%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 01:31:29 PM UTC 2026
% Result : Unsatisfiable 0.93s 1.10s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 19 unt; 0 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 258 ( 132 ~; 126 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f5,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f17,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f20,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
tcf(c_69,plain,
next(e_1,e_2),
inference(cnf_transformation,[],[f1]) ).
tcf(c_73,plain,
greater(e_3,e_2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_75,plain,
group_element(e_1),
inference(cnf_transformation,[],[f7]) ).
tcf(c_76,plain,
group_element(e_2),
inference(cnf_transformation,[],[f8]) ).
tcf(c_77,plain,
group_element(e_3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_78,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f10]) ).
tcf(c_79,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f13]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_88,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_160,plain,
! [X0: $i] :
( ~ greater(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[c_69,c_74]) ).
tcf(c_180,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_73,c_160]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_78,c_85]) ).
tcf(c_186,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_185]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_78,c_86]) ).
tcf(c_194,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_193]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_78,c_87]) ).
tcf(c_202,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_201]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_79,c_86]) ).
tcf(c_217,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_216]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[c_81,c_86]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[c_81,c_87]) ).
tcf(c_342,plain,
! [X0: $i] :
( product(e_1,e_1,e_3)
| ~ product(e_3,e_1,X0)
| ~ product(e_3,X0,e_1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_343,plain,
( product(e_1,e_1,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_2,X0)
| ~ product(X0,e_2,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X1,X0)
| ~ product(X0,X2,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_350,plain,
! [X0: $i] :
( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_352,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_350]) ).
tcf(c_353,plain,
! [X0: $i] :
( product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_355,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_356,plain,
! [X0: $i] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_357,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_1)
| ~ product(X0,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_242]) ).
tcf(c_359,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_356]) ).
tcf(c_361,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_1)
| ~ product(e_2,X0,e_1) ),
inference(instantiation,[status(thm)],[c_250]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_2)
| ~ product(e_2,X1,X2)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_370,plain,
! [X0: $i] :
( ~ product(e_2,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_201]) ).
tcf(c_382,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_242]) ).
tcf(c_386,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_382]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] :
( product(e_2,e_2,X0)
| ~ product(X0,e_2,X1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,e_2)
| ~ product(e_2,e_3,X0)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_364]) ).
tcf(c_455,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_361]) ).
tcf(c_492,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_3)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_242]) ).
tcf(c_494,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_492]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,X0)
| ~ product(X0,e_2,e_3)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_347]) ).
tcf(c_502,plain,
( product(e_3,e_1,e_1)
| ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_501]) ).
tcf(c_556,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(superposition,[status(thm)],[c_84,c_180]) ).
tcf(c_558,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_556,c_75]) ).
tcf(c_595,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(superposition,[status(thm)],[c_84,c_180]) ).
tcf(c_597,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_595,c_75]) ).
tcf(c_627,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_628,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_216]) ).
tcf(c_701,plain,
( ~ product(e_2,e_3,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_370]) ).
tcf(c_708,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(superposition,[status(thm)],[c_558,c_193]) ).
tcf(c_710,plain,
! [X0: $i] :
( product(e_1,e_1,e_1)
| product(X0,e_1,e_1)
| ~ product(e_1,e_2,X0) ),
inference(superposition,[status(thm)],[c_558,c_88]) ).
tcf(c_718,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_710]) ).
tcf(c_719,plain,
product(e_1,e_1,e_1),
inference(global_subsumption_just,[status(thm)],[c_597,c_76,c_75,c_91,c_180,c_343,c_352,c_502,c_708,c_718]) ).
tcf(c_815,plain,
! [X0: $i] :
( product(X0,e_3,e_2)
| ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_2,X0) ),
inference(instantiation,[status(thm)],[c_411]) ).
tcf(c_816,plain,
( product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_815]) ).
tcf(c_830,plain,
! [X0: $i] :
( product(e_2,e_2,X0)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_399]) ).
tcf(c_831,plain,
( product(e_2,e_2,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_830]) ).
tcf(c_879,plain,
! [X0: $i] :
( product(e_3,e_3,X0)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_501]) ).
tcf(c_880,plain,
( product(e_3,e_3,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_879]) ).
tcf(c_917,plain,
( ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_357]) ).
tcf(c_922,plain,
! [X0: $i] :
( product(e_1,X0,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_364]) ).
tcf(c_923,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_922]) ).
tcf(c_1027,plain,
! [X0: $i] :
( product(e_2,e_2,X0)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_399]) ).
tcf(c_1029,plain,
( product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1027]) ).
tcf(c_1221,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1029,c_923,c_917,c_880,c_831,c_816,c_719,c_701,c_628,c_627,c_494,c_455,c_386,c_359,c_355,c_352,c_217,c_202,c_194,c_186,c_75,c_76,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 13:41:47 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running EPR theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 0.93/1.10 % SZS status Started for theBenchmark.p
% 0.93/1.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.93/1.10
% 0.93/1.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.93/1.10
% 0.93/1.10 % ------ iProver source info
% 0.93/1.10
% 0.93/1.10 % git: date: 2026-07-19 20:42:38 +0200
% 0.93/1.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.93/1.10 % git: non_committed_changes: false
% 0.93/1.10
% 0.93/1.10 % ------ Parsing...% successful
% 0.93/1.10
% 0.93/1.10
% 0.93/1.10 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.93/1.10 %
% 0.93/1.10
% 0.93/1.10 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.93/1.10
% 0.93/1.10 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.93/1.10 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.93/1.10 % ------ Proving...
% 0.93/1.10 % ------ Problem Properties
% 0.93/1.10
% 0.93/1.10 %
% 0.93/1.10 % clauses 15
% 0.93/1.10 % conjectures 1
% 0.93/1.10 % EPR 15
% 0.93/1.10 % Horn 14
% 0.93/1.10 % unary 4
% 0.93/1.10 % binary 9
% 0.93/1.10 % lits 30
% 0.93/1.10 % lits eq 0
% 0.93/1.10 % fd_pure 0
% 0.93/1.10 % fd_pseudo 0
% 0.93/1.10 % fd_cond 0
% 0.93/1.10 % fd_pseudo_cond 0
% 0.93/1.10 % AC symbols 0
% 0.93/1.10
% 0.93/1.10 % ------ Schedule EPR non Horn non eq is on
% 0.93/1.10
% 0.93/1.10 % ------ no equalities: superposition off
% 0.93/1.10
% 0.93/1.10 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 0.93/1.10
% 0.93/1.10
% 0.93/1.10 % ------
% 0.93/1.10 % Current options:
% 0.93/1.10 % ------
% 0.93/1.10
% 0.93/1.10
% 0.93/1.10 %
% 0.93/1.10
% 0.93/1.10 % ------ Proving...
% 0.93/1.10 %
% 0.93/1.10
% 0.93/1.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.93/1.10
% 0.93/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.93/1.10
% 0.93/1.10
%------------------------------------------------------------------------------