%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN546-1 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 03:40:46 PM UTC 2026
% Result : Satisfiable 3.70s 6.17s
% Output : Model 3.38s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
%------ Positive definition of ndr1_0
fof(lit_def,axiom,
( ndr1_0
<=> $true ) ).
%------ Positive definition of c7_0
fof(lit_def_001,axiom,
( c7_0
<=> $true ) ).
%------ Positive definition of c3_0
fof(lit_def_002,axiom,
( c3_0
<=> $true ) ).
%------ Positive definition of c5_0
fof(lit_def_003,axiom,
( c5_0
<=> $false ) ).
%------ Positive definition of ssSkC0
fof(lit_def_004,axiom,
( ssSkC0
<=> $true ) ).
%------ Positive definition of c6_0
fof(lit_def_005,axiom,
( c6_0
<=> $true ) ).
%------ Positive definition of ssSkC27
fof(lit_def_006,axiom,
( ssSkC27
<=> $true ) ).
%------ Positive definition of ssSkC26
fof(lit_def_007,axiom,
( ssSkC26
<=> $false ) ).
%------ Positive definition of ssSkC24
fof(lit_def_008,axiom,
( ssSkC24
<=> $true ) ).
%------ Positive definition of ssSkC22
fof(lit_def_009,axiom,
( ssSkC22
<=> $true ) ).
%------ Positive definition of ssSkC20
fof(lit_def_010,axiom,
( ssSkC20
<=> $true ) ).
%------ Positive definition of ssSkC16
fof(lit_def_011,axiom,
( ssSkC16
<=> $true ) ).
%------ Positive definition of ssSkC15
fof(lit_def_012,axiom,
( ssSkC15
<=> $true ) ).
%------ Positive definition of ssSkC13
fof(lit_def_013,axiom,
( ssSkC13
<=> $true ) ).
%------ Positive definition of ssSkC12
fof(lit_def_014,axiom,
( ssSkC12
<=> $false ) ).
%------ Positive definition of ssSkC11
fof(lit_def_015,axiom,
( ssSkC11
<=> $true ) ).
%------ Positive definition of ssSkC10
fof(lit_def_016,axiom,
( ssSkC10
<=> $false ) ).
%------ Positive definition of ssSkC9
fof(lit_def_017,axiom,
( ssSkC9
<=> $true ) ).
%------ Positive definition of ssSkC8
fof(lit_def_018,axiom,
( ssSkC8
<=> $true ) ).
%------ Positive definition of ssSkC5
fof(lit_def_019,axiom,
( ssSkC5
<=> $true ) ).
%------ Positive definition of ssSkC4
fof(lit_def_020,axiom,
( ssSkC4
<=> $false ) ).
%------ Positive definition of ssSkC2
fof(lit_def_021,axiom,
( ssSkC2
<=> $false ) ).
%------ Positive definition of ssSkC1
fof(lit_def_022,axiom,
( ssSkC1
<=> $true ) ).
%------ Positive definition of c1_0
fof(lit_def_023,axiom,
( c1_0
<=> $false ) ).
%------ Positive definition of c4_0
fof(lit_def_024,axiom,
( c4_0
<=> $false ) ).
%------ Positive definition of ndr1_1
fof(lit_def_025,axiom,
! [X0] :
( ndr1_1(X0)
<=> ( X0 = a362
| X0 = a326
| X0 = a351
| X0 = a376
| X0 = a417
| X0 = a305
| X0 = a347
| X0 = a385
| X0 = a425
| X0 = a442
| X0 = a445
| X0 = a454
| X0 = a315
| X0 = a371
| X0 = a379
| X0 = a380
| X0 = a323
| X0 = a345
| X0 = a397
| X0 = a423
| X0 = a438
| X0 = a302
| X0 = a309
| X0 = a402 ) ) ).
%------ Positive definition of c6_1
fof(lit_def_026,axiom,
! [X0] :
( c6_1(X0)
<=> $false ) ).
%------ Positive definition of ssSkC18
fof(lit_def_027,axiom,
( ssSkC18
<=> $false ) ).
%------ Positive definition of c2_0
fof(lit_def_028,axiom,
( c2_0
<=> $false ) ).
%------ Positive definition of ssSkC7
fof(lit_def_029,axiom,
( ssSkC7
<=> $true ) ).
%------ Positive definition of c3_1
fof(lit_def_030,axiom,
! [X0] :
( c3_1(X0)
<=> ( X0 = a305
| X0 = a385
| X0 = a425
| X0 = a428
| X0 = a454
| X0 = a315
| X0 = a371
| X0 = a379
| X0 = a380
| X0 = a453
| X0 = a345
| X0 = a302
| X0 = a309
| ( X0 != a413
& X0 != a397 ) ) ) ).
%------ Positive definition of c8_0
fof(lit_def_031,axiom,
( c8_0
<=> $true ) ).
%------ Positive definition of c2_1
fof(lit_def_032,axiom,
! [X0] :
( c2_1(X0)
<=> ( X0 = a385
| X0 = a454
| X0 = a315
| X0 = a302 ) ) ).
%------ Positive definition of c5_1
fof(lit_def_033,axiom,
! [X0] :
( c5_1(X0)
<=> ( X0 = a417
| X0 = a385
| X0 = a400
| X0 = a354
| X0 = a441
| ( X0 != a362
& X0 != a326
& X0 != a376
& X0 != a305
& X0 != a413
& X0 != a442
& X0 != a454
& X0 != a315
& X0 != a371
& X0 != a379
& X0 != a380
& X0 != a323
& X0 != a397
& X0 != a302
& X0 != a309
& X0 != a402 ) ) ) ).
%------ Positive definition of ssSkP4
fof(lit_def_034,axiom,
! [X0] :
( ssSkP4(X0)
<=> $true ) ).
%------ Positive definition of c4_1
fof(lit_def_035,axiom,
! [X0] :
( c4_1(X0)
<=> ( X0 = a417
| X0 = a316
| X0 = a347
| X0 = a413
| X0 = a423 ) ) ).
%------ Positive definition of ssSkP3
fof(lit_def_036,axiom,
! [X0] :
( ssSkP3(X0)
<=> ( X0 = a413
| ( X0 != a362
& X0 != a326
& X0 != a351
& X0 != a376
& X0 != a417
& X0 != a305
& X0 != a347
& X0 != a385
& X0 != a413
& X0 != a442
& X0 != a445
& X0 != a454
& X0 != a315
& X0 != a371
& X0 != a379
& X0 != a380
& X0 != a323
& X0 != a345
& X0 != a397
& X0 != a423
& X0 != a438
& X0 != a302
& X0 != a309
& X0 != a402 ) ) ) ).
%------ Positive definition of ssSkP2
fof(lit_def_037,axiom,
! [X0] :
( ssSkP2(X0)
<=> ( X0 = a362
| X0 = a351
| X0 = a385
| X0 = a442
| X0 = a379
| X0 = a345
| X0 = a397
| X0 = a423
| X0 = a309
| X0 = a402
| ( X0 != a362
& X0 != a326
& X0 != a351
& X0 != a442
& X0 != a454
& X0 != a315
& X0 != a371
& X0 != a379
& X0 != a309 ) ) ) ).
%------ Positive definition of c1_1
fof(lit_def_038,axiom,
! [X0] :
( c1_1(X0)
<=> ( X0 = a413
| X0 = a338
| X0 = a323 ) ) ).
%------ Positive definition of ssSkP1
fof(lit_def_039,axiom,
! [X0] :
( ssSkP1(X0)
<=> $true ) ).
%------ Positive definition of ssSkP0
fof(lit_def_040,axiom,
! [X0] :
( ssSkP0(X0)
<=> ( X0 = a362
| X0 = a326
| X0 = a351
| X0 = a305
| X0 = a385
| X0 = a425
| X0 = a442
| X0 = a454
| X0 = a315
| X0 = a371
| X0 = a379
| X0 = a345
| X0 = a302
| X0 = a309
| X0 = a402
| ( X0 != a362
& X0 != a326
& X0 != a351
& X0 != a442
& X0 != a454
& X0 != a315
& X0 != a371
& X0 != a379
& X0 != a309 ) ) ) ).
%------ Positive definition of c8_1
fof(lit_def_041,axiom,
! [X0] :
( c8_1(X0)
<=> ( X0 = a314
| X0 = a347
| X0 = a413
| X0 = a425
| X0 = a442
| X0 = a317
| X0 = a423
| X0 = a441
| ( X0 != a362
& X0 != a326
& X0 != a351
& X0 != a314
& X0 != a413
& X0 != a442
& X0 != a454
& X0 != a315
& X0 != a371
& X0 != a379
& X0 != a423
& X0 != a441
& X0 != a309 ) ) ) ).
%------ Positive definition of ssSkC23
fof(lit_def_042,axiom,
( ssSkC23
<=> $false ) ).
%------ Positive definition of c6_2
fof(lit_def_043,axiom,
! [X0,X1] :
( c6_2(X0,X1)
<=> ( ( X0 != a305
& X0 != a385
& X0 != a454
& X0 != a315
& X0 != a345
& X0 != a302
& X0 != a402
& X1 = a340 )
| ( X1 = a430
& X0 = a413 )
| ( X1 = a383
& X0 = a380 )
| ( X1 = a303
& X0 = a302 )
| ( X1 = a403
& X0 = a402 ) ) ) ).
%------ Positive definition of c3_2
fof(lit_def_044,axiom,
! [X0,X1] :
( c3_2(X0,X1)
<=> ( ( X0 != a397
& X1 = a411 )
| ( X1 = a377
& X0 = a376 )
| ( X1 = a348
& X0 = a347 )
| ( X1 = a320
& X0 = a385 )
| ( X1 = a390
& X0 = a385 )
| ( X1 = a310
& X0 = a425 )
| ( X1 = a430
& X0 = a425 )
| ( X1 = a434
& X0 = a425 )
| ( X1 = a404
& X0 = a425 )
| ( X1 = a426
& X0 = a425 )
| ( X1 = a340
& X0 = a425 )
| ( X1 != a310
& X1 != a430
& X1 != a434
& X1 != a404
& X1 != a340
& X0 = a425 )
| ( X1 = a446
& X0 = a445 )
| ( X1 = a310
& X0 = a379 )
| ( X1 = a430
& X0 = a379 )
| ( X1 = a434
& X0 = a379 )
| ( X1 != a310
& X1 != a430
& X1 != a434
& X1 != a404
& X1 != a340
& X0 = a379 )
| ( X1 = a382
& X0 = a380 )
| ( X1 = a390
& X0 = a345 )
| ( X1 = a411
& X0 = a397 )
| ( X1 = a390
& X0 = a302 )
| ( X1 = a389
& X0 = a309 )
| ( X1 = a434
& X0 = a402 )
| ( X1 = a403
& X0 = a402 ) ) ) ).
%------ Positive definition of c7_1
fof(lit_def_045,axiom,
! [X0] :
( c7_1(X0)
<=> ( X0 = a425
| X0 = a380
| X0 = a400
| X0 = a345
| X0 = a397
| ( X0 != a362
& X0 != a326
& X0 != a351
& X0 != a385
& X0 != a442
& X0 != a315
& X0 != a371
& X0 != a379
& X0 != a309
& X0 != a402 ) ) ) ).
%------ Positive definition of ssSkC19
fof(lit_def_046,axiom,
( ssSkC19
<=> $true ) ).
%------ Positive definition of ssSkC17
fof(lit_def_047,axiom,
( ssSkC17
<=> $true ) ).
%------ Positive definition of ssSkC6
fof(lit_def_048,axiom,
( ssSkC6
<=> $false ) ).
%------ Positive definition of c4_2
fof(lit_def_049,axiom,
! [X0,X1] :
( c4_2(X0,X1)
<=> ( ( X1 = a319
& X0 = a305 )
| ( X1 = a340
& X0 = a305 )
| ( X1 = a320
& X0 = a385 )
| ( X1 = a391
& X0 = a385 )
| ( X1 = a341
& X0 = a385 )
| ( X1 = a426
& X0 = a425 )
| ( X1 = a447
& X0 = a445 )
| ( X1 = a320
& X0 = a454 )
| ( X1 = a341
& X0 = a454 )
| ( X1 = a455
& X0 = a454 )
| ( X1 = a320
& X0 = a315 )
| ( X1 = a341
& X0 = a315 )
| ( X1 = a404
& X0 = a379 )
| ( X1 = a340
& X0 = a379 )
| ( X1 = a319
& X0 = a380 )
| ( X1 = a372
& X0 = a323 )
| ( X1 = a324
& X0 = a323 )
| ( X1 = a319
& X0 = a345 )
| ( X1 = a320
& X0 = a345 )
| ( X1 = a341
& X0 = a345 )
| ( X1 = a319
& X0 = a397 )
| ( X1 = a367
& X0 = a397 )
| ( X1 = a440
& X0 = a438 )
| ( X1 = a320
& X0 = a302 )
| ( X1 = a341
& X0 = a302 ) ) ) ).
%------ Positive definition of c1_2
fof(lit_def_050,axiom,
! [X0,X1] :
( c1_2(X0,X1)
<=> ( ( X1 = a341
& X0 = a385 )
| ( X1 = a341
& X0 = a454 )
| ( X1 = a341
& X0 = a315 )
| ( X1 = a383
& X0 = a380 )
| ( X1 = a399
& X0 = a397 )
| ( X1 = a404
& X0 = a423 )
| ( X1 = a424
& X0 = a423 )
| ( X1 = a439
& X0 = a438 )
| ( X1 = a341
& X0 = a302 ) ) ) ).
%------ Positive definition of c8_2
fof(lit_def_051,axiom,
! [X0,X1] :
( c8_2(X0,X1)
<=> ( ( X1 = a412
& X0 = a376 )
| ( X1 = a306
& X0 = a305 )
| ( X1 = a412
& X0 = a385 )
| ( X1 = a391
& X0 = a385 )
| ( X1 = a412
& X0 = a425 )
| ( X1 = a412
& X0 = a454 )
| ( X1 = a455
& X0 = a454 )
| ( X1 = a344
& X0 = a380 )
| ( X1 = a412
& X0 = a380 )
| ( X1 = a434
& X0 = a380 )
| ( X1 = a382
& X0 = a380 )
| ( X1 = a412
& X0 = a323 )
| ( X1 = a344
& X0 = a345 )
| ( X1 = a412
& X0 = a345 )
| ( X1 = a434
& X0 = a345 )
| ( X1 = a344
& X0 = a397 )
| ( X1 = a412
& X0 = a397 )
| ( X1 = a434
& X0 = a397 )
| ( X1 = a398
& X0 = a397 )
| ( X1 = a424
& X0 = a423 )
| ( X1 = a412
& X0 = a302 )
| ( X1 = a412
& X0 = a402 )
| ( X1 = a403
& X0 = a402 ) ) ) ).
%------ Positive definition of c5_2
fof(lit_def_052,axiom,
! [X0,X1] :
( c5_2(X0,X1)
<=> ( ( X1 = a398
& X0 = a397 )
| ( X1 = a424
& X0 = a423 ) ) ) ).
%------ Positive definition of c2_2
fof(lit_def_053,axiom,
! [X0,X1] :
( c2_2(X0,X1)
<=> ( ( X0 != a362
& X0 != a453
& X0 != a309
& X1 = a389 )
| ( X1 = a306
& X0 = a305 )
| ( X1 = a348
& X0 = a347 )
| ( X1 = a430
& X0 = a413 )
| ( X1 = a412
& X0 = a425 )
| ( X1 = a381
& X0 = a380 )
| ( X1 = a389
& X0 = a453 )
| ( X1 = a346
& X0 = a345 )
| ( X1 = a399
& X0 = a397 )
| ( X1 = a389
& X0 = a309 ) ) ) ).
%------ Positive definition of c7_2
fof(lit_def_054,axiom,
! [X0,X1] :
( c7_2(X0,X1)
<=> ( ( X0 != a351
& X0 != a385
& X0 != a442
& X0 != a379
& X0 != a380
& X0 != a345
& X0 != a397
& X0 != a423
& X0 != a309
& X0 != a402
& X1 = a389 )
| ( X1 = a341
& X0 = a385 )
| ( X1 = a341
& X0 = a454 )
| ( X1 = a341
& X0 = a315 )
| ( X1 = a389
& X0 = a380 )
| ( X1 = a398
& X0 = a397 )
| ( X1 = a341
& X0 = a302 ) ) ) ).
%------ Positive definition of ssSkC28
fof(lit_def_055,axiom,
( ssSkC28
<=> $true ) ).
%------ Positive definition of ssSkC25
fof(lit_def_056,axiom,
( ssSkC25
<=> $false ) ).
%------ Positive definition of ssSkC14
fof(lit_def_057,axiom,
( ssSkC14
<=> $false ) ).
%------ Positive definition of ssSkC21
fof(lit_def_058,axiom,
( ssSkC21
<=> $false ) ).
%------ Positive definition of ssSkC3
fof(lit_def_059,axiom,
( ssSkC3
<=> $false ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN546-1 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.37 % Computer : n017.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Fri Sep 25 01:39:08 UTC 2026
% 0.12/5.37 % CPUTime :
% 0.12/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.41 Running EPR theorem proving
% 0.16/5.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42
% 0.16/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.42
% 0.16/5.42 % Detected problem language: tptp
% 0.16/5.43 % Proving...
% 3.70/6.17 % SZS status Started for theBenchmark.p
% 3.70/6.17 % SZS status Satisfiable for theBenchmark.p
% 3.70/6.17
% 3.70/6.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.70/6.17
% 3.70/6.17 % ------ iProver source info
% 3.70/6.17
% 3.70/6.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.70/6.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.70/6.17 % git: non_committed_changes: false
% 3.70/6.17
% 3.70/6.17 % ------ Parsing...% successful
% 3.70/6.17
% 3.70/6.17
% 3.70/6.17 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.70/6.17 % ------ Proving...
% 3.70/6.17 % ------ Problem Properties
% 3.70/6.17
% 3.70/6.17 %
% 3.70/6.17 % clauses 525
% 3.70/6.17 % conjectures 525
% 3.70/6.17 % EPR 525
% 3.70/6.17 % Horn 212
% 3.70/6.17 % unary 0
% 3.70/6.17 % binary 141
% 3.70/6.17 % lits 2379
% 3.70/6.17 % lits eq 0
% 3.70/6.17 % fd_pure 0
% 3.70/6.17 % fd_pseudo 0
% 3.70/6.17 % fd_cond 0
% 3.70/6.17 % fd_pseudo_cond 0
% 3.70/6.17 % AC symbols 0
% 3.70/6.17
% 3.70/6.17 % ------ Input Options Time Limit: Unbounded
% 3.70/6.17
% 3.70/6.17
% 3.70/6.17 % ------
% 3.70/6.17 % Current options:
% 3.70/6.17 % ------
% 3.70/6.17
% 3.70/6.17
% 3.70/6.17 %
% 3.70/6.17
% 3.70/6.17 % ------ Proving...
% 3.70/6.17 %
% 3.70/6.17
% 3.70/6.17 % SZS status Satisfiable for theBenchmark.p
% 3.70/6.17
% 3.70/6.17 ------ Building Model...Done
% 3.70/6.17
% 3.70/6.17 %------ The model is defined over ground terms (initial term algebra).
% 3.70/6.17 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n))))
% 3.70/6.17 %------ where \phi is a formula over the term algebra.
% 3.70/6.17 %------ If we have equality in the problem then it is also defined as a predicate above,
% 3.70/6.17 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type
% 3.70/6.17 %------ See help for --sat_out_model for different model outputs.
% 3.70/6.17 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
% 3.70/6.17 %------ where the first argument stands for the sort ($i in the unsorted case)
% 3.70/6.17 % SZS output start Model for theBenchmark.p
% See solution above
% 3.38/6.19
%------------------------------------------------------------------------------