%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC153+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 : n006.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 03:08:06 PM UTC 2026
% Result : Theorem 1.08s 1.29s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 22 unt; 0 def)
% Number of atoms : 279 ( 30 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 376 ( 144 ~; 136 |; 76 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 76 !; 32 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ! [X13] :
( ssList(X13)
=> ! [X14] :
( ssList(X14)
=> ( ( leq(X10,X11)
& ! [X15] :
( ssItem(X15)
=> ( ( leq(X10,X15)
& leq(X15,X11) )
| ~ memberP(X13,X15) ) ) )
| ~ leq(X11,X10)
| app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X0 ) ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ( ? [X9] :
( ( ~ leq(X9,X5)
| ~ leq(X4,X9) )
& memberP(X7,X9)
& ssItem(X9) )
| ~ leq(X4,X5) )
& leq(X5,X4)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X2
& ssList(X8) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| X2 != X0
| X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ! [X13] :
( ssList(X13)
=> ! [X14] :
( ssList(X14)
=> ( ( leq(X10,X11)
& ! [X15] :
( ssItem(X15)
=> ( ( leq(X10,X15)
& leq(X15,X11) )
| ~ memberP(X13,X15) ) ) )
| ~ leq(X11,X10)
| app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X0 ) ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ( ? [X9] :
( ( ~ leq(X9,X5)
| ~ leq(X4,X9) )
& memberP(X7,X9)
& ssItem(X9) )
| ~ leq(X4,X5) )
& leq(X5,X4)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X2
& ssList(X8) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| X2 != X0
| X3 != X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& ( ~ leq(X10,X11)
| ? [X15] :
( ssItem(X15)
& ( ~ leq(X10,X15)
| ~ leq(X15,X11) )
& memberP(X13,X15) ) )
& leq(X11,X10)
& app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) = X0 ) ) ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ( ! [X9] :
( ( leq(X9,X5)
& leq(X4,X9) )
| ~ memberP(X7,X9)
| ~ ssItem(X9) )
& leq(X4,X5) )
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X2
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& ( ~ leq(X10,X11)
| ? [X15] :
( ssItem(X15)
& ( ~ leq(X10,X15)
| ~ leq(X15,X11) )
& memberP(X13,X15) ) )
& leq(X11,X10)
& app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) = X0 ) ) ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ( ! [X9] :
( ( leq(X9,X5)
& leq(X4,X9) )
| ~ memberP(X7,X9)
| ~ ssItem(X9) )
& leq(X4,X5) )
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X2
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f137,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssItem(sK4)
& ssItem(sK5)
& ssList(sK6)
& ssList(sK7)
& ssList(sK8)
& ( ~ leq(sK4,sK5)
| ( ssItem(sK9)
& ( ~ leq(sK4,sK9)
| ~ leq(sK9,sK5) )
& memberP(sK7,sK9) ) )
& leq(sK5,sK4)
& sK0 = app(app(app(app(sK6,cons(sK4,nil)),sK7),cons(sK5,nil)),sK8)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ( ! [X9] :
( ( leq(X9,X5)
& leq(X4,X9) )
| ~ memberP(X7,X9)
| ~ ssItem(X9) )
& leq(X4,X5) )
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != sK2
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X10,sK4),skolemize(X11,sK5),skolemize(X12,sK6),skolemize(X13,sK7),skolemize(X14,sK8),skolemize(X15,sK9)],[f99]) ).
fof(f155,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f137]) ).
fof(f156,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f137]) ).
fof(f157,plain,
ssList(sK6),
inference(cnf_transformation,[],[f137]) ).
fof(f158,plain,
ssList(sK7),
inference(cnf_transformation,[],[f137]) ).
fof(f159,plain,
ssList(sK8),
inference(cnf_transformation,[],[f137]) ).
fof(f160,plain,
( ~ leq(sK4,sK5)
| ssItem(sK9) ),
inference(cnf_transformation,[],[f137]) ).
fof(f161,plain,
( ~ leq(sK4,sK5)
| ~ leq(sK4,sK9)
| ~ leq(sK9,sK5) ),
inference(cnf_transformation,[],[f137]) ).
fof(f162,plain,
( ~ leq(sK4,sK5)
| memberP(sK7,sK9) ),
inference(cnf_transformation,[],[f137]) ).
fof(f163,plain,
leq(sK5,sK4),
inference(cnf_transformation,[],[f137]) ).
fof(f164,plain,
sK0 = app(app(app(app(sK6,cons(sK4,nil)),sK7),cons(sK5,nil)),sK8),
inference(cnf_transformation,[],[f137]) ).
fof(f165,plain,
! [X8,X6,X9,X7,X4,X5] :
( leq(X9,X5)
| ~ memberP(X7,X9)
| ~ ssItem(X9)
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != sK2
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f166,plain,
! [X8,X6,X9,X7,X4,X5] :
( leq(X4,X9)
| ~ memberP(X7,X9)
| ~ ssItem(X9)
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != sK2
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f167,plain,
! [X8,X6,X7,X4,X5] :
( leq(X4,X5)
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != sK2
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f168,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f137]) ).
fof(f215,plain,
sK2 = app(app(app(app(sK6,cons(sK4,nil)),sK7),cons(sK5,nil)),sK8),
inference(definition_unfolding,[],[f164,f168]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ leq(X3,X1)
| ( app(app(app(app(X0,cons(X1,nil)),X2),cons(X3,nil)),X4) != sK2 ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( leq(X1,X5)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ memberP(X2,X5)
| ~ leq(X3,X1)
| ( app(app(app(app(X0,cons(X1,nil)),X2),cons(X3,nil)),X4) != sK2 ) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( leq(X5,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ memberP(X2,X5)
| ~ leq(X3,X1)
| ( app(app(app(app(X0,cons(X1,nil)),X2),cons(X3,nil)),X4) != sK2 ) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_52,negated_conjecture,
app(app(app(app(sK6,cons(sK4,nil)),sK7),cons(sK5,nil)),sK8) = sK2,
inference(cnf_transformation,[],[f215]) ).
tcf(c_53,negated_conjecture,
leq(sK5,sK4),
inference(cnf_transformation,[],[f163]) ).
tcf(c_54,negated_conjecture,
( memberP(sK7,sK9)
| ~ leq(sK4,sK5) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_55,negated_conjecture,
( ~ leq(sK9,sK5)
| ~ leq(sK4,sK9)
| ~ leq(sK4,sK5) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_56,negated_conjecture,
( ssItem(sK9)
| ~ leq(sK4,sK5) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_57,negated_conjecture,
ssList(sK8),
inference(cnf_transformation,[],[f159]) ).
tcf(c_58,negated_conjecture,
ssList(sK7),
inference(cnf_transformation,[],[f158]) ).
tcf(c_59,negated_conjecture,
ssList(sK6),
inference(cnf_transformation,[],[f157]) ).
tcf(c_60,negated_conjecture,
ssItem(sK5),
inference(cnf_transformation,[],[f156]) ).
tcf(c_61,negated_conjecture,
ssItem(sK4),
inference(cnf_transformation,[],[f155]) ).
tcf(c_2688,plain,
( leq(sK4,sK5)
| ~ ssList(sK8)
| ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5)
| ~ ssItem(sK4)
| ~ leq(sK5,sK4) ),
inference(superposition,[status(thm)],[c_52,c_49]) ).
tcf(c_2690,plain,
leq(sK4,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_2688,c_57,c_58,c_59,c_60,c_61,c_53]) ).
tcf(c_2698,plain,
ssItem(sK9),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_2690]) ).
tcf(c_2699,plain,
( ~ leq(sK9,sK5)
| ~ leq(sK4,sK9) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_2690]) ).
tcf(c_2700,plain,
memberP(sK7,sK9),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_2690]) ).
tcf(c_2724,plain,
! [X0: $i] :
( leq(sK4,X0)
| ~ ssList(sK8)
| ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5)
| ~ ssItem(sK4)
| ~ ssItem(X0)
| ~ leq(sK5,sK4)
| ~ memberP(sK7,X0) ),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_2726,plain,
! [X0: $i] :
( leq(sK4,X0)
| ~ ssItem(X0)
| ~ memberP(sK7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2724,c_57,c_58,c_59,c_60,c_61,c_53]) ).
tcf(c_2760,plain,
! [X0: $i] :
( leq(X0,sK5)
| ~ ssList(sK8)
| ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5)
| ~ ssItem(sK4)
| ~ ssItem(X0)
| ~ leq(sK5,sK4)
| ~ memberP(sK7,X0) ),
inference(superposition,[status(thm)],[c_52,c_51]) ).
tcf(c_2762,plain,
! [X0: $i] :
( leq(X0,sK5)
| ~ ssItem(X0)
| ~ memberP(sK7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2760,c_57,c_58,c_59,c_60,c_61,c_53]) ).
tcf(c_2782,plain,
( leq(sK4,sK9)
| ~ ssItem(sK9) ),
inference(superposition,[status(thm)],[c_2700,c_2726]) ).
tcf(c_2783,plain,
leq(sK4,sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2782,c_2698]) ).
tcf(c_2822,plain,
~ leq(sK9,sK5),
inference(global_subsumption_just,[status(thm)],[c_2699,c_55,c_2690,c_2783]) ).
tcf(c_2830,plain,
( leq(sK9,sK5)
| ~ ssItem(sK9) ),
inference(superposition,[status(thm)],[c_2700,c_2762]) ).
tcf(c_2831,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2830,c_2822,c_2698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC153+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n006.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 16:40:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.08/1.29 % SZS status Started for theBenchmark.p
% 1.08/1.29 % SZS status Theorem for theBenchmark.p
% 1.08/1.29
% 1.08/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.08/1.29
% 1.08/1.29 % ------ iProver source info
% 1.08/1.29
% 1.08/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.08/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.08/1.29 % git: non_committed_changes: false
% 1.08/1.29
% 1.08/1.29 % ------ Parsing...
% 1.08/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.08/1.29
% 1.08/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.08/1.29
% 1.08/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.08/1.29
% 1.08/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.08/1.29 % ------ Proving...
% 1.08/1.29 % ------ Problem Properties
% 1.08/1.29
% 1.08/1.29 %
% 1.08/1.29 % clauses 58
% 1.08/1.29 % conjectures 15
% 1.08/1.29 % EPR 25
% 1.08/1.29 % Horn 52
% 1.08/1.29 % unary 14
% 1.08/1.29 % binary 7
% 1.08/1.29 % lits 204
% 1.08/1.29 % lits eq 33
% 1.08/1.29 % fd_pure 0
% 1.08/1.29 % fd_pseudo 0
% 1.08/1.29 % fd_cond 4
% 1.08/1.29 % fd_pseudo_cond 7
% 1.08/1.29 % AC symbols 0
% 1.08/1.29
% 1.08/1.29 % ------ Schedule dynamic 5 is on
% 1.08/1.29
% 1.08/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.08/1.29
% 1.08/1.29
% 1.08/1.29 % ------
% 1.08/1.29 % Current options:
% 1.08/1.29 % ------
% 1.08/1.29
% 1.08/1.29
% 1.08/1.29 %
% 1.08/1.29
% 1.08/1.29 % ------ Proving...
% 1.08/1.29 %
% 1.08/1.29
% 1.08/1.29 % SZS status Theorem for theBenchmark.p
% 1.08/1.29
% 1.08/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.08/1.29
% 1.08/1.29
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