%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC218+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 03:08:54 PM UTC 2026
% Result : Theorem 4.14s 1.28s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 113 ( 55 unt; 4 def)
% Number of atoms : 376 ( 110 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 341 ( 135 ~; 121 |; 49 &)
% ( 8 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 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; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 99 !; 18 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax52) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> app(app(X4,cons(X6,nil)),X5) != X2 )
| app(X4,X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> app(app(X4,cons(X6,nil)),X5) != X2 )
| app(X4,X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f167,plain,
! [X0] :
( ~ ssList(X0)
| ( rearsegP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f200,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ~ neq(X0,nil)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& app(app(X4,cons(X6,nil)),X5) = X2 )
& app(X4,X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ~ neq(X0,nil)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& app(app(X4,cons(X6,nil)),X5) = X2 )
& app(X4,X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f243,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f244,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X3] :
( app(X3,X1) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f243]) ).
fof(f245,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ( app(sK12(X0,X1),X1) = X0
& ssList(sK12(X0,X1)) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1))],[f244]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f284,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ rearsegP(nil,X0)
| nil = X0 )
& ( nil != X0
| rearsegP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f167]) ).
fof(f292,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f200]) ).
fof(f293,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f292]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ~ neq(sK53,nil)
& ssList(sK57)
& ssList(sK58)
& ssItem(sK59)
& sK55 = app(app(sK57,cons(sK59,nil)),sK58)
& sK56 = app(sK57,sK58)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59)],[f222]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f245]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f436,plain,
! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f284]) ).
fof(f480,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f293]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
~ neq(sK53,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssList(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssItem(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK55 = app(app(sK57,cons(sK59,nil)),sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK56 = app(sK57,sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
~ neq(sK55,nil),
inference(definition_unfolding,[],[f500,f506]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f515,plain,
! [X2,X1] :
( ~ ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X2,X1),X1) ),
inference(equality_resolution,[],[f314]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_189,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(cnf_transformation,[],[f436]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f480]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
app(sK57,sK58) = sK56,
inference(cnf_transformation,[],[f505]) ).
tcf(c_247,negated_conjecture,
app(app(sK57,cons(sK59,nil)),sK58) = sK55,
inference(cnf_transformation,[],[f504]) ).
tcf(c_248,negated_conjecture,
ssItem(sK59),
inference(cnf_transformation,[],[f503]) ).
tcf(c_249,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f502]) ).
tcf(c_250,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f501]) ).
tcf(c_251,negated_conjecture,
~ neq(sK55,nil),
inference(cnf_transformation,[],[f508]) ).
tcf(c_254,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_255,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_153,c_64]) ).
tcf(c_3207,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_251]) ).
tcf(c_3208,plain,
( ( sK55 = nil )
| ~ ssList(sK55)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3207]) ).
tcf(c_3209,plain,
sK55 = nil,
inference(global_subsumption_just,[status(thm)],[c_3208,c_255,c_141,c_3208]) ).
tcf(c_6289,plain,
app(app(sK57,cons(sK59,nil)),sK58) = nil,
inference(light_normalisation,[status(thm)],[c_247,c_3209]) ).
tcf(c_12838,definition,
iPr_def_10 = cons(sK59,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_12839,definition,
iPr_def_11 = app(sK57,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_12840,definition,
iPr_def_12 = app(iPr_def_11,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_12841,definition,
iPr_def_13 = app(sK57,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_12842,plain,
iPr_def_12 = nil,
inference(demodulation,[status(thm)],[c_6289,c_12838,c_12839,c_12840]) ).
tcf(c_12844,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_12845,negated_conjecture,
ssList(sK57),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_12846,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_12847,negated_conjecture,
ssItem(sK59),
inference(demodulation,[status(thm)],[c_248]) ).
tcf(c_12848,negated_conjecture,
iPr_def_13 = sK56,
inference(demodulation,[status(thm)],[c_246,c_12841]) ).
tcf(c_15664,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_12844,c_12848]) ).
tcf(c_15667,plain,
ssList(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_141,c_12842]) ).
tcf(c_15685,plain,
cons(sK59,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_12838,c_12842]) ).
tcf(c_16097,plain,
! [X0: $i] :
( ( app(X0,iPr_def_12) = X0 )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_232,c_12842]) ).
tcf(c_16126,plain,
app(sK57,iPr_def_12) = sK57,
inference(superposition,[status(thm)],[c_12845,c_16097]) ).
tcf(c_16190,plain,
( ssList(iPr_def_10)
| ~ ssList(iPr_def_12)
| ~ ssItem(sK59) ),
inference(superposition,[status(thm)],[c_15685,c_140]) ).
tcf(c_16193,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_16190,c_15667,c_12847]) ).
tcf(c_16393,plain,
( ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ~ ssList(sK57) ),
inference(superposition,[status(thm)],[c_12839,c_153]) ).
tcf(c_16406,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_16393,c_16193,c_12845]) ).
tcf(c_16432,plain,
app(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_16406,c_16097]) ).
tcf(c_17058,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ ssList(X0)
| ~ rearsegP(iPr_def_12,X0) ),
inference(light_normalisation,[status(thm)],[c_189,c_12842]) ).
tcf(c_17319,plain,
( rearsegP(iPr_def_12,sK58)
| ~ ssList(iPr_def_11)
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_12840,c_374]) ).
tcf(c_17351,plain,
rearsegP(iPr_def_12,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_17319,c_16406,c_12846]) ).
tcf(c_17538,plain,
( ( sK58 = iPr_def_12 )
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_17351,c_17058]) ).
tcf(c_17539,plain,
sK58 = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_17538,c_12846]) ).
tcf(c_17549,plain,
app(sK57,iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_12841,c_17539]) ).
tcf(c_17550,plain,
app(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_12840,c_17539]) ).
tcf(c_17552,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_17550,c_16432]) ).
tcf(c_17598,plain,
app(sK57,iPr_def_11) = sK57,
inference(demodulation,[status(thm)],[c_16126,c_17552]) ).
tcf(c_17613,plain,
cons(sK59,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_15685,c_17552]) ).
tcf(c_17628,plain,
nil = iPr_def_11,
inference(demodulation,[status(thm)],[c_12842,c_17552]) ).
tcf(c_17761,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_148,c_17628]) ).
tcf(c_18644,plain,
sK57 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_17549,c_17552,c_17598]) ).
tcf(c_18658,plain,
app(iPr_def_13,iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_12839,c_18644]) ).
tcf(c_19566,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_11 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_230,c_17628]) ).
tcf(c_19679,plain,
( ~ ssList(iPr_def_11)
| ~ ssItem(sK59)
| ( iPr_def_10 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_17613,c_17761]) ).
tcf(c_19683,plain,
iPr_def_10 != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_19679,c_16406,c_12847]) ).
tcf(c_19997,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_18658,c_19566]) ).
tcf(c_20004,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_19997,c_19683,c_15664,c_16193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC218+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 17:02:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 4.14/1.28 % SZS status Started for theBenchmark.p
% 4.14/1.28 % SZS status Theorem for theBenchmark.p
% 4.14/1.28
% 4.14/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.14/1.28
% 4.14/1.28 % ------ iProver source info
% 4.14/1.28
% 4.14/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.14/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.14/1.28 % git: non_committed_changes: false
% 4.14/1.28
% 4.14/1.28 % ------ Parsing...
% 4.14/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.14/1.28
% 4.14/1.28 % ------ 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: 3 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 %
% 4.14/1.28
% 4.14/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.14/1.28
% 4.14/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.14/1.28 % ------ Proving...
% 4.14/1.28 % ------ Problem Properties
% 4.14/1.28
% 4.14/1.28 %
% 4.14/1.28 % clauses 191
% 4.14/1.28 % conjectures 5
% 4.14/1.28 % EPR 56
% 4.14/1.28 % Horn 123
% 4.14/1.28 % unary 27
% 4.14/1.28 % binary 40
% 4.14/1.28 % lits 629
% 4.14/1.28 % lits eq 85
% 4.14/1.28 % fd_pure 0
% 4.14/1.28 % fd_pseudo 0
% 4.14/1.28 % fd_cond 21
% 4.14/1.28 % fd_pseudo_cond 14
% 4.14/1.28 % AC symbols 0
% 4.14/1.28
% 4.14/1.28 % ------ Schedule dynamic 5 is on
% 4.14/1.28
% 4.14/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.14/1.28
% 4.14/1.28
% 4.14/1.28 % ------
% 4.14/1.28 % Current options:
% 4.14/1.28 % ------
% 4.14/1.28
% 4.14/1.28
% 4.14/1.28 %
% 4.14/1.28
% 4.14/1.28 % ------ Proving...
% 4.14/1.28 %
% 4.14/1.28
% 4.14/1.28 % SZS status Theorem for theBenchmark.p
% 4.14/1.28
% 4.14/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.14/1.28
% 4.14/1.28
%------------------------------------------------------------------------------