%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP037-3 : 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 : 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 01:30:00 PM UTC 2026
% Result : Unsatisfiable 3.18s 16.55s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 27 unt; 2 def)
% Number of atoms : 99 ( 28 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 32 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_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(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(f11,axiom,
! [X0] :
( product(X0,another_identity,X0)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_identity) ).
fof(f13,axiom,
! [X0] :
( product(another_inverse(X0),X0,another_identity)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_left_inverse) ).
fof(f17,axiom,
! [X2,X3,X0,X1] :
( X3 = X0
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f20,axiom,
subgroup_member(another_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_identity_in_subgroup) ).
fof(f21,negated_conjecture,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
tcf(c_68,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f3]) ).
tcf(c_71,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,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_78,plain,
! [X0: $i] :
( product(X0,another_identity,X0)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_80,plain,
! [X0: $i] :
( product(another_inverse(X0),X0,another_identity)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,plain,
subgroup_member(a),
inference(cnf_transformation,[],[f19]) ).
tcf(c_85,plain,
subgroup_member(another_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_86,negated_conjecture,
another_inverse(a) != inverse(a),
inference(cnf_transformation,[],[f21]) ).
tcf(c_98,plain,
! [X0: $i] :
( ( multiply(X0,another_identity) = X0 )
| ~ subgroup_member(X0) ),
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_100,plain,
! [X0: $i] :
( ( multiply(another_inverse(X0),X0) = another_identity )
| ~ subgroup_member(X0) ),
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( multiply(X3,X1) != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_105,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_76]) ).
tcf(c_107,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_109,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_110,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(unflattening,[status(thm)],[c_105]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( multiply(X0,X1) != multiply(X2,X1) ) ),
inference(unflattening,[status(thm)],[c_103]) ).
tcf(c_342,definition,
iPr_def_10 = another_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_343,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_344,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_86,c_343,c_342]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] :
( ( inverse(X1) = X0 )
| ( multiply(X0,X1) != identity ) ),
inference(superposition,[status(thm)],[c_109,c_231]) ).
tcf(c_654,plain,
multiply(another_inverse(a),a) = another_identity,
inference(superposition,[status(thm)],[c_84,c_100]) ).
tcf(c_657,plain,
multiply(iPr_def_10,a) = another_identity,
inference(light_normalisation,[status(thm)],[c_654,c_342]) ).
tcf(c_687,plain,
! [X0: $i] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(superposition,[status(thm)],[c_110,c_223]) ).
tcf(c_715,plain,
( subgroup_member(identity)
| ~ subgroup_member(another_identity) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_722,plain,
subgroup_member(identity),
inference(global_subsumption_just,[status(thm)],[c_687,c_85,c_715]) ).
tcf(c_726,plain,
multiply(identity,another_identity) = identity,
inference(superposition,[status(thm)],[c_722,c_98]) ).
tcf(c_741,plain,
another_identity = identity,
inference(demodulation,[status(thm)],[c_726,c_107]) ).
tcf(c_743,plain,
multiply(iPr_def_10,a) = identity,
inference(demodulation,[status(thm)],[c_657,c_741]) ).
tcf(c_810,plain,
inverse(a) = iPr_def_10,
inference(superposition,[status(thm)],[c_743,c_589]) ).
tcf(c_816,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_343,c_810]) ).
tcf(c_817,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_816,c_344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.63 % CPULimit : 300
% 0.07/15.63 % WCLimit : 300
% 0.07/15.63 % DateTime : Wed Sep 23 13:19:53 UTC 2026
% 0.07/15.63 % CPUTime :
% 0.07/15.63 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/15.67 Running first-order theorem proving
% 0.07/15.67 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
% 0.07/15.68
% 0.07/15.68 % ======== iProver multi-core TPTP/SMT =========
% 0.07/15.68
% 0.07/15.68 % Detected problem language: tptp
% 0.07/15.70 % Proving...
% 3.18/16.55 % SZS status Started for theBenchmark.p
% 3.18/16.55 % SZS status Unsatisfiable for theBenchmark.p
% 3.18/16.55
% 3.18/16.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.18/16.55
% 3.18/16.55 % ------ iProver source info
% 3.18/16.55
% 3.18/16.55 % git: date: 2026-07-19 20:42:38 +0200
% 3.18/16.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.18/16.55 % git: non_committed_changes: false
% 3.18/16.55
% 3.18/16.55 % ------ Parsing...% successful
% 3.18/16.55
% 3.18/16.55
% 3.18/16.55 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.18/16.55
% 3.18/16.55 % ------ Preprocessing... sup_sim: 7 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 %
% 3.18/16.55
% 3.18/16.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.18/16.55
% 3.18/16.55 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.18/16.55 % ------ Proving...
% 3.18/16.55 % ------ Problem Properties
% 3.18/16.55
% 3.18/16.55 %
% 3.18/16.55 % clauses 18
% 3.18/16.55 % conjectures 1
% 3.18/16.55 % EPR 3
% 3.18/16.55 % Horn 18
% 3.18/16.55 % unary 10
% 3.18/16.55 % binary 7
% 3.18/16.55 % lits 27
% 3.18/16.55 % lits eq 16
% 3.18/16.55 % fd_pure 0
% 3.18/16.55 % fd_pseudo 0
% 3.18/16.55 % fd_cond 0
% 3.18/16.55 % fd_pseudo_cond 2
% 3.18/16.55 % AC symbols 0
% 3.18/16.55
% 3.18/16.55 % ------ Schedule dynamic 5 is on
% 3.18/16.55
% 3.18/16.55 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.18/16.55
% 3.18/16.55
% 3.18/16.55 % ------
% 3.18/16.55 % Current options:
% 3.18/16.55 % ------
% 3.18/16.55
% 3.18/16.55
% 3.18/16.55 %
% 3.18/16.55
% 3.18/16.55 % ------ Proving...
% 3.18/16.55 %
% 3.18/16.55
% 3.18/16.55 % SZS status Unsatisfiable for theBenchmark.p
% 3.18/16.55
% 3.18/16.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.18/16.55
% 3.18/16.55
%------------------------------------------------------------------------------