%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC259+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 : n009.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 03:09:03 PM UTC 2026
% Result : Theorem 3.73s 6.28s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 10 unt; 1 def)
% Number of atoms : 175 ( 52 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 211 ( 71 ~; 65 |; 64 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 48 !; 24 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax66) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| totalorderedP(X0)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| totalorderedP(X0)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) )
& ~ totalorderedP(X0)
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f132,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f65]) ).
fof(f163,plain,
( ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ( ( nil = sK6
& nil = sK7 )
| sP0(sK6,sK7) )
& ~ totalorderedP(sK4)
& sK4 = sK6
& sK5 = sK7
& ssList(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f159]) ).
fof(f194,plain,
( nil = sK6
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f163]) ).
fof(f196,plain,
~ totalorderedP(sK4),
inference(cnf_transformation,[],[f163]) ).
fof(f197,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f163]) ).
fof(f247,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f248,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f272,plain,
~ totalorderedP(sK6),
inference(definition_unfolding,[],[f196,f197]) ).
tcf(c_57,negated_conjecture,
~ totalorderedP(sK6),
inference(cnf_transformation,[],[f272]) ).
tcf(c_59,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK6 ) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_109,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f247]) ).
tcf(c_110,plain,
! [X0: $i] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f158,definition,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f159,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ~ totalorderedP(X0)
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(definition_folding,[],[f98,f158]) ).
fof(f160,plain,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) ),
inference(nnf_transformation,[],[f158]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X6] :
( ~ lt(X6,X2)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(X2,X5)
| ~ memberP(X3,X5)
| ~ ssItem(X5) )
& app(app(X3,X0),X4) = X1
& cons(X2,nil) = X0
& ssList(X4) ) ) ) ),
inference(rectify,[],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ssItem(sK1(X0,X1))
& ssList(sK2(X0,X1))
& ! [X6] :
( ~ lt(X6,sK1(X0,X1))
| ~ memberP(sK3(X0,X1),X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(sK1(X0,X1),X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ ssItem(X5) )
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& cons(sK1(X0,X1),nil) = X0
& ssList(sK3(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f161]) ).
fof(f184,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f162]) ).
fof(f189,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK1(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( cons(sK1(X0,X1),nil) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_1275,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ( nil = sK6 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_59]) ).
tcf(c_1276,plain,
( ssItem(sK1(sK6,sK7))
| ( nil = sK6 ) ),
inference(unflattening,[status(thm)],[c_1275]) ).
tcf(c_1383,plain,
! [X0: $i,X1: $i] :
( ( nil = sK6 )
| ( cons(sK1(X0,X1),nil) = X0 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_59]) ).
tcf(c_1384,plain,
( ( nil = sK6 )
| ( cons(sK1(sK6,sK7),nil) = sK6 ) ),
inference(unflattening,[status(thm)],[c_1383]) ).
tcf(c_2909,plain,
( totalorderedP(sK6)
| ( nil = sK6 )
| ~ ssItem(sK1(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_1384,c_110]) ).
tcf(c_2910,plain,
( ( nil = sK6 )
| ~ ssItem(sK1(sK6,sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2909,c_57]) ).
tcf(c_2987,plain,
nil = sK6,
inference(global_subsumption_just,[status(thm)],[c_2910,c_1276,c_2910]) ).
tcf(c_3000,plain,
~ totalorderedP(nil),
inference(demodulation,[status(thm)],[c_57,c_2987]) ).
tcf(c_3002,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3000,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC259+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 17:16:50 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.42 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 3.73/6.28 % SZS status Started for theBenchmark.p
% 3.73/6.28 % SZS status Theorem for theBenchmark.p
% 3.73/6.28
% 3.73/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.73/6.28
% 3.73/6.28 % ------ iProver source info
% 3.73/6.28
% 3.73/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.73/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.73/6.28 % git: non_committed_changes: false
% 3.73/6.28
% 3.73/6.28 % ------ Parsing...
% 3.73/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.73/6.28
% 3.73/6.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 3.73/6.28
% 3.73/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.73/6.28
% 3.73/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.73/6.28 % ------ Proving...
% 3.73/6.28 % ------ Problem Properties
% 3.73/6.28
% 3.73/6.28 %
% 3.73/6.28 % clauses 85
% 3.73/6.28 % conjectures 3
% 3.73/6.28 % EPR 18
% 3.73/6.28 % Horn 50
% 3.73/6.28 % unary 9
% 3.73/6.28 % binary 16
% 3.73/6.28 % lits 289
% 3.73/6.28 % lits eq 72
% 3.73/6.28 % fd_pure 0
% 3.73/6.28 % fd_pseudo 0
% 3.73/6.28 % fd_cond 15
% 3.73/6.28 % fd_pseudo_cond 8
% 3.73/6.28 % AC symbols 0
% 3.73/6.28
% 3.73/6.28 % ------ Schedule dynamic 5 is on
% 3.73/6.28
% 3.73/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.73/6.28
% 3.73/6.28
% 3.73/6.28 % ------
% 3.73/6.28 % Current options:
% 3.73/6.28 % ------
% 3.73/6.28
% 3.73/6.28
% 3.73/6.28 %
% 3.73/6.28
% 3.73/6.28 % ------ Proving...
% 3.73/6.28 %
% 3.73/6.28
% 3.73/6.28 % SZS status Theorem for theBenchmark.p
% 3.73/6.28
% 3.73/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.73/6.28
% 3.73/6.28
%------------------------------------------------------------------------------