%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC104+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 : n007.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 03:07:54 PM UTC 2026
% Result : Theorem 4.00s 6.28s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f297ERROR: Could not build tree for root c_3684ERROR: 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(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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( frontsegP(X1,X0)
& neq(X0,nil) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ totalorderedP(X2)
| app(X2,X4) != X3 ) )
| ~ 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)
=> ( ( frontsegP(X1,X0)
& neq(X0,nil) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ totalorderedP(X2)
| app(X2,X4) != X3 ) )
| ~ neq(X1,nil)
| 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)
& ( ~ frontsegP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& totalorderedP(X2)
& app(X2,X4) = X3 )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ frontsegP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& totalorderedP(X2)
& app(X2,X4) = X3 )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f168,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( nil != sK2
| nil = sK3 )
& ssList(sK4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != sK2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& totalorderedP(sK2)
& sK3 = app(sK2,sK4)
& neq(sK1,nil)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f173,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f178,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,[],[f130]) ).
fof(f179,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,[],[f178]) ).
fof(f180,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK9(X0,X1)) = X0
& ssList(sK9(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1))],[f179]) ).
fof(f190,plain,
ssList(sK0),
inference(cnf_transformation,[],[f168]) ).
fof(f191,plain,
ssList(sK1),
inference(cnf_transformation,[],[f168]) ).
fof(f194,plain,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(cnf_transformation,[],[f168]) ).
fof(f195,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f168]) ).
fof(f196,plain,
ssList(sK4),
inference(cnf_transformation,[],[f168]) ).
fof(f199,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f168]) ).
fof(f200,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f168]) ).
fof(f201,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f168]) ).
fof(f202,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f168]) ).
fof(f224,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f226,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
fof(f229,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f281,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f200,f202]) ).
fof(f282,plain,
( ~ frontsegP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(definition_unfolding,[],[f194,f201,f202,f201]) ).
fof(f283,plain,
ssList(sK3),
inference(definition_unfolding,[],[f191,f202]) ).
fof(f284,plain,
ssList(sK2),
inference(definition_unfolding,[],[f190,f201]) ).
fof(f291,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f242]) ).
tcf(c_49,negated_conjecture,
neq(sK3,nil),
inference(cnf_transformation,[],[f281]) ).
tcf(c_50,negated_conjecture,
app(sK2,sK4) = sK3,
inference(cnf_transformation,[],[f199]) ).
tcf(c_53,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f196]) ).
tcf(c_54,negated_conjecture,
( ( sK3 = nil )
| ( nil != sK2 ) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_55,negated_conjecture,
( ~ frontsegP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_58,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f283]) ).
tcf(c_59,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f284]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_83,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f297]) ).
tcf(c_86,plain,
ssList(nil),
inference(cnf_transformation,[],[f229]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_97,c_81]) ).
tcf(c_1319,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_83]) ).
tcf(c_1320,plain,
( ~ ssList(sK3)
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_1319]) ).
tcf(c_1339,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK3,sK2)
| ( X1 != sK2 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_82]) ).
tcf(c_1340,plain,
( ( nil = sK2 )
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ frontsegP(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_1339]) ).
tcf(c_1341,plain,
~ frontsegP(sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_1340,c_59,c_58,c_86,c_54,c_1320,c_1340]) ).
tcf(c_3682,plain,
( frontsegP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_50,c_311]) ).
tcf(c_3684,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3682,c_1341,c_53,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC104+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 16:22:13 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 4.00/6.28 % SZS status Started for theBenchmark.p
% 4.00/6.28 % SZS status Theorem for theBenchmark.p
% 4.00/6.28
% 4.00/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.00/6.28
% 4.00/6.28 % ------ iProver source info
% 4.00/6.28
% 4.00/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.00/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.00/6.28 % git: non_committed_changes: false
% 4.00/6.28
% 4.00/6.28 % ------ Parsing...
% 4.00/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.00/6.28
% 4.00/6.28 % ------ 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 %
% 4.00/6.28
% 4.00/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.00/6.28
% 4.00/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.00/6.28 % ------ Proving...
% 4.00/6.28 % ------ Problem Properties
% 4.00/6.28
% 4.00/6.28 %
% 4.00/6.28 % clauses 79
% 4.00/6.28 % conjectures 6
% 4.00/6.28 % EPR 27
% 4.00/6.28 % Horn 56
% 4.00/6.28 % unary 15
% 4.00/6.28 % binary 7
% 4.00/6.28 % lits 268
% 4.00/6.28 % lits eq 61
% 4.00/6.28 % fd_pure 0
% 4.00/6.28 % fd_pseudo 0
% 4.00/6.28 % fd_cond 16
% 4.00/6.28 % fd_pseudo_cond 9
% 4.00/6.28 % AC symbols 0
% 4.00/6.28
% 4.00/6.28 % ------ Schedule dynamic 5 is on
% 4.00/6.28
% 4.00/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.00/6.28
% 4.00/6.28
% 4.00/6.28 % ------
% 4.00/6.28 % Current options:
% 4.00/6.28 % ------
% 4.00/6.28
% 4.00/6.28
% 4.00/6.28 %
% 4.00/6.28
% 4.00/6.28 % ------ Proving...
% 4.00/6.28 %
% 4.00/6.28
% 4.00/6.28 % SZS status Theorem for theBenchmark.p
% 4.00/6.28
% 4.00/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.00/6.28
% 4.00/6.28
%------------------------------------------------------------------------------