%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP039-4 : 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 : n002.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 0.83s 1.23s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 90 ( 55 unt; 3 def)
% Number of atoms : 309 ( 38 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 122 ( 58 ~; 64 |; 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 : 75 ( 0 sgn 75 !; 0 ?; 57 :)
% 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,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP003-1.ax',closure_of_product) ).
fof(f12,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(f13,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(f14,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f15,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f16,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f17,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
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] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_75,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_77,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_79,negated_conjecture,
subgroup_member(b),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,negated_conjecture,
product(b,inverse(a),c),
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,negated_conjecture,
product(a,c,d),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,negated_conjecture,
~ subgroup_member(d),
inference(cnf_transformation,[],[f17]) ).
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_78]) ).
tcf(c_90,plain,
multiply(b,inverse(a)) = c,
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_91,plain,
multiply(a,c) = d,
inference(well_definedness,[status(thm)],[c_81]) ).
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_75]) ).
tcf(c_94,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_66]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_67]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_97,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_69]) ).
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_73]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(unflattening,[status(thm)],[c_92]) ).
tcf(c_198,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_276,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_277,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_278,definition,
iPr_def_12 = multiply(b,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_279,plain,
iPr_def_10 = d,
inference(demodulation,[status(thm)],[c_91,c_276]) ).
tcf(c_280,plain,
iPr_def_12 = c,
inference(demodulation,[status(thm)],[c_90,c_277,c_278]) ).
tcf(c_281,negated_conjecture,
~ subgroup_member(d),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_282,negated_conjecture,
subgroup_member(b),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_438,plain,
~ subgroup_member(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_281,c_279]) ).
tcf(c_441,plain,
( subgroup_member(iPr_def_11)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_277,c_74]) ).
tcf(c_454,plain,
multiply(a,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_276,c_280]) ).
tcf(c_455,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_454,c_190]) ).
tcf(c_456,plain,
( ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_455,c_438]) ).
tcf(c_459,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11)
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_278,c_190]) ).
tcf(c_460,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_459,c_282]) ).
tcf(c_475,plain,
~ subgroup_member(a),
inference(global_subsumption_just,[status(thm)],[c_456,c_441,c_456,c_460]) ).
tcf(c_478,plain,
multiply(iPr_def_11,a) = identity,
inference(superposition,[status(thm)],[c_277,c_96]) ).
tcf(c_485,plain,
multiply(a,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_277,c_97]) ).
tcf(c_496,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_438]) ).
tcf(c_499,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(iPr_def_10,element_in_O2(iPr_def_10,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_89,c_438]) ).
tcf(c_526,plain,
multiply(a,element_in_O2(a,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_496,c_475]) ).
tcf(c_547,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_278,c_198]) ).
tcf(c_549,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_478,c_198]) ).
tcf(c_550,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_11,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_485,c_198]) ).
tcf(c_554,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_198,c_190]) ).
tcf(c_557,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_11,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_550,c_94]) ).
tcf(c_558,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_549,c_94]) ).
tcf(c_586,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(b)
| ~ subgroup_member(multiply(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_547,c_190]) ).
tcf(c_588,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(multiply(iPr_def_11,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_586,c_282]) ).
tcf(c_610,plain,
multiply(a,identity) = inverse(iPr_def_11),
inference(superposition,[status(thm)],[c_97,c_557]) ).
tcf(c_615,plain,
inverse(iPr_def_11) = a,
inference(demodulation,[status(thm)],[c_610,c_95]) ).
tcf(c_618,plain,
( subgroup_member(a)
| ~ subgroup_member(iPr_def_11) ),
inference(superposition,[status(thm)],[c_615,c_74]) ).
tcf(c_619,plain,
~ subgroup_member(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_618,c_475]) ).
tcf(c_633,plain,
multiply(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_454,c_558]) ).
tcf(c_635,plain,
element_in_O2(a,iPr_def_10) = multiply(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_526,c_558]) ).
tcf(c_643,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(iPr_def_10,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_633,c_198]) ).
tcf(c_724,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(multiply(b,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_547,c_554]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(iPr_def_12,multiply(X0,X1)))
| ~ subgroup_member(X1)
| ~ subgroup_member(multiply(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_554,c_588]) ).
tcf(c_747,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(X0) ),
inference(light_normalisation,[status(thm)],[c_724,c_278]) ).
tcf(c_894,plain,
element_in_O2(a,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_635,c_633]) ).
tcf(c_895,plain,
( subgroup_member(iPr_def_12)
| subgroup_member(iPr_def_10)
| subgroup_member(a) ),
inference(superposition,[status(thm)],[c_894,c_77]) ).
tcf(c_896,plain,
subgroup_member(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_895,c_438,c_475]) ).
tcf(c_910,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(multiply(iPr_def_11,identity)) ),
inference(superposition,[status(thm)],[c_94,c_742]) ).
tcf(c_1211,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(X0) ),
inference(global_subsumption_just,[status(thm)],[c_910,c_747,c_896]) ).
tcf(c_3220,plain,
multiply(iPr_def_12,inverse(iPr_def_10)) = multiply(iPr_def_11,identity),
inference(superposition,[status(thm)],[c_97,c_643]) ).
tcf(c_3324,plain,
multiply(iPr_def_12,inverse(iPr_def_10)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3220,c_95]) ).
tcf(c_3335,plain,
( subgroup_member(iPr_def_11)
| ~ subgroup_member(inverse(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3324,c_1211]) ).
tcf(c_3343,plain,
~ subgroup_member(inverse(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3335,c_619]) ).
tcf(c_3388,plain,
multiply(iPr_def_10,element_in_O2(iPr_def_10,inverse(iPr_def_10))) = inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_499,c_3343]) ).
tcf(c_3623,plain,
( subgroup_member(multiply(iPr_def_12,inverse(iPr_def_10)))
| ~ subgroup_member(multiply(iPr_def_11,iPr_def_10))
| ~ subgroup_member(element_in_O2(iPr_def_10,inverse(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_3388,c_742]) ).
tcf(c_3632,plain,
( subgroup_member(iPr_def_11)
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(element_in_O2(iPr_def_10,inverse(iPr_def_10))) ),
inference(light_normalisation,[status(thm)],[c_3623,c_633,c_3324]) ).
tcf(c_3633,plain,
~ subgroup_member(element_in_O2(iPr_def_10,inverse(iPr_def_10))),
inference(forward_subsumption_resolution,[status(thm)],[c_3632,c_619,c_896]) ).
tcf(c_3635,plain,
( subgroup_member(iPr_def_10)
| subgroup_member(inverse(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_77,c_3633]) ).
tcf(c_3647,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3635,c_438,c_3343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n002.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 13:24:03 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.43
% 0.15/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.43
% 0.15/0.43 % Detected problem language: tptp
% 0.15/0.44 % Proving...
% 0.83/1.23 % SZS status Started for theBenchmark.p
% 0.83/1.23 % SZS status Unsatisfiable for theBenchmark.p
% 0.83/1.23
% 0.83/1.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.83/1.23
% 0.83/1.23 % ------ iProver source info
% 0.83/1.23
% 0.83/1.23 % git: date: 2026-07-19 20:42:38 +0200
% 0.83/1.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.83/1.23 % git: non_committed_changes: false
% 0.83/1.23
% 0.83/1.23 % ------ Parsing...% successful
% 0.83/1.23
% 0.83/1.23
% 0.83/1.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.83/1.23
% 0.83/1.23 % ------ 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 %
% 0.83/1.23
% 0.83/1.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.83/1.23
% 0.83/1.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.83/1.23 % ------ Proving...
% 0.83/1.23 % ------ Problem Properties
% 0.83/1.23
% 0.83/1.23 %
% 0.83/1.23 % clauses 17
% 0.83/1.23 % conjectures 2
% 0.83/1.23 % EPR 5
% 0.83/1.23 % Horn 15
% 0.83/1.23 % unary 13
% 0.83/1.23 % binary 1
% 0.83/1.23 % lits 24
% 0.83/1.23 % lits eq 11
% 0.83/1.23 % fd_pure 0
% 0.83/1.23 % fd_pseudo 0
% 0.83/1.23 % fd_cond 0
% 0.83/1.23 % fd_pseudo_cond 0
% 0.83/1.23 % AC symbols 0
% 0.83/1.23
% 0.83/1.23 % ------ Schedule dynamic 5 is on
% 0.83/1.23
% 0.83/1.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.83/1.23
% 0.83/1.23
% 0.83/1.23 % ------
% 0.83/1.23 % Current options:
% 0.83/1.23 % ------
% 0.83/1.23
% 0.83/1.23
% 0.83/1.23 %
% 0.83/1.23
% 0.83/1.23 % ------ Proving...
% 0.83/1.23 %
% 0.83/1.23
% 0.83/1.23 % SZS status Unsatisfiable for theBenchmark.p
% 0.83/1.23
% 0.83/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.83/1.24
% 0.83/1.24
%------------------------------------------------------------------------------