%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC118+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 : n004.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 03:07:58 PM UTC 2026
% Result : Theorem 2.79s 1.16s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 20 unt; 0 def)
% Number of atoms : 286 ( 89 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 381 ( 145 ~; 130 |; 86 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 74 !; 36 ?; 7 :)
% 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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),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)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| 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)
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f129,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(f167,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK2
| nil = sK3 )
& ssList(sK4)
& ssList(sK5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X12,X10)
| app(X13,cons(X12,nil)) != sK2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != sK5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X6,X8)
| app(cons(X8,nil),X9) != sK2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != sK4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& totalorderedP(sK2)
& sK3 = app(app(sK4,sK2),sK5)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f99]) ).
fof(f172,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f175,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,[],[f129]) ).
fof(f176,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,[],[f175]) ).
fof(f177,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK10(X0,X1),X1),sK11(X0,X1)) = X0
& ssList(sK11(X0,X1))
& ssList(sK10(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f176]) ).
fof(f187,plain,
ssList(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f188,plain,
ssList(sK1),
inference(cnf_transformation,[],[f167]) ).
fof(f191,plain,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(cnf_transformation,[],[f167]) ).
fof(f192,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f167]) ).
fof(f193,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f167]) ).
fof(f194,plain,
ssList(sK4),
inference(cnf_transformation,[],[f167]) ).
fof(f195,plain,
ssList(sK5),
inference(cnf_transformation,[],[f167]) ).
fof(f199,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f167]) ).
fof(f200,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f167]) ).
fof(f201,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f167]) ).
fof(f225,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
fof(f228,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f239,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,[],[f177]) ).
fof(f278,plain,
( nil != sK2
| nil != sK3 ),
inference(definition_unfolding,[],[f192,f201,f200]) ).
fof(f279,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(definition_unfolding,[],[f191,f200,f201,f200]) ).
fof(f280,plain,
ssList(sK3),
inference(definition_unfolding,[],[f188,f201]) ).
fof(f281,plain,
ssList(sK2),
inference(definition_unfolding,[],[f187,f200]) ).
fof(f287,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,[],[f239]) ).
tcf(c_49,negated_conjecture,
app(app(sK4,sK2),sK5) = sK3,
inference(cnf_transformation,[],[f199]) ).
tcf(c_53,negated_conjecture,
ssList(sK5),
inference(cnf_transformation,[],[f195]) ).
tcf(c_54,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f194]) ).
tcf(c_55,negated_conjecture,
( ( sK3 = nil )
| ( sK2 != nil ) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_56,negated_conjecture,
( ( sK2 != nil )
| ( sK3 != nil ) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_57,negated_conjecture,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_60,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f280]) ).
tcf(c_61,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f281]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_88,plain,
ssList(nil),
inference(cnf_transformation,[],[f228]) ).
tcf(c_96,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,[],[f287]) ).
tcf(c_183,negated_conjecture,
sK2 != nil,
inference(global_subsumption_just,[status(thm)],[c_55,c_55,c_56]) ).
tcf(c_1299,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK3,sK2)
| ( X1 != nil )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_84]) ).
tcf(c_1300,plain,
( ( sK2 = nil )
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ segmentP(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_1299]) ).
tcf(c_1301,plain,
~ segmentP(sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_1300,c_61,c_88,c_183,c_1300]) ).
tcf(c_8210,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK5)
| ~ ssList(sK2)
| ~ ssList(sK4)
| ~ ssList(app(app(sK4,sK2),sK5)) ),
inference(superposition,[status(thm)],[c_49,c_96]) ).
tcf(c_8233,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK5)
| ~ ssList(sK2)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(light_normalisation,[status(thm)],[c_8210,c_49]) ).
tcf(c_8234,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8233,c_1301,c_53,c_61,c_54,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC118+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 16:29:24 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 Running first-order theorem proving
% 0.11/0.38 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
% 0.11/0.39
% 0.11/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.39
% 0.11/0.39 % Detected problem language: tptp
% 0.11/0.40 % Proving...
% 2.79/1.16 % SZS status Started for theBenchmark.p
% 2.79/1.16 % SZS status Theorem for theBenchmark.p
% 2.79/1.16
% 2.79/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.79/1.16
% 2.79/1.16 % ------ iProver source info
% 2.79/1.16
% 2.79/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.79/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.79/1.16 % git: non_committed_changes: false
% 2.79/1.16
% 2.79/1.16 % ------ Parsing...
% 2.79/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.79/1.16
% 2.79/1.16 % ------ 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 %
% 2.79/1.16
% 2.79/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.79/1.16
% 2.79/1.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.79/1.16 % ------ Proving...
% 2.79/1.16 % ------ Problem Properties
% 2.79/1.16
% 2.79/1.16 %
% 2.79/1.16 % clauses 78
% 2.79/1.16 % conjectures 9
% 2.79/1.16 % EPR 27
% 2.79/1.16 % Horn 55
% 2.79/1.16 % unary 15
% 2.79/1.16 % binary 7
% 2.79/1.16 % lits 265
% 2.79/1.16 % lits eq 61
% 2.79/1.16 % fd_pure 0
% 2.79/1.16 % fd_pseudo 0
% 2.79/1.16 % fd_cond 16
% 2.79/1.16 % fd_pseudo_cond 8
% 2.79/1.16 % AC symbols 0
% 2.79/1.16
% 2.79/1.16 % ------ Schedule dynamic 5 is on
% 2.79/1.16
% 2.79/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.79/1.16
% 2.79/1.16
% 2.79/1.16 % ------
% 2.79/1.16 % Current options:
% 2.79/1.16 % ------
% 2.79/1.16
% 2.79/1.16
% 2.79/1.16 %
% 2.79/1.16
% 2.79/1.16 % ------ Proving...
% 2.79/1.16 %
% 2.79/1.16
% 2.79/1.16 % SZS status Theorem for theBenchmark.p
% 2.79/1.16
% 2.79/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.79/1.16
%------------------------------------------------------------------------------