%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 01:30:01 PM UTC 2026
% Result : Unsatisfiable 0.64s 1.20s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 43 unt; 3 def)
% Number of atoms : 137 ( 37 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 29 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).
fof(f6,axiom,
! [X2,X0,X1] :
( subgroup_member(X2)
| multiply(X0,X1) != X2
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
fof(f8,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f9,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_inverse) ).
fof(f14,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f15,axiom,
! [X0,X1] :
( multiply(X0,element_in_O2(X0,X1)) = X1
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f16,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
fof(f17,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f18,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f19,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f20,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(equality_resolution,[],[f6]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_71,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,X1)) = X1 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_77,negated_conjecture,
subgroup_member(b),
inference(cnf_transformation,[],[f16]) ).
tcf(c_78,negated_conjecture,
multiply(b,inverse(a)) = c,
inference(cnf_transformation,[],[f17]) ).
tcf(c_79,negated_conjecture,
multiply(a,c) = d,
inference(cnf_transformation,[],[f18]) ).
tcf(c_80,negated_conjecture,
~ subgroup_member(d),
inference(cnf_transformation,[],[f19]) ).
tcf(c_160,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_161,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_162,definition,
iPr_def_12 = multiply(b,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_163,negated_conjecture,
~ subgroup_member(d),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_164,negated_conjecture,
iPr_def_10 = d,
inference(demodulation,[status(thm)],[c_79,c_160]) ).
tcf(c_165,negated_conjecture,
iPr_def_12 = c,
inference(demodulation,[status(thm)],[c_78,c_161,c_162]) ).
tcf(c_166,negated_conjecture,
subgroup_member(b),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_331,plain,
~ subgroup_member(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_163,c_164]) ).
tcf(c_332,plain,
multiply(a,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_160,c_165]) ).
tcf(c_339,plain,
inverse(iPr_def_11) = a,
inference(superposition,[status(thm)],[c_161,c_72]) ).
tcf(c_348,plain,
( subgroup_member(a)
| ~ subgroup_member(iPr_def_11) ),
inference(superposition,[status(thm)],[c_339,c_68]) ).
tcf(c_372,plain,
multiply(a,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_339,c_66]) ).
tcf(c_397,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11)
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_162,c_69]) ).
tcf(c_398,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_332,c_69]) ).
tcf(c_401,plain,
( ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_398,c_331]) ).
tcf(c_404,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_397,c_166]) ).
tcf(c_407,plain,
~ subgroup_member(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_404,c_348,c_404,c_401]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_71,c_67]) ).
tcf(c_420,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_11,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_372,c_67]) ).
tcf(c_425,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_11,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_420,c_65]) ).
tcf(c_451,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(iPr_def_11,element_in_O2(iPr_def_11,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_76,c_407]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_413,c_65]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_72,c_624]) ).
tcf(c_694,plain,
multiply(inverse(b),iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_162,c_631]) ).
tcf(c_740,plain,
( subgroup_member(iPr_def_11)
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(inverse(b)) ),
inference(superposition,[status(thm)],[c_694,c_69]) ).
tcf(c_742,plain,
( ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(inverse(b)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_740,c_407]) ).
tcf(c_753,plain,
( ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_68,c_742]) ).
tcf(c_754,plain,
~ subgroup_member(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_753,c_166]) ).
tcf(c_867,plain,
multiply(iPr_def_11,element_in_O2(iPr_def_11,iPr_def_12)) = iPr_def_12,
inference(superposition,[status(thm)],[c_451,c_754]) ).
tcf(c_893,plain,
multiply(a,iPr_def_12) = element_in_O2(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_867,c_425]) ).
tcf(c_894,plain,
element_in_O2(iPr_def_11,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_893,c_332]) ).
tcf(c_939,plain,
( subgroup_member(iPr_def_12)
| subgroup_member(iPr_def_11)
| subgroup_member(iPr_def_10) ),
inference(superposition,[status(thm)],[c_894,c_75]) ).
tcf(c_940,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_939,c_754,c_407,c_331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 13:21:42 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 0.64/1.20 % SZS status Started for theBenchmark.p
% 0.64/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 0.64/1.20
% 0.64/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.64/1.20
% 0.64/1.20 % ------ iProver source info
% 0.64/1.20
% 0.64/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 0.64/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.64/1.20 % git: non_committed_changes: false
% 0.64/1.20
% 0.64/1.20 % ------ Parsing...% successful
% 0.64/1.20
% 0.64/1.20
% 0.64/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.64/1.20
% 0.64/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.64/1.20
% 0.64/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.64/1.20
% 0.64/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.64/1.20 % ------ Proving...
% 0.64/1.20 % ------ Problem Properties
% 0.64/1.20
% 0.64/1.20 %
% 0.64/1.20 % clauses 19
% 0.64/1.20 % conjectures 4
% 0.64/1.20 % EPR 5
% 0.64/1.20 % Horn 17
% 0.64/1.20 % unary 15
% 0.64/1.20 % binary 1
% 0.64/1.20 % lits 26
% 0.64/1.20 % lits eq 13
% 0.64/1.20 % fd_pure 0
% 0.64/1.20 % fd_pseudo 0
% 0.64/1.20 % fd_cond 0
% 0.64/1.20 % fd_pseudo_cond 0
% 0.64/1.20 % AC symbols 0
% 0.64/1.20
% 0.64/1.20 % ------ Schedule dynamic 5 is on
% 0.64/1.20
% 0.64/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.64/1.20
% 0.64/1.20
% 0.64/1.20 % ------
% 0.64/1.20 % Current options:
% 0.64/1.20 % ------
% 0.64/1.20
% 0.64/1.20
% 0.64/1.20 %
% 0.64/1.20
% 0.64/1.20 % ------ Proving...
% 0.64/1.20 %
% 0.64/1.20
% 0.64/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 0.64/1.20
% 0.64/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.64/1.20
% 0.64/1.20
%------------------------------------------------------------------------------