%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC068+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 : n002.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 03:07:45 PM UTC 2026
% Result : Theorem 4.28s 11.31s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f198ERROR: Could not build tree for root c_5359ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
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)
=> ( ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3
| app(X3,X3) != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3
| app(X3,X3) != X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X0
| nil != X1 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3
& app(X3,X3) = X2 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X0
| nil != X1 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3
& app(X3,X3) = X2 ) ) ) ),
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(f111,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f130,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( nil != sK0
| nil != sK1 )
& ! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& sK0 = sK2
& sK1 = sK3
& sK2 = app(sK3,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(f132,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(f133,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,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f111]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f125]) ).
fof(f139,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK8(X0,X1),X1),sK9(X0,X1)) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f139]) ).
fof(f141,plain,
ssList(sK0),
inference(cnf_transformation,[],[f130]) ).
fof(f142,plain,
ssList(sK1),
inference(cnf_transformation,[],[f130]) ).
fof(f145,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f130]) ).
fof(f146,plain,
! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f130]) ).
fof(f147,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f130]) ).
fof(f148,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f130]) ).
fof(f149,plain,
sK2 = app(sK3,sK3),
inference(cnf_transformation,[],[f130]) ).
fof(f153,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f100]) ).
fof(f155,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f133]) ).
fof(f161,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f108]) ).
fof(f165,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f172,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f177,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f188,plain,
! [X4] :
( ~ segmentP(sK2,X4)
| ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f146,f148,f147]) ).
fof(f189,plain,
( nil != sK2
| nil != sK3 ),
inference(definition_unfolding,[],[f145,f148,f147]) ).
fof(f190,plain,
ssList(sK3),
inference(definition_unfolding,[],[f142,f148]) ).
fof(f191,plain,
ssList(sK2),
inference(definition_unfolding,[],[f141,f147]) ).
fof(f197,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f183]) ).
tcf(c_49,negated_conjecture,
app(sK3,sK3) = sK2,
inference(cnf_transformation,[],[f149]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_51,negated_conjecture,
( ( sK3 != nil )
| ( sK2 != nil ) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_54,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f190]) ).
tcf(c_55,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f191]) ).
tcf(c_59,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_60,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_67,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_78,plain,
ssList(nil),
inference(cnf_transformation,[],[f172]) ).
tcf(c_83,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_97,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_120,plain,
app(nil,nil) = nil,
inference(global_subsumption_just,[status(thm)],[c_60,c_78,c_97]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_70]) ).
tcf(c_669,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK3,X0)
| ~ segmentP(sK2,X0) ),
inference(unflattening,[status(thm)],[c_668]) ).
tcf(c_671,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_669,c_78,c_669]) ).
tcf(c_672,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK3,X0)
| ~ segmentP(sK2,X0) ),
inference(renaming,[status(thm)],[c_671]) ).
tcf(c_1787,plain,
app(sK2,nil) = sK2,
inference(superposition,[status(thm)],[c_55,c_59]) ).
tcf(c_2384,plain,
( ( sK3 = nil )
| ~ ssList(sK3)
| ( sK2 != nil ) ),
inference(superposition,[status(thm)],[c_49,c_61]) ).
tcf(c_2397,plain,
( ( sK3 = nil )
| ( sK2 != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2384,c_54]) ).
tcf(c_2421,plain,
sK2 != nil,
inference(global_subsumption_just,[status(thm)],[c_2397,c_51,c_2397]) ).
tcf(c_4494,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK3)
| ~ ssList(sK3)
| ~ ssList(X0)
| ~ ssList(app(app(sK3,sK3),X0)) ),
inference(superposition,[status(thm)],[c_49,c_86]) ).
tcf(c_4523,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK3)
| ~ ssList(sK3)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_4494,c_49]) ).
tcf(c_4524,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK3)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4523,c_54]) ).
tcf(c_5058,plain,
( segmentP(sK2,sK3)
| ~ ssList(nil)
| ~ ssList(app(sK2,nil)) ),
inference(superposition,[status(thm)],[c_1787,c_4524]) ).
tcf(c_5063,plain,
( segmentP(sK2,sK3)
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(light_normalisation,[status(thm)],[c_5058,c_1787]) ).
tcf(c_5064,plain,
segmentP(sK2,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_5063,c_78,c_55]) ).
tcf(c_5104,plain,
( ( sK3 = nil )
| ~ ssList(sK3)
| ~ segmentP(sK3,sK3) ),
inference(superposition,[status(thm)],[c_5064,c_672]) ).
tcf(c_5108,plain,
( ( sK3 = nil )
| ~ segmentP(sK3,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5104,c_54]) ).
tcf(c_5315,plain,
( ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_83,c_5108]) ).
tcf(c_5316,plain,
sK3 = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_5315,c_54]) ).
tcf(c_5356,plain,
app(nil,nil) = sK2,
inference(demodulation,[status(thm)],[c_49,c_5316]) ).
tcf(c_5358,plain,
sK2 = nil,
inference(light_normalisation,[status(thm)],[c_5356,c_120]) ).
tcf(c_5359,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5358,c_2421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC068+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.39 % Computer : n002.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Thu Sep 24 16:15:33 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.12/10.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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
% 0.15/10.45
% 0.15/10.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.45
% 0.15/10.45 % Detected problem language: tptp
% 0.15/10.46 % Proving...
% 4.28/11.31 % SZS status Started for theBenchmark.p
% 4.28/11.31 % SZS status Theorem for theBenchmark.p
% 4.28/11.31
% 4.28/11.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.28/11.31
% 4.28/11.31 % ------ iProver source info
% 4.28/11.31
% 4.28/11.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.28/11.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.28/11.31 % git: non_committed_changes: false
% 4.28/11.31
% 4.28/11.31 % ------ Parsing...
% 4.28/11.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.28/11.31
% 4.28/11.31 % ------ 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 %
% 4.28/11.31
% 4.28/11.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.28/11.31
% 4.28/11.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.28/11.31 % ------ Proving...
% 4.28/11.31 % ------ Problem Properties
% 4.28/11.31
% 4.28/11.31 %
% 4.28/11.31 % clauses 39
% 4.28/11.31 % conjectures 4
% 4.28/11.31 % EPR 14
% 4.28/11.31 % Horn 36
% 4.28/11.31 % unary 9
% 4.28/11.31 % binary 5
% 4.28/11.31 % lits 122
% 4.28/11.31 % lits eq 32
% 4.28/11.31 % fd_pure 0
% 4.28/11.31 % fd_pseudo 0
% 4.28/11.31 % fd_cond 6
% 4.28/11.31 % fd_pseudo_cond 5
% 4.28/11.31 % AC symbols 0
% 4.28/11.31
% 4.28/11.31 % ------ Schedule dynamic 5 is on
% 4.28/11.31
% 4.28/11.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.28/11.31
% 4.28/11.31
% 4.28/11.31 % ------
% 4.28/11.31 % Current options:
% 4.28/11.31 % ------
% 4.28/11.31
% 4.28/11.31
% 4.28/11.31 %
% 4.28/11.31
% 4.28/11.31 % ------ Proving...
% 4.28/11.31 %
% 4.28/11.31
% 4.28/11.31 % SZS status Theorem for theBenchmark.p
% 4.28/11.31
% 4.28/11.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/11.32
% 4.28/11.32
%------------------------------------------------------------------------------