%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC185+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 : n016.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 03:08:29 PM UTC 2026
% Result : Theorem 1.53s 1.29s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 21 unt; 3 def)
% Number of atoms : 217 ( 44 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 253 ( 107 ~; 86 |; 46 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 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; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 59 !; 20 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( ~ memberP(X9,X7)
& ~ memberP(X8,X7) )
| app(app(X8,cons(X7,nil)),X9) != X0 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ( memberP(X6,X4)
| memberP(X5,X4) )
& app(app(X5,cons(X4,nil)),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| 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)
=> ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( ~ memberP(X9,X7)
& ~ memberP(X8,X7) )
| app(app(X8,cons(X7,nil)),X9) != X0 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ( memberP(X6,X4)
| memberP(X5,X4) )
& app(app(X5,cons(X4,nil)),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| 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)
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ( memberP(X9,X7)
| memberP(X8,X7) )
& app(app(X8,cons(X7,nil)),X9) = X0 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X2
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ( memberP(X9,X7)
| memberP(X8,X7) )
& app(app(X8,cons(X7,nil)),X9) = X0 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X2
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ssItem(sK57)
& ssList(sK58)
& ssList(sK59)
& ( memberP(sK59,sK57)
| memberP(sK58,sK57) )
& sK53 = app(app(sK58,cons(sK57,nil)),sK59)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57),skolemize(X8,sK58),skolemize(X9,sK59)],[f222]) ).
fof(f500,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( memberP(sK59,sK57)
| memberP(sK58,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK53 = app(app(sK58,cons(sK57,nil)),sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
! [X6,X4,X5] :
( ~ memberP(X6,X4)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
! [X6,X4,X5] :
( ~ memberP(X5,X4)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK55 = app(app(sK58,cons(sK57,nil)),sK59),
inference(definition_unfolding,[],[f504,f507]) ).
tcf(c_246,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_247,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X2,X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_248,negated_conjecture,
app(app(sK58,cons(sK57,nil)),sK59) = sK55,
inference(cnf_transformation,[],[f509]) ).
tcf(c_249,negated_conjecture,
( memberP(sK59,sK57)
| memberP(sK58,sK57) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_250,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f502]) ).
tcf(c_251,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f501]) ).
tcf(c_252,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f500]) ).
tcf(c_8882,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8883,definition,
iPr_def_11 = app(sK58,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8884,definition,
iPr_def_12 = app(iPr_def_11,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8887,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_8888,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_251]) ).
tcf(c_8889,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_8890,negated_conjecture,
( memberP(sK59,sK57)
| memberP(sK58,sK57) ),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8891,negated_conjecture,
iPr_def_12 = sK55,
inference(demodulation,[status(thm)],[c_248,c_8882,c_8883,c_8884]) ).
tcf(c_8892,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X2,X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_8893,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_11756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X2,X1)
| ( app(app(X0,cons(X1,nil)),X2) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_8892,c_8891]) ).
tcf(c_11772,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1)
| ( app(app(X0,cons(X1,nil)),X2) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_8893,c_8891]) ).
tcf(c_11788,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(sK57)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X0,sK57)
| ( app(app(X0,iPr_def_10),X1) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8882,c_11772]) ).
tcf(c_11789,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(sK57)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X1,sK57)
| ( app(app(X0,iPr_def_10),X1) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8882,c_11756]) ).
tcf(c_11790,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X1,sK57)
| ( app(app(X0,iPr_def_10),X1) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11789,c_8887]) ).
tcf(c_11795,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X0,sK57)
| ( app(app(X0,iPr_def_10),X1) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11788,c_8887]) ).
tcf(c_11873,plain,
! [X0: $i] :
( ~ ssList(sK58)
| ~ ssList(X0)
| ~ memberP(sK58,sK57)
| ( app(iPr_def_11,X0) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8883,c_11795]) ).
tcf(c_11874,plain,
! [X0: $i] :
( ~ ssList(sK58)
| ~ ssList(X0)
| ~ memberP(X0,sK57)
| ( app(iPr_def_11,X0) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8883,c_11790]) ).
tcf(c_11875,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ memberP(X0,sK57)
| ( app(iPr_def_11,X0) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11874,c_8888]) ).
tcf(c_11879,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ memberP(sK58,sK57)
| ( app(iPr_def_11,X0) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11873,c_8888]) ).
tcf(c_11933,plain,
( ~ ssList(sK59)
| ~ memberP(sK58,sK57) ),
inference(superposition,[status(thm)],[c_8884,c_11879]) ).
tcf(c_11934,plain,
( ~ ssList(sK59)
| ~ memberP(sK59,sK57) ),
inference(superposition,[status(thm)],[c_8884,c_11875]) ).
tcf(c_11935,plain,
~ memberP(sK59,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_11934,c_8889]) ).
tcf(c_11936,plain,
~ memberP(sK58,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_11933,c_8889]) ).
tcf(c_11937,plain,
memberP(sK58,sK57),
inference(backward_subsumption_resolution,[status(thm)],[c_8890,c_11935]) ).
tcf(c_11938,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11937,c_11936]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC185+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 16:56:27 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.43 % Detected problem language: tptp
% 0.15/0.44 % Proving...
% 1.53/1.29 % SZS status Started for theBenchmark.p
% 1.53/1.29 % SZS status Theorem for theBenchmark.p
% 1.53/1.29
% 1.53/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.53/1.29
% 1.53/1.29 % ------ iProver source info
% 1.53/1.29
% 1.53/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.53/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.53/1.29 % git: non_committed_changes: false
% 1.53/1.29
% 1.53/1.29 % ------ Parsing...
% 1.53/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.53/1.29
% 1.53/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 1.53/1.29
% 1.53/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.53/1.29
% 1.53/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.53/1.29 % ------ Proving...
% 1.53/1.29 % ------ Problem Properties
% 1.53/1.29
% 1.53/1.29 %
% 1.53/1.29 % clauses 192
% 1.53/1.29 % conjectures 9
% 1.53/1.29 % EPR 56
% 1.53/1.29 % Horn 123
% 1.53/1.29 % unary 25
% 1.53/1.29 % binary 41
% 1.53/1.29 % lits 639
% 1.53/1.29 % lits eq 84
% 1.53/1.29 % fd_pure 0
% 1.53/1.29 % fd_pseudo 0
% 1.53/1.29 % fd_cond 21
% 1.53/1.29 % fd_pseudo_cond 14
% 1.53/1.29 % AC symbols 0
% 1.53/1.29
% 1.53/1.29 % ------ Schedule dynamic 5 is on
% 1.53/1.29
% 1.53/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.53/1.29
% 1.53/1.29
% 1.53/1.29 % ------
% 1.53/1.29 % Current options:
% 1.53/1.29 % ------
% 1.53/1.29
% 1.53/1.29
% 1.53/1.29 %
% 1.53/1.29
% 1.53/1.29 % ------ Proving...
% 1.53/1.29 %
% 1.53/1.29
% 1.53/1.29 % SZS status Theorem for theBenchmark.p
% 1.53/1.29
% 1.53/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.53/1.29
% 1.53/1.29
%------------------------------------------------------------------------------