%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP034-3 : 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 01:29:59 PM UTC 2026
% Result : Unsatisfiable 2.07s 1.18s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 16 unt; 1 def)
% Number of atoms : 54 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f9,axiom,
! [X2,X0,X1] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
fof(f10,axiom,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f11,negated_conjecture,
~ subgroup_member(inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_is_in_subgroup) ).
tcf(c_60,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ product(X0,inverse(X1),X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
subgroup_member(a),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
~ subgroup_member(inverse(a)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| ( multiply(X0,inverse(X1)) != X2 ) ),
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_60]) ).
tcf(c_81,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_63]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(unflattening,[status(thm)],[c_76]) ).
tcf(c_182,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_183,negated_conjecture,
~ subgroup_member(iPr_def_10),
inference(demodulation,[status(thm)],[c_70,c_182]) ).
tcf(c_296,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,iPr_def_10))
| ~ subgroup_member(a)
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_182,c_138]) ).
tcf(c_302,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,iPr_def_10))
| ~ subgroup_member(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_296,c_69]) ).
tcf(c_311,plain,
multiply(a,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_182,c_81]) ).
tcf(c_321,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(identity) ),
inference(superposition,[status(thm)],[c_78,c_302]) ).
tcf(c_323,plain,
( subgroup_member(identity)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_311,c_302]) ).
tcf(c_324,plain,
subgroup_member(identity),
inference(forward_subsumption_resolution,[status(thm)],[c_323,c_69]) ).
tcf(c_325,plain,
subgroup_member(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_321,c_324]) ).
tcf(c_326,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_325,c_183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:25:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.07/1.18 % SZS status Started for theBenchmark.p
% 2.07/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.18
% 2.07/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.07/1.18
% 2.07/1.18 % ------ iProver source info
% 2.07/1.18
% 2.07/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.07/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.07/1.18 % git: non_committed_changes: false
% 2.07/1.18
% 2.07/1.18 % ------ Parsing...% successful
% 2.07/1.18
% 2.07/1.18
% 2.07/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.07/1.18
% 2.07/1.18 % ------ Preprocessing... sup_sim: 5 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 %
% 2.07/1.18
% 2.07/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.07/1.18
% 2.07/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.07/1.18 % ------ Proving...
% 2.07/1.18 % ------ Problem Properties
% 2.07/1.18
% 2.07/1.18 %
% 2.07/1.18 % clauses 9
% 2.07/1.18 % conjectures 1
% 2.07/1.18 % EPR 2
% 2.07/1.18 % Horn 9
% 2.07/1.18 % unary 8
% 2.07/1.18 % binary 0
% 2.07/1.18 % lits 11
% 2.07/1.18 % lits eq 6
% 2.07/1.18 % fd_pure 0
% 2.07/1.18 % fd_pseudo 0
% 2.07/1.18 % fd_cond 0
% 2.07/1.18 % fd_pseudo_cond 0
% 2.07/1.18 % AC symbols 0
% 2.07/1.18
% 2.07/1.18 % ------ Schedule dynamic 5 is on
% 2.07/1.18
% 2.07/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.07/1.18
% 2.07/1.18
% 2.07/1.18 % ------
% 2.07/1.18 % Current options:
% 2.07/1.18 % ------
% 2.07/1.18
% 2.07/1.18
% 2.07/1.18 %
% 2.07/1.18
% 2.07/1.18 % ------ Proving...
% 2.07/1.18 %
% 2.07/1.18
% 2.07/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.18
% 2.07/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.07/1.18
% 2.07/1.18
%------------------------------------------------------------------------------