%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC279-1 : 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 : 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 03:09:08 PM UTC 2026
% Result : Unsatisfiable 4.17s 6.32s
% Output : CNFRefutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 62 ( 26 unt; 3 def)
% Number of atoms : 211 ( 27 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 247 ( 122 ~; 125 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 64 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ memberP(X2,X3)
| leq(X0,X3)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( ~ memberP(X2,X3)
| leq(X0,X3)
| ~ ssItem(X3)
| sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ memberP(X1,X3)
| leq(X3,X0)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( ~ memberP(X1,X3)
| leq(X3,X0)
| ~ ssItem(X3)
| sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f208]) ).
fof(f210,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f211,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f212,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
sk1 = app(app(sk6,cons(sk5,nil)),sk7),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f216,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f217,negated_conjecture,
( ~ leq(sk5,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f218,negated_conjecture,
( memberP(sk7,sk8)
| ~ leq(sk8,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f219,negated_conjecture,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f222,plain,
sk3 = app(app(sk6,cons(sk5,nil)),sk7),
inference(definition_unfolding,[],[f214,f205]) ).
tcf(c_440,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X1,X3)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X2,X3)
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_441,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X3)
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_442,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f210]) ).
tcf(c_443,negated_conjecture,
ssList(sk6),
inference(cnf_transformation,[],[f211]) ).
tcf(c_444,negated_conjecture,
ssList(sk7),
inference(cnf_transformation,[],[f212]) ).
tcf(c_445,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(cnf_transformation,[],[f222]) ).
tcf(c_446,negated_conjecture,
ssItem(sk8),
inference(cnf_transformation,[],[f215]) ).
tcf(c_447,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_448,negated_conjecture,
( memberP(sk6,sk8)
| ~ leq(sk5,sk8) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_449,negated_conjecture,
( memberP(sk7,sk8)
| ~ leq(sk8,sk5) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_450,negated_conjecture,
( ~ leq(sk8,sk5)
| ~ leq(sk5,sk8) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_6622,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6623,definition,
iPr_def_13 = app(sk6,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6624,definition,
iPr_def_14 = app(iPr_def_13,sk7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6625,negated_conjecture,
iPr_def_14 = sk3,
inference(demodulation,[status(thm)],[c_445,c_6622,c_6623,c_6624]) ).
tcf(c_6627,negated_conjecture,
( memberP(sk7,sk8)
| ~ leq(sk8,sk5) ),
inference(demodulation,[status(thm)],[c_449]) ).
tcf(c_6629,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(demodulation,[status(thm)],[c_447]) ).
tcf(c_6630,negated_conjecture,
ssItem(sk8),
inference(demodulation,[status(thm)],[c_446]) ).
tcf(c_6631,negated_conjecture,
ssList(sk7),
inference(demodulation,[status(thm)],[c_444]) ).
tcf(c_6632,negated_conjecture,
ssList(sk6),
inference(demodulation,[status(thm)],[c_443]) ).
tcf(c_6633,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_442]) ).
tcf(c_6634,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X3)
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(demodulation,[status(thm)],[c_441]) ).
tcf(c_6635,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X1,X3)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X2,X3)
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(demodulation,[status(thm)],[c_440]) ).
tcf(c_9249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X3)
| ( app(app(X0,cons(X1,nil)),X2) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6634,c_6625]) ).
tcf(c_9271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X1,X3)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X2,X3)
| ( app(app(X0,cons(X1,nil)),X2) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6635,c_6625]) ).
tcf(c_9297,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(sk5,X2)
| ~ ssItem(sk5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X1,X2)
| ( app(app(X0,iPr_def_12),X1) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6622,c_9271]) ).
tcf(c_9298,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X2,sk5)
| ~ ssItem(sk5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X0,X2)
| ( app(app(X0,iPr_def_12),X1) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6622,c_9249]) ).
tcf(c_9299,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X2,sk5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X0,X2)
| ( app(app(X0,iPr_def_12),X1) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9298,c_6633]) ).
tcf(c_9306,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(sk5,X2)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X1,X2)
| ( app(app(X0,iPr_def_12),X1) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9297,c_6633]) ).
tcf(c_9337,plain,
! [X0: $i,X1: $i] :
( leq(sk5,X1)
| ~ ssList(sk6)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6623,c_9306]) ).
tcf(c_9338,plain,
! [X0: $i,X1: $i] :
( leq(X1,sk5)
| ~ ssList(sk6)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(sk6,X1)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6623,c_9299]) ).
tcf(c_9339,plain,
! [X0: $i,X1: $i] :
( leq(X1,sk5)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(sk6,X1)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9338,c_6632]) ).
tcf(c_9345,plain,
! [X0: $i,X1: $i] :
( leq(sk5,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9337,c_6632]) ).
tcf(c_9372,plain,
! [X0: $i] :
( leq(sk5,X0)
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(superposition,[status(thm)],[c_6624,c_9345]) ).
tcf(c_9373,plain,
! [X0: $i] :
( leq(X0,sk5)
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(superposition,[status(thm)],[c_6624,c_9339]) ).
tcf(c_9374,plain,
! [X0: $i] :
( leq(X0,sk5)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9373,c_6631]) ).
tcf(c_9378,plain,
! [X0: $i] :
( leq(sk5,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9372,c_6631]) ).
tcf(c_9396,plain,
( memberP(sk6,sk8)
| leq(sk5,sk8)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm)],[c_6629,c_9378]) ).
tcf(c_9397,plain,
( memberP(sk6,sk8)
| leq(sk5,sk8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9396,c_6630]) ).
tcf(c_9400,plain,
memberP(sk6,sk8),
inference(global_subsumption_just,[status(thm)],[c_9397,c_448,c_9397]) ).
tcf(c_9402,plain,
( leq(sk8,sk5)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm)],[c_9400,c_9374]) ).
tcf(c_9403,plain,
leq(sk8,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_9402,c_6630]) ).
tcf(c_9405,plain,
memberP(sk7,sk8),
inference(backward_subsumption_resolution,[status(thm)],[c_6627,c_9403]) ).
tcf(c_9406,plain,
( leq(sk5,sk8)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm)],[c_9405,c_9378]) ).
tcf(c_9407,plain,
leq(sk5,sk8),
inference(forward_subsumption_resolution,[status(thm)],[c_9406,c_6630]) ).
tcf(c_9408,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9407,c_9403,c_450]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC279-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.40 % Computer : n002.cluster.edu
% 0.15/5.40 % Model : x86_64 x86_64
% 0.15/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.40 % Memory : 8046.5625MB
% 0.15/5.40 % OS : Linux 6.8.0-71-generic
% 0.15/5.40 % CPULimit : 300
% 0.15/5.40 % WCLimit : 300
% 0.15/5.40 % DateTime : Thu Sep 24 17:25:56 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 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
% 0.15/5.45
% 0.15/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.45
% 0.15/5.45 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 4.17/6.32 % SZS status Started for theBenchmark.p
% 4.17/6.32 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/6.32
% 4.17/6.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.17/6.32
% 4.17/6.32 % ------ iProver source info
% 4.17/6.32
% 4.17/6.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.17/6.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.17/6.32 % git: non_committed_changes: false
% 4.17/6.32
% 4.17/6.32 % ------ Parsing...% successful
% 4.17/6.32
% 4.17/6.32
% 4.17/6.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.17/6.32
% 4.17/6.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.17/6.32
% 4.17/6.32 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.17/6.32
% 4.17/6.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.17/6.32 % ------ Proving...
% 4.17/6.32 % ------ Problem Properties
% 4.17/6.32
% 4.17/6.32 %
% 4.17/6.32 % clauses 193
% 4.17/6.32 % conjectures 13
% 4.17/6.32 % EPR 63
% 4.17/6.32 % Horn 164
% 4.17/6.32 % unary 68
% 4.17/6.32 % binary 25
% 4.17/6.32 % lits 573
% 4.17/6.32 % lits eq 75
% 4.17/6.32 % fd_pure 0
% 4.17/6.32 % fd_pseudo 0
% 4.17/6.32 % fd_cond 15
% 4.17/6.32 % fd_pseudo_cond 14
% 4.17/6.32 % AC symbols 0
% 4.17/6.32
% 4.17/6.32 % ------ Schedule dynamic 5 is on
% 4.17/6.32
% 4.17/6.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.17/6.32
% 4.17/6.32
% 4.17/6.32 % ------
% 4.17/6.32 % Current options:
% 4.17/6.32 % ------
% 4.17/6.32
% 4.17/6.32
% 4.17/6.32 %
% 4.17/6.32
% 4.17/6.32 % ------ Proving...
% 4.17/6.32 %
% 4.17/6.32
% 4.17/6.32 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/6.32
% 4.17/6.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.17/6.32
% 4.17/6.32
%------------------------------------------------------------------------------