%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC211+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 03:08:53 PM UTC 2026
% Result : Theorem 10.36s 2.27s
% Output : CNFRefutation 10.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 105 ( 33 unt; 0 def)
% Number of atoms : 353 ( 131 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 406 ( 158 ~; 162 |; 58 &)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 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; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 100 !; 26 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| neq(X0,nil)
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| neq(X0,nil)
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f176,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f186,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f192]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X3
| nil = X2 )
& ~ neq(X0,nil)
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X3
| nil = X2 )
& ~ neq(X0,nil)
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f235,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f235]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f285,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
fof(f290,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(X1,sK51(X0))],[f187]) ).
fof(f291,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f189]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( nil != sK56
| nil = sK55 )
& ~ neq(sK53,nil)
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK56
| app(X5,cons(X4,nil)) = sK55
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f443,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f444,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK51(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f290]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f291]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
~ neq(sK53,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4,X5] :
( app(cons(X4,nil),X5) != sK56
| app(X5,cons(X4,nil)) = sK55
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f503,f505]) ).
fof(f507,plain,
~ neq(sK55,nil),
inference(definition_unfolding,[],[f501,f504]) ).
fof(f508,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f505]) ).
fof(f509,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f504]) ).
fof(f511,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f305]) ).
fof(f529,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f444]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f529]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK51(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK51(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f469]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f506]) ).
tcf(c_247,negated_conjecture,
! [X0: $i,X1: $i] :
( ( app(X1,cons(X0,nil)) = sK55 )
| ~ ssList(X1)
| ~ ssItem(X0)
| ( app(cons(X0,nil),X1) != sK56 ) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_248,negated_conjecture,
~ neq(sK55,nil),
inference(cnf_transformation,[],[f507]) ).
tcf(c_252,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f508]) ).
tcf(c_253,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f509]) ).
tcf(c_303,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_3222,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_248]) ).
tcf(c_3223,plain,
( ( sK55 = nil )
| ~ ssList(sK55)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3222]) ).
tcf(c_3224,plain,
sK55 = nil,
inference(global_subsumption_just,[status(thm)],[c_3223,c_253,c_141,c_3223]) ).
tcf(c_3240,plain,
( ( sK56 != sK55 )
| ( nil != nil ) ),
inference(resolution_lifted,[status(thm)],[c_246,c_248]) ).
tcf(c_3241,plain,
sK56 != sK55,
inference(global_subsumption_just,[status(thm)],[c_3240,c_141,c_195,c_303,c_3240]) ).
tcf(c_6057,plain,
nil != sK56,
inference(light_normalisation,[status(thm)],[c_3241,c_3224]) ).
tcf(c_7060,plain,
! [X0: $i,X1: $i] :
( ( app(X1,cons(X0,nil)) = nil )
| ~ ssList(X1)
| ~ ssItem(X0)
| ( app(cons(X0,nil),X1) != sK56 ) ),
inference(light_normalisation,[status(thm)],[c_247,c_3224]) ).
tcf(c_12894,plain,
! [X0: $i,X1: $i] :
( ( app(X1,cons(X0,nil)) = nil )
| ~ ssList(X1)
| ~ ssItem(X0)
| ( app(cons(X0,nil),X1) != sK56 ) ),
inference(demodulation,[status(thm)],[c_7060]) ).
tcf(c_12895,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_6057]) ).
tcf(c_12897,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_17641,plain,
( ( nil = sK56 )
| ( hd(sK56) = sK51(sK56) ) ),
inference(superposition,[status(thm)],[c_12897,c_220]) ).
tcf(c_17642,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_17641,c_12895]) ).
tcf(c_17799,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_12897,c_222]) ).
tcf(c_17800,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_17799,c_12895]) ).
tcf(c_17939,plain,
( ssItem(hd(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_17642,c_219]) ).
tcf(c_17940,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_17939,c_12895,c_12897]) ).
tcf(c_17961,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_17800,c_221]) ).
tcf(c_17962,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_17961,c_12895,c_12897]) ).
tcf(c_19073,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_12897,c_224]) ).
tcf(c_19076,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_19073,c_12895]) ).
tcf(c_19878,plain,
! [X0: $i] :
( ( app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_17940,c_227]) ).
tcf(c_20431,plain,
app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
inference(superposition,[status(thm)],[c_17962,c_19878]) ).
tcf(c_20433,plain,
app(cons(hd(sK56),nil),tl(sK56)) = sK56,
inference(light_normalisation,[status(thm)],[c_20431,c_19076]) ).
tcf(c_23368,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) = nil )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_20433,c_12894]) ).
tcf(c_23375,plain,
app(tl(sK56),cons(hd(sK56),nil)) = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_23368,c_17962,c_17940]) ).
tcf(c_23455,plain,
( memberP(nil,hd(sK56))
| ~ ssList(nil)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil))) ),
inference(superposition,[status(thm)],[c_23375,c_54]) ).
tcf(c_23497,plain,
( memberP(nil,hd(sK56))
| ~ ssList(nil)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56)) ),
inference(light_normalisation,[status(thm)],[c_23455,c_23375]) ).
tcf(c_23498,plain,
memberP(nil,hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_23497,c_141,c_17962,c_17940]) ).
tcf(c_23504,plain,
~ ssItem(hd(sK56)),
inference(superposition,[status(thm)],[c_23498,c_171]) ).
tcf(c_23505,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23504,c_17940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC211+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 17:00:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 10.36/2.27 % SZS status Started for theBenchmark.p
% 10.36/2.27 % SZS status Theorem for theBenchmark.p
% 10.36/2.27
% 10.36/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.36/2.27
% 10.36/2.27 % ------ iProver source info
% 10.36/2.27
% 10.36/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 10.36/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.36/2.27 % git: non_committed_changes: false
% 10.36/2.27
% 10.36/2.27 % ------ Parsing...
% 10.36/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.36/2.27
% 10.36/2.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 5 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 10.36/2.27
% 10.36/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.36/2.27
% 10.36/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.36/2.27 % ------ Proving...
% 10.36/2.27 % ------ Problem Properties
% 10.36/2.27
% 10.36/2.27 %
% 10.36/2.27 % clauses 184
% 10.36/2.27 % conjectures 1
% 10.36/2.27 % EPR 52
% 10.36/2.27 % Horn 116
% 10.36/2.27 % unary 19
% 10.36/2.27 % binary 40
% 10.36/2.27 % lits 625
% 10.36/2.27 % lits eq 82
% 10.36/2.27 % fd_pure 0
% 10.36/2.27 % fd_pseudo 0
% 10.36/2.27 % fd_cond 21
% 10.36/2.27 % fd_pseudo_cond 14
% 10.36/2.27 % AC symbols 0
% 10.36/2.27
% 10.36/2.27 % ------ Schedule dynamic 5 is on
% 10.36/2.27
% 10.36/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.36/2.27
% 10.36/2.27
% 10.36/2.27 % ------
% 10.36/2.27 % Current options:
% 10.36/2.27 % ------
% 10.36/2.27
% 10.36/2.27
% 10.36/2.27 %
% 10.36/2.27
% 10.36/2.27 % ------ Proving...
% 10.36/2.27 %
% 10.36/2.27
% 10.36/2.27 % SZS status Theorem for theBenchmark.p
% 10.36/2.27
% 10.36/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.36/2.27
% 10.36/2.27
%------------------------------------------------------------------------------