%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC096+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 : n002.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 03:07:52 PM UTC 2026
% Result : Theorem 4.28s 1.31s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 20 unt; 5 def)
% Number of atoms : 263 ( 89 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 275 ( 114 ~; 99 |; 54 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 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 : 12 ( 10 usr; 5 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 118 !; 20 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( app(X7,cons(X6,nil)) != X3
| cons(X6,nil) != X2
| ~ ssList(X7) ) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X0
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( app(X7,cons(X6,nil)) != X3
| cons(X6,nil) != X2
| ~ ssList(X7) ) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X0
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( app(X7,cons(X6,nil)) = X3
& cons(X6,nil) = X2
& ssList(X7) ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f300,plain,
( ssList(sK56)
& ssList(sK57)
& ssList(sK58)
& ( ( ~ neq(sK59,nil)
& neq(sK57,nil) )
| sP6(sK57,sK56,sK58,sK59) )
& sK56 = sK58
& sK57 = sK59
& ssList(sK59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59]),skolemize(X0,sK56),skolemize(X1,sK57),skolemize(X2,sK58),skolemize(X3,sK59)],[f232]) ).
fof(f509,plain,
( ~ neq(sK59,nil)
| sP6(sK57,sK56,sK58,sK59) ),
inference(cnf_transformation,[],[f300]) ).
fof(f510,plain,
( neq(sK57,nil)
| sP6(sK57,sK56,sK58,sK59) ),
inference(cnf_transformation,[],[f300]) ).
fof(f511,plain,
sK56 = sK58,
inference(cnf_transformation,[],[f300]) ).
fof(f512,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f300]) ).
fof(f514,plain,
( neq(sK59,nil)
| sP6(sK59,sK58,sK58,sK59) ),
inference(definition_unfolding,[],[f510,f512,f511,f512]) ).
fof(f515,plain,
( ~ neq(sK59,nil)
| sP6(sK59,sK58,sK58,sK59) ),
inference(definition_unfolding,[],[f509,f512,f511]) ).
tcf(c_253,negated_conjecture,
( neq(sK59,nil)
| sP6(sK59,sK58,sK58,sK59) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_254,negated_conjecture,
( sP6(sK59,sK58,sK58,sK59)
| ~ neq(sK59,nil) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_376,negated_conjecture,
sP6(sK59,sK58,sK58,sK59),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_254]) ).
tcf(c_378,negated_conjecture,
sP6(sK59,sK58,sK58,sK59),
inference(global_subsumption_just,[status(thm)],[c_254,c_376]) ).
tcf(c_8925,definition,
iPr_def_10 = sK55(sK58,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8926,definition,
iPr_def_11 = app(iPr_def_10,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8927,definition,
iPr_def_12 = sK54(sK58,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8928,definition,
iPr_def_13 = cons(iPr_def_12,nil),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
fof(f231,definition,
! [X1,X0,X2,X3] :
( ~ sP6(X1,X0,X2,X3)
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( app(X7,cons(X6,nil)) = X3
& cons(X6,nil) = X2
& ssList(X7) ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f232,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X1,X0,X2,X3) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(definition_folding,[],[f221,f231]) ).
fof(f297,plain,
! [X1,X0,X2,X3] :
( ~ sP6(X1,X0,X2,X3)
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( app(X7,cons(X6,nil)) = X3
& cons(X6,nil) = X2
& ssList(X7) ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f231]) ).
fof(f298,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( app(X7,cons(X6,nil)) = X3
& cons(X6,nil) = X2
& ssList(X7) ) )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f297]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ssItem(sK54(X2,X3))
& app(sK55(X2,X3),cons(sK54(X2,X3),nil)) = X3
& cons(sK54(X2,X3),nil) = X2
& ssList(sK55(X2,X3))
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55]),skolemize(X6,sK54(X2,X3)),skolemize(X7,sK55(X2,X3))],[f298]) ).
fof(f500,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssItem(sK54(X2,X3)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f501,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| app(sK55(X2,X3),cons(sK54(X2,X3),nil)) = X3 ),
inference(cnf_transformation,[],[f299]) ).
fof(f502,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| cons(sK54(X2,X3),nil) = X2 ),
inference(cnf_transformation,[],[f299]) ).
fof(f503,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssList(sK55(X2,X3)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f504,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP6(X0,X1,X2,X3)
| app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f299]) ).
fof(f545,plain,
! [X2,X3,X0,X4,X5] :
( ~ sP6(X0,cons(X4,nil),X2,X3)
| app(X5,cons(X4,nil)) != X0
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f504]) ).
fof(f546,plain,
! [X2,X3,X4,X5] :
( ~ sP6(app(X5,cons(X4,nil)),cons(X4,nil),X2,X3)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f545]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ sP6(app(X0,cons(X1,nil)),cons(X1,nil),X2,X3) ),
inference(cnf_transformation,[],[f546]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK55(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK54(X2,X3),nil) = X2 )
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK55(X2,X3),cons(sK54(X2,X3),nil)) = X3 )
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_3135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X2,X3))
| ( X3 != sK59 )
| ( X2 != sK58 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_251,c_378]) ).
tcf(c_3136,plain,
ssItem(sK54(sK58,sK59)),
inference(unflattening,[status(thm)],[c_3135]) ).
tcf(c_3140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK55(X2,X3),cons(sK54(X2,X3),nil)) = X3 )
| ( X3 != sK59 )
| ( X2 != sK58 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_250,c_378]) ).
tcf(c_3141,plain,
app(sK55(sK58,sK59),cons(sK54(sK58,sK59),nil)) = sK59,
inference(unflattening,[status(thm)],[c_3140]) ).
tcf(c_3145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK54(X2,X3),nil) = X2 )
| ( X3 != sK59 )
| ( X2 != sK58 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_249,c_378]) ).
tcf(c_3146,plain,
cons(sK54(sK58,sK59),nil) = sK58,
inference(unflattening,[status(thm)],[c_3145]) ).
tcf(c_3150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK55(X2,X3))
| ( X3 != sK59 )
| ( X2 != sK58 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_248,c_378]) ).
tcf(c_3151,plain,
ssList(sK55(sK58,sK59)),
inference(unflattening,[status(thm)],[c_3150]) ).
tcf(c_3160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ( X3 != sK59 )
| ( X2 != sK58 )
| ( cons(X1,nil) != sK58 )
| ( app(X0,cons(X1,nil)) != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_247,c_378]) ).
tcf(c_3161,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ( cons(X1,nil) != sK58 )
| ( app(X0,cons(X1,nil)) != sK59 ) ),
inference(unflattening,[status(thm)],[c_3160]) ).
tcf(c_6518,plain,
app(sK55(sK58,sK59),sK58) = sK59,
inference(light_normalisation,[status(thm)],[c_3141,c_3146]) ).
tcf(c_8929,plain,
iPr_def_11 = sK59,
inference(demodulation,[status(thm)],[c_6518,c_8925,c_8926]) ).
tcf(c_8931,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ( cons(X1,nil) != sK58 )
| ( app(X0,cons(X1,nil)) != sK59 ) ),
inference(demodulation,[status(thm)],[c_3161]) ).
tcf(c_8932,plain,
ssList(iPr_def_10),
inference(demodulation,[status(thm)],[c_3151]) ).
tcf(c_8933,plain,
iPr_def_13 = sK58,
inference(demodulation,[status(thm)],[c_3146,c_8927,c_8928]) ).
tcf(c_8934,plain,
ssItem(iPr_def_12),
inference(demodulation,[status(thm)],[c_3136]) ).
tcf(c_11798,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ( cons(X1,nil) != iPr_def_13 )
| ( app(X0,cons(X1,nil)) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_8931,c_8929,c_8933]) ).
tcf(c_11873,plain,
app(iPr_def_10,iPr_def_13) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8926,c_8933]) ).
tcf(c_11899,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(X0)
| ( cons(iPr_def_12,nil) != iPr_def_13 )
| ( app(X0,iPr_def_13) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8928,c_11798]) ).
tcf(c_11900,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(X0)
| ( app(X0,iPr_def_13) != iPr_def_11 ) ),
inference(ground_joinability,[status(thm)],[c_11899,c_8928]) ).
tcf(c_11901,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(X0,iPr_def_13) != iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11900,c_8934]) ).
tcf(c_11909,plain,
~ ssList(iPr_def_10),
inference(superposition,[status(thm)],[c_11873,c_11901]) ).
tcf(c_11910,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11909,c_8932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC096+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 16:24:35 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 4.28/1.31 % SZS status Started for theBenchmark.p
% 4.28/1.31 % SZS status Theorem for theBenchmark.p
% 4.28/1.31
% 4.28/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.28/1.31
% 4.28/1.31 % ------ iProver source info
% 4.28/1.31
% 4.28/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.28/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.28/1.31 % git: non_committed_changes: false
% 4.28/1.31
% 4.28/1.31 % ------ Parsing...
% 4.28/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.28/1.31
% 4.28/1.31 % ------ 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: 1 sf_s rm: 6 0s sf_e pe_s pe_e %
% 4.28/1.31
% 4.28/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.28/1.31
% 4.28/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.28/1.31 % ------ Proving...
% 4.28/1.31 % ------ Problem Properties
% 4.28/1.31
% 4.28/1.31 %
% 4.28/1.31 % clauses 192
% 4.28/1.31 % conjectures 2
% 4.28/1.31 % EPR 56
% 4.28/1.31 % Horn 124
% 4.28/1.31 % unary 27
% 4.28/1.31 % binary 40
% 4.28/1.31 % lits 633
% 4.28/1.31 % lits eq 87
% 4.28/1.31 % fd_pure 0
% 4.28/1.31 % fd_pseudo 0
% 4.28/1.31 % fd_cond 21
% 4.28/1.31 % fd_pseudo_cond 14
% 4.28/1.31 % AC symbols 0
% 4.28/1.31
% 4.28/1.31 % ------ Schedule dynamic 5 is on
% 4.28/1.31
% 4.28/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.28/1.31
% 4.28/1.31
% 4.28/1.31 % ------
% 4.28/1.31 % Current options:
% 4.28/1.31 % ------
% 4.28/1.31
% 4.28/1.31
% 4.28/1.31 %
% 4.28/1.31
% 4.28/1.31 % ------ Proving...
% 4.28/1.31 %
% 4.28/1.31
% 4.28/1.31 % SZS status Theorem for theBenchmark.p
% 4.28/1.31
% 4.28/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/1.31
% 4.28/1.31
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