%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP040-4 : 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 : n013.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 1.02s 1.74s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 62 ( 42 unt; 0 def)
% Number of atoms : 146 ( 29 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 78 ( 35 ~; 43 |; 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 : 72 ( 0 sgn 72 !; 0 ?; 53 :)
% 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,
! [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] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f16,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(f17,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(f18,axiom,
~ subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_in_subgroup) ).
fof(f19,axiom,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f20,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_in_subgroup) ).
fof(f21,axiom,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f22,axiom,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f23,negated_conjecture,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
tcf(c_70,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f3]) ).
tcf(c_73,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_77,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_78,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_80,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_85,plain,
~ subgroup_member(a),
inference(cnf_transformation,[],[f18]) ).
tcf(c_86,plain,
subgroup_member(b),
inference(cnf_transformation,[],[f19]) ).
tcf(c_87,plain,
~ subgroup_member(d),
inference(cnf_transformation,[],[f20]) ).
tcf(c_88,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[],[f21]) ).
tcf(c_89,plain,
product(a,c,d),
inference(cnf_transformation,[],[f22]) ).
tcf(c_90,negated_conjecture,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_102,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_84]) ).
tcf(c_103,plain,
multiply(b,inverse(a)) = c,
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_104,plain,
multiply(a,c) = d,
inference(well_definedness,[status(thm)],[c_89]) ).
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_78]) ).
tcf(c_107,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_108,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_109,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_110,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_73]) ).
tcf(c_116,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_77]) ).
tcf(c_219,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_237,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_116]) ).
tcf(c_336,negated_conjecture,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X1,X0))
| ~ subgroup_member(X1)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[status(thm)],[c_336,c_219]) ).
tcf(c_573,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,a)) = a ) ),
inference(superposition,[status(thm)],[c_102,c_85]) ).
tcf(c_703,plain,
multiply(d,element_in_O2(d,a)) = a,
inference(superposition,[status(thm)],[c_573,c_87]) ).
tcf(c_2104,plain,
! [X0: $i] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[c_103,c_237]) ).
tcf(c_2105,plain,
! [X0: $i] : multiply(a,multiply(c,X0)) = multiply(d,X0),
inference(superposition,[status(thm)],[c_104,c_237]) ).
tcf(c_2108,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_109,c_237]) ).
tcf(c_2271,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(superposition,[status(thm)],[c_110,c_2105]) ).
tcf(c_2276,plain,
multiply(d,inverse(c)) = a,
inference(demodulation,[status(thm)],[c_2271,c_108]) ).
tcf(c_4865,plain,
multiply(b,identity) = multiply(c,a),
inference(superposition,[status(thm)],[c_109,c_2104]) ).
tcf(c_5364,plain,
multiply(c,a) = b,
inference(demodulation,[status(thm)],[c_4865,c_108]) ).
tcf(c_5830,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2108,c_107]) ).
tcf(c_5843,plain,
multiply(inverse(d),a) = element_in_O2(d,a),
inference(superposition,[status(thm)],[c_703,c_5830]) ).
tcf(c_5860,plain,
multiply(inverse(d),a) = inverse(c),
inference(superposition,[status(thm)],[c_2276,c_5830]) ).
tcf(c_5871,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(inverse(multiply(X0,X1))) ),
inference(superposition,[status(thm)],[c_5830,c_541]) ).
tcf(c_6538,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_80,c_5871]) ).
tcf(c_7102,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[status(thm)],[c_5364,c_6538]) ).
tcf(c_7105,plain,
~ subgroup_member(inverse(c)),
inference(forward_subsumption_resolution,[status(thm)],[c_7102,c_85,c_86]) ).
tcf(c_8410,plain,
element_in_O2(d,a) = inverse(c),
inference(light_normalisation,[status(thm)],[c_5843,c_5860]) ).
tcf(c_8411,plain,
( subgroup_member(d)
| subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(superposition,[status(thm)],[c_8410,c_83]) ).
tcf(c_8412,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8411,c_87,c_85,c_7105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 13:21:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 1.02/1.74 % SZS status Started for theBenchmark.p
% 1.02/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.02/1.74
% 1.02/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.02/1.74
% 1.02/1.74 % ------ iProver source info
% 1.02/1.74
% 1.02/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.02/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.02/1.74 % git: non_committed_changes: false
% 1.02/1.74
% 1.02/1.74 % ------ Parsing...% successful
% 1.02/1.74
% 1.02/1.74
% 1.02/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.02/1.74
% 1.02/1.74 % ------ 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 %
% 1.02/1.74
% 1.02/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.02/1.74
% 1.02/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.02/1.74 % ------ Proving...
% 1.02/1.74 % ------ Problem Properties
% 1.02/1.74
% 1.02/1.74 %
% 1.02/1.74 % clauses 18
% 1.02/1.74 % conjectures 1
% 1.02/1.74 % EPR 4
% 1.02/1.74 % Horn 16
% 1.02/1.74 % unary 12
% 1.02/1.74 % binary 3
% 1.02/1.74 % lits 27
% 1.02/1.74 % lits eq 13
% 1.02/1.74 % fd_pure 0
% 1.02/1.74 % fd_pseudo 0
% 1.02/1.74 % fd_cond 0
% 1.02/1.74 % fd_pseudo_cond 2
% 1.02/1.74 % AC symbols 0
% 1.02/1.74
% 1.02/1.74 % ------ Schedule dynamic 5 is on
% 1.02/1.74
% 1.02/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.02/1.74
% 1.02/1.74
% 1.02/1.74 % ------
% 1.02/1.74 % Current options:
% 1.02/1.74 % ------
% 1.02/1.74
% 1.02/1.74
% 1.02/1.74 %
% 1.02/1.74
% 1.02/1.74 % ------ Proving...
% 1.02/1.74 %
% 1.02/1.74
% 1.02/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.02/1.74
% 1.02/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.02/1.74
% 1.02/1.74
%------------------------------------------------------------------------------