%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC317+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 : n006.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 03:09:17 PM UTC 2026
% Result : Theorem 4.74s 1.54s
% Output : CNFRefutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 45 ( 9 unt; 1 def)
% Number of atoms : 213 ( 80 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 270 ( 102 ~; 90 |; 66 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 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 : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn 113 !; 26 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X3
| app(cons(X6,nil),X7) != X2 ) ) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& app(cons(X4,nil),X5) = X0
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| 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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X3
| app(cons(X6,nil),X7) != X2 ) ) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& app(cons(X4,nil),X5) = X0
& ssList(X5) )
& ssItem(X4) )
| ~ 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)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& app(cons(X6,nil),X7) = X2 ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| app(cons(X4,nil),X5) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& 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)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& app(cons(X6,nil),X7) = X2 ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| app(cons(X4,nil),X5) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f125,plain,
( ssList(sK3)
& ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ( ( ~ neq(sK6,nil)
& neq(sK4,nil) )
| sP0(sK4,sK3,sK5,sK6) )
& sK3 = sK5
& sK4 = sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f121]) ).
fof(f142,plain,
( ~ neq(sK6,nil)
| sP0(sK4,sK3,sK5,sK6) ),
inference(cnf_transformation,[],[f125]) ).
fof(f143,plain,
( neq(sK4,nil)
| sP0(sK4,sK3,sK5,sK6) ),
inference(cnf_transformation,[],[f125]) ).
fof(f144,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f125]) ).
fof(f145,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f125]) ).
fof(f173,plain,
( neq(sK6,nil)
| sP0(sK6,sK5,sK5,sK6) ),
inference(definition_unfolding,[],[f143,f145,f144,f145]) ).
fof(f174,plain,
( ~ neq(sK6,nil)
| sP0(sK6,sK5,sK5,sK6) ),
inference(definition_unfolding,[],[f142,f145,f144]) ).
tcf(c_55,negated_conjecture,
( neq(sK6,nil)
| sP0(sK6,sK5,sK5,sK6) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_56,negated_conjecture,
( sP0(sK6,sK5,sK5,sK6)
| ~ neq(sK6,nil) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_111,negated_conjecture,
sP0(sK6,sK5,sK5,sK6),
inference(global_subsumption_just,[status(thm)],[c_55,c_55,c_56]) ).
tcf(c_113,negated_conjecture,
sP0(sK6,sK5,sK5,sK6),
inference(global_subsumption_just,[status(thm)],[c_56,c_111]) ).
fof(f120,definition,
! [X1,X0,X2,X3] :
( ~ sP0(X1,X0,X2,X3)
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& app(cons(X6,nil),X7) = X2 ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| app(cons(X4,nil),X5) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f121,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP0(X1,X0,X2,X3) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f120]) ).
fof(f122,plain,
! [X1,X0,X2,X3] :
( ~ sP0(X1,X0,X2,X3)
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& app(cons(X6,nil),X7) = X2 ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| app(cons(X4,nil),X5) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& app(cons(X6,nil),X7) = X2 ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ssItem(sK1(X2,X3))
& ssList(sK2(X2,X3))
& app(sK2(X2,X3),cons(sK1(X2,X3),nil)) = X3
& app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X2
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X6,sK1(X2,X3)),skolemize(X7,sK2(X2,X3))],[f123]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK2(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(sK2(X2,X3),cons(sK1(X2,X3),nil)) = X3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X2 ),
inference(cnf_transformation,[],[f124]) ).
fof(f136,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP0(X0,X1,X2,X3)
| app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f124]) ).
fof(f177,plain,
! [X2,X3,X0,X4,X5] :
( ~ sP0(X0,app(cons(X4,nil),X5),X2,X3)
| app(X5,cons(X4,nil)) != X0
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f136]) ).
fof(f178,plain,
! [X2,X3,X4,X5] :
( ~ sP0(app(X5,cons(X4,nil)),app(cons(X4,nil),X5),X2,X3)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f177]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ sP0(app(X0,cons(X1,nil)),app(cons(X1,nil),X0),X2,X3) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X2 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK2(X2,X3),cons(sK1(X2,X3),nil)) = X3 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK2(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X2,X3))
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_113]) ).
tcf(c_505,plain,
ssItem(sK1(sK5,sK6)),
inference(unflattening,[status(thm)],[c_504]) ).
tcf(c_509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK2(X2,X3))
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_113]) ).
tcf(c_510,plain,
ssList(sK2(sK5,sK6)),
inference(unflattening,[status(thm)],[c_509]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK2(X2,X3),cons(sK1(X2,X3),nil)) = X3 )
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_113]) ).
tcf(c_515,plain,
app(sK2(sK5,sK6),cons(sK1(sK5,sK6),nil)) = sK6,
inference(unflattening,[status(thm)],[c_514]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X2 )
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_113]) ).
tcf(c_520,plain,
app(cons(sK1(sK5,sK6),nil),sK2(sK5,sK6)) = sK5,
inference(unflattening,[status(thm)],[c_519]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( app(X1,cons(X0,nil)) != sK6 )
| ( app(cons(X0,nil),X1) != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_113]) ).
tcf(c_530,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( app(X1,cons(X0,nil)) != sK6 )
| ( app(cons(X0,nil),X1) != sK5 ) ),
inference(unflattening,[status(thm)],[c_529]) ).
tcf(c_1325,plain,
( ~ ssList(sK2(sK5,sK6))
| ~ ssItem(sK1(sK5,sK6))
| ( app(sK2(sK5,sK6),cons(sK1(sK5,sK6),nil)) != sK6 ) ),
inference(superposition,[status(thm)],[c_520,c_530]) ).
tcf(c_1326,plain,
( ~ ssList(sK2(sK5,sK6))
| ~ ssItem(sK1(sK5,sK6)) ),
inference(ground_joinability,[status(thm)],[c_1325,c_515]) ).
tcf(c_1327,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1326,c_510,c_505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC317+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.20/0.45 % Computer : n006.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Thu Sep 24 17:35:11 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.53
% 0.24/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.53
% 0.24/0.53 % Detected problem language: tptp
% 0.24/0.55 % Proving...
% 4.74/1.54 % SZS status Started for theBenchmark.p
% 4.74/1.54 % SZS status Theorem for theBenchmark.p
% 4.74/1.54
% 4.74/1.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.74/1.54
% 4.74/1.54 % ------ iProver source info
% 4.74/1.54
% 4.74/1.54 % git: date: 2026-07-19 20:42:38 +0200
% 4.74/1.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.74/1.54 % git: non_committed_changes: false
% 4.74/1.54
% 4.74/1.54 % ------ Parsing...
% 4.74/1.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.74/1.54
% 4.74/1.54 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.74/1.54
% 4.74/1.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.74/1.54
% 4.74/1.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.74/1.54 % ------ Proving...
% 4.74/1.54 % ------ Problem Properties
% 4.74/1.54
% 4.74/1.54 %
% 4.74/1.54 % clauses 31
% 4.74/1.54 % conjectures 2
% 4.74/1.54 % EPR 7
% 4.74/1.54 % Horn 28
% 4.74/1.54 % unary 12
% 4.74/1.54 % binary 2
% 4.74/1.54 % lits 82
% 4.74/1.54 % lits eq 30
% 4.74/1.54 % fd_pure 0
% 4.74/1.54 % fd_pseudo 0
% 4.74/1.54 % fd_cond 4
% 4.74/1.54 % fd_pseudo_cond 4
% 4.74/1.54 % AC symbols 0
% 4.74/1.54
% 4.74/1.54 % ------ Schedule dynamic 5 is on
% 4.74/1.54
% 4.74/1.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.74/1.54
% 4.74/1.54
% 4.74/1.54 % ------
% 4.74/1.54 % Current options:
% 4.74/1.54 % ------
% 4.74/1.54
% 4.74/1.54
% 4.74/1.54 %
% 4.74/1.54
% 4.74/1.54 % ------ Proving...
% 4.74/1.54 %
% 4.74/1.54
% 4.74/1.54 % SZS status Theorem for theBenchmark.p
% 4.74/1.54
% 4.74/1.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.74/1.54
% 4.74/1.54
%------------------------------------------------------------------------------