%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP039-6 : 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 : 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 01:30:01 PM UTC 2026
% Result : Unsatisfiable 0.71s 1.21s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 29 unt; 1 def)
% Number of atoms : 128 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 51 ~; 54 |; 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 : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subgroup_member_substitution) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f6,axiom,
! [X2,X0,X1] :
( subgroup_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
fof(f7,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f9,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f10,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f17,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(f18,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(f19,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f20,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f21,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f22,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( subgroup_member(X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_77,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f9]) ).
tcf(c_80,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f10]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_89,negated_conjecture,
subgroup_member(b),
inference(cnf_transformation,[],[f19]) ).
tcf(c_90,negated_conjecture,
product(b,inverse(a),c),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,negated_conjecture,
product(a,c,d),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,negated_conjecture,
~ subgroup_member(d),
inference(cnf_transformation,[],[f22]) ).
tcf(c_195,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_196,negated_conjecture,
~ subgroup_member(d),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_197,negated_conjecture,
product(a,c,d),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_198,negated_conjecture,
product(b,iPr_def_10,c),
inference(demodulation,[status(thm)],[c_90,c_195]) ).
tcf(c_199,negated_conjecture,
subgroup_member(b),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_480,plain,
product(iPr_def_10,a,identity),
inference(superposition,[status(thm)],[c_195,c_79]) ).
tcf(c_484,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_195,c_75]) ).
tcf(c_627,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_197,c_76]) ).
tcf(c_628,plain,
( subgroup_member(c)
| ~ subgroup_member(iPr_def_10)
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_198,c_76]) ).
tcf(c_633,plain,
( subgroup_member(c)
| ~ subgroup_member(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_628,c_199]) ).
tcf(c_636,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_627,c_196]) ).
tcf(c_721,plain,
! [X0: $i] :
( equalish(X0,c)
| ~ product(a,X0,d) ),
inference(superposition,[status(thm)],[c_197,c_85]) ).
tcf(c_723,plain,
! [X0: $i] :
( equalish(X0,a)
| ~ product(iPr_def_10,X0,identity) ),
inference(superposition,[status(thm)],[c_480,c_85]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_79,c_81]) ).
tcf(c_913,plain,
~ subgroup_member(a),
inference(global_subsumption_just,[status(thm)],[c_636,c_484,c_633,c_636]) ).
tcf(c_1007,plain,
( subgroup_member(d)
| subgroup_member(a)
| equalish(element_in_O2(a,d),c) ),
inference(superposition,[status(thm)],[c_88,c_721]) ).
tcf(c_1013,plain,
equalish(element_in_O2(a,d),c),
inference(forward_subsumption_resolution,[status(thm)],[c_1007,c_196,c_913]) ).
tcf(c_1021,plain,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(a,d)) ),
inference(superposition,[status(thm)],[c_1013,c_71]) ).
tcf(c_1088,plain,
( subgroup_member(d)
| subgroup_member(c)
| subgroup_member(a) ),
inference(superposition,[status(thm)],[c_87,c_1021]) ).
tcf(c_1089,plain,
subgroup_member(c),
inference(forward_subsumption_resolution,[status(thm)],[c_1088,c_196,c_913]) ).
tcf(c_1943,plain,
equalish(inverse(iPr_def_10),a),
inference(superposition,[status(thm)],[c_80,c_723]) ).
tcf(c_1952,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1943,c_71]) ).
tcf(c_1953,plain,
~ subgroup_member(inverse(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_1952,c_913]) ).
tcf(c_1958,plain,
~ subgroup_member(iPr_def_10),
inference(superposition,[status(thm)],[c_75,c_1953]) ).
tcf(c_2003,plain,
! [X0: $i] :
( product(inverse(b),c,X0)
| ~ product(identity,iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_198,c_839]) ).
tcf(c_2172,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(c)
| ~ subgroup_member(inverse(b))
| ~ product(identity,iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_2003,c_76]) ).
tcf(c_2186,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(b))
| ~ product(identity,iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2172,c_1089]) ).
tcf(c_4044,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(inverse(b)) ),
inference(superposition,[status(thm)],[c_77,c_2186]) ).
tcf(c_4046,plain,
~ subgroup_member(inverse(b)),
inference(forward_subsumption_resolution,[status(thm)],[c_4044,c_1958]) ).
tcf(c_4097,plain,
~ subgroup_member(b),
inference(superposition,[status(thm)],[c_75,c_4046]) ).
tcf(c_4098,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4097,c_199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:24:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.71/1.21 % SZS status Started for theBenchmark.p
% 0.71/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.71/1.21
% 0.71/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.71/1.21
% 0.71/1.21 % ------ iProver source info
% 0.71/1.21
% 0.71/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.71/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.71/1.21 % git: non_committed_changes: false
% 0.71/1.21
% 0.71/1.21 % ------ Parsing...% successful
% 0.71/1.21
% 0.71/1.21
% 0.71/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.71/1.21
% 0.71/1.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.71/1.21
% 0.71/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.71/1.21
% 0.71/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.71/1.21 % ------ Proving...
% 0.71/1.21 % ------ Problem Properties
% 0.71/1.21
% 0.71/1.21 %
% 0.71/1.21 % clauses 23
% 0.71/1.21 % conjectures 4
% 0.71/1.21 % EPR 15
% 0.71/1.21 % Horn 21
% 0.71/1.21 % unary 10
% 0.71/1.21 % binary 3
% 0.71/1.21 % lits 49
% 0.71/1.21 % lits eq 1
% 0.71/1.21 % fd_pure 0
% 0.71/1.21 % fd_pseudo 0
% 0.71/1.21 % fd_cond 0
% 0.71/1.21 % fd_pseudo_cond 0
% 0.71/1.21 % AC symbols 0
% 0.71/1.21
% 0.71/1.21 % ------ Schedule dynamic 5 is on
% 0.71/1.21
% 0.71/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.71/1.21
% 0.71/1.21
% 0.71/1.21 % ------
% 0.71/1.21 % Current options:
% 0.71/1.21 % ------
% 0.71/1.21
% 0.71/1.21
% 0.71/1.21 %
% 0.71/1.21
% 0.71/1.21 % ------ Proving...
% 0.71/1.21 %
% 0.71/1.21
% 0.71/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.71/1.21
% 0.71/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.71/1.21
% 0.71/1.21
%------------------------------------------------------------------------------