%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 10:16:45 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 37
% Syntax : Number of formulae : 175 ( 43 unt; 20 def)
% Number of atoms : 375 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 380 ( 180 ~; 180 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 24 ( 23 usr; 21 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f29,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f32,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f33,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f35,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f36,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f37,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f38,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f40,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(f41,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(f42,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f44,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_2) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_4)
| ~ product(X3,e_1,X1) ),
inference(resolution,[],[f28,f44]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X2,X3,e_2)
| ~ product(X2,X0,e_4)
| ~ product(X3,e_2,X1) ),
inference(resolution,[],[f31,f44]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(e_1,X0,e_4)
| ~ product(e_1,e_1,X1) ),
inference(resolution,[],[f42,f49]) ).
fof(f84,plain,
! [X0,X1] :
( ~ product(X0,e_4,e_2)
| ~ product(X1,e_2,e_2)
| ~ product(X1,X0,e_4) ),
inference(resolution,[],[f42,f55]) ).
fof(f106,plain,
! [X0] :
( ~ product(X0,e_4,e_1)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[],[f69,f42]) ).
fof(f112,definition,
( spl0_2
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f114,plain,
( ~ product(e_1,e_4,e_4)
| spl0_2 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f138,definition,
( spl0_4
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f140,plain,
( ~ product(e_1,e_3,e_3)
| spl0_4 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f145,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f40,f29]) ).
fof(f148,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f40,f32]) ).
fof(f149,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f40,f33]) ).
fof(f151,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f40,f35]) ).
fof(f152,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f40,f36]) ).
fof(f153,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[],[f40,f37]) ).
fof(f157,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f41,f29]) ).
fof(f160,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f41,f32]) ).
fof(f161,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f41,f33]) ).
fof(f163,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f41,f35]) ).
fof(f164,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f41,f36]) ).
fof(f289,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| product(e_1,X0,e_3)
| product(e_1,X0,e_4) ),
inference(resolution,[],[f38,f22]) ).
fof(f290,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_3)
| product(e_2,X0,e_4) ),
inference(resolution,[],[f38,f23]) ).
fof(f293,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| product(X0,e_1,e_3)
| product(X0,e_1,e_4) ),
inference(resolution,[],[f38,f22]) ).
fof(f386,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[],[f145,f42]) ).
fof(f396,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[],[f157,f42]) ).
fof(f398,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[],[f160,f42]) ).
fof(f399,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f398,f138]) ).
fof(f400,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[],[f161,f42]) ).
fof(f402,plain,
~ product(e_1,e_4,e_4),
inference(resolution,[],[f163,f42]) ).
fof(f403,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f402,f112]) ).
fof(f404,plain,
~ product(e_2,e_4,e_4),
inference(resolution,[],[f164,f42]) ).
fof(f481,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,[],[f289,f23]) ).
fof(f482,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolution,[],[f289,f24]) ).
fof(f483,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(resolution,[],[f289,f25]) ).
fof(f484,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f483,f114]) ).
fof(f485,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_4)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f482,f140]) ).
fof(f486,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(forward_subsumption_resolution,[],[f481,f396]) ).
fof(f488,definition,
( spl0_39
<=> product(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f490,plain,
( product(e_1,e_4,e_3)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f492,definition,
( spl0_40
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f494,plain,
( product(e_1,e_4,e_2)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f496,definition,
( spl0_41
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f498,plain,
( product(e_1,e_4,e_1)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f499,plain,
( spl0_39
| spl0_40
| spl0_41
| spl0_2 ),
inference(avatar_split_clause,[],[f484,f112,f496,f492,f488]) ).
fof(f501,definition,
( spl0_42
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f503,plain,
( product(e_1,e_3,e_4)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f505,definition,
( spl0_43
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f509,definition,
( spl0_44
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f511,plain,
( product(e_1,e_3,e_1)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f512,plain,
( spl0_42
| spl0_43
| spl0_44
| spl0_4 ),
inference(avatar_split_clause,[],[f485,f138,f509,f505,f501]) ).
fof(f514,definition,
( spl0_45
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f516,plain,
( product(e_1,e_2,e_4)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f518,definition,
( spl0_46
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f522,definition,
( spl0_47
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f524,plain,
( product(e_1,e_2,e_1)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f525,plain,
( spl0_45
| spl0_46
| spl0_47 ),
inference(avatar_split_clause,[],[f486,f522,f518,f514]) ).
fof(f533,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_39 ),
inference(resolution,[],[f490,f152]) ).
fof(f539,plain,
( ~ spl0_46
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f533,f488,f518]) ).
fof(f542,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(resolution,[],[f290,f24]) ).
fof(f543,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(resolution,[],[f290,f25]) ).
fof(f544,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(forward_subsumption_resolution,[],[f543,f404]) ).
fof(f545,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(forward_subsumption_resolution,[],[f542,f400]) ).
fof(f548,definition,
( spl0_48
<=> product(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f550,plain,
( product(e_2,e_4,e_3)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f552,definition,
( spl0_49
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f554,plain,
( product(e_2,e_4,e_2)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f556,definition,
( spl0_50
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f558,plain,
( product(e_2,e_4,e_1)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( spl0_48
| spl0_49
| spl0_50 ),
inference(avatar_split_clause,[],[f544,f556,f552,f548]) ).
fof(f561,definition,
( spl0_51
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f563,plain,
( product(e_2,e_3,e_4)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f565,definition,
( spl0_52
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f567,plain,
( product(e_2,e_3,e_2)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f569,definition,
( spl0_53
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_53])],[avatar_definition]) ).
fof(f571,plain,
( product(e_2,e_3,e_1)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f572,plain,
( spl0_51
| spl0_52
| spl0_53 ),
inference(avatar_split_clause,[],[f545,f569,f565,f561]) ).
fof(f672,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(resolution,[],[f293,f23]) ).
fof(f708,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_40 ),
inference(resolution,[],[f494,f153]) ).
fof(f718,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_41 ),
inference(resolution,[],[f498,f151]) ).
fof(f722,plain,
( $false
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f718,f42]) ).
fof(f723,plain,
~ spl0_41,
inference(avatar_contradiction_clause,[],[f722]) ).
fof(f738,plain,
( ~ spl0_43
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f708,f492,f505]) ).
fof(f774,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_44 ),
inference(resolution,[],[f511,f148]) ).
fof(f777,plain,
( $false
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f774,f42]) ).
fof(f778,plain,
~ spl0_44,
inference(avatar_contradiction_clause,[],[f777]) ).
fof(f841,plain,
( ! [X0] :
( ~ product(X0,e_2,e_2)
| ~ product(X0,e_1,e_4) )
| ~ spl0_40 ),
inference(resolution,[],[f494,f84]) ).
fof(f861,plain,
( ~ product(e_2,e_1,e_4)
| ~ spl0_40 ),
inference(resolution,[],[f841,f42]) ).
fof(f885,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_47 ),
inference(resolution,[],[f524,f145]) ).
fof(f886,plain,
( $false
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f885,f42]) ).
fof(f887,plain,
~ spl0_47,
inference(avatar_contradiction_clause,[],[f886]) ).
fof(f889,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(forward_subsumption_resolution,[],[f672,f386]) ).
fof(f893,definition,
( spl0_74
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_74])],[avatar_definition]) ).
fof(f897,definition,
( spl0_75
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_75])],[avatar_definition]) ).
fof(f899,plain,
( product(e_2,e_1,e_1)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f902,plain,
( ~ spl0_74
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f861,f492,f893]) ).
fof(f904,definition,
( spl0_76
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_76])],[avatar_definition]) ).
fof(f906,plain,
( product(e_2,e_1,e_3)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f904]) ).
fof(f908,plain,
( spl0_74
| spl0_76
| spl0_75 ),
inference(avatar_split_clause,[],[f889,f897,f904,f893]) ).
fof(f987,plain,
( ~ product(e_1,e_4,e_3)
| ~ spl0_48 ),
inference(resolution,[],[f550,f157]) ).
fof(f995,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_48 ),
inference(resolution,[],[f550,f151]) ).
fof(f1002,plain,
( $false
| ~ spl0_48
| ~ spl0_76 ),
inference(forward_subsumption_resolution,[],[f995,f906]) ).
fof(f1003,plain,
( ~ spl0_48
| ~ spl0_76 ),
inference(avatar_contradiction_clause,[],[f1002]) ).
fof(f1017,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_49 ),
inference(resolution,[],[f554,f152]) ).
fof(f1022,plain,
( $false
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1017,f42]) ).
fof(f1023,plain,
~ spl0_49,
inference(avatar_contradiction_clause,[],[f1022]) ).
fof(f1029,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_50 ),
inference(resolution,[],[f558,f106]) ).
fof(f1037,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_50 ),
inference(resolution,[],[f558,f153]) ).
fof(f1039,plain,
( ~ product(e_1,e_3,e_4)
| ~ spl0_51 ),
inference(resolution,[],[f563,f157]) ).
fof(f1053,plain,
( $false
| ~ spl0_42
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[],[f1039,f503]) ).
fof(f1054,plain,
( ~ spl0_42
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f1053]) ).
fof(f1068,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_52 ),
inference(resolution,[],[f567,f149]) ).
fof(f1070,plain,
( $false
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1068,f42]) ).
fof(f1071,plain,
~ spl0_52,
inference(avatar_contradiction_clause,[],[f1070]) ).
fof(f1072,plain,
( $false
| ~ spl0_50
| ~ spl0_53 ),
inference(forward_subsumption_resolution,[],[f1037,f571]) ).
fof(f1073,plain,
( ~ spl0_50
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f1072]) ).
fof(f1077,plain,
( $false
| ~ spl0_45
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f1029,f516]) ).
fof(f1078,plain,
( ~ spl0_45
| ~ spl0_50 ),
inference(avatar_contradiction_clause,[],[f1077]) ).
fof(f1079,plain,
( $false
| ~ spl0_39
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f987,f490]) ).
fof(f1080,plain,
( ~ spl0_39
| ~ spl0_48 ),
inference(avatar_contradiction_clause,[],[f1079]) ).
fof(f1127,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_75 ),
inference(resolution,[],[f899,f157]) ).
fof(f1138,plain,
( $false
| ~ spl0_75 ),
inference(forward_subsumption_resolution,[],[f1127,f42]) ).
fof(f1139,plain,
~ spl0_75,
inference(avatar_contradiction_clause,[],[f1138]) ).
cnf(s22,plain,
~ spl0_4,
inference(sat_conversion,[],[f399]) ).
cnf(s23,plain,
~ spl0_2,
inference(sat_conversion,[],[f403]) ).
cnf(s29,plain,
( spl0_2
| spl0_39
| spl0_40
| spl0_41 ),
inference(sat_conversion,[],[f499]) ).
cnf(s30,plain,
( spl0_4
| spl0_42
| spl0_43
| spl0_44 ),
inference(sat_conversion,[],[f512]) ).
cnf(s31,plain,
( spl0_45
| spl0_46
| spl0_47 ),
inference(sat_conversion,[],[f525]) ).
cnf(s34,plain,
( ~ spl0_39
| ~ spl0_46 ),
inference(sat_conversion,[],[f539]) ).
cnf(s35,plain,
( spl0_48
| spl0_49
| spl0_50 ),
inference(sat_conversion,[],[f559]) ).
cnf(s36,plain,
( spl0_51
| spl0_52
| spl0_53 ),
inference(sat_conversion,[],[f572]) ).
cnf(s49,plain,
~ spl0_41,
inference(sat_conversion,[],[f723]) ).
cnf(s53,plain,
( ~ spl0_40
| ~ spl0_43 ),
inference(sat_conversion,[],[f738]) ).
cnf(s58,plain,
~ spl0_44,
inference(sat_conversion,[],[f778]) ).
cnf(s75,plain,
~ spl0_47,
inference(sat_conversion,[],[f887]) ).
cnf(s82,plain,
( ~ spl0_40
| ~ spl0_74 ),
inference(sat_conversion,[],[f902]) ).
cnf(s89,plain,
( spl0_74
| spl0_75
| spl0_76 ),
inference(sat_conversion,[],[f908]) ).
cnf(s110,plain,
( ~ spl0_48
| ~ spl0_76 ),
inference(sat_conversion,[],[f1003]) ).
cnf(s113,plain,
~ spl0_49,
inference(sat_conversion,[],[f1023]) ).
cnf(s116,plain,
( ~ spl0_42
| ~ spl0_51 ),
inference(sat_conversion,[],[f1054]) ).
cnf(s117,plain,
~ spl0_52,
inference(sat_conversion,[],[f1071]) ).
cnf(s118,plain,
( ~ spl0_50
| ~ spl0_53 ),
inference(sat_conversion,[],[f1073]) ).
cnf(s130,plain,
( ~ spl0_45
| ~ spl0_50 ),
inference(sat_conversion,[],[f1078]) ).
cnf(s131,plain,
( ~ spl0_39
| ~ spl0_48 ),
inference(sat_conversion,[],[f1080]) ).
cnf(s146,plain,
~ spl0_75,
inference(sat_conversion,[],[f1139]) ).
cnf(s147,plain,
( spl0_74
| spl0_76 ),
inference(rat,[],[s89,s146]) ).
cnf(s155,plain,
( spl0_51
| spl0_53 ),
inference(rat,[],[s36,s117]) ).
cnf(s156,plain,
( spl0_48
| spl0_50 ),
inference(rat,[],[s35,s113]) ).
cnf(s157,plain,
( spl0_45
| spl0_46 ),
inference(rat,[],[s31,s75]) ).
cnf(s158,plain,
( spl0_4
| spl0_42
| spl0_43 ),
inference(rat,[],[s30,s58]) ).
cnf(s159,plain,
( spl0_2
| spl0_39
| spl0_40 ),
inference(rat,[],[s29,s49]) ).
cnf(s166,plain,
~ spl0_40,
inference(rat,[],[s118,s155,s156,s116,s110,s158,s147,s53,s82,s22]) ).
cnf(s167,plain,
spl0_39,
inference(rat,[],[s159,s23,s166]) ).
cnf(s168,plain,
~ spl0_48,
inference(rat,[],[s131,s167]) ).
cnf(s172,plain,
~ spl0_46,
inference(rat,[],[s34,s167]) ).
cnf(s173,plain,
spl0_50,
inference(rat,[],[s156,s168]) ).
cnf(s176,plain,
spl0_45,
inference(rat,[],[s157,s172]) ).
cnf(s177,plain,
$false,
inference(rat,[],[s130,s173,s176]) ).
fof(f1140,plain,
$false,
inference(avatar_sat_refutation,[],[s177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 % Computer : n011.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Sun Sep 27 09:21:15 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (2142363)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2142373)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2979158925:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2142370)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2142370)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2528517423:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2142369)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2136023770_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2142371)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3103324932:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2142372)dis+10_1_sil=32000:sp=arity:random_seed=926235701:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2142374)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=70787929:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % Detected minimum model sizes of [1]
% 0.17/0.47 % Detected maximum model sizes of [5]
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2142375)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=374420045:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (2142373) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2142363-2142373"...
% 0.17/0.47 % (2142373)...printing done.
% 0.17/0.47 % (2142373)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2142373)------------------------------
% 0.17/0.48 % (2142373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2142373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2142373)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2142373)Termination reason: Refutation
% 0.17/0.48 % (2142373)Time elapsed: 0.014 s
% 0.17/0.48 % (2142373)Peak memory usage: 12 MB
% 0.17/0.48 % (2142373)Instructions burned: 42 (million)
% 0.17/0.48 % (2142363)Success in time 0.03 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------