%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC353+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 : n005.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 03:09:25 PM UTC 2026
% Result : Theorem 3.53s 1.18s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 19 unt; 1 def)
% Number of atoms : 183 ( 50 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 221 ( 80 ~; 70 |; 55 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 52 !; 22 ?; 6 :)
% 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(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)
=> ( ( nil = X2
& nil != X3 )
| frontsegP(X1,X0)
| ! [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 ) )
| 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)
=> ( ( nil = X2
& nil != X3 )
| frontsegP(X1,X0)
| ! [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 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X2
| nil = X3 )
& ~ frontsegP(X1,X0)
& ? [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 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X2
| nil = X3 )
& ~ frontsegP(X1,X0)
& ? [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 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f240,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,[],[f101]) ).
fof(f241,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,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( nil != sK55
| nil = sK56 )
& ~ frontsegP(sK54,sK53)
& ssList(sK57)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != sK55
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK57
| ~ ssList(X6) )
| ~ ssItem(X5) )
& totalorderedP(sK55)
& sK56 = app(sK55,sK57)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
~ frontsegP(sK54,sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK56 = app(sK55,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
~ frontsegP(sK56,sK55),
inference(definition_unfolding,[],[f501,f507,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f514,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_246,negated_conjecture,
app(sK55,sK57) = sK56,
inference(cnf_transformation,[],[f505]) ).
tcf(c_249,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f502]) ).
tcf(c_250,negated_conjecture,
~ frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f508]) ).
tcf(c_255,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
tcf(c_8858,definition,
iPr_def_10 = app(sK55,sK57),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8859,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_255]) ).
tcf(c_8862,negated_conjecture,
~ frontsegP(sK56,sK55),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_8863,negated_conjecture,
ssList(sK57),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8866,negated_conjecture,
iPr_def_10 = sK56,
inference(demodulation,[status(thm)],[c_246,c_8858]) ).
tcf(c_11703,plain,
~ frontsegP(iPr_def_10,sK55),
inference(light_normalisation,[status(thm)],[c_8862,c_8866]) ).
tcf(c_11796,plain,
( frontsegP(iPr_def_10,sK55)
| ~ ssList(sK57)
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8858,c_378]) ).
tcf(c_11797,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11796,c_11703,c_8863,c_8859]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC353+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 17:47:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 3.53/1.18 % SZS status Started for theBenchmark.p
% 3.53/1.18 % SZS status Theorem for theBenchmark.p
% 3.53/1.18
% 3.53/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.53/1.18
% 3.53/1.18 % ------ iProver source info
% 3.53/1.18
% 3.53/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.53/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.53/1.18 % git: non_committed_changes: false
% 3.53/1.18
% 3.53/1.18 % ------ Parsing...
% 3.53/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.53/1.18
% 3.53/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 3.53/1.18
% 3.53/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.53/1.18
% 3.53/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.53/1.18 % ------ Proving...
% 3.53/1.18 % ------ Problem Properties
% 3.53/1.18
% 3.53/1.18 %
% 3.53/1.18 % clauses 189
% 3.53/1.18 % conjectures 8
% 3.53/1.18 % EPR 56
% 3.53/1.18 % Horn 121
% 3.53/1.18 % unary 23
% 3.53/1.18 % binary 41
% 3.53/1.18 % lits 634
% 3.53/1.18 % lits eq 84
% 3.53/1.18 % fd_pure 0
% 3.53/1.18 % fd_pseudo 0
% 3.53/1.18 % fd_cond 21
% 3.53/1.18 % fd_pseudo_cond 14
% 3.53/1.18 % AC symbols 0
% 3.53/1.18
% 3.53/1.18 % ------ Schedule dynamic 5 is on
% 3.53/1.18
% 3.53/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.53/1.18
% 3.53/1.18
% 3.53/1.18 % ------
% 3.53/1.18 % Current options:
% 3.53/1.18 % ------
% 3.53/1.18
% 3.53/1.18
% 3.53/1.18 %
% 3.53/1.18
% 3.53/1.18 % ------ Proving...
% 3.53/1.18 %
% 3.53/1.18
% 3.53/1.18 % SZS status Theorem for theBenchmark.p
% 3.53/1.18
% 3.53/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.53/1.18
% 3.53/1.18
%------------------------------------------------------------------------------