%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC029+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 : n018.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 03:07:35 PM UTC 2026
% Result : Theorem 3.31s 1.35s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 13 unt; 0 def)
% Number of atoms : 255 ( 124 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 310 ( 119 ~; 115 |; 52 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 58 !; 12 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
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(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3 ) ) ) )
| ( nil = X3
& nil != X2 )
| 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 = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3 ) ) ) )
| ( nil = X3
& nil != X2 )
| 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 != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3 ) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3 ) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f110,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( nil != sK1
& nil = sK0 )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(sK3,nil)
| ( ssItem(sK4)
& ssList(sK5)
& sK2 = app(sK5,cons(sK4,nil))
& sK3 = app(cons(sK4,nil),sK5) ) )
& ( nil != sK3
| nil = sK2 )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f99]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f128,plain,
ssList(sK1),
inference(cnf_transformation,[],[f120]) ).
fof(f131,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f134,plain,
( nil = sK0
| nil = sK1 ),
inference(cnf_transformation,[],[f120]) ).
fof(f135,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f120]) ).
fof(f136,plain,
( ~ neq(sK3,nil)
| ssList(sK5) ),
inference(cnf_transformation,[],[f120]) ).
fof(f137,plain,
( ~ neq(sK3,nil)
| sK2 = app(sK5,cons(sK4,nil)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f139,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f140,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f141,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f120]) ).
fof(f147,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f154,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f157,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f165,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f168,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f169,plain,
( nil = sK2
| nil = sK3 ),
inference(definition_unfolding,[],[f134,f141,f140]) ).
fof(f172,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f131,f140,f141]) ).
fof(f173,plain,
ssList(sK3),
inference(definition_unfolding,[],[f128,f141]) ).
tcf(c_49,negated_conjecture,
( ( nil = sK2 )
| ( nil != sK3 ) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_51,negated_conjecture,
( ( app(sK5,cons(sK4,nil)) = sK2 )
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_52,negated_conjecture,
( ssList(sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_53,negated_conjecture,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_54,negated_conjecture,
( ( nil = sK3 )
| ( nil = sK2 ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_55,negated_conjecture,
( ( nil != sK3 )
| ( nil != sK2 ) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_58,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f173]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_86,plain,
ssList(nil),
inference(cnf_transformation,[],[f168]) ).
tcf(c_104,negated_conjecture,
nil = sK2,
inference(global_subsumption_just,[status(thm)],[c_54,c_54,c_49]) ).
tcf(c_106,negated_conjecture,
nil = sK2,
inference(global_subsumption_just,[status(thm)],[c_49,c_104]) ).
tcf(c_349,plain,
( ( app(sK5,cons(sK4,nil)) = nil )
| ~ neq(sK3,nil) ),
inference(light_normalisation,[status(thm)],[c_51,c_106]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(sK5,cons(sK4,nil)) = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_349,c_82]) ).
tcf(c_498,plain,
( ( nil = sK3 )
| ( app(sK5,cons(sK4,nil)) = nil )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_497]) ).
tcf(c_499,plain,
app(sK5,cons(sK4,nil)) = nil,
inference(global_subsumption_just,[status(thm)],[c_498,c_58,c_86,c_55,c_104,c_498]) ).
tcf(c_517,plain,
! [X0: $i,X1: $i] :
( ssItem(sK4)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_82]) ).
tcf(c_518,plain,
( ssItem(sK4)
| ( nil = sK3 )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_517]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i] :
( ssList(sK5)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_82]) ).
tcf(c_538,plain,
( ssList(sK5)
| ( nil = sK3 )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_537]) ).
tcf(c_539,plain,
ssList(sK5),
inference(global_subsumption_just,[status(thm)],[c_538,c_58,c_86,c_54,c_49,c_55,c_538]) ).
tcf(c_1423,plain,
( ( cons(sK4,nil) = nil )
| ~ ssList(sK5)
| ~ ssList(cons(sK4,nil)) ),
inference(superposition,[status(thm)],[c_499,c_75]) ).
tcf(c_1429,plain,
( ( cons(sK4,nil) = nil )
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1423,c_539]) ).
tcf(c_1553,plain,
! [X0: $i] :
( ~ ssItem(sK4)
| ~ ssList(X0)
| ( cons(sK4,X0) != nil ) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1554,plain,
( ~ ssItem(sK4)
| ~ ssList(nil)
| ( cons(sK4,nil) != nil ) ),
inference(instantiation,[status(thm)],[c_1553]) ).
tcf(c_1570,plain,
! [X0: $i] :
( ssList(cons(sK4,X0))
| ~ ssItem(sK4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_1571,plain,
( ssList(cons(sK4,nil))
| ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_1570]) ).
tcf(c_1572,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1571,c_1554,c_1429,c_518,c_104,c_55,c_86,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC029+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Thu Sep 24 16:02:04 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 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
% 0.17/0.46
% 0.17/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.46
% 0.17/0.46 % Detected problem language: tptp
% 0.17/0.48 % Proving...
% 3.31/1.35 % SZS status Started for theBenchmark.p
% 3.31/1.35 % SZS status Theorem for theBenchmark.p
% 3.31/1.35
% 3.31/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/1.35
% 3.31/1.35 % ------ iProver source info
% 3.31/1.35
% 3.31/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/1.35 % git: non_committed_changes: false
% 3.31/1.35
% 3.31/1.35 % ------ Parsing...
% 3.31/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.31/1.35
% 3.31/1.35 % ------ Preprocessing... sup_sim: 3 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 %
% 3.31/1.35
% 3.31/1.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.31/1.35
% 3.31/1.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.31/1.35 % ------ Proving...
% 3.31/1.35 % ------ Problem Properties
% 3.31/1.35
% 3.31/1.35 %
% 3.31/1.35 % clauses 30
% 3.31/1.35 % conjectures 3
% 3.31/1.35 % EPR 9
% 3.31/1.35 % Horn 27
% 3.31/1.35 % unary 12
% 3.31/1.35 % binary 2
% 3.31/1.35 % lits 78
% 3.31/1.35 % lits eq 29
% 3.31/1.35 % fd_pure 0
% 3.31/1.35 % fd_pseudo 0
% 3.31/1.35 % fd_cond 4
% 3.31/1.35 % fd_pseudo_cond 4
% 3.31/1.35 % AC symbols 0
% 3.31/1.35
% 3.31/1.35 % ------ Schedule dynamic 5 is on
% 3.31/1.35
% 3.31/1.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.31/1.35
% 3.31/1.35
% 3.31/1.35 % ------
% 3.31/1.35 % Current options:
% 3.31/1.35 % ------
% 3.31/1.35
% 3.31/1.35
% 3.31/1.35 %
% 3.31/1.35
% 3.31/1.35 % ------ Proving...
% 3.31/1.35 %
% 3.31/1.35
% 3.31/1.35 % SZS status Theorem for theBenchmark.p
% 3.31/1.35
% 3.31/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/1.35
%------------------------------------------------------------------------------