%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP035-3 : 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 3.23s 1.33s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 27 unt; 0 def)
% Number of atoms : 99 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 37 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 40 :)
% 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(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,
! [X2,X0,X1] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
fof(f10,axiom,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f11,axiom,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f12,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f13,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
tcf(c_62,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,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_70,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_71,plain,
subgroup_member(a),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
subgroup_member(b),
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
product(a,b,c),
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,negated_conjecture,
~ subgroup_member(c),
inference(cnf_transformation,[],[f13]) ).
tcf(c_80,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_73]) ).
tcf(c_81,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_70]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_62]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_63]) ).
tcf(c_86,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_65]) ).
tcf(c_92,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_69]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(unflattening,[status(thm)],[c_81]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_92]) ).
tcf(c_193,negated_conjecture,
~ subgroup_member(c),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_297,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_83,c_147]) ).
tcf(c_310,plain,
! [X0: $i] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_86,c_147]) ).
tcf(c_316,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[c_80,c_152]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(multiply(X0,multiply(X1,inverse(X2))))
| ~ subgroup_member(X2)
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_152,c_147]) ).
tcf(c_340,plain,
subgroup_member(identity),
inference(superposition,[status(thm)],[c_71,c_310]) ).
tcf(c_343,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(global_subsumption_just,[status(thm)],[c_297,c_297,c_340]) ).
tcf(c_353,plain,
multiply(c,inverse(b)) = multiply(a,identity),
inference(superposition,[status(thm)],[c_86,c_316]) ).
tcf(c_359,plain,
multiply(c,inverse(b)) = a,
inference(demodulation,[status(thm)],[c_353,c_84]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,identity))
| ~ subgroup_member(X1)
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_86,c_323]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ subgroup_member(multiply(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_418,c_84]) ).
tcf(c_467,plain,
( subgroup_member(c)
| ~ subgroup_member(a)
| ~ subgroup_member(inverse(b)) ),
inference(superposition,[status(thm)],[c_359,c_425]) ).
tcf(c_470,plain,
~ subgroup_member(inverse(b)),
inference(forward_subsumption_resolution,[status(thm)],[c_467,c_193,c_71]) ).
tcf(c_558,plain,
~ subgroup_member(b),
inference(superposition,[status(thm)],[c_343,c_470]) ).
tcf(c_559,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_558,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.52 % Computer : n026.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Wed Sep 23 13:23:09 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.56 Running first-order theorem proving
% 0.13/0.56 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
% 0.13/0.57
% 0.13/0.57 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.57
% 0.13/0.57 % Detected problem language: tptp
% 0.13/0.58 % Proving...
% 3.23/1.33 % SZS status Started for theBenchmark.p
% 3.23/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/1.33
% 3.23/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.23/1.33
% 3.23/1.33 % ------ iProver source info
% 3.23/1.33
% 3.23/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 3.23/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.23/1.33 % git: non_committed_changes: false
% 3.23/1.33
% 3.23/1.33 % ------ Parsing...% successful
% 3.23/1.33
% 3.23/1.33
% 3.23/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.23/1.33
% 3.23/1.33 % ------ 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 %
% 3.23/1.33
% 3.23/1.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.23/1.33
% 3.23/1.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.33 % ------ Proving...
% 3.23/1.33 % ------ Problem Properties
% 3.23/1.33
% 3.23/1.33 %
% 3.23/1.33 % clauses 10
% 3.23/1.33 % conjectures 1
% 3.23/1.33 % EPR 3
% 3.23/1.33 % Horn 10
% 3.23/1.33 % unary 9
% 3.23/1.33 % binary 0
% 3.23/1.33 % lits 12
% 3.23/1.33 % lits eq 6
% 3.23/1.33 % fd_pure 0
% 3.23/1.33 % fd_pseudo 0
% 3.23/1.33 % fd_cond 0
% 3.23/1.33 % fd_pseudo_cond 0
% 3.23/1.33 % AC symbols 0
% 3.23/1.33
% 3.23/1.33 % ------ Schedule dynamic 5 is on
% 3.23/1.33
% 3.23/1.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.23/1.33
% 3.23/1.33
% 3.23/1.33 % ------
% 3.23/1.33 % Current options:
% 3.23/1.33 % ------
% 3.23/1.33
% 3.23/1.33
% 3.23/1.33 %
% 3.23/1.33
% 3.23/1.33 % ------ Proving...
% 3.23/1.33 %
% 3.23/1.33
% 3.23/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/1.33
% 3.23/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.33
% 3.23/1.33
%------------------------------------------------------------------------------