%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC254+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 : n019.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 03:09:02 PM UTC 2026
% Result : Theorem 4.04s 1.27s
% Output : CNFRefutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 11 unt; 1 def)
% Number of atoms : 210 ( 55 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 241 ( 82 ~; 74 |; 68 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 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 : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 86 !; 26 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( singletonP(X0)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X3
| cons(X4,nil) != X2 ) ) )
| ~ 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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( singletonP(X0)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X3
| cons(X4,nil) != X2 ) ) )
| ~ 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) )
| ( ~ singletonP(X0)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2 ) )
& 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) )
| ( ~ singletonP(X0)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2 ) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f126,plain,
( ssList(sK3)
& ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ( ( ~ neq(sK6,nil)
& neq(sK4,nil) )
| sP0(sK4,sK5,sK6,sK3) )
& 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)],[f122]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0))],[f134]) ).
fof(f146,plain,
( ~ neq(sK6,nil)
| sP0(sK4,sK5,sK6,sK3) ),
inference(cnf_transformation,[],[f126]) ).
fof(f147,plain,
( neq(sK4,nil)
| sP0(sK4,sK5,sK6,sK3) ),
inference(cnf_transformation,[],[f126]) ).
fof(f148,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f126]) ).
fof(f149,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f126]) ).
fof(f162,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f176,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f180,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f181,plain,
( neq(sK6,nil)
| sP0(sK6,sK5,sK6,sK5) ),
inference(definition_unfolding,[],[f147,f149,f148,f149]) ).
fof(f182,plain,
( ~ neq(sK6,nil)
| sP0(sK6,sK5,sK6,sK5) ),
inference(definition_unfolding,[],[f146,f149,f148]) ).
fof(f189,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f180]) ).
tcf(c_55,negated_conjecture,
( neq(sK6,nil)
| sP0(sK6,sK5,sK6,sK5) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_56,negated_conjecture,
( sP0(sK6,sK5,sK6,sK5)
| ~ neq(sK6,nil) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_87,plain,
ssList(nil),
inference(cnf_transformation,[],[f176]) ).
tcf(c_89,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_115,negated_conjecture,
sP0(sK6,sK5,sK6,sK5),
inference(global_subsumption_just,[status(thm)],[c_55,c_55,c_56]) ).
tcf(c_117,negated_conjecture,
sP0(sK6,sK5,sK6,sK5),
inference(global_subsumption_just,[status(thm)],[c_56,c_115]) ).
tcf(c_1640,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_73,c_89]) ).
tcf(c_1642,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1640,c_87]) ).
fof(f121,definition,
! [X1,X2,X3,X0] :
( ~ sP0(X1,X2,X3,X0)
| ( ~ singletonP(X0)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2 ) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f122,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP0(X1,X2,X3,X0) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f121]) ).
fof(f123,plain,
! [X1,X2,X3,X0] :
( ~ sP0(X1,X2,X3,X0)
| ( ~ singletonP(X0)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2 ) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ~ singletonP(X3)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X2
& cons(X4,nil) = X1 ) )
& neq(X0,nil) ) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ~ singletonP(X3)
& ssItem(sK1(X1,X2))
& ssList(sK2(X1,X2))
& app(sK2(X1,X2),cons(sK1(X1,X2),nil)) = X2
& cons(sK1(X1,X2),nil) = X1
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X4,sK1(X1,X2)),skolemize(X5,sK2(X1,X2))],[f124]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ~ singletonP(X3) ),
inference(cnf_transformation,[],[f125]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X1,X2)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| cons(sK1(X1,X2),nil) = X1 ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK1(X1,X2),nil) = X1 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X1,X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ singletonP(X3)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ singletonP(X3)
| ( X3 != sK5 )
| ( X2 != sK6 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_117]) ).
tcf(c_544,plain,
~ singletonP(sK5),
inference(unflattening,[status(thm)],[c_543]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X1,X2))
| ( X3 != sK5 )
| ( X2 != sK6 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_117]) ).
tcf(c_549,plain,
ssItem(sK1(sK5,sK6)),
inference(unflattening,[status(thm)],[c_548]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK1(X1,X2),nil) = X1 )
| ( X3 != sK5 )
| ( X2 != sK6 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_117]) ).
tcf(c_564,plain,
cons(sK1(sK5,sK6),nil) = sK5,
inference(unflattening,[status(thm)],[c_563]) ).
tcf(c_1660,plain,
( singletonP(sK5)
| ~ ssItem(sK1(sK5,sK6)) ),
inference(superposition,[status(thm)],[c_564,c_1642]) ).
tcf(c_1661,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1660,c_544,c_549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 17:15:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 4.04/1.27 % SZS status Started for theBenchmark.p
% 4.04/1.27 % SZS status Theorem for theBenchmark.p
% 4.04/1.27
% 4.04/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.04/1.27
% 4.04/1.27 % ------ iProver source info
% 4.04/1.27
% 4.04/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.04/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.04/1.27 % git: non_committed_changes: false
% 4.04/1.27
% 4.04/1.27 % ------ Parsing...
% 4.04/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.04/1.27
% 4.04/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 1 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.04/1.27
% 4.04/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.04/1.27
% 4.04/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.04/1.27 % ------ Proving...
% 4.04/1.27 % ------ Problem Properties
% 4.04/1.27
% 4.04/1.27 %
% 4.04/1.27 % clauses 35
% 4.04/1.27 % conjectures 2
% 4.04/1.27 % EPR 9
% 4.04/1.27 % Horn 32
% 4.04/1.27 % unary 14
% 4.04/1.27 % binary 2
% 4.04/1.27 % lits 89
% 4.04/1.27 % lits eq 29
% 4.04/1.27 % fd_pure 0
% 4.04/1.27 % fd_pseudo 0
% 4.04/1.27 % fd_cond 4
% 4.04/1.27 % fd_pseudo_cond 4
% 4.04/1.27 % AC symbols 0
% 4.04/1.27
% 4.04/1.27 % ------ Schedule dynamic 5 is on
% 4.04/1.27
% 4.04/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.04/1.27
% 4.04/1.27
% 4.04/1.27 % ------
% 4.04/1.27 % Current options:
% 4.04/1.27 % ------
% 4.04/1.27
% 4.04/1.27
% 4.04/1.27 %
% 4.04/1.27
% 4.04/1.27 % ------ Proving...
% 4.04/1.27 %
% 4.04/1.27
% 4.04/1.27 % SZS status Theorem for theBenchmark.p
% 4.04/1.27
% 4.04/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.04/1.27
% 4.04/1.27
%------------------------------------------------------------------------------