%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC309+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 : n014.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 03:09:14 PM UTC 2026
% Result : Theorem 25.87s 4.19s
% Output : CNFRefutation 25.87s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f173ERROR: Could not build tree for root c_50156ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) != X2
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X0
& app(cons(X4,nil),X5) = X1
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| 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 = X3
& nil != X2 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) != X2
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X0
& app(cons(X4,nil),X5) = X1
& 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)
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ 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)
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f103,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(flattening,[],[f103]) ).
fof(f120,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( nil != sK3
| nil = sK2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != sK3
| app(X7,cons(X6,nil)) = sK2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK0
| app(cons(X4,nil),X5) != sK1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK1,nil)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| ( cons(sK7(X0),sK6(X0)) = X0
& ssItem(sK7(X0))
& ssList(sK6(X0)) )
| nil = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0))],[f104]) ).
fof(f128,plain,
ssList(sK1),
inference(cnf_transformation,[],[f120]) ).
fof(f132,plain,
! [X6,X7] :
( app(cons(X6,nil),X7) != sK3
| app(X7,cons(X6,nil)) = sK2
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f120]) ).
fof(f133,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK0
| app(cons(X4,nil),X5) != sK1
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f120]) ).
fof(f134,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f120]) ).
fof(f135,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f136,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f120]) ).
fof(f140,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f143,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK7(X0),sK6(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f144,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK7(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f145,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK6(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f164,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f134,f136]) ).
fof(f165,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK2
| app(cons(X4,nil),X5) != sK3
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f133,f136,f135]) ).
fof(f166,plain,
ssList(sK3),
inference(definition_unfolding,[],[f128,f136]) ).
tcf(c_49,negated_conjecture,
neq(sK3,nil),
inference(cnf_transformation,[],[f164]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( app(X1,cons(X0,nil)) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( ( app(X1,cons(X0,nil)) = sK2 )
| ~ ssList(X1)
| ~ ssItem(X0)
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_55,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f166]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_63,plain,
! [X0: $i] :
( ssList(sK6(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_64,plain,
! [X0: $i] :
( ssItem(sK7(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(sK7(X0),sK6(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_80,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) != sK3 )
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_51,c_50]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(renaming,[status(thm)],[c_105]) ).
tcf(c_108,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_106]) ).
tcf(c_472,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_80]) ).
tcf(c_473,plain,
( ~ ssList(sK3)
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_472]) ).
tcf(c_474,plain,
sK3 != nil,
inference(global_subsumption_just,[status(thm)],[c_473,c_55,c_473]) ).
tcf(c_785,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_787,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1261,plain,
( ( sK3 = nil )
| ( cons(sK7(sK3),sK6(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_1269,plain,
cons(sK7(sK3),sK6(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_1261,c_474]) ).
tcf(c_1440,plain,
( ssList(sK6(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1452,plain,
( ssItem(sK7(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1957,plain,
! [X0: $i] :
( ( app(cons(sK7(sK3),nil),X0) = cons(sK7(sK3),X0) )
| ~ ssList(X0)
| ~ ssItem(sK7(sK3)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1961,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(sK7(sK3))
| ( app(cons(sK7(sK3),nil),X0) != sK3 ) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_2321,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_785]) ).
tcf(c_2322,plain,
! [X0: $i,X1: $i] :
( ( sK3 = X0 )
| ( sK3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_787]) ).
tcf(c_3417,plain,
! [X0: $i,X1: $i] :
( ( app(cons(sK7(sK3),nil),X0) = sK3 )
| ( sK3 != X1 )
| ( app(cons(sK7(sK3),nil),X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_787]) ).
tcf(c_4421,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ( sK3 != sK3 )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_2322]) ).
tcf(c_14246,plain,
( ( sK3 = cons(sK7(sK3),sK6(sK3)) )
| ( sK3 != sK3 )
| ( cons(sK7(sK3),sK6(sK3)) != sK3 ) ),
inference(instantiation,[status(thm)],[c_4421]) ).
tcf(c_21614,plain,
! [X0: $i] :
( ( app(cons(sK7(sK3),nil),X0) = sK3 )
| ( sK3 != cons(sK7(sK3),sK6(sK3)) )
| ( app(cons(sK7(sK3),nil),X0) != cons(sK7(sK3),sK6(sK3)) ) ),
inference(instantiation,[status(thm)],[c_3417]) ).
tcf(c_35588,plain,
( ( app(cons(sK7(sK3),nil),sK6(sK3)) = sK3 )
| ( sK3 != cons(sK7(sK3),sK6(sK3)) )
| ( app(cons(sK7(sK3),nil),sK6(sK3)) != cons(sK7(sK3),sK6(sK3)) ) ),
inference(instantiation,[status(thm)],[c_21614]) ).
tcf(c_35589,plain,
( ( app(cons(sK7(sK3),nil),sK6(sK3)) = cons(sK7(sK3),sK6(sK3)) )
| ~ ssList(sK6(sK3))
| ~ ssItem(sK7(sK3)) ),
inference(instantiation,[status(thm)],[c_1957]) ).
tcf(c_50155,plain,
( ~ ssList(sK6(sK3))
| ~ ssItem(sK7(sK3))
| ( app(cons(sK7(sK3),nil),sK6(sK3)) != sK3 ) ),
inference(instantiation,[status(thm)],[c_1961]) ).
tcf(c_50156,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_50155,c_35589,c_35588,c_14246,c_2321,c_1452,c_1440,c_1269,c_473,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC309+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 : n014.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 17:33:04 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 25.87/4.19 % SZS status Started for theBenchmark.p
% 25.87/4.19 % SZS status Theorem for theBenchmark.p
% 25.87/4.19
% 25.87/4.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.87/4.19
% 25.87/4.19 % ------ iProver source info
% 25.87/4.19
% 25.87/4.19 % git: date: 2026-07-19 20:42:38 +0200
% 25.87/4.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.87/4.19 % git: non_committed_changes: false
% 25.87/4.19
% 25.87/4.19 % ------ Parsing...
% 25.87/4.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.87/4.19
% 25.87/4.19 % ------ 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 %
% 25.87/4.19
% 25.87/4.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 25.87/4.19
% 25.87/4.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.87/4.19 % ------ Proving...
% 25.87/4.19 % ------ Problem Properties
% 25.87/4.19
% 25.87/4.19 %
% 25.87/4.19 % clauses 27
% 25.87/4.19 % conjectures 3
% 25.87/4.19 % EPR 7
% 25.87/4.19 % Horn 24
% 25.87/4.19 % unary 8
% 25.87/4.19 % binary 2
% 25.87/4.19 % lits 77
% 25.87/4.19 % lits eq 27
% 25.87/4.19 % fd_pure 0
% 25.87/4.19 % fd_pseudo 0
% 25.87/4.19 % fd_cond 4
% 25.87/4.19 % fd_pseudo_cond 4
% 25.87/4.19 % AC symbols 0
% 25.87/4.19
% 25.87/4.19 % ------ Schedule dynamic 5 is on
% 25.87/4.19
% 25.87/4.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 25.87/4.19
% 25.87/4.19
% 25.87/4.19 % ------
% 25.87/4.19 % Current options:
% 25.87/4.19 % ------
% 25.87/4.19
% 25.87/4.19
% 25.87/4.19 %
% 25.87/4.19
% 25.87/4.19 % ------ Proving...
% 25.87/4.19 %
% 25.87/4.19
% 25.87/4.19 % SZS status Theorem for theBenchmark.p
% 25.87/4.19
% 25.87/4.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.87/4.19
% 25.87/4.19
%------------------------------------------------------------------------------