%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP029-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 01:29:58 PM UTC 2026
% Result : Unsatisfiable 3.29s 1.29s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 38 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f14,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f15,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f16,negated_conjecture,
! [X0] : ~ product(not_right_identity(X0),X0,not_right_identity(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_79,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f15]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] : ~ product(not_right_identity(X0),X0,not_right_identity(X0)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,plain,
product(identity,identity,identity),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_85,plain,
~ product(not_right_identity(identity),identity,not_right_identity(identity)),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(not_right_identity(X2),X2,not_right_identity(X2))
| ~ product(X1,X2,X3)
| ~ product(X0,X3,not_right_identity(X2))
| ~ product(X0,X1,not_right_identity(X2)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X3,X5,not_right_identity(X2))
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| ~ product(X0,X1,not_right_identity(X2)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_203,plain,
! [X0: $i] : product(identity,not_right_identity(X0),not_right_identity(X0)),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_205,plain,
product(identity,not_right_identity(identity),not_right_identity(identity)),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,not_right_identity(X0))
| ~ product(X3,X1,identity)
| ~ product(X1,not_right_identity(X0),X2)
| ~ product(identity,not_right_identity(X0),not_right_identity(X0)) ),
inference(instantiation,[status(thm)],[c_200]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i] :
( product(X1,identity,not_right_identity(X0))
| ~ product(identity,not_right_identity(X0),not_right_identity(X0))
| ~ product(X1,inverse(not_right_identity(X0)),identity)
| ~ product(inverse(not_right_identity(X0)),not_right_identity(X0),identity) ),
inference(instantiation,[status(thm)],[c_329]) ).
tcf(c_546,plain,
! [X0: $i] : product(inverse(not_right_identity(X0)),not_right_identity(X0),identity),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_548,plain,
product(inverse(not_right_identity(identity)),not_right_identity(identity),identity),
inference(instantiation,[status(thm)],[c_546]) ).
tcf(c_1472,plain,
! [X0: $i] :
( product(inverse(inverse(not_right_identity(X0))),identity,not_right_identity(X0))
| ~ product(identity,not_right_identity(X0),not_right_identity(X0))
| ~ product(inverse(not_right_identity(X0)),not_right_identity(X0),identity)
| ~ product(inverse(inverse(not_right_identity(X0))),inverse(not_right_identity(X0)),identity) ),
inference(instantiation,[status(thm)],[c_545]) ).
tcf(c_1473,plain,
! [X0: $i] : product(inverse(inverse(not_right_identity(X0))),inverse(not_right_identity(X0)),identity),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_1474,plain,
( product(inverse(inverse(not_right_identity(identity))),identity,not_right_identity(identity))
| ~ product(identity,not_right_identity(identity),not_right_identity(identity))
| ~ product(inverse(not_right_identity(identity)),not_right_identity(identity),identity)
| ~ product(inverse(inverse(not_right_identity(identity))),inverse(not_right_identity(identity)),identity) ),
inference(instantiation,[status(thm)],[c_1472]) ).
tcf(c_1475,plain,
product(inverse(inverse(not_right_identity(identity))),inverse(not_right_identity(identity)),identity),
inference(instantiation,[status(thm)],[c_1473]) ).
tcf(c_6842,plain,
! [X0: $i,X1: $i] :
( product(not_right_identity(X0),X0,not_right_identity(X0))
| ~ product(identity,X0,X1)
| ~ product(inverse(inverse(not_right_identity(X0))),identity,not_right_identity(X0))
| ~ product(inverse(inverse(not_right_identity(X0))),X1,not_right_identity(X0)) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_6843,plain,
( product(not_right_identity(identity),identity,not_right_identity(identity))
| ~ product(identity,identity,identity)
| ~ product(inverse(inverse(not_right_identity(identity))),identity,not_right_identity(identity)) ),
inference(instantiation,[status(thm)],[c_6842]) ).
tcf(c_6844,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6843,c_1475,c_1474,c_548,c_205,c_85,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP029-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n001.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 13:24:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.29/1.29 % SZS status Started for theBenchmark.p
% 3.29/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.29/1.29
% 3.29/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.29/1.29
% 3.29/1.29 % ------ iProver source info
% 3.29/1.29
% 3.29/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.29/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.29/1.29 % git: non_committed_changes: false
% 3.29/1.29
% 3.29/1.29 % ------ Parsing...% successful
% 3.29/1.29
% 3.29/1.29
% 3.29/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.29/1.29
% 3.29/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.29/1.29
% 3.29/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.29/1.29 % ------ Proving...
% 3.29/1.29 % ------ Problem Properties
% 3.29/1.29
% 3.29/1.29 %
% 3.29/1.29 % clauses 16
% 3.29/1.29 % conjectures 1
% 3.29/1.29 % EPR 10
% 3.29/1.29 % Horn 16
% 3.29/1.29 % unary 5
% 3.29/1.29 % binary 4
% 3.29/1.29 % lits 36
% 3.29/1.29 % lits eq 0
% 3.29/1.29 % fd_pure 0
% 3.29/1.29 % fd_pseudo 0
% 3.29/1.30 % fd_cond 0
% 3.29/1.30 % fd_pseudo_cond 0
% 3.29/1.30 % AC symbols 0
% 3.29/1.30
% 3.29/1.30 % ------ Schedule dynamic 5 is on
% 3.29/1.30
% 3.29/1.30 % ------ no equalities: superposition off
% 3.29/1.30
% 3.29/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.29/1.30
% 3.29/1.30
% 3.29/1.30 % ------
% 3.29/1.30 % Current options:
% 3.29/1.30 % ------
% 3.29/1.30
% 3.29/1.30
% 3.29/1.30 %
% 3.29/1.30
% 3.29/1.30 % ------ Proving...
% 3.29/1.30 %
% 3.29/1.30
% 3.29/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.29/1.30
% 3.29/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.29/1.30
% 3.29/1.30
%------------------------------------------------------------------------------