%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC029-1 : 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 : n019.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 03:07:35 PM UTC 2026
% Result : Unsatisfiable 3.96s 1.27s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 85 ( 35 unt; 3 def)
% Number of atoms : 224 ( 80 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 187 ( 90 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f84,axiom,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f101]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
( ~ neq(sk4,nil)
| sk4 = app(cons(sk5,nil),sk6) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,plain,
( ~ neq(sk4,nil)
| sk3 = app(sk6,cons(sk5,nil)) ),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
( nil = sk1
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f216,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f219,plain,
( nil = sk3
| nil = sk4 ),
inference(definition_unfolding,[],[f213,f204,f205]) ).
fof(f222,plain,
( nil != sk4
| nil != sk3 ),
inference(definition_unfolding,[],[f216,f205,f204]) ).
fof(f234,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
tcf(c_256,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_321,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_322,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_332,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_437,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_438,negated_conjecture,
( ( sk3 = nil )
| ( sk4 != nil ) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_439,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_440,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_441,negated_conjecture,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_442,negated_conjecture,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_443,negated_conjecture,
( ( sk4 = nil )
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_444,negated_conjecture,
( ( sk4 != nil )
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_558,negated_conjecture,
sk3 = nil,
inference(global_subsumption_just,[status(thm)],[c_443,c_443,c_438]) ).
tcf(c_560,negated_conjecture,
sk3 = nil,
inference(global_subsumption_just,[status(thm)],[c_438,c_443,c_438]) ).
tcf(c_564,negated_conjecture,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_444,c_444,c_558]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_392,c_333]) ).
tcf(c_1913,plain,
( ( app(sk6,cons(sk5,nil)) = nil )
| ~ neq(sk4,nil) ),
inference(light_normalisation,[status(thm)],[c_442,c_560]) ).
tcf(c_3583,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(sk6,cons(sk5,nil)) = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_1913,c_348]) ).
tcf(c_3584,plain,
( ( sk4 = nil )
| ( app(sk6,cons(sk5,nil)) = nil )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_3583]) ).
tcf(c_3585,plain,
app(sk6,cons(sk5,nil)) = nil,
inference(global_subsumption_just,[status(thm)],[c_3584,c_437,c_256,c_443,c_438,c_444,c_3584]) ).
tcf(c_3603,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(cons(sk5,nil),sk6) = sk4 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_441,c_348]) ).
tcf(c_3604,plain,
( ( sk4 = nil )
| ( app(cons(sk5,nil),sk6) = sk4 )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_3603]) ).
tcf(c_3605,plain,
app(cons(sk5,nil),sk6) = sk4,
inference(global_subsumption_just,[status(thm)],[c_3604,c_437,c_256,c_443,c_438,c_444,c_3604]) ).
tcf(c_3623,plain,
! [X0: $i,X1: $i] :
( ssList(sk6)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_440,c_348]) ).
tcf(c_3624,plain,
( ssList(sk6)
| ( sk4 = nil )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_3623]) ).
tcf(c_3625,plain,
ssList(sk6),
inference(global_subsumption_just,[status(thm)],[c_3624,c_437,c_256,c_443,c_438,c_444,c_3624]) ).
tcf(c_3643,plain,
! [X0: $i,X1: $i] :
( ssItem(sk5)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_439,c_348]) ).
tcf(c_3644,plain,
( ssItem(sk5)
| ( sk4 = nil )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_3643]) ).
tcf(c_3645,plain,
ssItem(sk5),
inference(global_subsumption_just,[status(thm)],[c_3644,c_437,c_256,c_443,c_438,c_444,c_3644]) ).
tcf(c_6561,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6562,definition,
iPr_def_13 = app(iPr_def_12,sk6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6563,definition,
iPr_def_14 = app(sk6,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6564,plain,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_3645]) ).
tcf(c_6565,plain,
ssList(sk6),
inference(demodulation,[status(thm)],[c_3625]) ).
tcf(c_6566,plain,
iPr_def_13 = sk4,
inference(demodulation,[status(thm)],[c_3605,c_6561,c_6562]) ).
tcf(c_6567,plain,
iPr_def_14 = nil,
inference(demodulation,[status(thm)],[c_3585,c_6563]) ).
tcf(c_6568,negated_conjecture,
sk4 != nil,
inference(demodulation,[status(thm)],[c_564]) ).
tcf(c_9077,plain,
iPr_def_13 != iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6568,c_6566,c_6567]) ).
tcf(c_9086,plain,
ssList(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_256,c_6567]) ).
tcf(c_9090,plain,
cons(sk5,iPr_def_14) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_6561,c_6567]) ).
tcf(c_9131,plain,
! [X0: $i] :
( ( app(X0,iPr_def_14) = X0 )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_321,c_6567]) ).
tcf(c_9277,plain,
! [X0: $i] :
( ( app(iPr_def_14,X0) = X0 )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_322,c_6567]) ).
tcf(c_9566,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(iPr_def_14) ),
inference(superposition,[status(thm)],[c_9090,c_334]) ).
tcf(c_9570,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9566,c_6564,c_9086]) ).
tcf(c_9584,plain,
app(iPr_def_14,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_9570,c_9277]) ).
tcf(c_9585,plain,
app(iPr_def_12,iPr_def_14) = iPr_def_12,
inference(superposition,[status(thm)],[c_9570,c_9131]) ).
tcf(c_9670,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ~ ssList(X0)
| ~ frontsegP(iPr_def_14,X0) ),
inference(light_normalisation,[status(thm)],[c_332,c_6567]) ).
tcf(c_9935,plain,
( frontsegP(iPr_def_14,sk6)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6563,c_818]) ).
tcf(c_10006,plain,
frontsegP(iPr_def_14,sk6),
inference(forward_subsumption_resolution,[status(thm)],[c_9935,c_9570,c_6565]) ).
tcf(c_10497,plain,
( ( sk6 = iPr_def_14 )
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_10006,c_9670]) ).
tcf(c_10498,plain,
sk6 = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_10497,c_6565]) ).
tcf(c_10505,plain,
app(iPr_def_14,iPr_def_12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_6563,c_10498]) ).
tcf(c_10506,plain,
app(iPr_def_12,iPr_def_14) = iPr_def_13,
inference(demodulation,[status(thm)],[c_6562,c_10498]) ).
tcf(c_10508,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_10506,c_9585]) ).
tcf(c_10518,plain,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_9077,c_10508]) ).
tcf(c_10520,plain,
iPr_def_12 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_10505,c_9584]) ).
tcf(c_10521,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_10518,c_10520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC029-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.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 16:00:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.96/1.27 % SZS status Started for theBenchmark.p
% 3.96/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.96/1.27
% 3.96/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.96/1.27
% 3.96/1.27 % ------ iProver source info
% 3.96/1.27
% 3.96/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.96/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.96/1.27 % git: non_committed_changes: false
% 3.96/1.27
% 3.96/1.27 % ------ Parsing...% successful
% 3.96/1.27
% 3.96/1.27
% 3.96/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.96/1.27
% 3.96/1.27 % ------ Preprocessing... sup_sim: 3 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 %
% 3.96/1.27
% 3.96/1.27 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.96/1.27
% 3.96/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.96/1.27 % ------ Proving...
% 3.96/1.27 % ------ Problem Properties
% 3.96/1.27
% 3.96/1.27 %
% 3.96/1.27 % clauses 187
% 3.96/1.27 % conjectures 3
% 3.96/1.27 % EPR 59
% 3.96/1.27 % Horn 159
% 3.96/1.27 % unary 68
% 3.96/1.27 % binary 21
% 3.96/1.27 % lits 551
% 3.96/1.27 % lits eq 76
% 3.96/1.27 % fd_pure 0
% 3.96/1.27 % fd_pseudo 0
% 3.96/1.27 % fd_cond 15
% 3.96/1.27 % fd_pseudo_cond 14
% 3.96/1.27 % AC symbols 0
% 3.96/1.27
% 3.96/1.27 % ------ Schedule dynamic 5 is on
% 3.96/1.27
% 3.96/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.96/1.27
% 3.96/1.27
% 3.96/1.27 % ------
% 3.96/1.27 % Current options:
% 3.96/1.27 % ------
% 3.96/1.27
% 3.96/1.27
% 3.96/1.27 %
% 3.96/1.27
% 3.96/1.27 % ------ Proving...
% 3.96/1.27 %
% 3.96/1.27
% 3.96/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.96/1.27
% 3.96/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.96/1.27
% 3.96/1.27
%------------------------------------------------------------------------------