%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP039-1 : 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 : n007.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 01:30:00 PM UTC 2026
% Result : Unsatisfiable 3.16s 1.20s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 80 ( 55 unt; 3 def)
% Number of atoms : 243 ( 37 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 92 ( 44 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 70 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-1.ax',closure_of_inverse) ).
fof(f10,axiom,
! [X2,X0,X1] :
( subgroup_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-1.ax',closure_of_product) ).
fof(f11,axiom,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f12,axiom,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f13,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f14,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f15,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f16,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
tcf(c_65,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_67,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f3]) ).
tcf(c_68,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_72,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_73,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ product(X0,X1,X2) ),
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,[],[f11]) ).
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,[],[f12]) ).
tcf(c_77,negated_conjecture,
subgroup_member(b),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,negated_conjecture,
product(b,inverse(a),c),
inference(cnf_transformation,[],[f14]) ).
tcf(c_79,negated_conjecture,
product(a,c,d),
inference(cnf_transformation,[],[f15]) ).
tcf(c_80,negated_conjecture,
~ subgroup_member(d),
inference(cnf_transformation,[],[f16]) ).
tcf(c_89,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_90,plain,
multiply(b,inverse(a)) = c,
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_91,plain,
multiply(a,c) = d,
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_94,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_65]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_66]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_67]) ).
tcf(c_97,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_103,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_72]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(unflattening,[status(thm)],[c_92]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_103]) ).
tcf(c_273,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_274,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_275,definition,
iPr_def_12 = multiply(b,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_276,plain,
iPr_def_10 = d,
inference(demodulation,[status(thm)],[c_91,c_273]) ).
tcf(c_277,plain,
iPr_def_12 = c,
inference(demodulation,[status(thm)],[c_90,c_274,c_275]) ).
tcf(c_278,negated_conjecture,
~ subgroup_member(d),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_279,negated_conjecture,
subgroup_member(b),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_431,plain,
~ subgroup_member(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_278,c_276]) ).
tcf(c_434,plain,
( subgroup_member(iPr_def_11)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_274,c_73]) ).
tcf(c_448,plain,
multiply(a,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_273,c_277]) ).
tcf(c_449,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_448,c_189]) ).
tcf(c_450,plain,
( ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_449,c_431]) ).
tcf(c_453,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11)
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_275,c_189]) ).
tcf(c_454,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_453,c_279]) ).
tcf(c_468,plain,
~ subgroup_member(a),
inference(global_subsumption_just,[status(thm)],[c_450,c_434,c_450,c_454]) ).
tcf(c_471,plain,
multiply(iPr_def_11,a) = identity,
inference(superposition,[status(thm)],[c_274,c_96]) ).
tcf(c_502,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,iPr_def_10)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_89,c_431]) ).
tcf(c_532,plain,
multiply(a,element_in_O2(a,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_502,c_468]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_197]) ).
tcf(c_544,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_275,c_197]) ).
tcf(c_545,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_12,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_448,c_197]) ).
tcf(c_546,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_471,c_197]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(multiply(X0,multiply(X1,X2)))
| ~ subgroup_member(X2)
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_197,c_189]) ).
tcf(c_555,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_546,c_94]) ).
tcf(c_585,plain,
multiply(b,identity) = multiply(iPr_def_12,a),
inference(superposition,[status(thm)],[c_471,c_544]) ).
tcf(c_626,plain,
multiply(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_448,c_555]) ).
tcf(c_628,plain,
element_in_O2(a,iPr_def_10) = multiply(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_532,c_555]) ).
tcf(c_641,plain,
multiply(iPr_def_12,a) = b,
inference(demodulation,[status(thm)],[c_585,c_95]) ).
tcf(c_910,plain,
element_in_O2(a,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_628,c_626]) ).
tcf(c_911,plain,
( subgroup_member(iPr_def_12)
| subgroup_member(iPr_def_10)
| subgroup_member(a) ),
inference(superposition,[status(thm)],[c_910,c_75]) ).
tcf(c_912,plain,
subgroup_member(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_911,c_431,c_468]) ).
tcf(c_1120,plain,
multiply(iPr_def_10,inverse(iPr_def_12)) = multiply(a,identity),
inference(superposition,[status(thm)],[c_97,c_545]) ).
tcf(c_1121,plain,
multiply(a,b) = multiply(iPr_def_10,a),
inference(superposition,[status(thm)],[c_641,c_545]) ).
tcf(c_1147,plain,
multiply(iPr_def_10,inverse(iPr_def_12)) = a,
inference(demodulation,[status(thm)],[c_1120,c_95]) ).
tcf(c_2103,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,multiply(iPr_def_10,a)))
| ~ subgroup_member(b)
| ~ subgroup_member(multiply(X0,a)) ),
inference(superposition,[status(thm)],[c_1121,c_551]) ).
tcf(c_2110,plain,
! [X0: $i] :
( subgroup_member(multiply(X0,multiply(iPr_def_10,a)))
| ~ subgroup_member(multiply(X0,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2103,c_279]) ).
tcf(c_2338,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_541,c_94]) ).
tcf(c_2365,plain,
multiply(inverse(iPr_def_10),a) = inverse(iPr_def_12),
inference(superposition,[status(thm)],[c_1147,c_2338]) ).
tcf(c_2380,plain,
( subgroup_member(a)
| ~ subgroup_member(multiply(inverse(iPr_def_10),a)) ),
inference(superposition,[status(thm)],[c_2338,c_2110]) ).
tcf(c_2386,plain,
~ subgroup_member(multiply(inverse(iPr_def_10),a)),
inference(forward_subsumption_resolution,[status(thm)],[c_2380,c_468]) ).
tcf(c_2487,plain,
~ subgroup_member(inverse(iPr_def_12)),
inference(light_normalisation,[status(thm)],[c_2386,c_2365]) ).
tcf(c_2499,plain,
~ subgroup_member(iPr_def_12),
inference(superposition,[status(thm)],[c_73,c_2487]) ).
tcf(c_2500,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2499,c_912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % 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 13:18:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.16/1.20 % SZS status Started for theBenchmark.p
% 3.16/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.16/1.20
% 3.16/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.16/1.20
% 3.16/1.20 % ------ iProver source info
% 3.16/1.20
% 3.16/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.16/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.16/1.20 % git: non_committed_changes: false
% 3.16/1.20
% 3.16/1.20 % ------ Parsing...% successful
% 3.16/1.20
% 3.16/1.20
% 3.16/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.16/1.20
% 3.16/1.20 % ------ 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 %
% 3.16/1.20
% 3.16/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.16/1.20
% 3.16/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.16/1.20 % ------ Proving...
% 3.16/1.20 % ------ Problem Properties
% 3.16/1.20
% 3.16/1.20 %
% 3.16/1.20 % clauses 16
% 3.16/1.20 % conjectures 2
% 3.16/1.20 % EPR 4
% 3.16/1.20 % Horn 14
% 3.16/1.20 % unary 12
% 3.16/1.20 % binary 1
% 3.16/1.20 % lits 23
% 3.16/1.20 % lits eq 11
% 3.16/1.20 % fd_pure 0
% 3.16/1.20 % fd_pseudo 0
% 3.16/1.20 % fd_cond 0
% 3.16/1.20 % fd_pseudo_cond 0
% 3.16/1.20 % AC symbols 0
% 3.16/1.20
% 3.16/1.20 % ------ Schedule dynamic 5 is on
% 3.16/1.20
% 3.16/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.16/1.20
% 3.16/1.20
% 3.16/1.20 % ------
% 3.16/1.20 % Current options:
% 3.16/1.20 % ------
% 3.16/1.20
% 3.16/1.20
% 3.16/1.20 %
% 3.16/1.20
% 3.16/1.20 % ------ Proving...
% 3.16/1.20 %
% 3.16/1.20
% 3.16/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.16/1.20
% 3.16/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.16/1.20
% 3.16/1.20
%------------------------------------------------------------------------------