%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 01:30:01 PM UTC 2026
% Result : Unsatisfiable 4.39s 1.31s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 43 unt; 0 def)
% Number of atoms : 197 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 124 ( 58 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 89 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f8,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/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
fof(f10,axiom,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f11,axiom,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f12,axiom,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).
fof(f13,axiom,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f14,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).
fof(f15,axiom,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f16,axiom,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f17,negated_conjecture,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
tcf(c_66,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_73,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,[],[f8]) ).
tcf(c_74,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_75,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,plain,
~ subgroup_member(a),
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,plain,
subgroup_member(b),
inference(cnf_transformation,[],[f13]) ).
tcf(c_79,plain,
~ subgroup_member(d),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,plain,
product(a,c,d),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,negated_conjecture,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f17]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,X1)) = X1 ) ),
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_92,plain,
multiply(b,inverse(a)) = c,
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_93,plain,
multiply(a,c) = d,
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_94,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_74]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_66]) ).
tcf(c_97,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_67]) ).
tcf(c_98,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_99,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_69]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( multiply(X2,X5) = X4 )
| ( multiply(X1,X5) != X3 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_73]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(unflattening,[status(thm)],[c_94]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_105]) ).
tcf(c_265,negated_conjecture,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_423,plain,
! [X0: $i] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_99,c_186]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X1,X0))
| ~ subgroup_member(X1)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[status(thm)],[c_265,c_186]) ).
tcf(c_443,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(identity)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[status(thm)],[c_96,c_424]) ).
tcf(c_465,plain,
subgroup_member(identity),
inference(superposition,[status(thm)],[c_78,c_423]) ).
tcf(c_470,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_443,c_443,c_465]) ).
tcf(c_476,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_265,c_470]) ).
tcf(c_497,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,d)) = d ) ),
inference(superposition,[status(thm)],[c_91,c_79]) ).
tcf(c_581,plain,
! [X0: $i] :
( subgroup_member(a)
| subgroup_member(X0)
| subgroup_member(element_in_O2(a,X0)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_586,plain,
! [X0: $i] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[c_92,c_194]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_98,c_194]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(multiply(X0,multiply(X1,X2)))
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_194,c_424]) ).
tcf(c_629,plain,
( subgroup_member(d)
| subgroup_member(a)
| subgroup_member(element_in_O2(a,d)) ),
inference(instantiation,[status(thm)],[c_581]) ).
tcf(c_642,plain,
multiply(a,element_in_O2(a,d)) = d,
inference(superposition,[status(thm)],[c_497,c_77]) ).
tcf(c_689,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,d))
| ~ subgroup_member(multiply(X0,a))
| ~ subgroup_member(inverse(element_in_O2(a,d))) ),
inference(superposition,[status(thm)],[c_642,c_597]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X1,X0))
| ~ subgroup_member(X1)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[status(thm)],[c_265,c_186]) ).
tcf(c_851,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(identity)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[status(thm)],[c_96,c_746]) ).
tcf(c_907,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,d))
| ~ subgroup_member(element_in_O2(a,d))
| ~ subgroup_member(multiply(X0,a)) ),
inference(superposition,[status(thm)],[c_476,c_689]) ).
tcf(c_958,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,d))
| ~ subgroup_member(multiply(X0,a)) ),
inference(global_subsumption_just,[status(thm)],[c_907,c_79,c_77,c_629,c_907]) ).
tcf(c_977,plain,
( subgroup_member(multiply(inverse(a),d))
| ~ subgroup_member(identity) ),
inference(superposition,[status(thm)],[c_98,c_958]) ).
tcf(c_979,plain,
subgroup_member(multiply(inverse(a),d)),
inference(forward_subsumption_resolution,[status(thm)],[c_977,c_465]) ).
tcf(c_1020,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_851,c_470]) ).
tcf(c_1026,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_265,c_1020]) ).
tcf(c_1184,plain,
multiply(b,identity) = multiply(c,a),
inference(superposition,[status(thm)],[c_98,c_586]) ).
tcf(c_1346,plain,
multiply(c,a) = b,
inference(demodulation,[status(thm)],[c_1184,c_97]) ).
tcf(c_1350,plain,
( subgroup_member(multiply(c,d))
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_1346,c_958]) ).
tcf(c_1352,plain,
subgroup_member(multiply(c,d)),
inference(forward_subsumption_resolution,[status(thm)],[c_1350,c_78]) ).
tcf(c_1750,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(multiply(X0,multiply(X1,X2)))
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_194,c_746]) ).
tcf(c_1879,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_590,c_96]) ).
tcf(c_1883,plain,
multiply(inverse(a),d) = c,
inference(superposition,[status(thm)],[c_93,c_1879]) ).
tcf(c_1902,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(inverse(multiply(X0,X1))) ),
inference(superposition,[status(thm)],[c_1879,c_424]) ).
tcf(c_1929,plain,
subgroup_member(c),
inference(demodulation,[status(thm)],[c_979,c_1883]) ).
tcf(c_2127,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_476,c_1902]) ).
tcf(c_2245,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,d))
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(multiply(X0,a)) ),
inference(superposition,[status(thm)],[c_93,c_1750]) ).
tcf(c_2308,plain,
( subgroup_member(d)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[status(thm)],[c_1352,c_2127]) ).
tcf(c_2320,plain,
~ subgroup_member(inverse(c)),
inference(forward_subsumption_resolution,[status(thm)],[c_2308,c_79]) ).
tcf(c_2524,plain,
~ subgroup_member(inverse(c)),
inference(global_subsumption_just,[status(thm)],[c_2245,c_2320]) ).
tcf(c_2538,plain,
~ subgroup_member(c),
inference(superposition,[status(thm)],[c_1026,c_2524]) ).
tcf(c_2555,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2538,c_1929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 13:24:53 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.39/1.31 % SZS status Started for theBenchmark.p
% 4.39/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.39/1.31
% 4.39/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.39/1.31
% 4.39/1.31 % ------ iProver source info
% 4.39/1.31
% 4.39/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.39/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.39/1.31 % git: non_committed_changes: false
% 4.39/1.31
% 4.39/1.31 % ------ Parsing...% successful
% 4.39/1.31
% 4.39/1.31
% 4.39/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.39/1.31
% 4.39/1.31 % ------ 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 %
% 4.39/1.31
% 4.39/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.39/1.31
% 4.39/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.39/1.31 % ------ Proving...
% 4.39/1.31 % ------ Problem Properties
% 4.39/1.31
% 4.39/1.31 %
% 4.39/1.31 % clauses 14
% 4.39/1.31 % conjectures 1
% 4.39/1.31 % EPR 3
% 4.39/1.31 % Horn 12
% 4.39/1.31 % unary 11
% 4.39/1.31 % binary 0
% 4.39/1.31 % lits 20
% 4.39/1.31 % lits eq 9
% 4.39/1.31 % fd_pure 0
% 4.39/1.31 % fd_pseudo 0
% 4.39/1.31 % fd_cond 0
% 4.39/1.31 % fd_pseudo_cond 0
% 4.39/1.31 % AC symbols 0
% 4.39/1.31
% 4.39/1.31 % ------ Schedule dynamic 5 is on
% 4.39/1.31
% 4.39/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.39/1.31
% 4.39/1.31
% 4.39/1.31 % ------
% 4.39/1.31 % Current options:
% 4.39/1.31 % ------
% 4.39/1.31
% 4.39/1.31
% 4.39/1.31 %
% 4.39/1.31
% 4.39/1.31 % ------ Proving...
% 4.39/1.31 %
% 4.39/1.31
% 4.39/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.39/1.31
% 4.39/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.39/1.31
% 4.39/1.31
%------------------------------------------------------------------------------