%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP124-8.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 01:31:11 PM UTC 2026
% Result : Satisfiable 3.45s 1.18s
% Output : Model 3.45s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
%------ Positive definition of next
fof(lit_def,axiom,
! [X0,X1] :
( next(X0,X1)
<=> ( ( X1 = e_5
& X0 = e_4 )
| ( X1 = e_4
& X0 = e_3 )
| ( X1 = e_3
& X0 = e_2 )
| ( X1 = e_2
& X0 = e_1 )
| ( X1 = e_1
& X0 = e_0 ) ) ) ).
%------ Positive definition of greater
fof(lit_def_001,axiom,
! [X0,X1] :
( greater(X0,X1)
<=> ( ( X1 = e_4
& X0 = e_5 )
| ( X1 = e_3
& X0 = e_5 )
| ( X1 = e_2
& X0 = e_5 )
| ( X1 = e_1
& X0 = e_5 )
| ( X1 = e_0
& X0 = e_5 )
| ( X1 = e_3
& X0 = e_4 )
| ( X1 = e_2
& X0 = e_4 )
| ( X1 = e_1
& X0 = e_4 )
| ( X1 = e_0
& X0 = e_4 )
| ( X1 = e_2
& X0 = e_3 )
| ( X1 = e_1
& X0 = e_3 )
| ( X1 = e_0
& X0 = e_3 )
| ( X1 = e_1
& X0 = e_2 )
| ( X1 = e_0
& X0 = e_2 )
| ( X1 = e_0
& X0 = e_1 ) ) ) ).
%------ Positive definition of cycle
fof(lit_def_002,axiom,
! [X0,X1] :
( cycle(X0,X1)
<=> ( ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X0 != e_0
& X1 = e_0 )
| ( X1 = e_0
& X0 = e_5 )
| ( X1 = e_1
& X0 = e_4 )
| ( X1 = e_0
& X0 = e_3 )
| ( X1 = e_1
& X0 = e_2 )
| ( X1 = e_0
& X0 = e_1 ) ) ) ).
%------ Positive definition of equalish
fof(lit_def_003,axiom,
! [X0,X1] :
( equalish(X0,X1)
<=> ( ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X1 = e_1 )
| ( ( X1 != e_4
| X0 != e_5 )
& ( X1 != e_3
| X0 != e_5 )
& ( X1 != e_2
| X0 != e_5 )
& ( X1 != e_1
| X0 != e_5 )
& ( X1 != e_5
| X0 != e_4 )
& ( X1 != e_3
| X0 != e_4 )
& ( X1 != e_2
| X0 != e_4 )
& ( X1 != e_1
| X0 != e_4 )
& ( X1 != e_5
| X0 != e_3 )
& ( X1 != e_4
| X0 != e_3 )
& ( X1 != e_2
| X0 != e_3 )
& ( X1 != e_1
| X0 != e_3 )
& ( X1 != e_5
| X0 != e_2 )
& ( X1 != e_4
| X0 != e_2 )
& ( X1 != e_3
| X0 != e_2 )
& ( X1 != e_1
| X0 != e_2 )
& ( X1 != e_5
| X0 != e_1 )
& ( X1 != e_4
| X0 != e_1 )
& ( X1 != e_3
| X0 != e_1 )
& ( X1 != e_2
| X0 != e_1 ) ) ) ) ).
%------ Positive definition of group_element
fof(lit_def_004,axiom,
! [X0] :
( group_element(X0)
<=> ( X0 = e_5
| X0 = e_4
| X0 = e_3
| X0 = e_2
| X0 = e_1 ) ) ).
%------ Positive definition of product1
fof(lit_def_005,axiom,
! [X0,X1,X2] :
( product1(X0,X1,X2)
<=> ( ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& ( X1 != e_5
| X0 != e_5 )
& ( X1 != e_3
| X0 != e_5 )
& ( X1 != e_2
| X0 != e_5 )
& X0 != e_5
& ( X1 != e_4
| X0 != e_4 )
& ( X1 != e_3
| X0 != e_4 )
& ( X1 != e_2
| X0 != e_4 )
& ( X1 != e_1
| X0 != e_4 )
& X0 != e_4
& ( X1 != e_5
| X0 != e_3 )
& ( X1 != e_4
| X0 != e_3 )
& ( X1 != e_3
| X0 != e_3 )
& ( X1 != e_2
| X0 != e_3 )
& X0 != e_3
& ( X1 != e_5
| X0 != e_2 )
& ( X1 != e_4
| X0 != e_2 )
& ( X1 != e_3
| X0 != e_2 )
& ( X1 != e_2
| X0 != e_2 )
& X0 != e_2
& ( X1 != e_5
| X0 != e_1 )
& ( X1 != e_4
| X0 != e_1 )
& ( X1 != e_3
| X0 != e_1 )
& ( X1 != e_2
| X0 != e_1 )
& X2 = e_1 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X2 = X0
& X1 = X0 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_3
& X1 = e_5 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_2
& X1 = e_4 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_4
& X1 = e_3 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_5
& X1 = e_2 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_3
& X0 = e_5 )
| ( X2 = e_5
& X1 = e_5
& X0 = e_5 )
| ( X2 = e_1
& X1 = e_4
& X0 = e_5 )
| ( X2 = e_2
& X1 = e_3
& X0 = e_5 )
| ( X2 = e_4
& X1 = e_2
& X0 = e_5 )
| ( X2 = e_3
& X1 = e_1
& X0 = e_5 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_2
& X0 = e_4 )
| ( X2 = e_1
& X1 = e_5
& X0 = e_4 )
| ( X2 = e_4
& X1 = e_4
& X0 = e_4 )
| ( X2 = e_5
& X1 = e_3
& X0 = e_4 )
| ( X2 = e_3
& X1 = e_2
& X0 = e_4 )
| ( X2 = e_2
& X1 = e_1
& X0 = e_4 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_4
& X0 = e_3 )
| ( X2 = e_2
& X1 = e_5
& X0 = e_3 )
| ( X2 = e_5
& X1 = e_4
& X0 = e_3 )
| ( X2 = e_3
& X1 = e_3
& X0 = e_3 )
| ( X2 = e_1
& X1 = e_2
& X0 = e_3 )
| ( X2 = e_4
& X1 = e_1
& X0 = e_3 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_5
& X0 = e_2 )
| ( X2 = e_4
& X1 = e_5
& X0 = e_2 )
| ( X2 = e_3
& X1 = e_4
& X0 = e_2 )
| ( X2 = e_1
& X1 = e_3
& X0 = e_2 )
| ( X2 = e_2
& X1 = e_2
& X0 = e_2 )
| ( X2 = e_5
& X1 = e_1
& X0 = e_2 )
| ( X2 = e_3
& X1 = e_5
& X0 = e_1 )
| ( X2 = e_2
& X1 = e_4
& X0 = e_1 )
| ( X2 = e_4
& X1 = e_3
& X0 = e_1 )
| ( X2 = e_5
& X1 = e_2
& X0 = e_1 ) ) ) ).
%------ Positive definition of product2
fof(lit_def_006,axiom,
! [X0,X1,X2] :
( product2(X0,X1,X2)
<=> ( ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& ( X1 != e_5
| X0 != e_5 )
& ( X1 != e_3
| X0 != e_5 )
& ( X1 != e_2
| X0 != e_5 )
& ( X1 != e_1
| X0 != e_5 )
& X0 != e_5
& ( X1 != e_4
| X0 != e_4 )
& ( X1 != e_3
| X0 != e_4 )
& ( X1 != e_2
| X0 != e_4 )
& X0 != e_4
& ( X1 != e_5
| X0 != e_3 )
& ( X1 != e_4
| X0 != e_3 )
& ( X1 != e_3
| X0 != e_3 )
& ( X1 != e_2
| X0 != e_3 )
& X0 != e_3
& ( X1 != e_5
| X0 != e_2 )
& ( X1 != e_4
| X0 != e_2 )
& ( X1 != e_3
| X0 != e_2 )
& ( X1 != e_2
| X0 != e_2 )
& X0 != e_2
& ( X1 != e_5
| X0 != e_1 )
& ( X1 != e_4
| X0 != e_1 )
& ( X1 != e_2
| X0 != e_1 )
& X2 = e_1 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X2 = X0
& X1 = X0 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_3
& X1 = e_5 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_2
& X1 = e_4 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_4
& X1 = e_3 )
| ( X0 != e_5
& X0 != e_4
& X0 != e_3
& X0 != e_2
& X0 != e_1
& X2 = e_5
& X1 = e_2 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_3
& X0 = e_5 )
| ( X2 = e_5
& X1 = e_5
& X0 = e_5 )
| ( X2 = e_1
& X1 = e_4
& X0 = e_5 )
| ( X2 != e_5
& X2 != e_4
& X2 != e_3
& X2 != e_2
& X1 = e_4
& X0 = e_5 )
| ( X2 = e_2
& X1 = e_3
& X0 = e_5 )
| ( X2 = e_4
& X1 = e_2
& X0 = e_5 )
| ( X2 = e_3
& X1 = e_1
& X0 = e_5 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_2
& X0 = e_4 )
| ( X2 = e_1
& X1 = e_5
& X0 = e_4 )
| ( X2 != e_5
& X2 != e_4
& X2 != e_3
& X2 != e_2
& X2 != e_1
& X1 = e_5
& X0 = e_4 )
| ( X2 = e_4
& X1 = e_4
& X0 = e_4 )
| ( X2 = e_5
& X1 = e_3
& X0 = e_4 )
| ( X2 = e_3
& X1 = e_2
& X0 = e_4 )
| ( X2 = e_2
& X1 = e_1
& X0 = e_4 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_4
& X0 = e_3 )
| ( X2 = e_2
& X1 = e_5
& X0 = e_3 )
| ( X2 = e_5
& X1 = e_4
& X0 = e_3 )
| ( X2 = e_3
& X1 = e_3
& X0 = e_3 )
| ( X2 = e_1
& X1 = e_2
& X0 = e_3 )
| ( X2 != e_5
& X2 != e_4
& X2 != e_3
& X2 != e_2
& X2 != e_1
& X1 = e_2
& X0 = e_3 )
| ( X2 = e_4
& X1 = e_1
& X0 = e_3 )
| ( X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& X1 != e_1
& X2 = e_5
& X0 = e_2 )
| ( X2 = e_4
& X1 = e_5
& X0 = e_2 )
| ( X2 = e_3
& X1 = e_4
& X0 = e_2 )
| ( X2 = e_1
& X1 = e_3
& X0 = e_2 )
| ( X2 != e_5
& X2 != e_4
& X2 != e_3
& X2 != e_2
& X1 = e_3
& X0 = e_2 )
| ( X2 = e_2
& X1 = e_2
& X0 = e_2 )
| ( X2 = e_5
& X1 = e_1
& X0 = e_2 )
| ( X2 = e_3
& X1 = e_5
& X0 = e_1 )
| ( X2 = e_2
& X1 = e_4
& X0 = e_1 )
| ( X2 = e_4
& X1 = e_3
& X0 = e_1 )
| ( X2 = e_5
& X1 = e_2
& X0 = e_1 )
| ( X2 != e_5
& X2 != e_4
& X2 != e_3
& X2 != e_2
& X1 != e_5
& X1 != e_4
& X1 != e_3
& X1 != e_2
& ( X2 != e_2
| X0 != e_5 )
& X0 != e_5
& ( X2 != e_3
| X0 != e_4 )
& X0 != e_4
& ( X2 != e_5
| X0 != e_3 )
& ( X2 != e_4
| X0 != e_3 )
& ( X2 != e_2
| X0 != e_3 )
& X0 != e_3
& ( X2 != e_4
| X0 != e_2 )
& ( X2 != e_3
| X0 != e_2 )
& ( X2 != e_2
| X0 != e_2 )
& X0 != e_2 ) ) ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-8.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:34:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.41 Running EPR theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 3.45/1.18 % SZS status Started for theBenchmark.p
% 3.45/1.18 % SZS status Satisfiable for theBenchmark.p
% 3.45/1.18
% 3.45/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.45/1.18
% 3.45/1.18 % ------ iProver source info
% 3.45/1.18
% 3.45/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.45/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.45/1.18 % git: non_committed_changes: false
% 3.45/1.18
% 3.45/1.18 % ------ Parsing...% successful
% 3.45/1.18
% 3.45/1.18
% 3.45/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.45/1.18 % ------ Proving...
% 3.45/1.18 % ------ Problem Properties
% 3.45/1.18
% 3.45/1.18 %
% 3.45/1.18 % clauses 61
% 3.45/1.18 % conjectures 1
% 3.45/1.18 % EPR 61
% 3.45/1.18 % Horn 58
% 3.45/1.18 % unary 48
% 3.45/1.18 % binary 0
% 3.45/1.18 % lits 104
% 3.45/1.18 % lits eq 0
% 3.45/1.18 % fd_pure 0
% 3.45/1.18 % fd_pseudo 0
% 3.45/1.18 % fd_cond 0
% 3.45/1.18 % fd_pseudo_cond 0
% 3.45/1.18 % AC symbols 0
% 3.45/1.18
% 3.45/1.18 % ------ Input Options Time Limit: Unbounded
% 3.45/1.18
% 3.45/1.18
% 3.45/1.18 % ------
% 3.45/1.18 % Current options:
% 3.45/1.18 % ------
% 3.45/1.18
% 3.45/1.18
% 3.45/1.18 %
% 3.45/1.18
% 3.45/1.18 % ------ Proving...
% 3.45/1.18 %
% 3.45/1.18
% 3.45/1.18 % SZS status Satisfiable for theBenchmark.p
% 3.45/1.18
% 3.45/1.18 ------ Building Model...Done
% 3.45/1.18
% 3.45/1.18 %------ The model is defined over ground terms (initial term algebra).
% 3.45/1.18 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n))))
% 3.45/1.18 %------ where \phi is a formula over the term algebra.
% 3.45/1.18 %------ If we have equality in the problem then it is also defined as a predicate above,
% 3.45/1.18 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type
% 3.45/1.18 %------ See help for --sat_out_model for different model outputs.
% 3.45/1.18 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
% 3.45/1.18 %------ where the first argument stands for the sort ($i in the unsorted case)
% 3.45/1.18 % SZS output start Model for theBenchmark.p
% See solution above
% 3.45/1.19
%------------------------------------------------------------------------------