm)],[c_2078,c_94]) ).
tcf(c_2138,plain,
( ( prop(sK6) = true )
| ~ forallprefers(false1,lazy_impl(false1,sK6)) ),
inference(superposition,[status(thm)],[c_1745,c_2009]) ).
tcf(c_3496,plain,
( ( prop(sK6) = true )
| ~ forallprefers(false1,true) ),
inference(demodulation,[status(thm)],[c_2138,c_76]) ).
tcf(c_3497,plain,
prop(sK6) = true,
inference(forward_subsumption_resolution,[status(thm)],[c_3496,c_60]) ).
tcf(c_3498,plain,
( ( err = false2 )
| ( lazy_impl(true,sK6) = false2 ) ),
inference(demodulation,[status(thm)],[c_2085,c_3497]) ).
tcf(c_3501,plain,
~ forallprefers(false1,lazy_impl(true,sK6)),
inference(demodulation,[status(thm)],[c_2009,c_3497]) ).
tcf(c_3502,plain,
! [X0: $i] : ~ forallprefers(lazy_impl(prop(X0),X0),lazy_impl(true,sK6)),
inference(demodulation,[status(thm)],[c_95,c_3497]) ).
tcf(c_3503,plain,
lazy_impl(true,lazy_impl(true,sK6)) = false2,
inference(demodulation,[status(thm)],[c_94,c_3497]) ).
tcf(c_3518,plain,
bool(sK6),
inference(superposition,[status(thm)],[c_3497,c_68]) ).
tcf(c_3528,plain,
( ( true = sK6 )
| ( false1 = sK6 ) ),
inference(superposition,[status(thm)],[c_3518,c_51]) ).
tcf(c_3533,plain,
impl(true,sK6) = sK6,
inference(superposition,[status(thm)],[c_3518,c_74]) ).
tcf(c_3534,plain,
impl(false1,sK6) = true,
inference(superposition,[status(thm)],[c_3518,c_73]) ).
tcf(c_3590,plain,
( ( false2 = sK6 )
| ( lazy_impl(true,sK6) = err ) ),
inference(superposition,[status(thm)],[c_66,c_3503]) ).
tcf(c_3686,plain,
! [X0: $i] :
( ( true = sK6 )
| ~ forallprefers(lazy_impl(prop(X0),X0),lazy_impl(true,false1)) ),
inference(superposition,[status(thm)],[c_3528,c_3502]) ).
tcf(c_3689,plain,
! [X0: $i] :
( ( true = sK6 )
| ~ forallprefers(lazy_impl(prop(X0),X0),false1) ),
inference(light_normalisation,[status(thm)],[c_3686,c_1768]) ).
tcf(c_4015,plain,
( ( false2 = sK6 )
| ( true = sK6 )
| ( lazy_impl(true,false1) = err ) ),
inference(superposition,[status(thm)],[c_3528,c_3590]) ).
tcf(c_4017,plain,
( ( false2 = sK6 )
| ( err = false2 ) ),
inference(superposition,[status(thm)],[c_3590,c_3498]) ).
tcf(c_4038,plain,
( ( false2 = sK6 )
| ( true = sK6 )
| ( false1 = err ) ),
inference(light_normalisation,[status(thm)],[c_4015,c_1768]) ).
tcf(c_4039,plain,
( ( false2 = sK6 )
| ( true = sK6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4038,c_54]) ).
tcf(c_4058,plain,
( ( err = false2 )
| ( impl(sK7,sK6) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4017,c_822]) ).
tcf(c_4144,plain,
( ( true = sK6 )
| ( impl(sK7,sK6) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4039,c_822]) ).
tcf(c_4860,plain,
! [X0: $i] :
( d(lazy_impl(prop(X0),X0))
| ( true = sK6 )
| ~ d(false1) ),
inference(superposition,[status(thm)],[c_58,c_3689]) ).
tcf(c_4870,plain,
! [X0: $i] :
( d(lazy_impl(prop(X0),X0))
| ( true = sK6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4860,c_56]) ).
tcf(c_4890,plain,
( d(lazy_impl(true,sK6))
| ( true = sK6 ) ),
inference(superposition,[status(thm)],[c_3497,c_4870]) ).
tcf(c_4913,plain,
( ( true = sK6 )
| ( lazy_impl(true,lazy_impl(true,sK6)) = lazy_impl(true,sK6) ) ),
inference(superposition,[status(thm)],[c_4890,c_65]) ).
tcf(c_4917,plain,
( ( true = sK6 )
| ( lazy_impl(true,sK6) = false2 ) ),
inference(light_normalisation,[status(thm)],[c_4913,c_3503]) ).
tcf(c_5148,plain,
( ( true = sK6 )
| ( lazy_impl(true,false1) = false2 ) ),
inference(superposition,[status(thm)],[c_3528,c_4917]) ).
tcf(c_9817,plain,
( ( prop(sK7) = true )
| ( lazy_impl(true,sK7) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1877,c_822]) ).
tcf(c_9970,plain,
( ( not1(sK7) = iPr_def_10 )
| ( prop(sK7) = true ) ),
inference(superposition,[status(thm)],[c_9817,c_1852]) ).
tcf(c_9973,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( prop(sK7) = true ) ),
inference(light_normalisation,[status(thm)],[c_9970,c_823]) ).
tcf(c_9974,plain,
prop(sK7) = true,
inference(forward_subsumption_resolution,[status(thm)],[c_9973,c_824]) ).
tcf(c_10100,plain,
bool(sK7),
inference(superposition,[status(thm)],[c_9974,c_68]) ).
tcf(c_10205,plain,
( ( true = sK7 )
| ( false1 = sK7 ) ),
inference(superposition,[status(thm)],[c_10100,c_51]) ).
tcf(c_11024,plain,
( ( err = false2 )
| ( true = sK7 )
| ( impl(false1,sK6) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_10205,c_4058]) ).
tcf(c_11026,plain,
( ( true = sK7 )
| ( not1(false1) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_10205,c_823]) ).
tcf(c_11028,plain,
( ( true = iPr_def_11 )
| ( true = sK7 ) ),
inference(light_normalisation,[status(thm)],[c_11026,c_97]) ).
tcf(c_11042,plain,
( ( err = false2 )
| ( true = iPr_def_10 )
| ( true = sK7 ) ),
inference(light_normalisation,[status(thm)],[c_11024,c_3534]) ).
tcf(c_16958,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_11042,c_11028,c_5148,c_4144,c_4039,c_3533,c_3501,c_1768,c_1767,c_824,c_823,c_98,c_60,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW102+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.43 % Computer : n006.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Thu Sep 24 21:39:09 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.47 Running first-order theorem proving
% 0.17/5.47 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
% 0.17/5.48
% 0.17/5.48 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.48
% 0.17/5.48 % Detected problem language: tptp
% 0.17/5.49 % Proving...
% 8.35/6.80 % SZS status Started for theBenchmark.p
% 8.35/6.80 % SZS status Theorem for theBenchmark.p
% 8.35/6.80
% 8.35/6.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.35/6.80
% 8.35/6.80 % ------ iProver source info
% 8.35/6.80
% 8.35/6.80 % git: date: 2026-07-19 20:42:38 +0200
% 8.35/6.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.35/6.80 % git: non_committed_changes: false
% 8.35/6.80
% 8.35/6.80 % ------ Parsing...
% 8.35/6.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.35/6.80
% 8.35/6.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 8.35/6.80
% 8.35/6.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.35/6.80
% 8.35/6.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.35/6.80 % ------ Proving...
% 8.35/6.80 % ------ Problem Properties
% 8.35/6.80
% 8.35/6.80 %
% 8.35/6.80 % clauses 53
% 8.35/6.80 % conjectures 1
% 8.35/6.80 % EPR 16
% 8.35/6.80 % Horn 36
% 8.35/6.80 % unary 26
% 8.35/6.80 % binary 19
% 8.35/6.80 % lits 90
% 8.35/6.80 % lits eq 37
% 8.35/6.80 % fd_pure 0
% 8.35/6.80 % fd_pseudo 0
% 8.35/6.80 % fd_cond 1
% 8.35/6.80 % fd_pseudo_cond 0
% 8.35/6.80 % AC symbols 0
% 8.35/6.80
% 8.35/6.80 % ------ Schedule dynamic 5 is on
% 8.35/6.80
% 8.35/6.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.35/6.80
% 8.35/6.80
% 8.35/6.80 % ------
% 8.35/6.80 % Current options:
% 8.35/6.80 % ------
% 8.35/6.80
% 8.35/6.80
% 8.35/6.80 %
% 8.35/6.80
% 8.35/6.80 % ------ Proving...
% 8.35/6.80 %
% 8.35/6.80
% 8.35/6.80 % SZS status Theorem for theBenchmark.p
% 8.35/6.80
% 8.35/6.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.35/6.81
% 8.35/6.81
%------------------------------------------------------------------------------