%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC101+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 : n016.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 2.86s 1.28s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 228 ( 79 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 293 ( 114 ~; 100 |; 59 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 61 !; 20 ?; 10 :)
% 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 = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(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)
=> ( ( frontsegP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != 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)
& ( ~ frontsegP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& 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 != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& 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(f134,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK2
| nil = sK3 )
& ssList(sK4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& sK3 = app(sK2,sK4)
& 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(f139,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f144,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(f145,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,[],[f144]) ).
fof(f146,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))],[f145]) ).
fof(f150,plain,
ssList(sK0),
inference(cnf_transformation,[],[f134]) ).
fof(f154,plain,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(cnf_transformation,[],[f134]) ).
fof(f155,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f134]) ).
fof(f157,plain,
ssList(sK4),
inference(cnf_transformation,[],[f134]) ).
fof(f160,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f134]) ).
fof(f161,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f134]) ).
fof(f162,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f134]) ).
fof(f184,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f186,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f189,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f212,plain,
( nil != sK2
| nil != sK3 ),
inference(definition_unfolding,[],[f155,f162,f161]) ).
fof(f213,plain,
( ~ frontsegP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(definition_unfolding,[],[f154,f161,f162,f161]) ).
fof(f215,plain,
ssList(sK2),
inference(definition_unfolding,[],[f150,f161]) ).
fof(f222,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f202]) ).
tcf(c_49,negated_conjecture,
app(sK2,sK4) = sK3,
inference(cnf_transformation,[],[f160]) ).
tcf(c_52,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f157]) ).
tcf(c_53,negated_conjecture,
( ( sK3 = nil )
| ( sK2 != nil ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_54,negated_conjecture,
( ( sK2 != nil )
| ( sK3 != nil ) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_55,negated_conjecture,
( ~ frontsegP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_59,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f215]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_86,plain,
ssList(nil),
inference(cnf_transformation,[],[f189]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_139,negated_conjecture,
sK2 != nil,
inference(global_subsumption_just,[status(thm)],[c_53,c_53,c_54]) ).
tcf(c_251,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_846,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK3,sK2)
| ( X1 != nil )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_82]) ).
tcf(c_847,plain,
( ( sK2 = nil )
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ frontsegP(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_846]) ).
tcf(c_848,plain,
~ frontsegP(sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_847,c_59,c_86,c_139,c_847]) ).
tcf(c_2950,plain,
( frontsegP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_49,c_251]) ).
tcf(c_2964,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2950,c_848,c_52,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC101+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n016.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Thu Sep 24 16:28:12 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.40 Running first-order theorem proving
% 0.16/0.40 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
% 0.16/0.41
% 0.16/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.41
% 0.16/0.41 % Detected problem language: tptp
% 0.16/0.42 % Proving...
% 2.86/1.28 % SZS status Started for theBenchmark.p
% 2.86/1.28 % SZS status Theorem for theBenchmark.p
% 2.86/1.28
% 2.86/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.86/1.28
% 2.86/1.28 % ------ iProver source info
% 2.86/1.28
% 2.86/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.86/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.86/1.28 % git: non_committed_changes: false
% 2.86/1.28
% 2.86/1.28 % ------ Parsing...
% 2.86/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.86/1.28
% 2.86/1.28 % ------ 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 %
% 2.86/1.28
% 2.86/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.86/1.28
% 2.86/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.86/1.28 % ------ Proving...
% 2.86/1.28 % ------ Problem Properties
% 2.86/1.28
% 2.86/1.28 %
% 2.86/1.28 % clauses 53
% 2.86/1.28 % conjectures 7
% 2.86/1.28 % EPR 17
% 2.86/1.28 % Horn 45
% 2.86/1.28 % unary 14
% 2.86/1.28 % binary 5
% 2.86/1.28 % lits 163
% 2.86/1.28 % lits eq 36
% 2.86/1.28 % fd_pure 0
% 2.86/1.28 % fd_pseudo 0
% 2.86/1.28 % fd_cond 5
% 2.86/1.28 % fd_pseudo_cond 7
% 2.86/1.28 % AC symbols 0
% 2.86/1.28
% 2.86/1.28 % ------ Schedule dynamic 5 is on
% 2.86/1.28
% 2.86/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.86/1.28
% 2.86/1.28
% 2.86/1.28 % ------
% 2.86/1.28 % Current options:
% 2.86/1.28 % ------
% 2.86/1.28
% 2.86/1.28
% 2.86/1.28 %
% 2.86/1.28
% 2.86/1.28 % ------ Proving...
% 2.86/1.28 %
% 2.86/1.28
% 2.86/1.28 % SZS status Theorem for theBenchmark.p
% 2.86/1.28
% 2.86/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.86/1.28
% 2.86/1.28
%------------------------------------------------------------------------------