%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 10:13:01 AM UTC 2026
% Result : Unsatisfiable 2.30s 1.17s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 90 ( 13 unt; 6 def)
% Number of atoms : 448 ( 0 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 618 ( 260 ~; 352 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 186 ( 0 sgn 186 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
! [X0,X1] :
( product(X0,X1,e_2)
| ~ group_element(X1)
| product(X0,X1,e_1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f9,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X5,X4,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
fof(f10,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X5,X4,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X0,X1,X2)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
fof(f11,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| equalish(X2,X1) ),
inference(resolution,[],[f5,f8]) ).
fof(f12,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| equalish(X2,X0) ),
inference(resolution,[],[f5,f7]) ).
fof(f13,plain,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| equalish(X2,e_2) ),
inference(resolution,[],[f5,f6]) ).
fof(f14,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(e_2,X0,X2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ product(X1,X3,X4)
| ~ product(X4,X3,X2)
| equalish(X3,X0) ),
inference(resolution,[],[f5,f10]) ).
fof(f15,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(e_2,X0,X2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ product(X1,X3,X4)
| ~ product(X4,X3,X2)
| equalish(X4,e_2) ),
inference(resolution,[],[f5,f9]) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( product(X0,X1,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| ~ product(X0,X2,X3)
| ~ product(X3,X2,e_2)
| equalish(X2,X1)
| ~ group_element(X1)
| product(e_2,X1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[],[f14,f5]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( product(X0,X1,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| ~ product(X0,X2,X3)
| ~ product(X3,X2,e_2)
| equalish(X2,X1)
| product(e_2,X1,e_1)
| ~ group_element(e_2) ),
inference(duplicate_literal_removal,[],[f16]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X2,e_2)
| ~ group_element(X0)
| ~ group_element(X1)
| ~ product(X0,X2,X3)
| product(X0,X1,e_1)
| equalish(X2,X1)
| product(e_2,X1,e_1) ),
inference(forward_subsumption_resolution,[],[f17,f2]) ).
fof(f19,plain,
! [X2,X3,X0,X1] :
( product(X0,X1,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| ~ product(X0,X2,X3)
| ~ product(X3,X2,e_2)
| equalish(X3,e_2)
| ~ group_element(X1)
| product(e_2,X1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[],[f15,f5]) ).
fof(f20,plain,
! [X2,X3,X0,X1] :
( product(X0,X1,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| ~ product(X0,X2,X3)
| ~ product(X3,X2,e_2)
| equalish(X3,e_2)
| product(e_2,X1,e_1)
| ~ group_element(e_2) ),
inference(duplicate_literal_removal,[],[f19]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X2,e_2)
| ~ group_element(X0)
| ~ group_element(X1)
| ~ product(X0,X2,X3)
| product(X0,X1,e_1)
| equalish(X3,e_2)
| product(e_2,X1,e_1) ),
inference(forward_subsumption_resolution,[],[f20,f2]) ).
fof(f22,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X2,X3)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_1)
| equalish(X2,X1)
| product(e_2,X1,e_1)
| ~ group_element(X2)
| product(X3,X2,e_1)
| ~ group_element(X3) ),
inference(resolution,[],[f18,f5]) ).
fof(f23,plain,
! [X2,X0,X1] :
( product(X0,X1,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| equalish(X2,X0)
| ~ group_element(X1)
| product(X2,X1,e_1)
| ~ group_element(X2) ),
inference(resolution,[],[f11,f5]) ).
fof(f24,plain,
! [X2,X0,X1] :
( product(X2,X1,e_1)
| product(X0,X1,e_1)
| equalish(X2,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2) ),
inference(duplicate_literal_removal,[],[f23]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X2,X3)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_1)
| equalish(X3,e_2)
| product(e_2,X1,e_1)
| ~ group_element(X2)
| product(X3,X2,e_1)
| ~ group_element(X3) ),
inference(resolution,[],[f21,f5]) ).
fof(f26,plain,
! [X2,X0,X1] :
( product(X0,X1,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| equalish(X2,X1)
| ~ group_element(X2)
| product(X0,X2,e_1)
| ~ group_element(X0) ),
inference(resolution,[],[f12,f5]) ).
fof(f27,plain,
! [X2,X0,X1] :
( product(X0,X2,e_1)
| product(X0,X1,e_1)
| equalish(X2,X1)
| ~ group_element(X1)
| ~ group_element(X2)
| ~ group_element(X0) ),
inference(duplicate_literal_removal,[],[f26]) ).
fof(f70,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,e_1)
| equalish(X0,X2)
| ~ group_element(X1)
| ~ group_element(X2)
| ~ group_element(X0)
| product(X2,X1,e_1)
| equalish(X3,X1) ),
inference(resolution,[],[f24,f7]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( product(X2,X1,e_1)
| equalish(X2,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| ~ group_element(X3)
| ~ group_element(X0)
| product(X0,X3,e_1)
| equalish(X1,X3)
| product(e_2,X3,e_1)
| ~ group_element(X1)
| product(e_1,X1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[],[f24,f22]) ).
fof(f97,plain,
! [X2,X3,X0,X1] :
( product(X2,X1,e_1)
| equalish(X2,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| ~ group_element(X3)
| product(X0,X3,e_1)
| equalish(X1,X3)
| product(e_2,X3,e_1)
| product(e_1,X1,e_1)
| ~ group_element(e_1) ),
inference(duplicate_literal_removal,[],[f86]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( product(X0,X2,e_1)
| equalish(X1,X2)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ product(X3,X1,e_1)
| equalish(X3,X0) ),
inference(resolution,[],[f27,f8]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( equalish(X2,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| ~ group_element(X3)
| product(X0,X3,e_1)
| equalish(X1,X3)
| product(e_2,X3,e_1)
| product(e_1,X1,e_1)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f97,f70]) ).
fof(f204,plain,
! [X2,X3,X0,X1] :
( product(e_2,X3,e_1)
| product(e_1,X1,e_1)
| product(X0,X3,e_1)
| equalish(X2,X0)
| equalish(X1,X3)
| ~ group_element(X3)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ group_element(X1) ),
inference(forward_subsumption_resolution,[],[f190,f1]) ).
fof(f268,definition,
( spl0_6
<=> ! [X3] :
( ~ group_element(X3)
| product(e_2,X3,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f269,plain,
( ! [X3] :
( product(e_2,X3,e_1)
| ~ group_element(X3) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f316,plain,
! [X2,X0,X1] :
( product(e_2,X0,e_1)
| product(e_1,X1,e_1)
| equalish(X2,e_2)
| equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X2)
| ~ group_element(e_2)
| ~ group_element(X1) ),
inference(factoring,[],[f204]) ).
fof(f331,plain,
! [X2,X0,X1] :
( product(e_2,X0,e_1)
| product(e_1,X1,e_1)
| equalish(X2,e_2)
| equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X2)
| ~ group_element(X1) ),
inference(forward_subsumption_resolution,[],[f316,f2]) ).
fof(f333,definition,
( spl0_8
<=> ! [X2] :
( equalish(X2,e_2)
| ~ group_element(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f334,plain,
( ! [X2] :
( equalish(X2,e_2)
| ~ group_element(X2) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f336,definition,
( spl0_9
<=> ! [X0,X1] :
( product(e_2,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_1,X1,e_1)
| equalish(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f337,plain,
( ! [X0,X1] :
( product(e_2,X0,e_1)
| product(e_1,X1,e_1)
| equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X1) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f338,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f331,f336,f333]) ).
fof(f356,plain,
( ~ group_element(e_1)
| ~ spl0_8 ),
inference(resolution,[],[f334,f3]) ).
fof(f357,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f356,f1]) ).
fof(f358,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f383,plain,
( ! [X0,X1] :
( product(e_1,X1,e_1)
| equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X1)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| equalish(e_1,e_2) )
| ~ spl0_9 ),
inference(resolution,[],[f337,f13]) ).
fof(f405,plain,
( ! [X0,X1] :
( product(e_1,X1,e_1)
| equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X1)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| equalish(e_1,e_2) )
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f383]) ).
fof(f408,plain,
( ! [X0,X1] :
( equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X1)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| equalish(e_1,e_2) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f405,f111]) ).
fof(f409,plain,
( ! [X0,X1] :
( equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X1)
| product(e_2,X0,e_1)
| equalish(e_1,e_2) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f408,f2]) ).
fof(f410,plain,
( ! [X0,X1] :
( product(e_2,X0,e_1)
| equalish(X1,X0)
| ~ group_element(X1)
| ~ group_element(X0) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f409,f3]) ).
fof(f434,plain,
( ! [X2,X0,X1] :
( ~ product(X2,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| equalish(X1,X0)
| equalish(X2,e_2) )
| ~ spl0_9 ),
inference(resolution,[],[f410,f8]) ).
fof(f439,plain,
( ! [X2,X0,X1] :
( equalish(X1,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| ~ group_element(e_2)
| product(e_2,X2,e_1)
| equalish(e_1,e_2)
| product(e_2,X2,e_1)
| ~ group_element(X0)
| product(e_1,X0,e_1)
| ~ group_element(e_1) )
| ~ spl0_9 ),
inference(resolution,[],[f410,f25]) ).
fof(f440,plain,
( ! [X2,X0,X1] :
( equalish(X1,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| ~ group_element(e_2)
| product(e_2,X2,e_1)
| equalish(e_1,e_2)
| product(e_1,X0,e_1)
| ~ group_element(e_1) )
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f439]) ).
fof(f445,plain,
( ! [X2,X0,X1] :
( equalish(X1,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| product(e_2,X2,e_1)
| equalish(e_1,e_2)
| product(e_1,X0,e_1)
| ~ group_element(e_1) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f440,f2]) ).
fof(f446,plain,
( ! [X2,X0,X1] :
( equalish(X1,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| product(e_2,X2,e_1)
| product(e_1,X0,e_1)
| ~ group_element(e_1) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f445,f3]) ).
fof(f447,plain,
( ! [X2,X0,X1] :
( equalish(X1,X0)
| ~ group_element(X1)
| ~ group_element(X0)
| ~ group_element(X2)
| product(e_2,X2,e_1)
| product(e_1,X0,e_1) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f446,f1]) ).
fof(f449,definition,
( spl0_10
<=> ! [X0,X1] :
( equalish(X1,X0)
| product(e_1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f450,plain,
( ! [X0,X1] :
( product(e_1,X0,e_1)
| equalish(X1,X0)
| ~ group_element(X0)
| ~ group_element(X1) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f451,plain,
( spl0_6
| spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f447,f336,f449,f268]) ).
fof(f534,definition,
( spl0_13
<=> ! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| equalish(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f535,plain,
( ! [X0,X1] :
( equalish(X1,X0)
| ~ group_element(X1)
| ~ group_element(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f793,plain,
( ! [X0,X1] :
( ~ product(e_2,X1,e_1)
| ~ group_element(X0)
| equalish(X1,X0) )
| ~ spl0_6 ),
inference(resolution,[],[f269,f7]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ group_element(X0)
| equalish(X1,X0)
| ~ group_element(X1) )
| ~ spl0_6 ),
inference(resolution,[],[f793,f269]) ).
fof(f857,plain,
( spl0_13
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f847,f268,f534]) ).
fof(f871,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| ~ spl0_13 ),
inference(resolution,[],[f535,f3]) ).
fof(f874,plain,
( ~ group_element(e_2)
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f871,f1]) ).
fof(f877,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f874,f2]) ).
fof(f878,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f877]) ).
fof(f1208,definition,
( spl0_30
<=> ! [X2,X0,X1] :
( ~ group_element(X0)
| ~ group_element(X2)
| equalish(X2,X1)
| equalish(X0,X1)
| ~ group_element(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f1209,plain,
( ! [X2,X0,X1] :
( equalish(X2,X1)
| equalish(X0,X1)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ group_element(X1) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f1299,plain,
( ! [X2,X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| equalish(X0,X1)
| equalish(e_1,e_2)
| equalish(X2,X1)
| ~ group_element(X1)
| ~ group_element(X2) )
| ~ spl0_9
| ~ spl0_10 ),
inference(resolution,[],[f434,f450]) ).
fof(f1304,plain,
( ! [X2,X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| equalish(X0,X1)
| equalish(e_1,e_2)
| equalish(X2,X1)
| ~ group_element(X2) )
| ~ spl0_9
| ~ spl0_10 ),
inference(duplicate_literal_removal,[],[f1299]) ).
fof(f1315,plain,
( ! [X2,X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| equalish(X0,X1)
| equalish(X2,X1)
| ~ group_element(X2) )
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f1304,f3]) ).
fof(f1316,plain,
( spl0_30
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f1315,f449,f336,f1208]) ).
fof(f1349,plain,
( ! [X0,X1] :
( equalish(X0,X1)
| ~ group_element(X0)
| ~ group_element(X0)
| ~ group_element(X1) )
| ~ spl0_30 ),
inference(factoring,[],[f1209]) ).
fof(f1350,plain,
( ! [X0,X1] :
( equalish(X0,X1)
| ~ group_element(X0)
| ~ group_element(X1) )
| ~ spl0_30 ),
inference(duplicate_literal_removal,[],[f1349]) ).
fof(f1351,plain,
( spl0_13
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1350,f1208,f534]) ).
cnf(s8,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f338]) ).
cnf(s9,plain,
~ spl0_8,
inference(sat_conversion,[],[f358]) ).
cnf(s10,plain,
( spl0_6
| ~ spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f451]) ).
cnf(s28,plain,
( ~ spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f857]) ).
cnf(s31,plain,
~ spl0_13,
inference(sat_conversion,[],[f878]) ).
cnf(s37,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_30 ),
inference(sat_conversion,[],[f1316]) ).
cnf(s38,plain,
( spl0_13
| ~ spl0_30 ),
inference(sat_conversion,[],[f1351]) ).
cnf(s43,plain,
~ spl0_30,
inference(rat,[],[s38,s31]) ).
cnf(s45,plain,
~ spl0_6,
inference(rat,[],[s28,s31]) ).
cnf(s47,plain,
( ~ spl0_9
| spl0_10 ),
inference(rat,[],[s10,s45]) ).
cnf(s48,plain,
spl0_9,
inference(rat,[],[s8,s9]) ).
cnf(s49,plain,
~ spl0_10,
inference(rat,[],[s37,s43,s48]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s47,s49,s48]) ).
fof(f1362,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n014.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 09:28:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.30/1.17 % (544847)Input is clausal, will run a generic CNF schedule.
% 2.30/1.17 % (544855)lrs+10_1_sil=8000:sp=occurrence:random_seed=2791029407:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.30/1.17 % (544853)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2736111274:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.30/1.17 % (544855)First to succeed.
% 2.30/1.17 % (544855)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-544847"
% 2.30/1.17 % (544852)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=3010532911:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.30/1.17 % (544854)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1599256666:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.30/1.17 % (544858)dis-21_1_sil=8000:lcm=predicate:random_seed=549982161: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)
% 2.30/1.17 % (544857)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=868609892:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.30/1.17 % (544856)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2888600669:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.30/1.17 % (544856)Refutation not found, incomplete strategy
% 2.30/1.17 % (544856)------------------------------
% 2.30/1.17 % (544856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.17 % (544856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.17 % (544856)CaDiCaL version: 2.1.3
% 2.30/1.17 % (544856)Termination reason: Refutation not found, incomplete strategy
% 2.30/1.17 % (544856)Time elapsed: 0.001 s
% 2.30/1.17 % (544856)Peak memory usage: 86 MB
% 2.30/1.17 % (544857)Also succeeded, but the first one will report.
% 2.30/1.17 % (544858)Also succeeded, but the first one will report.
% 2.30/1.17 % (544855)Refutation found. Thanks to Tanya!
% 2.30/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.30/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.37 % (544855)------------------------------
% 2.77/1.37 % (544855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.37 % (544855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.37 % (544855)CaDiCaL version: 2.1.3
% 2.77/1.37 % (544855)Termination reason: Refutation
% 2.77/1.37 % (544855)Time elapsed: 0.027 s
% 2.77/1.37 % (544855)Peak memory usage: 89 MB
% 2.77/1.37 % (544855)Instructions burned: 92 (million)
% 2.77/1.37 % (544855)------------------------------
% 2.77/1.37 % (544855)------------------------------
% 2.77/1.37 % (544847)Success in time 0.313 s
% 2.77/1.37 % Vampire exiting
%------------------------------------------------------------------------------