%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC179+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 : n017.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 03:08:17 PM UTC 2026
% Result : Theorem 3.31s 1.19s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 11 unt; 1 def)
% Number of atoms : 203 ( 63 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 238 ( 75 ~; 70 |; 78 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 52 !; 31 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax71) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax72) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2 ) ) ) ) )
| duplicatefreeP(X0)
| 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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2 ) ) ) ) )
| duplicatefreeP(X0)
| 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 = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2 ) ) ) )
& ~ duplicatefreeP(X0)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2 ) ) ) )
& ~ duplicatefreeP(X0)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f132,plain,
! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f71]) ).
fof(f145,plain,
( ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ssList(sK7)
& ( ( nil = sK6
& nil = sK7 )
| sP0(sK6,sK7) )
& ~ duplicatefreeP(sK4)
& sK4 = sK6
& sK5 = sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f141]) ).
fof(f173,plain,
( nil = sK6
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f145]) ).
fof(f174,plain,
( nil = sK7
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f145]) ).
fof(f175,plain,
~ duplicatefreeP(sK4),
inference(cnf_transformation,[],[f145]) ).
fof(f176,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f145]) ).
fof(f220,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f221,plain,
! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f233,plain,
~ duplicatefreeP(sK6),
inference(definition_unfolding,[],[f175,f176]) ).
tcf(c_56,negated_conjecture,
~ duplicatefreeP(sK6),
inference(cnf_transformation,[],[f233]) ).
tcf(c_57,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK7 ) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_58,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK6 ) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_105,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f220]) ).
tcf(c_106,plain,
! [X0: $i] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_1178,plain,
nil != sK6,
inference(resolution_lifted,[status(thm)],[c_56,c_105]) ).
fof(f140,definition,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f141,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ~ duplicatefreeP(X0)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f140]) ).
fof(f142,plain,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2 ) ) ) ),
inference(nnf_transformation,[],[f140]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ! [X6] :
( ~ lt(X6,X2)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(X2,X5)
| ~ memberP(X3,X5)
| ~ ssItem(X5) )
& app(app(X3,X0),X4) = X1
& cons(X2,nil) = X0 ) ) ) ),
inference(rectify,[],[f142]) ).
fof(f144,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ssItem(sK1(X0,X1))
& ssList(sK2(X0,X1))
& ssList(sK3(X0,X1))
& ! [X6] :
( ~ lt(X6,sK1(X0,X1))
| ~ memberP(sK3(X0,X1),X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(sK1(X0,X1),X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ ssItem(X5) )
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& cons(sK1(X0,X1),nil) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f143]) ).
fof(f162,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f168,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK1(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( cons(sK1(X0,X1),nil) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_1002,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ( nil = sK6 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_58]) ).
tcf(c_1003,plain,
( ssItem(sK1(sK6,sK7))
| ( nil = sK6 ) ),
inference(unflattening,[status(thm)],[c_1002]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ( nil = sK7 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
tcf(c_1011,plain,
( ssItem(sK1(sK6,sK7))
| ( nil = sK7 ) ),
inference(unflattening,[status(thm)],[c_1010]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i] :
( ( nil = sK6 )
| ( cons(sK1(X0,X1),nil) = X0 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_1127,plain,
( ( nil = sK6 )
| ( cons(sK1(sK6,sK7),nil) = sK6 ) ),
inference(unflattening,[status(thm)],[c_1126]) ).
tcf(c_1433,plain,
cons(sK1(sK6,sK7),nil) = sK6,
inference(backward_subsumption_resolution,[status(thm)],[c_1127,c_1178]) ).
tcf(c_1507,plain,
ssItem(sK1(sK6,sK7)),
inference(global_subsumption_just,[status(thm)],[c_1011,c_1003,c_1178]) ).
tcf(c_4723,plain,
( duplicatefreeP(sK6)
| ~ ssItem(sK1(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_1433,c_106]) ).
tcf(c_4724,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4723,c_56,c_1507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC179+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 16:45:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.31/1.19 % SZS status Started for theBenchmark.p
% 3.31/1.19 % SZS status Theorem for theBenchmark.p
% 3.31/1.19
% 3.31/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/1.19
% 3.31/1.19 % ------ iProver source info
% 3.31/1.19
% 3.31/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/1.19 % git: non_committed_changes: false
% 3.31/1.19
% 3.31/1.19 % ------ Parsing...
% 3.31/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.31/1.19
% 3.31/1.19 % ------ 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 sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.31/1.19
% 3.31/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.31/1.19
% 3.31/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.31/1.19 % ------ Proving...
% 3.31/1.19 % ------ Problem Properties
% 3.31/1.19
% 3.31/1.19 %
% 3.31/1.19 % clauses 63
% 3.31/1.19 % conjectures 3
% 3.31/1.19 % EPR 18
% 3.31/1.19 % Horn 50
% 3.31/1.19 % unary 14
% 3.31/1.19 % binary 6
% 3.31/1.19 % lits 204
% 3.31/1.19 % lits eq 33
% 3.31/1.19 % fd_pure 0
% 3.31/1.19 % fd_pseudo 0
% 3.31/1.19 % fd_cond 4
% 3.31/1.19 % fd_pseudo_cond 7
% 3.31/1.19 % AC symbols 0
% 3.31/1.19
% 3.31/1.19 % ------ Schedule dynamic 5 is on
% 3.31/1.19
% 3.31/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.31/1.19
% 3.31/1.19
% 3.31/1.19 % ------
% 3.31/1.19 % Current options:
% 3.31/1.19 % ------
% 3.31/1.19
% 3.31/1.19
% 3.31/1.19 %
% 3.31/1.19
% 3.31/1.19 % ------ Proving...
% 3.31/1.19 %
% 3.31/1.19
% 3.31/1.19 % SZS status Theorem for theBenchmark.p
% 3.31/1.19
% 3.31/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/1.19
% 3.31/1.19
%------------------------------------------------------------------------------