%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC008+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 : n013.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 03:07:29 PM UTC 2026
% Result : Theorem 4.46s 1.27s
% Output : CNFRefutation 4.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f247ERROR: Could not build tree for root c_5711ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X7] :
( equalelemsP(X7)
& segmentP(X7,X2)
& frontsegP(X3,X7)
& neq(X2,X7)
& ssList(X7) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| 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)
=> ( ? [X7] :
( equalelemsP(X7)
& segmentP(X7,X2)
& frontsegP(X3,X7)
& neq(X2,X7)
& ssList(X7) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ! [X7] :
( ~ equalelemsP(X7)
| ~ segmentP(X7,X2)
| ~ frontsegP(X3,X7)
| ~ neq(X2,X7)
| ~ ssList(X7) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ! [X7] :
( ~ equalelemsP(X7)
| ~ segmentP(X7,X2)
| ~ frontsegP(X3,X7)
| ~ neq(X2,X7)
| ~ ssList(X7) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f144,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ! [X7] :
( ~ equalelemsP(X7)
| ~ segmentP(X7,sK2)
| ~ frontsegP(sK3,X7)
| ~ neq(sK2,X7)
| ~ ssList(X7) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X4,X6) != sK0
| app(app(X4,X5),X6) != sK1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& equalelemsP(sK2)
& frontsegP(sK3,sK2)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f146,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,[],[f101]) ).
fof(f147,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,[],[f146]) ).
fof(f153,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f123]) ).
fof(f154,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f153]) ).
fof(f155,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK6(X0,X1)) = X0
& ssList(sK6(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1))],[f154]) ).
fof(f164,plain,
ssList(sK0),
inference(cnf_transformation,[],[f144]) ).
fof(f165,plain,
ssList(sK1),
inference(cnf_transformation,[],[f144]) ).
fof(f169,plain,
! [X6,X4,X5] :
( app(X4,X6) != sK0
| app(app(X4,X5),X6) != sK1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f144]) ).
fof(f171,plain,
frontsegP(sK3,sK2),
inference(cnf_transformation,[],[f144]) ).
fof(f172,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f144]) ).
fof(f173,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f144]) ).
fof(f177,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f100]) ).
fof(f178,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f185,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f108]) ).
fof(f202,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK6(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f155]) ).
fof(f203,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ssList(sK6(X0,X1)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f229,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f234,plain,
! [X6,X4,X5] :
( app(X4,X6) != sK2
| app(app(X4,X5),X6) != sK3
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f169,f173,f172]) ).
fof(f235,plain,
ssList(sK3),
inference(definition_unfolding,[],[f165,f173]) ).
fof(f236,plain,
ssList(sK2),
inference(definition_unfolding,[],[f164,f172]) ).
tcf(c_49,negated_conjecture,
frontsegP(sK3,sK2),
inference(cnf_transformation,[],[f171]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X2) != sK2 )
| ( app(app(X0,X1),X2) != sK3 ) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_55,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f235]) ).
tcf(c_56,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f236]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_61,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ssList(sK6(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ( app(X1,sK6(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_112,plain,
ssList(nil),
inference(cnf_transformation,[],[f229]) ).
tcf(c_122,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_157,plain,
app(nil,nil) = nil,
inference(global_subsumption_just,[status(thm)],[c_61,c_112,c_122]) ).
tcf(c_3841,plain,
app(sK3,nil) = sK3,
inference(superposition,[status(thm)],[c_55,c_60]) ).
tcf(c_3842,plain,
app(sK2,nil) = sK2,
inference(superposition,[status(thm)],[c_56,c_60]) ).
tcf(c_3856,plain,
app(nil,sK3) = sK3,
inference(superposition,[status(thm)],[c_55,c_68]) ).
tcf(c_3918,plain,
! [X0: $i] :
( ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssList(X0)
| ( app(nil,X0) != sK2 )
| ( app(sK3,X0) != sK3 ) ),
inference(superposition,[status(thm)],[c_3856,c_51]) ).
tcf(c_3923,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(nil,X0) != sK2 )
| ( app(sK3,X0) != sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3918,c_112,c_55]) ).
tcf(c_3959,plain,
( ~ ssList(nil)
| ( sK2 != nil )
| ( app(sK3,nil) != sK3 ) ),
inference(superposition,[status(thm)],[c_157,c_3923]) ).
tcf(c_3963,plain,
( ~ ssList(nil)
| ( sK2 != nil ) ),
inference(ground_joinability,[status(thm)],[c_3959,c_3841]) ).
tcf(c_3964,plain,
sK2 != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_3963,c_112]) ).
tcf(c_5286,plain,
( ( app(sK2,sK6(sK3,sK2)) = sK3 )
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_49,c_87]) ).
tcf(c_5306,plain,
app(sK2,sK6(sK3,sK2)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_5286,c_56,c_55]) ).
tcf(c_5614,plain,
( ( sK2 = nil )
| ~ ssList(sK2)
| ~ ssList(sK6(sK3,sK2))
| ( sK3 != nil ) ),
inference(superposition,[status(thm)],[c_5306,c_63]) ).
tcf(c_5618,plain,
! [X0: $i] :
( ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK6(sK3,sK2))
| ( app(sK2,X0) != sK2 )
| ( app(sK3,X0) != sK3 ) ),
inference(superposition,[status(thm)],[c_5306,c_51]) ).
tcf(c_5622,plain,
( ~ ssList(sK6(sK3,sK2))
| ( sK3 != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5614,c_3964,c_56]) ).
tcf(c_5630,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssList(sK6(sK3,sK2))
| ( app(sK2,X0) != sK2 )
| ( app(sK3,X0) != sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5618,c_56]) ).
tcf(c_5635,plain,
( ~ ssList(nil)
| ~ ssList(sK6(sK3,sK2))
| ( app(sK2,nil) != sK2 )
| ( app(sK3,nil) != sK3 ) ),
inference(instantiation,[status(thm)],[c_5630]) ).
tcf(c_5708,plain,
~ ssList(sK6(sK3,sK2)),
inference(global_subsumption_just,[status(thm)],[c_5622,c_112,c_3842,c_3841,c_5635]) ).
tcf(c_5710,plain,
( ~ ssList(sK2)
| ~ ssList(sK3)
| ~ frontsegP(sK3,sK2) ),
inference(superposition,[status(thm)],[c_86,c_5708]) ).
tcf(c_5711,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5710,c_56,c_55,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC008+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.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 15:52:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 4.46/1.27 % SZS status Started for theBenchmark.p
% 4.46/1.27 % SZS status Theorem for theBenchmark.p
% 4.46/1.27
% 4.46/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.46/1.27
% 4.46/1.27 % ------ iProver source info
% 4.46/1.27
% 4.46/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.46/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.46/1.27 % git: non_committed_changes: false
% 4.46/1.27
% 4.46/1.27 % ------ Parsing...
% 4.46/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.46/1.27
% 4.46/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.46/1.27
% 4.46/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.46/1.27
% 4.46/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.46/1.27 % ------ Proving...
% 4.46/1.27 % ------ Problem Properties
% 4.46/1.27
% 4.46/1.27 %
% 4.46/1.27 % clauses 62
% 4.46/1.27 % conjectures 5
% 4.46/1.27 % EPR 22
% 4.46/1.27 % Horn 54
% 4.46/1.27 % unary 12
% 4.46/1.27 % binary 7
% 4.46/1.27 % lits 207
% 4.46/1.27 % lits eq 38
% 4.46/1.27 % fd_pure 0
% 4.46/1.27 % fd_pseudo 0
% 4.46/1.27 % fd_cond 7
% 4.46/1.27 % fd_pseudo_cond 8
% 4.46/1.27 % AC symbols 0
% 4.46/1.27
% 4.46/1.27 % ------ Schedule dynamic 5 is on
% 4.46/1.27
% 4.46/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.46/1.27
% 4.46/1.27
% 4.46/1.27 % ------
% 4.46/1.27 % Current options:
% 4.46/1.27 % ------
% 4.46/1.27
% 4.46/1.27
% 4.46/1.27 %
% 4.46/1.27
% 4.46/1.27 % ------ Proving...
% 4.46/1.27 %
% 4.46/1.27
% 4.46/1.27 % SZS status Theorem for theBenchmark.p
% 4.46/1.27
% 4.46/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.46/1.27
% 4.46/1.27
%------------------------------------------------------------------------------