%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC322+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 : n012.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 03:09:18 PM UTC 2026
% Result : Theorem 0.07s 5.97s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 20 unt; 3 def)
% Number of atoms : 214 ( 119 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 210 ( 77 ~; 75 |; 46 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 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 : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 29 !; 16 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X0
| nil != X1 )
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) = X0
| app(X7,cons(X6,nil)) != X1 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& app(cons(X4,nil),X5) != X2
& 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)
=> ( ( ( nil = X0
| nil != X1 )
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) = X0
| app(X7,cons(X6,nil)) != X1 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& app(cons(X4,nil),X5) != X2
& 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)
& ( ( nil != X0
& nil = X1 )
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) != X0
& app(X7,cons(X6,nil)) = X1 ) ) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) = X2
| ~ 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)
& ( ( nil != X0
& nil = X1 )
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) != X0
& app(X7,cons(X6,nil)) = X1 ) ) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( nil != sK53
& nil = sK54 )
| ( ssItem(sK57)
& ssList(sK58)
& sK53 != app(cons(sK57,nil),sK58)
& sK54 = app(sK58,cons(sK57,nil)) ) )
& ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK56
| app(cons(X4,nil),X5) = sK55
| ~ ssList(X5) )
| ~ ssItem(X4) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X6,sK57),skolemize(X7,sK58)],[f222]) ).
fof(f500,plain,
( nil != sK53
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil = sK54
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil != sK53
| ssList(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK54
| ssList(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil != sK53
| sK53 != app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( nil = sK54
| sK53 != app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( nil != sK53
| sK54 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( nil = sK54
| sK54 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK56
| app(cons(X4,nil),X5) = sK55
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
( nil = sK56
| sK56 = app(sK58,cons(sK57,nil)) ),
inference(definition_unfolding,[],[f507,f511,f511]) ).
fof(f513,plain,
( nil != sK55
| sK56 = app(sK58,cons(sK57,nil)) ),
inference(definition_unfolding,[],[f506,f511,f510]) ).
fof(f514,plain,
( nil = sK56
| sK55 != app(cons(sK57,nil),sK58) ),
inference(definition_unfolding,[],[f505,f510,f511]) ).
fof(f515,plain,
( nil != sK55
| sK55 != app(cons(sK57,nil),sK58) ),
inference(definition_unfolding,[],[f504,f510,f510]) ).
fof(f516,plain,
( nil = sK56
| ssList(sK58) ),
inference(definition_unfolding,[],[f503,f511]) ).
fof(f517,plain,
( nil != sK55
| ssList(sK58) ),
inference(definition_unfolding,[],[f502,f510]) ).
fof(f518,plain,
( nil = sK56
| ssItem(sK57) ),
inference(definition_unfolding,[],[f501,f511]) ).
fof(f519,plain,
( nil != sK55
| ssItem(sK57) ),
inference(definition_unfolding,[],[f500,f510]) ).
tcf(c_246,negated_conjecture,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = sK55 )
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,cons(X1,nil)) != sK56 ) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_247,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_248,negated_conjecture,
( ( nil = sK56 )
| ( app(sK58,cons(sK57,nil)) = sK56 ) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_249,negated_conjecture,
( ( app(sK58,cons(sK57,nil)) = sK56 )
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f513]) ).
tcf(c_250,negated_conjecture,
( ( nil = sK56 )
| ( app(cons(sK57,nil),sK58) != sK55 ) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_251,negated_conjecture,
( ( nil != sK55 )
| ( app(cons(sK57,nil),sK58) != sK55 ) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_252,negated_conjecture,
( ssList(sK58)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_253,negated_conjecture,
( ssList(sK58)
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f517]) ).
tcf(c_254,negated_conjecture,
( ssItem(sK57)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f518]) ).
tcf(c_255,negated_conjecture,
( ssItem(sK57)
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f519]) ).
tcf(c_367,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_254,c_254,c_255,c_247]) ).
tcf(c_369,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_253,c_247]) ).
tcf(c_377,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_255,c_367]) ).
tcf(c_379,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_253,c_369]) ).
tcf(c_387,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK56,
inference(global_subsumption_just,[status(thm)],[c_248,c_247,c_248,c_249]) ).
tcf(c_389,negated_conjecture,
app(cons(sK57,nil),sK58) != sK55,
inference(global_subsumption_just,[status(thm)],[c_250,c_247,c_250,c_251]) ).
tcf(c_391,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK56,
inference(global_subsumption_just,[status(thm)],[c_249,c_387]) ).
tcf(c_393,negated_conjecture,
app(cons(sK57,nil),sK58) != sK55,
inference(global_subsumption_just,[status(thm)],[c_251,c_389]) ).
tcf(c_8854,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8855,definition,
iPr_def_11 = app(iPr_def_10,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8856,definition,
iPr_def_12 = app(sK58,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8857,negated_conjecture,
iPr_def_11 != sK55,
inference(demodulation,[status(thm)],[c_393,c_8854,c_8855]) ).
tcf(c_8858,negated_conjecture,
iPr_def_12 = sK56,
inference(demodulation,[status(thm)],[c_391,c_8856]) ).
tcf(c_8859,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_379]) ).
tcf(c_8860,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_377]) ).
tcf(c_8864,negated_conjecture,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = sK55 )
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,cons(X1,nil)) != sK56 ) ),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_11700,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = sK55 )
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,cons(X1,nil)) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_8864,c_8858]) ).
tcf(c_11717,plain,
! [X0: $i] :
( ( app(cons(sK57,nil),X0) = sK55 )
| ~ ssItem(sK57)
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8854,c_11700]) ).
tcf(c_11718,plain,
! [X0: $i] :
( ( app(iPr_def_10,X0) = sK55 )
| ~ ssItem(sK57)
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_11717,c_8854]) ).
tcf(c_11719,plain,
! [X0: $i] :
( ( app(iPr_def_10,X0) = sK55 )
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11718,c_8860]) ).
tcf(c_11818,plain,
( ( app(iPr_def_10,sK58) = sK55 )
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_8856,c_11719]) ).
tcf(c_11819,plain,
( ( sK55 = iPr_def_11 )
| ~ ssList(sK58) ),
inference(light_normalisation,[status(thm)],[c_11818,c_8855]) ).
tcf(c_11820,plain,
sK55 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_11819,c_8859]) ).
tcf(c_11824,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_8857,c_11820]) ).
tcf(c_11826,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_11824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC322+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.05/5.31 % Computer : n012.cluster.edu
% 0.05/5.31 % Model : x86_64 x86_64
% 0.05/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.31 % Memory : 8046.5625MB
% 0.05/5.31 % OS : Linux 6.8.0-71-generic
% 0.05/5.31 % CPULimit : 300
% 0.05/5.31 % WCLimit : 300
% 0.05/5.31 % DateTime : Thu Sep 24 17:36:51 UTC 2026
% 0.05/5.32 % CPUTime :
% 0.05/5.32 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.05/5.34 Running first-order theorem proving
% 0.05/5.34 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
% 0.05/5.34
% 0.05/5.34 % ======== iProver multi-core TPTP/SMT =========
% 0.05/5.34
% 0.05/5.34 % Detected problem language: tptp
% 0.05/5.35 % Proving...
% 0.07/5.97 % SZS status Started for theBenchmark.p
% 0.07/5.97 % SZS status Theorem for theBenchmark.p
% 0.07/5.97
% 0.07/5.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.07/5.97
% 0.07/5.97 % ------ iProver source info
% 0.07/5.97
% 0.07/5.97 % git: date: 2026-07-19 20:42:38 +0200
% 0.07/5.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.07/5.97 % git: non_committed_changes: false
% 0.07/5.97
% 0.07/5.97 % ------ Parsing...
% 0.07/5.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.07/5.97
% 0.07/5.97 % ------ 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 %
% 0.07/5.97
% 0.07/5.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.07/5.97
% 0.07/5.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.07/5.97 % ------ Proving...
% 0.07/5.97 % ------ Problem Properties
% 0.07/5.97
% 0.07/5.97 %
% 0.07/5.97 % clauses 191
% 0.07/5.97 % conjectures 8
% 0.07/5.97 % EPR 56
% 0.07/5.97 % Horn 123
% 0.07/5.97 % unary 25
% 0.07/5.97 % binary 41
% 0.07/5.97 % lits 633
% 0.07/5.97 % lits eq 87
% 0.07/5.97 % fd_pure 0
% 0.07/5.97 % fd_pseudo 0
% 0.07/5.97 % fd_cond 21
% 0.07/5.97 % fd_pseudo_cond 14
% 0.07/5.97 % AC symbols 0
% 0.07/5.97
% 0.07/5.97 % ------ Schedule dynamic 5 is on
% 0.07/5.97
% 0.07/5.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.07/5.97
% 0.07/5.97
% 0.07/5.97 % ------
% 0.07/5.97 % Current options:
% 0.07/5.97 % ------
% 0.07/5.97
% 0.07/5.97
% 0.07/5.97 %
% 0.07/5.97
% 0.07/5.97 % ------ Proving...
% 0.07/5.97 %
% 0.07/5.97
% 0.07/5.97 % SZS status Theorem for theBenchmark.p
% 0.07/5.97
% 0.07/5.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.07/5.97
% 0.07/5.97
%------------------------------------------------------------------------------