%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP134-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Tue Sep 29 10:13:03 AM UTC 2026
% Result : Unsatisfiable 2.49s 1.28s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 34
% Syntax : Number of formulae : 179 ( 21 unt; 20 def)
% Number of atoms : 444 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 477 ( 212 ~; 245 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 21 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f5,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f20,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
fof(f23,plain,
! [X0] :
( ~ next(X0,e_2)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[],[f5,f6]) ).
fof(f24,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f10,f19]) ).
fof(f25,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f10,f18]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f11,f19]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f11,f18]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f13,f19]) ).
fof(f34,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f13,f18]) ).
fof(f35,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_3) ),
inference(resolution,[],[f13,f17]) ).
fof(f42,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[],[f23,f1]) ).
fof(f50,definition,
( spl0_1
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f52,plain,
( ~ product(e_2,e_1,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f61,plain,
( ! [X0] :
( ~ product(e_2,X0,e_1)
| ~ product(X0,e_2,e_2) )
| spl0_1 ),
inference(resolution,[],[f52,f20]) ).
fof(f69,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| ~ group_element(e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f28,f16]) ).
fof(f70,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[],[f69,f9]) ).
fof(f84,definition,
( spl0_3
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f85,plain,
( product(e_3,e_1,e_3)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( ~ product(e_3,e_1,e_3)
| spl0_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_4
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f90,plain,
( ~ product(e_1,e_3,e_3)
| spl0_4 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f98,definition,
( spl0_5
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f100,plain,
( product(e_3,e_1,e_2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f102,definition,
( spl0_6
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f104,plain,
( product(e_3,e_1,e_1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f107,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f33,f16]) ).
fof(f108,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f107,f9]) ).
fof(f112,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| ~ group_element(e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f34,f16]) ).
fof(f113,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[],[f112,f9]) ).
fof(f119,definition,
( spl0_7
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f121,plain,
( product(e_1,e_3,e_2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f123,definition,
( spl0_8
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f125,plain,
( product(e_1,e_3,e_1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ product(e_2,X2,X1)
| ~ product(X0,X1,e_3)
| ~ product(X2,e_2,X0) ),
inference(resolution,[],[f35,f20]) ).
fof(f137,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_5 ),
inference(resolution,[],[f100,f27]) ).
fof(f160,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_7 ),
inference(resolution,[],[f121,f28]) ).
fof(f183,definition,
( spl0_10
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f184,plain,
( product(e_3,e_2,e_3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f185,plain,
( ~ product(e_3,e_2,e_3)
| spl0_10 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f187,definition,
( spl0_11
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f188,plain,
( product(e_2,e_3,e_3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( ~ product(e_2,e_3,e_3)
| spl0_11 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f197,definition,
( spl0_12
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f201,definition,
( spl0_13
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f203,plain,
( product(e_3,e_2,e_1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f219,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| ~ product(X0,X0,e_3) ),
inference(factoring,[],[f127]) ).
fof(f227,definition,
( spl0_14
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f229,plain,
( product(e_2,e_3,e_2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f231,definition,
( spl0_15
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f233,plain,
( product(e_2,e_3,e_1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ group_element(e_1) ),
inference(resolution,[],[f42,f16]) ).
fof(f236,plain,
! [X0] :
( ~ product(e_3,X0,e_1)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[],[f42,f20]) ).
fof(f237,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(duplicate_literal_removal,[],[f235]) ).
fof(f238,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f237,f7]) ).
fof(f240,definition,
( spl0_16
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f244,definition,
( spl0_17
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f247,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f238,f244,f240]) ).
fof(f289,definition,
( spl0_18
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f291,plain,
( product(e_2,e_2,e_2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f293,definition,
( spl0_19
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f298,plain,
! [X0,X1] :
( ~ product(X1,e_3,e_2)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ product(e_3,X1,X0)
| ~ group_element(X0) ),
inference(resolution,[],[f108,f20]) ).
fof(f307,plain,
! [X0,X1] :
( ~ product(e_3,X1,e_2)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| product(X0,e_3,e_1)
| ~ product(X1,e_3,X0) ),
inference(resolution,[],[f113,f20]) ).
fof(f312,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_14 ),
inference(resolution,[],[f229,f24]) ).
fof(f330,plain,
( ~ product(e_3,e_2,e_2)
| spl0_1
| ~ spl0_15 ),
inference(resolution,[],[f233,f61]) ).
fof(f334,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_15 ),
inference(resolution,[],[f233,f34]) ).
fof(f338,plain,
( ~ spl0_19
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f334,f231,f293]) ).
fof(f340,plain,
( ~ product(e_3,e_3,e_3)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ group_element(e_2) ),
inference(resolution,[],[f219,f16]) ).
fof(f341,plain,
( ~ product(e_3,e_3,e_3)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(duplicate_literal_removal,[],[f340]) ).
fof(f342,plain,
( ~ product(e_3,e_3,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(forward_subsumption_resolution,[],[f341,f8]) ).
fof(f344,definition,
( spl0_20
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f345,plain,
( product(e_3,e_3,e_3)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f346,plain,
( ~ product(e_3,e_3,e_3)
| spl0_20 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f347,plain,
( spl0_18
| spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f342,f344,f293,f289]) ).
fof(f353,definition,
( spl0_21
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f357,definition,
( spl0_22
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f361,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_13 ),
inference(resolution,[],[f236,f203]) ).
fof(f363,plain,
~ product(e_3,e_3,e_1),
inference(factoring,[],[f236]) ).
fof(f364,plain,
~ spl0_22,
inference(avatar_split_clause,[],[f363,f357]) ).
fof(f369,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ group_element(e_3)
| ~ spl0_10 ),
inference(resolution,[],[f184,f113]) ).
fof(f374,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f369,f9]) ).
fof(f375,plain,
( spl0_21
| spl0_22
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f374,f183,f357,f353]) ).
fof(f376,plain,
( ~ spl0_12
| spl0_1
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f330,f231,f50,f197]) ).
fof(f379,plain,
( ~ spl0_15
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f361,f201,f231]) ).
fof(f380,plain,
( ~ group_element(e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ group_element(e_3)
| spl0_10 ),
inference(resolution,[],[f185,f16]) ).
fof(f382,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ group_element(e_3)
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f380,f8]) ).
fof(f383,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f382,f9]) ).
fof(f384,plain,
( spl0_12
| spl0_13
| spl0_10 ),
inference(avatar_split_clause,[],[f383,f183,f201,f197]) ).
fof(f385,plain,
( ~ group_element(e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ spl0_11 ),
inference(resolution,[],[f188,f108]) ).
fof(f394,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f385,f9]) ).
fof(f395,plain,
( spl0_21
| spl0_22
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f394,f187,f357,f353]) ).
fof(f450,plain,
( ~ product(e_1,e_3,e_3)
| ~ spl0_20 ),
inference(resolution,[],[f345,f27]) ).
fof(f467,plain,
( ~ group_element(e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ group_element(e_3)
| spl0_20 ),
inference(resolution,[],[f346,f16]) ).
fof(f469,plain,
( ~ group_element(e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| spl0_20 ),
inference(duplicate_literal_removal,[],[f467]) ).
fof(f470,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f469,f9]) ).
fof(f471,plain,
( spl0_21
| spl0_22
| spl0_20 ),
inference(avatar_split_clause,[],[f470,f344,f357,f353]) ).
fof(f493,plain,
( ~ spl0_16
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f137,f98,f240]) ).
fof(f528,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_4 ),
inference(resolution,[],[f90,f16]) ).
fof(f530,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f528,f9]) ).
fof(f531,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f530,f7]) ).
fof(f532,plain,
( spl0_7
| spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f531,f88,f123,f119]) ).
fof(f550,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_8 ),
inference(resolution,[],[f125,f28]) ).
fof(f554,plain,
( ~ spl0_17
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f550,f123,f244]) ).
fof(f558,plain,
( ~ spl0_16
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f160,f119,f240]) ).
fof(f563,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ group_element(e_3)
| ~ spl0_3 ),
inference(resolution,[],[f85,f70]) ).
fof(f569,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f563,f9]) ).
fof(f570,plain,
( spl0_21
| spl0_22
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f569,f84,f357,f353]) ).
fof(f626,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_18 ),
inference(resolution,[],[f291,f25]) ).
fof(f638,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ group_element(e_2) ),
inference(factoring,[],[f298]) ).
fof(f641,plain,
( ~ product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[],[f307]) ).
fof(f642,plain,
( ~ product(e_3,e_3,e_2)
| ~ group_element(e_2)
| product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f641,f33]) ).
fof(f643,plain,
( ~ product(e_3,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f642,f8]) ).
fof(f646,plain,
( ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f312,f227,f119]) ).
fof(f655,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f638,f34]) ).
fof(f665,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(forward_subsumption_resolution,[],[f655,f8]) ).
fof(f667,plain,
( spl0_13
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f665,f353,f201]) ).
fof(f669,plain,
( ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_3)
| spl0_3 ),
inference(resolution,[],[f86,f16]) ).
fof(f672,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_3)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f669,f7]) ).
fof(f676,plain,
( ~ group_element(e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| spl0_11 ),
inference(resolution,[],[f189,f16]) ).
fof(f678,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f676,f9]) ).
fof(f684,plain,
( ~ product(e_1,e_3,e_1)
| ~ spl0_6 ),
inference(resolution,[],[f104,f236]) ).
fof(f686,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_6 ),
inference(resolution,[],[f104,f27]) ).
fof(f691,plain,
( ~ spl0_17
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f686,f102,f244]) ).
fof(f693,plain,
( ~ spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f684,f102,f123]) ).
fof(f694,plain,
( ~ spl0_4
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f450,f344,f88]) ).
fof(f702,plain,
( ~ spl0_1
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f626,f289,f50]) ).
fof(f705,plain,
( spl0_15
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f643,f353,f231]) ).
fof(f706,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f678,f8]) ).
fof(f709,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f672,f9]) ).
fof(f715,plain,
( spl0_14
| spl0_15
| spl0_11 ),
inference(avatar_split_clause,[],[f706,f187,f231,f227]) ).
fof(f717,plain,
( spl0_5
| spl0_6
| spl0_3 ),
inference(avatar_split_clause,[],[f709,f84,f102,f98]) ).
cnf(s16,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f247]) ).
cnf(s24,plain,
( ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f338]) ).
cnf(s25,plain,
( spl0_18
| spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f347]) ).
cnf(s27,plain,
~ spl0_22,
inference(sat_conversion,[],[f364]) ).
cnf(s29,plain,
( ~ spl0_10
| spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f375]) ).
cnf(s30,plain,
( spl0_1
| ~ spl0_12
| ~ spl0_15 ),
inference(sat_conversion,[],[f376]) ).
cnf(s34,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f379]) ).
cnf(s35,plain,
( spl0_10
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f384]) ).
cnf(s36,plain,
( ~ spl0_11
| spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f395]) ).
cnf(s42,plain,
( spl0_20
| spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f471]) ).
cnf(s44,plain,
( ~ spl0_5
| ~ spl0_16 ),
inference(sat_conversion,[],[f493]) ).
cnf(s54,plain,
( spl0_4
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f532]) ).
cnf(s58,plain,
( ~ spl0_8
| ~ spl0_17 ),
inference(sat_conversion,[],[f554]) ).
cnf(s63,plain,
( ~ spl0_7
| ~ spl0_16 ),
inference(sat_conversion,[],[f558]) ).
cnf(s65,plain,
( ~ spl0_3
| spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f570]) ).
cnf(s77,plain,
( ~ spl0_7
| ~ spl0_14 ),
inference(sat_conversion,[],[f646]) ).
cnf(s86,plain,
( spl0_13
| ~ spl0_21 ),
inference(sat_conversion,[],[f667]) ).
cnf(s91,plain,
( ~ spl0_6
| ~ spl0_17 ),
inference(sat_conversion,[],[f691]) ).
cnf(s93,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f693]) ).
cnf(s94,plain,
( ~ spl0_4
| ~ spl0_20 ),
inference(sat_conversion,[],[f694]) ).
cnf(s110,plain,
( ~ spl0_1
| ~ spl0_18 ),
inference(sat_conversion,[],[f702]) ).
cnf(s115,plain,
( spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f705]) ).
cnf(s121,plain,
( spl0_11
| spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f715]) ).
cnf(s123,plain,
( spl0_3
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f717]) ).
cnf(s126,plain,
( ~ spl0_6
| spl0_4 ),
inference(rat,[],[s63,s16,s54,s91,s93]) ).
cnf(s127,plain,
( ~ spl0_15
| spl0_10
| spl0_1 ),
inference(rat,[],[s35,s30,s34]) ).
cnf(s128,plain,
( spl0_15
| spl0_14 ),
inference(rat,[],[s36,s121,s115,s27]) ).
cnf(s129,plain,
( ~ spl0_15
| spl0_1 ),
inference(rat,[],[s29,s86,s127,s34,s27]) ).
cnf(s130,plain,
spl0_15,
inference(rat,[],[s123,s65,s44,s16,s58,s126,s54,s94,s77,s42,s128,s115,s27]) ).
cnf(s133,plain,
~ spl0_13,
inference(rat,[],[s34,s130]) ).
cnf(s134,plain,
~ spl0_19,
inference(rat,[],[s24,s130]) ).
cnf(s136,plain,
spl0_1,
inference(rat,[],[s129,s130]) ).
cnf(s137,plain,
~ spl0_21,
inference(rat,[],[s86,s133]) ).
cnf(s140,plain,
~ spl0_18,
inference(rat,[],[s110,s136]) ).
cnf(s144,plain,
spl0_20,
inference(rat,[],[s42,s27,s137]) ).
cnf(s149,plain,
$false,
inference(rat,[],[s25,s134,s144,s140]) ).
fof(f719,plain,
$false,
inference(avatar_sat_refutation,[],[s149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP134-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:33:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.49/1.28 % (247684)Input is clausal, will run a generic CNF schedule.
% 2.49/1.28 % (247692)lrs+10_1_sil=8000:sp=occurrence:random_seed=4291707476:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.49/1.28 % (247692)Instruction limit reached!
% 2.49/1.28 % (247692)------------------------------
% 2.49/1.28 % (247692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.28 % (247692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.28 % (247692)CaDiCaL version: 2.1.3
% 2.49/1.28 % (247692)Termination reason: Instruction limit
% 2.49/1.28 % (247692)Termination phase: Saturation
% 2.49/1.28 % (247692)Time elapsed: 0.034 s
% 2.49/1.28 % (247692)Peak memory usage: 88 MB
% 2.49/1.28 % (247692)Instructions burned: 107 (million)
% 2.49/1.28 % (247695)dis-21_1_sil=8000:lcm=predicate:random_seed=1950256787:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.49/1.28 % (247689)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=56121896:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.49/1.28 % (247690)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1691616382:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.49/1.28 % (247694)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3335713645:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.49/1.28 % (247691)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3139466827:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.49/1.28 % (247693)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1433067173:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.49/1.28 % (247694)First to succeed.
% 2.49/1.28 % (247694)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-247684"
% 2.49/1.28 % (247695)Also succeeded, but the first one will report.
% 2.49/1.28 % (247693)Instruction limit reached!
% 2.49/1.28 % (247693)------------------------------
% 2.49/1.28 % (247693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.28 % (247693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.28 % (247693)CaDiCaL version: 2.1.3
% 2.49/1.28 % (247693)Termination reason: Instruction limit
% 2.49/1.28 % (247693)Termination phase: Saturation
% 2.49/1.28 % (247693)Time elapsed: 0.060 s
% 2.49/1.28 % (247693)Peak memory usage: 88 MB
% 2.49/1.28 % (247693)Instructions burned: 115 (million)
% 2.49/1.28 % (247697)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=85973966:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.49/1.28 % (247697)Also succeeded, but the first one will report.
% 2.49/1.28 % (247704)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=225614075:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.49/1.28 % (247704)Refutation not found, incomplete strategy
% 2.49/1.28 % (247704)------------------------------
% 2.49/1.28 % (247704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.28 % (247704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.28 % (247704)CaDiCaL version: 2.1.3
% 2.49/1.28 % (247704)Termination reason: Refutation not found, incomplete strategy
% 2.49/1.28 % (247704)Time elapsed: 0.001 s
% 2.49/1.28 % (247704)Peak memory usage: 87 MB
% 2.49/1.28 % (247704)Instructions burned: 1 (million)
% 2.49/1.28 % (247694)Refutation found. Thanks to Tanya!
% 2.49/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.49/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.48 % (247694)------------------------------
% 3.55/1.48 % (247694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.48 % (247694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.48 % (247694)CaDiCaL version: 2.1.3
% 3.55/1.48 % (247694)Termination reason: Refutation
% 3.55/1.48 % (247694)Time elapsed: 0.019 s
% 3.55/1.48 % (247694)Peak memory usage: 89 MB
% 3.55/1.48 % (247694)Instructions burned: 25 (million)
% 3.55/1.48 % (247694)------------------------------
% 3.55/1.48 % (247694)------------------------------
% 3.55/1.48 % (247684)Success in time 0.421 s
% 3.55/1.48 % Vampire exiting
%------------------------------------------------------------------------------