%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP034-4 : 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 : n026.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 1.87s 1.30s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 12 unt; 1 def)
% Number of atoms : 32 ( 1 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 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 : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,axiom,
! [X2,X0,X1] :
( subgroup_member(X2)
| ~ product(X1,inverse(X0),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_subgroup) ).
fof(f8,axiom,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f9,negated_conjecture,
~ subgroup_member(inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_in_subgroup) ).
tcf(c_59,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ product(X0,inverse(X1),X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_65,plain,
subgroup_member(a),
inference(cnf_transformation,[],[f8]) ).
tcf(c_66,negated_conjecture,
~ subgroup_member(inverse(a)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_106,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_107,negated_conjecture,
~ subgroup_member(iPr_def_10),
inference(demodulation,[status(thm)],[c_66,c_106]) ).
tcf(c_257,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_59,c_64]) ).
tcf(c_258,plain,
! [X0: $i] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_61,c_64]) ).
tcf(c_336,plain,
subgroup_member(identity),
inference(superposition,[status(thm)],[c_65,c_258]) ).
tcf(c_337,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(global_subsumption_just,[status(thm)],[c_257,c_257,c_336]) ).
tcf(c_343,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_106,c_337]) ).
tcf(c_344,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_343,c_107,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 13:22:54 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 1.87/1.30 % SZS status Started for theBenchmark.p
% 1.87/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 1.87/1.30
% 1.87/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.87/1.30
% 1.87/1.30 % ------ iProver source info
% 1.87/1.30
% 1.87/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.87/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.87/1.30 % git: non_committed_changes: false
% 1.87/1.30
% 1.87/1.30 % ------ Parsing...% successful
% 1.87/1.30
% 1.87/1.30
% 1.87/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.87/1.30
% 1.87/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.87/1.30
% 1.87/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.87/1.30
% 1.87/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.87/1.30 % ------ Proving...
% 1.87/1.30 % ------ Problem Properties
% 1.87/1.30
% 1.87/1.30 %
% 1.87/1.30 % clauses 10
% 1.87/1.30 % conjectures 1
% 1.87/1.30 % EPR 6
% 1.87/1.30 % Horn 10
% 1.87/1.30 % unary 7
% 1.87/1.30 % binary 0
% 1.87/1.30 % lits 19
% 1.87/1.30 % lits eq 1
% 1.87/1.30 % fd_pure 0
% 1.87/1.30 % fd_pseudo 0
% 1.87/1.30 % fd_cond 0
% 1.87/1.30 % fd_pseudo_cond 0
% 1.87/1.30 % AC symbols 0
% 1.87/1.30
% 1.87/1.30 % ------ Schedule dynamic 5 is on
% 1.87/1.30
% 1.87/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.87/1.30
% 1.87/1.30
% 1.87/1.30 % ------
% 1.87/1.30 % Current options:
% 1.87/1.30 % ------
% 1.87/1.30
% 1.87/1.30
% 1.87/1.30 %
% 1.87/1.30
% 1.87/1.30 % ------ Proving...
% 1.87/1.30 %
% 1.87/1.30
% 1.87/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 1.87/1.30
% 1.87/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.87/1.30
% 1.87/1.30
%------------------------------------------------------------------------------