%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC381+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 : n015.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 03:09:33 PM UTC 2026
% Result : Theorem 3.30s 6.40s
% Output : CNFRefutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 13 unt; 3 def)
% Number of atoms : 208 ( 57 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 230 ( 87 ~; 75 |; 58 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 88 !; 19 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& 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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X5] :
( ssItem(X5)
& memberP(X3,X5)
& cons(X5,nil) = X2 )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X5] :
( ssItem(X5)
& memberP(X3,X5)
& cons(X5,nil) = X2 )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f301,plain,
( ssList(sK55)
& ssList(sK56)
& ssList(sK57)
& ssList(sK58)
& ( ( ~ neq(sK58,nil)
& neq(sK56,nil) )
| sP6(sK56,sK55,sK57,sK58) )
& sK55 = sK57
& sK56 = sK58 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58]),skolemize(X0,sK55),skolemize(X1,sK56),skolemize(X2,sK57),skolemize(X3,sK58)],[f233]) ).
fof(f510,plain,
( ~ neq(sK58,nil)
| sP6(sK56,sK55,sK57,sK58) ),
inference(cnf_transformation,[],[f301]) ).
fof(f511,plain,
( neq(sK56,nil)
| sP6(sK56,sK55,sK57,sK58) ),
inference(cnf_transformation,[],[f301]) ).
fof(f512,plain,
sK55 = sK57,
inference(cnf_transformation,[],[f301]) ).
fof(f513,plain,
sK56 = sK58,
inference(cnf_transformation,[],[f301]) ).
fof(f514,plain,
( neq(sK58,nil)
| sP6(sK58,sK57,sK57,sK58) ),
inference(definition_unfolding,[],[f511,f513,f512,f513]) ).
fof(f515,plain,
( ~ neq(sK58,nil)
| sP6(sK58,sK57,sK57,sK58) ),
inference(definition_unfolding,[],[f510,f513,f512]) ).
tcf(c_251,negated_conjecture,
( neq(sK58,nil)
| sP6(sK58,sK57,sK57,sK58) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_252,negated_conjecture,
( sP6(sK58,sK57,sK57,sK58)
| ~ neq(sK58,nil) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_373,negated_conjecture,
sP6(sK58,sK57,sK57,sK58),
inference(global_subsumption_just,[status(thm)],[c_251,c_251,c_252]) ).
tcf(c_375,negated_conjecture,
sP6(sK58,sK57,sK57,sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_373]) ).
tcf(c_8896,definition,
iPr_def_10 = sK54(sK57,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8897,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
fof(f232,definition,
! [X1,X0,X2,X3] :
( ~ sP6(X1,X0,X2,X3)
| ( ? [X5] :
( ssItem(X5)
& memberP(X3,X5)
& cons(X5,nil) = X2 )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f233,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X1,X0,X2,X3) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f298,plain,
! [X1,X0,X2,X3] :
( ~ sP6(X1,X0,X2,X3)
| ( ? [X5] :
( ssItem(X5)
& memberP(X3,X5)
& cons(X5,nil) = X2 )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ? [X5] :
( ssItem(X5)
& memberP(X3,X5)
& cons(X5,nil) = X2 )
& ! [X4] :
( ~ memberP(X0,X4)
| cons(X4,nil) != X1
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f298]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ssItem(sK54(X2,X3))
& memberP(X3,sK54(X2,X3))
& cons(sK54(X2,X3),nil) = X2
& ! [X4] :
( ~ memberP(X0,X4)
| cons(X4,nil) != X1
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X5,sK54(X2,X3))],[f299]) ).
fof(f501,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssItem(sK54(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f502,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| memberP(X3,sK54(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f503,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| cons(sK54(X2,X3),nil) = X2 ),
inference(cnf_transformation,[],[f300]) ).
fof(f504,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP6(X0,X1,X2,X3)
| ~ memberP(X0,X4)
| cons(X4,nil) != X1
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f300]) ).
fof(f545,plain,
! [X2,X3,X0,X4] :
( ~ sP6(X0,cons(X4,nil),X2,X3)
| ~ memberP(X0,X4)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f504]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X1)
| ~ memberP(X0,X1)
| ~ sP6(X0,cons(X1,nil),X2,X3) ),
inference(cnf_transformation,[],[f545]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK54(X2,X3),nil) = X2 )
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X3,sK54(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_3124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X2,X3))
| ( X3 != sK58 )
| ( X2 != sK57 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_250,c_375]) ).
tcf(c_3125,plain,
ssItem(sK54(sK57,sK58)),
inference(unflattening,[status(thm)],[c_3124]) ).
tcf(c_3129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X3,sK54(X2,X3))
| ( X3 != sK58 )
| ( X2 != sK57 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_249,c_375]) ).
tcf(c_3130,plain,
memberP(sK58,sK54(sK57,sK58)),
inference(unflattening,[status(thm)],[c_3129]) ).
tcf(c_3134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK54(X2,X3),nil) = X2 )
| ( X3 != sK58 )
| ( X2 != sK57 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_248,c_375]) ).
tcf(c_3135,plain,
cons(sK54(sK57,sK58),nil) = sK57,
inference(unflattening,[status(thm)],[c_3134]) ).
tcf(c_3144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X0)
| ~ memberP(X1,X0)
| ( X3 != sK58 )
| ( X2 != sK57 )
| ( X1 != sK58 )
| ( cons(X0,nil) != sK57 ) ),
inference(resolution_lifted,[status(thm)],[c_247,c_375]) ).
tcf(c_3145,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK58,X0)
| ( cons(X0,nil) != sK57 ) ),
inference(unflattening,[status(thm)],[c_3144]) ).
tcf(c_8899,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK58,X0)
| ( cons(X0,nil) != sK57 ) ),
inference(demodulation,[status(thm)],[c_3145]) ).
tcf(c_8900,plain,
iPr_def_11 = sK57,
inference(demodulation,[status(thm)],[c_3135,c_8896,c_8897]) ).
tcf(c_8901,plain,
memberP(sK58,iPr_def_10),
inference(demodulation,[status(thm)],[c_3130]) ).
tcf(c_8902,plain,
ssItem(iPr_def_10),
inference(demodulation,[status(thm)],[c_3125]) ).
tcf(c_11739,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK58,X0)
| ( cons(X0,nil) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_8899,c_8900]) ).
tcf(c_11816,plain,
( ~ ssItem(iPr_def_10)
| ~ memberP(sK58,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8897,c_11739]) ).
tcf(c_11817,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11816,c_8902,c_8901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC381+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.44 % Computer : n015.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.44 % CPULimit : 300
% 0.15/5.44 % WCLimit : 300
% 0.15/5.44 % DateTime : Thu Sep 24 17:59:48 UTC 2026
% 0.15/5.45 % CPUTime :
% 0.15/5.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.49 Running first-order theorem proving
% 0.15/5.49 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
% 0.21/5.50
% 0.21/5.50 % ======== iProver multi-core TPTP/SMT =========
% 0.21/5.50
% 0.21/5.51 % Detected problem language: tptp
% 0.21/5.52 % Proving...
% 3.30/6.40 % SZS status Started for theBenchmark.p
% 3.30/6.40 % SZS status Theorem for theBenchmark.p
% 3.30/6.40
% 3.30/6.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.30/6.40
% 3.30/6.40 % ------ iProver source info
% 3.30/6.40
% 3.30/6.40 % git: date: 2026-07-19 20:42:38 +0200
% 3.30/6.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.30/6.40 % git: non_committed_changes: false
% 3.30/6.40
% 3.30/6.40 % ------ Parsing...
% 3.30/6.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.30/6.40
% 3.30/6.40 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 3.30/6.40
% 3.30/6.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.30/6.40
% 3.30/6.40 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.30/6.40 % ------ Proving...
% 3.30/6.40 % ------ Problem Properties
% 3.30/6.40
% 3.30/6.40 %
% 3.30/6.40 % clauses 189
% 3.30/6.40 % conjectures 2
% 3.30/6.40 % EPR 55
% 3.30/6.40 % Horn 121
% 3.30/6.40 % unary 24
% 3.30/6.40 % binary 40
% 3.30/6.40 % lits 629
% 3.30/6.40 % lits eq 83
% 3.30/6.40 % fd_pure 0
% 3.30/6.40 % fd_pseudo 0
% 3.30/6.40 % fd_cond 21
% 3.30/6.40 % fd_pseudo_cond 14
% 3.30/6.40 % AC symbols 0
% 3.30/6.40
% 3.30/6.40 % ------ Schedule dynamic 5 is on
% 3.30/6.40
% 3.30/6.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.30/6.40
% 3.30/6.40
% 3.30/6.40 % ------
% 3.30/6.40 % Current options:
% 3.30/6.40 % ------
% 3.30/6.40
% 3.30/6.40
% 3.30/6.40 %
% 3.30/6.40
% 3.30/6.40 % ------ Proving...
% 3.30/6.40 %
% 3.30/6.40
% 3.30/6.40 % SZS status Theorem for theBenchmark.p
% 3.30/6.40
% 3.30/6.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.30/6.40
% 3.30/6.40
%------------------------------------------------------------------------------