%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 10:12:42 AM UTC 2026
% Result : Unsatisfiable 2.58s 1.32s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 60
% Syntax : Number of formulae : 277 ( 67 unt; 35 def)
% Number of atoms : 630 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 618 ( 265 ~; 318 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 39 ( 38 usr; 36 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| product(e_4,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f2,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1)
| product(X0,e_4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f6,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f7,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f8,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f9,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f10,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f11,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f12,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f13,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f14,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f15,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f16,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f17,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f18,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f19,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/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f20,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f23,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f24,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X0,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
fof(f25,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/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_1,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_2)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f7,f25]) ).
fof(f28,plain,
! [X0] :
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) ),
inference(factoring,[],[f26]) ).
fof(f31,definition,
( spl0_1
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f32,plain,
( product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f39,definition,
( spl0_3
<=> ! [X0] :
( ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f40,plain,
( ! [X0] :
( ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl0_4
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f44,plain,
( ~ product(e_1,e_1,e_1)
| spl0_4 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f28,f42,f39]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_1,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_3)
| ~ product(X0,e_3,X1) ),
inference(resolution,[],[f8,f25]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_1,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_4)
| ~ product(X0,e_4,X1) ),
inference(resolution,[],[f9,f25]) ).
fof(f63,definition,
( spl0_7
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f64,plain,
( product(e_2,e_2,e_1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_2,X1)
| ~ product(X2,X3,e_2)
| ~ product(X2,X0,e_4)
| ~ product(X0,e_4,X1) ),
inference(resolution,[],[f12,f25]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(X2,e_2,X3)
| ~ product(X2,e_4,X0)
| ~ product(e_2,X3,X1) ),
inference(resolution,[],[f12,f24]) ).
fof(f76,plain,
! [X0] :
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(factoring,[],[f46]) ).
fof(f79,definition,
( spl0_9
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f80,plain,
( product(e_1,e_3,e_3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( ~ product(e_1,e_3,e_3)
| spl0_9 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(X2,e_3,X3)
| ~ product(X2,e_4,X0)
| ~ product(e_3,X3,X1) ),
inference(resolution,[],[f15,f24]) ).
fof(f101,definition,
( spl0_13
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f102,plain,
( product(e_3,e_3,e_1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( ~ product(e_3,e_3,e_1)
| spl0_13 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f114,plain,
! [X0] :
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,X0,e_4)
| ~ product(X0,e_4,e_1) ),
inference(factoring,[],[f48]) ).
fof(f127,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f23,f44]) ).
fof(f134,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f127]) ).
fof(f135,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f76,f23]) ).
fof(f136,plain,
! [X0] :
( ~ product(e_1,X0,e_4)
| ~ product(X0,e_4,e_1) ),
inference(forward_subsumption_resolution,[],[f114,f23]) ).
fof(f137,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f20,f23]) ).
fof(f139,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f21,f23]) ).
fof(f141,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f22,f23]) ).
fof(f147,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,[],[f19,f3]) ).
fof(f154,definition,
( spl0_17
<=> product(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f155,plain,
( product(e_4,e_4,e_1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f156,plain,
( ~ product(e_4,e_4,e_1)
| spl0_17 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f178,definition,
( spl0_21
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f179,plain,
( product(e_3,e_3,e_2)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f180,plain,
( ~ product(e_3,e_3,e_2)
| spl0_21 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f186,plain,
! [X0] :
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_4,e_2) ),
inference(factoring,[],[f72]) ).
fof(f189,definition,
( spl0_23
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f190,plain,
( product(e_2,e_4,e_4)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f191,plain,
( ~ product(e_2,e_4,e_4)
| spl0_23 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f196,plain,
! [X0] :
( ~ product(e_2,X0,e_4)
| ~ product(X0,e_4,e_2) ),
inference(forward_subsumption_resolution,[],[f186,f23]) ).
fof(f199,plain,
! [X0] :
( ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_2,X0)
| ~ product(e_2,X0,e_4) ),
inference(factoring,[],[f73]) ).
fof(f200,plain,
! [X0] :
( ~ product(e_4,e_2,X0)
| ~ product(e_2,X0,e_4) ),
inference(forward_subsumption_resolution,[],[f199,f23]) ).
fof(f202,definition,
( spl0_25
<=> product(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f203,plain,
( product(e_4,e_4,e_2)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f213,definition,
( spl0_27
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f214,plain,
( product(e_3,e_4,e_4)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f215,plain,
( ~ product(e_3,e_4,e_4)
| spl0_27 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f223,plain,
! [X0] :
( ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_3,X0)
| ~ product(e_3,X0,e_4) ),
inference(factoring,[],[f89]) ).
fof(f224,plain,
! [X0] :
( ~ product(e_4,e_3,X0)
| ~ product(e_3,X0,e_4) ),
inference(forward_subsumption_resolution,[],[f223,f23]) ).
fof(f236,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,e_1,X0)
| product(e_2,e_2,X0)
| product(e_2,e_3,X0)
| product(e_2,e_4,X0) ),
inference(resolution,[],[f4,f2]) ).
fof(f237,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_2,X0)
| product(e_2,e_2,X0)
| product(e_3,e_2,X0)
| product(e_4,e_2,X0) ),
inference(resolution,[],[f4,f1]) ).
fof(f240,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,e_1,X0)
| product(e_3,e_2,X0)
| product(e_3,e_3,X0)
| product(e_3,e_4,X0) ),
inference(resolution,[],[f5,f2]) ).
fof(f241,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_3,X0)
| product(e_2,e_3,X0)
| product(e_3,e_3,X0)
| product(e_4,e_3,X0) ),
inference(resolution,[],[f5,f1]) ).
fof(f244,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_4,X0)
| product(e_2,e_4,X0)
| product(e_3,e_4,X0)
| product(e_4,e_4,X0) ),
inference(resolution,[],[f6,f1]) ).
fof(f272,definition,
( spl0_32
<=> product(e_3,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f276,definition,
( spl0_33
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f339,definition,
( spl0_43
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f341,plain,
( product(e_1,e_3,e_4)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f343,definition,
( spl0_44
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f345,plain,
( product(e_1,e_2,e_4)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f352,definition,
( spl0_46
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f353,plain,
( ~ product(e_1,e_2,e_3)
| spl0_46 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f354,plain,
( product(e_1,e_2,e_3)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f357,definition,
( spl0_47
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f359,plain,
( product(e_1,e_4,e_2)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f361,definition,
( spl0_48
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f363,plain,
( product(e_1,e_3,e_2)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f375,plain,
( equalish(e_3,e_1)
| ~ spl0_9 ),
inference(resolution,[],[f80,f141]) ).
fof(f376,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f375,f13]) ).
fof(f377,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f387,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,[],[f147,f4]) ).
fof(f388,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,[],[f147,f5]) ).
fof(f391,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_4)
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f388,f81]) ).
fof(f394,definition,
( spl0_49
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f395,plain,
( ~ product(e_1,e_4,e_1)
| spl0_49 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f396,plain,
( product(e_1,e_4,e_1)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f399,definition,
( spl0_50
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f401,plain,
( product(e_1,e_3,e_1)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f402,plain,
( spl0_43
| spl0_48
| spl0_50
| spl0_9 ),
inference(avatar_split_clause,[],[f391,f79,f399,f361,f339]) ).
fof(f404,definition,
( spl0_51
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f405,plain,
( ~ product(e_1,e_2,e_1)
| spl0_51 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f406,plain,
( product(e_1,e_2,e_1)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f409,plain,
( ~ product(e_3,e_4,e_1)
| ~ spl0_43 ),
inference(resolution,[],[f341,f136]) ).
fof(f430,definition,
( spl0_54
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f432,plain,
( product(e_2,e_4,e_2)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f434,definition,
( spl0_55
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_55])],[avatar_definition]) ).
fof(f439,definition,
( spl0_56
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_56])],[avatar_definition]) ).
fof(f441,plain,
( product(e_2,e_3,e_4)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f443,definition,
( spl0_57
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_57])],[avatar_definition]) ).
fof(f445,plain,
( product(e_2,e_3,e_2)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f447,definition,
( spl0_58
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_58])],[avatar_definition]) ).
fof(f452,definition,
( spl0_59
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_59])],[avatar_definition]) ).
fof(f453,plain,
( product(e_2,e_2,e_4)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f479,plain,
( equalish(e_4,e_2)
| ~ spl0_23 ),
inference(resolution,[],[f190,f141]) ).
fof(f480,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f479,f17]) ).
fof(f481,plain,
~ spl0_23,
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f483,plain,
( ~ product(e_2,e_4,e_1)
| ~ spl0_44 ),
inference(resolution,[],[f345,f136]) ).
fof(f489,plain,
( ~ spl0_55
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f483,f343,f434]) ).
fof(f508,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_4) ),
inference(resolution,[],[f236,f6]) ).
fof(f509,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_4)
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f508,f191]) ).
fof(f511,plain,
( spl0_56
| spl0_59
| spl0_33
| spl0_23 ),
inference(avatar_split_clause,[],[f509,f189,f276,f452,f439]) ).
fof(f513,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference(resolution,[],[f237,f3]) ).
fof(f528,definition,
( spl0_63
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_63])],[avatar_definition]) ).
fof(f530,plain,
( product(e_4,e_2,e_1)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f532,definition,
( spl0_64
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition]) ).
fof(f537,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_46 ),
inference(resolution,[],[f354,f135]) ).
fof(f545,plain,
( ~ spl0_58
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f537,f352,f447]) ).
fof(f552,definition,
( spl0_65
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_65])],[avatar_definition]) ).
fof(f570,definition,
( spl0_69
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_69])],[avatar_definition]) ).
fof(f574,definition,
( spl0_70
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_70])],[avatar_definition]) ).
fof(f579,definition,
( spl0_71
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_71])],[avatar_definition]) ).
fof(f580,plain,
( product(e_3,e_3,e_4)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f591,plain,
( equalish(e_4,e_3)
| ~ spl0_27 ),
inference(resolution,[],[f214,f141]) ).
fof(f592,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f591,f18]) ).
fof(f593,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f592]) ).
fof(f600,plain,
( equalish(e_1,e_2)
| ~ spl0_51 ),
inference(resolution,[],[f406,f139]) ).
fof(f601,plain,
( $false
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[],[f600,f7]) ).
fof(f602,plain,
~ spl0_51,
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f604,plain,
( spl0_63
| spl0_64
| spl0_7
| spl0_51 ),
inference(avatar_split_clause,[],[f513,f404,f63,f532,f528]) ).
fof(f610,plain,
( equalish(e_2,e_1)
| ~ spl0_7 ),
inference(resolution,[],[f64,f137]) ).
fof(f614,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f610,f10]) ).
fof(f615,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f614]) ).
fof(f619,plain,
( ~ product(e_3,e_4,e_2)
| ~ spl0_56 ),
inference(resolution,[],[f441,f196]) ).
fof(f625,plain,
( ~ spl0_69
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f619,f439,f570]) ).
fof(f629,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(resolution,[],[f240,f6]) ).
fof(f630,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f629,f215]) ).
fof(f633,plain,
( spl0_71
| spl0_65
| spl0_32
| spl0_27 ),
inference(avatar_split_clause,[],[f630,f213,f272,f552,f579]) ).
fof(f642,plain,
( equalish(e_3,e_1)
| ~ spl0_13 ),
inference(resolution,[],[f102,f137]) ).
fof(f646,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f642,f13]) ).
fof(f647,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f646]) ).
fof(f652,plain,
( equalish(e_3,e_2)
| ~ spl0_21 ),
inference(resolution,[],[f179,f137]) ).
fof(f656,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f652,f14]) ).
fof(f657,plain,
~ spl0_21,
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f658,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(resolution,[],[f241,f3]) ).
fof(f659,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference(resolution,[],[f241,f4]) ).
fof(f662,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_4,e_3,e_2)
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f659,f180]) ).
fof(f665,definition,
( spl0_72
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_72])],[avatar_definition]) ).
fof(f667,plain,
( product(e_4,e_3,e_2)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f668,plain,
( spl0_72
| spl0_57
| spl0_48
| spl0_21 ),
inference(avatar_split_clause,[],[f662,f178,f361,f443,f665]) ).
fof(f671,definition,
( spl0_73
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_73])],[avatar_definition]) ).
fof(f673,plain,
( product(e_4,e_3,e_1)
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f676,plain,
( ~ product(e_3,e_2,e_1)
| ~ spl0_3
| ~ spl0_48 ),
inference(resolution,[],[f363,f40]) ).
fof(f682,plain,
( ~ spl0_64
| ~ spl0_3
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f676,f361,f39,f532]) ).
fof(f726,plain,
( equalish(e_1,e_3)
| ~ spl0_50 ),
inference(resolution,[],[f401,f139]) ).
fof(f727,plain,
( $false
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f726,f8]) ).
fof(f728,plain,
~ spl0_50,
inference(avatar_contradiction_clause,[],[f727]) ).
fof(f729,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_4,e_3,e_1)
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f658,f103]) ).
fof(f730,plain,
( spl0_73
| spl0_58
| spl0_50
| spl0_13 ),
inference(avatar_split_clause,[],[f729,f101,f399,f447,f671]) ).
fof(f731,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_1) ),
inference(resolution,[],[f244,f3]) ).
fof(f732,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_4,e_4,e_2) ),
inference(resolution,[],[f244,f4]) ).
fof(f741,plain,
( spl0_25
| spl0_69
| spl0_54
| spl0_47 ),
inference(avatar_split_clause,[],[f732,f357,f430,f570,f202]) ).
fof(f748,plain,
( equalish(e_4,e_1)
| ~ spl0_17 ),
inference(resolution,[],[f155,f137]) ).
fof(f752,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f748,f16]) ).
fof(f753,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f752]) ).
fof(f758,plain,
( equalish(e_4,e_2)
| ~ spl0_25 ),
inference(resolution,[],[f203,f137]) ).
fof(f762,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f758,f17]) ).
fof(f763,plain,
~ spl0_25,
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f765,plain,
( ~ product(e_4,e_2,e_1)
| ~ spl0_3
| ~ spl0_47 ),
inference(resolution,[],[f359,f40]) ).
fof(f770,plain,
( ~ spl0_63
| ~ spl0_3
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f765,f357,f39,f528]) ).
fof(f775,plain,
( equalish(e_1,e_4)
| ~ spl0_49 ),
inference(resolution,[],[f396,f139]) ).
fof(f776,plain,
( $false
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f775,f9]) ).
fof(f777,plain,
~ spl0_49,
inference(avatar_contradiction_clause,[],[f776]) ).
fof(f783,plain,
( equalish(e_2,e_4)
| ~ spl0_54 ),
inference(resolution,[],[f432,f139]) ).
fof(f784,plain,
( $false
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[],[f783,f12]) ).
fof(f785,plain,
~ spl0_54,
inference(avatar_contradiction_clause,[],[f784]) ).
fof(f792,plain,
( equalish(e_2,e_3)
| ~ spl0_57 ),
inference(resolution,[],[f445,f139]) ).
fof(f793,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[],[f792,f11]) ).
fof(f794,plain,
~ spl0_57,
inference(avatar_contradiction_clause,[],[f793]) ).
fof(f802,plain,
( ~ product(e_2,e_1,e_4)
| ~ spl0_63 ),
inference(resolution,[],[f530,f200]) ).
fof(f812,plain,
( ~ spl0_33
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f802,f528,f276]) ).
fof(f819,plain,
( equalish(e_2,e_4)
| ~ spl0_59 ),
inference(resolution,[],[f453,f137]) ).
fof(f823,plain,
( $false
| ~ spl0_59 ),
inference(forward_subsumption_resolution,[],[f819,f12]) ).
fof(f824,plain,
~ spl0_59,
inference(avatar_contradiction_clause,[],[f823]) ).
fof(f865,plain,
( ~ product(e_3,e_2,e_4)
| ~ spl0_72 ),
inference(resolution,[],[f667,f224]) ).
fof(f874,plain,
( ~ spl0_65
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f865,f665,f552]) ).
fof(f875,plain,
( ~ product(e_3,e_1,e_4)
| ~ spl0_73 ),
inference(resolution,[],[f673,f224]) ).
fof(f884,plain,
( ~ spl0_32
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f875,f671,f272]) ).
fof(f890,plain,
( equalish(e_3,e_4)
| ~ spl0_71 ),
inference(resolution,[],[f580,f137]) ).
fof(f894,plain,
( $false
| ~ spl0_71 ),
inference(forward_subsumption_resolution,[],[f890,f15]) ).
fof(f895,plain,
~ spl0_71,
inference(avatar_contradiction_clause,[],[f894]) ).
fof(f917,plain,
( ~ spl0_70
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f409,f339,f574]) ).
fof(f918,plain,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_1)
| spl0_49 ),
inference(forward_subsumption_resolution,[],[f731,f395]) ).
fof(f921,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| spl0_51 ),
inference(forward_subsumption_resolution,[],[f387,f405]) ).
fof(f922,plain,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| spl0_17
| spl0_49 ),
inference(forward_subsumption_resolution,[],[f918,f156]) ).
fof(f924,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_4)
| spl0_46
| spl0_51 ),
inference(forward_subsumption_resolution,[],[f921,f353]) ).
fof(f925,plain,
( spl0_70
| spl0_55
| spl0_17
| spl0_49 ),
inference(avatar_split_clause,[],[f922,f394,f154,f434,f574]) ).
fof(f926,plain,
( spl0_44
| spl0_1
| spl0_46
| spl0_51 ),
inference(avatar_split_clause,[],[f924,f404,f352,f31,f343]) ).
fof(f934,plain,
( equalish(e_2,e_1)
| ~ spl0_1 ),
inference(resolution,[],[f32,f141]) ).
fof(f935,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f934,f10]) ).
fof(f936,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f935]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s11,plain,
spl0_4,
inference(sat_conversion,[],[f134]) ).
cnf(s30,plain,
~ spl0_9,
inference(sat_conversion,[],[f377]) ).
cnf(s33,plain,
( spl0_9
| spl0_43
| spl0_48
| spl0_50 ),
inference(sat_conversion,[],[f402]) ).
cnf(s43,plain,
~ spl0_23,
inference(sat_conversion,[],[f481]) ).
cnf(s44,plain,
( ~ spl0_44
| ~ spl0_55 ),
inference(sat_conversion,[],[f489]) ).
cnf(s46,plain,
( spl0_23
| spl0_33
| spl0_56
| spl0_59 ),
inference(sat_conversion,[],[f511]) ).
cnf(s51,plain,
( ~ spl0_46
| ~ spl0_58 ),
inference(sat_conversion,[],[f545]) ).
cnf(s57,plain,
~ spl0_27,
inference(sat_conversion,[],[f593]) ).
cnf(s58,plain,
~ spl0_51,
inference(sat_conversion,[],[f602]) ).
cnf(s59,plain,
( spl0_7
| spl0_51
| spl0_63
| spl0_64 ),
inference(sat_conversion,[],[f604]) ).
cnf(s61,plain,
~ spl0_7,
inference(sat_conversion,[],[f615]) ).
cnf(s63,plain,
( ~ spl0_56
| ~ spl0_69 ),
inference(sat_conversion,[],[f625]) ).
cnf(s64,plain,
( spl0_27
| spl0_32
| spl0_65
| spl0_71 ),
inference(sat_conversion,[],[f633]) ).
cnf(s69,plain,
~ spl0_13,
inference(sat_conversion,[],[f647]) ).
cnf(s70,plain,
~ spl0_21,
inference(sat_conversion,[],[f657]) ).
cnf(s71,plain,
( spl0_21
| spl0_48
| spl0_57
| spl0_72 ),
inference(sat_conversion,[],[f668]) ).
cnf(s73,plain,
( ~ spl0_3
| ~ spl0_48
| ~ spl0_64 ),
inference(sat_conversion,[],[f682]) ).
cnf(s80,plain,
~ spl0_50,
inference(sat_conversion,[],[f728]) ).
cnf(s81,plain,
( spl0_13
| spl0_50
| spl0_58
| spl0_73 ),
inference(sat_conversion,[],[f730]) ).
cnf(s85,plain,
( spl0_25
| spl0_47
| spl0_54
| spl0_69 ),
inference(sat_conversion,[],[f741]) ).
cnf(s88,plain,
~ spl0_17,
inference(sat_conversion,[],[f753]) ).
cnf(s89,plain,
~ spl0_25,
inference(sat_conversion,[],[f763]) ).
cnf(s90,plain,
( ~ spl0_3
| ~ spl0_47
| ~ spl0_63 ),
inference(sat_conversion,[],[f770]) ).
cnf(s91,plain,
~ spl0_49,
inference(sat_conversion,[],[f777]) ).
cnf(s92,plain,
~ spl0_54,
inference(sat_conversion,[],[f785]) ).
cnf(s93,plain,
~ spl0_57,
inference(sat_conversion,[],[f794]) ).
cnf(s94,plain,
( ~ spl0_33
| ~ spl0_63 ),
inference(sat_conversion,[],[f812]) ).
cnf(s96,plain,
~ spl0_59,
inference(sat_conversion,[],[f824]) ).
cnf(s104,plain,
( ~ spl0_65
| ~ spl0_72 ),
inference(sat_conversion,[],[f874]) ).
cnf(s105,plain,
( ~ spl0_32
| ~ spl0_73 ),
inference(sat_conversion,[],[f884]) ).
cnf(s106,plain,
~ spl0_71,
inference(sat_conversion,[],[f895]) ).
cnf(s112,plain,
( ~ spl0_43
| ~ spl0_70 ),
inference(sat_conversion,[],[f917]) ).
cnf(s115,plain,
( spl0_17
| spl0_49
| spl0_55
| spl0_70 ),
inference(sat_conversion,[],[f925]) ).
cnf(s116,plain,
( spl0_1
| spl0_44
| spl0_46
| spl0_51 ),
inference(sat_conversion,[],[f926]) ).
cnf(s117,plain,
~ spl0_1,
inference(sat_conversion,[],[f936]) ).
cnf(s118,plain,
( spl0_44
| spl0_46
| spl0_51 ),
inference(rat,[],[s116,s117]) ).
cnf(s121,plain,
( spl0_47
| spl0_69 ),
inference(rat,[],[s85,s92,s89]) ).
cnf(s128,plain,
( spl0_21
| spl0_48
| spl0_72 ),
inference(rat,[],[s71,s93]) ).
cnf(s133,plain,
( spl0_27
| spl0_32
| spl0_65 ),
inference(rat,[],[s64,s106]) ).
cnf(s135,plain,
( spl0_51
| spl0_63
| spl0_64 ),
inference(rat,[],[s59,s61]) ).
cnf(s140,plain,
( spl0_23
| spl0_33
| spl0_56 ),
inference(rat,[],[s46,s96]) ).
cnf(s146,plain,
( spl0_9
| spl0_43
| spl0_48 ),
inference(rat,[],[s33,s80]) ).
cnf(s156,plain,
spl0_3,
inference(rat,[],[s2,s11]) ).
cnf(s157,plain,
~ spl0_63,
inference(rat,[],[s63,s121,s140,s90,s94,s43,s156]) ).
cnf(s158,plain,
spl0_64,
inference(rat,[],[s135,s58,s157]) ).
cnf(s160,plain,
~ spl0_48,
inference(rat,[],[s73,s156,s158]) ).
cnf(s161,plain,
spl0_72,
inference(rat,[],[s128,s70,s160]) ).
cnf(s162,plain,
spl0_43,
inference(rat,[],[s146,s30,s160]) ).
cnf(s163,plain,
~ spl0_65,
inference(rat,[],[s104,s161]) ).
cnf(s164,plain,
~ spl0_70,
inference(rat,[],[s112,s162]) ).
cnf(s165,plain,
spl0_32,
inference(rat,[],[s133,s57,s163]) ).
cnf(s166,plain,
spl0_55,
inference(rat,[],[s115,s88,s91,s164]) ).
cnf(s169,plain,
~ spl0_73,
inference(rat,[],[s105,s165]) ).
cnf(s170,plain,
~ spl0_44,
inference(rat,[],[s44,s166]) ).
cnf(s173,plain,
spl0_58,
inference(rat,[],[s81,s69,s80,s169]) ).
cnf(s175,plain,
spl0_46,
inference(rat,[],[s118,s58,s170]) ).
cnf(s178,plain,
$false,
inference(rat,[],[s51,s173,s175]) ).
fof(f937,plain,
$false,
inference(avatar_sat_refutation,[],[s178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.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 : Sun Sep 27 09:20:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.58/1.32 % (3731702)Input is clausal, will run a generic CNF schedule.
% 2.58/1.32 % (3731710)lrs+10_1_sil=8000:sp=occurrence:random_seed=3786160647:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.58/1.32 % (3731710)Refutation not found, incomplete strategy
% 2.58/1.32 % (3731710)------------------------------
% 2.58/1.32 % (3731710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.32 % (3731710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.32 % (3731710)CaDiCaL version: 2.1.3
% 2.58/1.32 % (3731710)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.32 % (3731710)Time elapsed: 0.0000 s
% 2.58/1.32 % (3731710)Peak memory usage: 86 MB
% 2.58/1.32 % (3731708)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=895107881:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.58/1.32 % (3731711)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1913710679:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.58/1.32 % (3731707)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=1415716643:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.58/1.32 % (3731709)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3129606775:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.58/1.32 % (3731713)dis-21_1_sil=8000:lcm=predicate:random_seed=3576200324: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)
% 2.58/1.32 % (3731712)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=29970773:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.58/1.32 % (3731712)First to succeed.
% 2.58/1.32 % (3731712)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3731702"
% 2.58/1.32 % (3731711)Instruction limit reached!
% 2.58/1.32 % (3731711)------------------------------
% 2.58/1.32 % (3731711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.32 % (3731711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.32 % (3731711)CaDiCaL version: 2.1.3
% 2.58/1.32 % (3731711)Termination reason: Instruction limit
% 2.58/1.32 % (3731711)Termination phase: Saturation
% 2.58/1.32 % (3731711)Time elapsed: 0.059 s
% 2.58/1.32 % (3731711)Peak memory usage: 88 MB
% 2.58/1.32 % (3731711)Instructions burned: 114 (million)
% 2.58/1.32 % (3731713)Instruction limit reached!
% 2.58/1.32 % (3731713)------------------------------
% 2.58/1.32 % (3731713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.32 % (3731713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.32 % (3731713)CaDiCaL version: 2.1.3
% 2.58/1.32 % (3731713)Termination reason: Instruction limit
% 2.58/1.32 % (3731713)Termination phase: Saturation
% 2.58/1.32 % (3731713)Time elapsed: 0.072 s
% 2.58/1.32 % (3731713)Peak memory usage: 89 MB
% 2.58/1.32 % (3731713)Instructions burned: 118 (million)
% 2.58/1.32 % (3731710)------------------------------
% 2.58/1.32 % (3731710)------------------------------
% 2.58/1.32 % (3731721)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=2738102752:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.58/1.32 % (3731722)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3076331490: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)
% 2.58/1.32 % (3731722)Refutation not found, incomplete strategy
% 2.58/1.32 % (3731722)------------------------------
% 2.58/1.32 % (3731722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.32 % (3731722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.32 % (3731722)CaDiCaL version: 2.1.3
% 2.58/1.32 % (3731722)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.32 % (3731722)Time elapsed: 0.002 s
% 2.58/1.32 % (3731722)Peak memory usage: 87 MB
% 2.58/1.32 % (3731722)Instructions burned: 2 (million)
% 2.58/1.32 % (3731723)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1679734724:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 2.58/1.32 % (3731712)Refutation found. Thanks to Tanya!
% 2.58/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.76/1.41 % (3731712)------------------------------
% 3.76/1.41 % (3731712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.41 % (3731712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.41 % (3731712)CaDiCaL version: 2.1.3
% 3.76/1.41 % (3731712)Termination reason: Refutation
% 3.76/1.41 % (3731712)Time elapsed: 0.019 s
% 3.76/1.41 % (3731712)Peak memory usage: 89 MB
% 3.76/1.41 % (3731712)Instructions burned: 26 (million)
% 3.76/1.41 % (3731712)------------------------------
% 3.76/1.41 % (3731712)------------------------------
% 3.76/1.41 % (3731702)Success in time 0.452 s
% 3.76/1.41 % Vampire exiting
%------------------------------------------------------------------------------