%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP126-2.004 : 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 : 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 10:12:45 AM UTC 2026
% Result : Unsatisfiable 2.59s 1.31s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 164 ( 46 unt; 18 def)
% Number of atoms : 360 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 367 ( 171 ~; 178 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 24 ( 23 usr; 19 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
fof(f9,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_3) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
fof(f11,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f12,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f13,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f14,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f15,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f16,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f17,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f19,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f20,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f23,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f27,axiom,
! [X0,X1] :
( product(X0,X1,e_4)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f29,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(f30,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(f31,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f32,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
fof(f38,plain,
! [X0] :
( ~ next(X0,e_3)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[],[f9,f10]) ).
fof(f39,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f15,f30]) ).
fof(f40,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f15,f29]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f16,f29]) ).
fof(f45,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f17,f30]) ).
fof(f46,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f17,f29]) ).
fof(f51,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f19,f30]) ).
fof(f54,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f20,f30]) ).
fof(f55,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f20,f29]) ).
fof(f63,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[],[f23,f30]) ).
fof(f64,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[],[f23,f29]) ).
fof(f81,plain,
~ product(e_2,e_1,e_4),
inference(resolution,[],[f38,f2]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_2)
| ~ product(X0,e_1,X1)
| ~ product(X2,X1,X0) ),
inference(resolution,[],[f40,f32]) ).
fof(f102,definition,
( spl0_1
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f103,plain,
( product(e_2,e_1,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_4)
| ~ product(X0,e_1,X1)
| ~ product(X2,X1,X0) ),
inference(resolution,[],[f46,f32]) ).
fof(f163,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(X0,X0,e_2) ),
inference(factoring,[],[f89]) ).
fof(f183,plain,
~ product(e_2,e_4,e_4),
inference(resolution,[],[f54,f31]) ).
fof(f230,plain,
~ product(e_3,e_4,e_4),
inference(resolution,[],[f63,f31]) ).
fof(f237,plain,
~ product(e_4,e_3,e_4),
inference(resolution,[],[f64,f31]) ).
fof(f288,definition,
( spl0_14
<=> product(e_4,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f290,plain,
( product(e_4,e_1,e_3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f292,definition,
( spl0_15
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f294,plain,
( product(e_4,e_1,e_2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f296,definition,
( spl0_16
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f298,plain,
( product(e_4,e_1,e_1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f304,plain,
! [X0] :
( ~ product(e_4,e_1,X0)
| ~ product(X0,X0,e_4) ),
inference(factoring,[],[f144]) ).
fof(f395,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_14 ),
inference(resolution,[],[f290,f54]) ).
fof(f420,definition,
( spl0_25
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f422,plain,
( ~ product(e_2,e_4,e_4)
| spl0_25 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f445,definition,
( spl0_26
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f446,plain,
( product(e_4,e_3,e_3)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f447,plain,
( ~ product(e_4,e_3,e_3)
| spl0_26 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f449,definition,
( spl0_27
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f451,plain,
( ~ product(e_3,e_4,e_4)
| spl0_27 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f459,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ group_element(e_2) ),
inference(resolution,[],[f81,f27]) ).
fof(f460,plain,
! [X0] :
( ~ product(X0,e_4,e_2)
| ~ product(e_4,X0,e_1) ),
inference(resolution,[],[f81,f32]) ).
fof(f461,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f459,f11]) ).
fof(f465,definition,
( spl0_28
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f467,plain,
( product(e_2,e_1,e_3)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f469,definition,
( spl0_29
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f471,plain,
( product(e_2,e_1,e_1)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f475,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution,[],[f461,f12]) ).
fof(f476,plain,
( spl0_28
| spl0_1
| spl0_29 ),
inference(avatar_split_clause,[],[f475,f469,f102,f465]) ).
fof(f477,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f103,f163]) ).
fof(f490,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f477,f31]) ).
fof(f491,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f515,definition,
( spl0_30
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f517,plain,
( ~ product(e_4,e_3,e_4)
| spl0_30 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f556,definition,
( spl0_32
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f558,plain,
( product(e_4,e_3,e_2)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f560,definition,
( spl0_33
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f562,plain,
( product(e_4,e_3,e_1)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f566,plain,
~ spl0_25,
inference(avatar_split_clause,[],[f183,f420]) ).
fof(f567,plain,
( ~ group_element(e_4)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| ~ group_element(e_2)
| spl0_25 ),
inference(resolution,[],[f422,f27]) ).
fof(f569,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| ~ group_element(e_2)
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f567,f14]) ).
fof(f570,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f569,f12]) ).
fof(f572,definition,
( spl0_34
<=> product(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f574,plain,
( product(e_2,e_4,e_3)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f576,definition,
( spl0_35
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f578,plain,
( product(e_2,e_4,e_2)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f580,definition,
( spl0_36
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f582,plain,
( product(e_2,e_4,e_1)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f583,plain,
( spl0_34
| spl0_35
| spl0_36
| spl0_25 ),
inference(avatar_split_clause,[],[f570,f420,f580,f576,f572]) ).
fof(f607,plain,
~ spl0_27,
inference(avatar_split_clause,[],[f230,f449]) ).
fof(f608,plain,
( ~ group_element(e_4)
| product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| ~ group_element(e_3)
| spl0_27 ),
inference(resolution,[],[f451,f27]) ).
fof(f610,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| ~ group_element(e_3)
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f608,f14]) ).
fof(f611,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f610,f13]) ).
fof(f613,definition,
( spl0_39
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f615,plain,
( product(e_3,e_4,e_3)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f617,definition,
( spl0_40
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f619,plain,
( product(e_3,e_4,e_2)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f621,definition,
( spl0_41
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f623,plain,
( product(e_3,e_4,e_1)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f624,plain,
( spl0_39
| spl0_40
| spl0_41
| spl0_27 ),
inference(avatar_split_clause,[],[f611,f449,f621,f617,f613]) ).
fof(f713,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_16 ),
inference(resolution,[],[f298,f45]) ).
fof(f717,plain,
( $false
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f713,f31]) ).
fof(f718,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f754,plain,
( ~ spl0_28
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f395,f288,f465]) ).
fof(f783,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_29 ),
inference(resolution,[],[f471,f39]) ).
fof(f787,plain,
( $false
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f783,f31]) ).
fof(f788,plain,
~ spl0_29,
inference(avatar_contradiction_clause,[],[f787]) ).
fof(f842,plain,
( ~ product(e_4,e_4,e_4)
| ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4) ),
inference(resolution,[],[f304,f27]) ).
fof(f843,plain,
( ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4) ),
inference(forward_subsumption_resolution,[],[f842,f31]) ).
fof(f844,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4) ),
inference(forward_subsumption_resolution,[],[f843,f11]) ).
fof(f845,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(forward_subsumption_resolution,[],[f844,f14]) ).
fof(f846,plain,
( spl0_14
| spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f845,f296,f292,f288]) ).
fof(f975,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_34 ),
inference(resolution,[],[f574,f46]) ).
fof(f985,plain,
( $false
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f975,f467]) ).
fof(f986,plain,
( ~ spl0_28
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[],[f985]) ).
fof(f999,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_35 ),
inference(resolution,[],[f578,f55]) ).
fof(f1007,plain,
( $false
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f999,f31]) ).
fof(f1008,plain,
~ spl0_35,
inference(avatar_contradiction_clause,[],[f1007]) ).
fof(f1035,plain,
( ~ product(e_4,e_3,e_1)
| ~ spl0_40 ),
inference(resolution,[],[f619,f460]) ).
fof(f1046,plain,
( $false
| ~ spl0_33
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1035,f562]) ).
fof(f1047,plain,
( ~ spl0_33
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1046]) ).
fof(f1054,plain,
( ~ product(e_3,e_3,e_3)
| ~ spl0_26 ),
inference(resolution,[],[f446,f63]) ).
fof(f1071,plain,
( $false
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1054,f31]) ).
fof(f1072,plain,
~ spl0_26,
inference(avatar_contradiction_clause,[],[f1071]) ).
fof(f1074,plain,
~ spl0_30,
inference(avatar_split_clause,[],[f237,f515]) ).
fof(f1076,plain,
( ~ group_element(e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| ~ group_element(e_4)
| spl0_30 ),
inference(resolution,[],[f517,f27]) ).
fof(f1078,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| ~ group_element(e_4)
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f1076,f13]) ).
fof(f1079,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| ~ group_element(e_4)
| spl0_26
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f1078,f447]) ).
fof(f1080,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| spl0_26
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f1079,f14]) ).
fof(f1081,plain,
( spl0_32
| spl0_33
| spl0_26
| spl0_30 ),
inference(avatar_split_clause,[],[f1080,f515,f445,f560,f556]) ).
fof(f1090,plain,
( ~ product(e_4,e_1,e_2)
| ~ spl0_32 ),
inference(resolution,[],[f558,f43]) ).
fof(f1097,plain,
( $false
| ~ spl0_15
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f1090,f294]) ).
fof(f1098,plain,
( ~ spl0_15
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f1097]) ).
fof(f1130,plain,
( ~ product(e_3,e_3,e_3)
| ~ spl0_39 ),
inference(resolution,[],[f615,f64]) ).
fof(f1142,plain,
( $false
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f1130,f31]) ).
fof(f1143,plain,
~ spl0_39,
inference(avatar_contradiction_clause,[],[f1142]) ).
fof(f1175,plain,
( ~ product(e_2,e_4,e_1)
| ~ spl0_41 ),
inference(resolution,[],[f623,f51]) ).
fof(f1186,plain,
( $false
| ~ spl0_36
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1175,f582]) ).
fof(f1187,plain,
( ~ spl0_36
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1186]) ).
cnf(s25,plain,
( spl0_1
| spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f476]) ).
cnf(s28,plain,
~ spl0_1,
inference(sat_conversion,[],[f491]) ).
cnf(s42,plain,
~ spl0_25,
inference(sat_conversion,[],[f566]) ).
cnf(s43,plain,
( spl0_25
| spl0_34
| spl0_35
| spl0_36 ),
inference(sat_conversion,[],[f583]) ).
cnf(s46,plain,
~ spl0_27,
inference(sat_conversion,[],[f607]) ).
cnf(s47,plain,
( spl0_27
| spl0_39
| spl0_40
| spl0_41 ),
inference(sat_conversion,[],[f624]) ).
cnf(s53,plain,
~ spl0_16,
inference(sat_conversion,[],[f718]) ).
cnf(s65,plain,
( ~ spl0_14
| ~ spl0_28 ),
inference(sat_conversion,[],[f754]) ).
cnf(s72,plain,
~ spl0_29,
inference(sat_conversion,[],[f788]) ).
cnf(s81,plain,
( spl0_14
| spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f846]) ).
cnf(s95,plain,
( ~ spl0_28
| ~ spl0_34 ),
inference(sat_conversion,[],[f986]) ).
cnf(s98,plain,
~ spl0_35,
inference(sat_conversion,[],[f1008]) ).
cnf(s102,plain,
( ~ spl0_33
| ~ spl0_40 ),
inference(sat_conversion,[],[f1047]) ).
cnf(s109,plain,
~ spl0_26,
inference(sat_conversion,[],[f1072]) ).
cnf(s111,plain,
~ spl0_30,
inference(sat_conversion,[],[f1074]) ).
cnf(s112,plain,
( spl0_26
| spl0_30
| spl0_32
| spl0_33 ),
inference(sat_conversion,[],[f1081]) ).
cnf(s114,plain,
( ~ spl0_15
| ~ spl0_32 ),
inference(sat_conversion,[],[f1098]) ).
cnf(s118,plain,
~ spl0_39,
inference(sat_conversion,[],[f1143]) ).
cnf(s121,plain,
( ~ spl0_36
| ~ spl0_41 ),
inference(sat_conversion,[],[f1187]) ).
cnf(s125,plain,
( spl0_27
| spl0_40
| spl0_41 ),
inference(rat,[],[s47,s118]) ).
cnf(s127,plain,
( spl0_25
| spl0_34
| spl0_36 ),
inference(rat,[],[s43,s98]) ).
cnf(s131,plain,
spl0_28,
inference(rat,[],[s25,s72,s28]) ).
cnf(s132,plain,
~ spl0_34,
inference(rat,[],[s95,s131]) ).
cnf(s134,plain,
~ spl0_14,
inference(rat,[],[s65,s131]) ).
cnf(s135,plain,
spl0_36,
inference(rat,[],[s127,s42,s132]) ).
cnf(s136,plain,
spl0_15,
inference(rat,[],[s81,s53,s134]) ).
cnf(s137,plain,
~ spl0_41,
inference(rat,[],[s121,s135]) ).
cnf(s138,plain,
~ spl0_32,
inference(rat,[],[s114,s136]) ).
cnf(s140,plain,
spl0_40,
inference(rat,[],[s125,s46,s137]) ).
cnf(s141,plain,
spl0_33,
inference(rat,[],[s112,s109,s111,s138]) ).
cnf(s144,plain,
$false,
inference(rat,[],[s102,s140,s141]) ).
fof(f1190,plain,
$false,
inference(avatar_sat_refutation,[],[s144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP126-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:27:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.59/1.31 % (243963)Input is clausal, will run a generic CNF schedule.
% 2.59/1.31 % (243972)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3615289638:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.59/1.31 % (243973)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2345401607:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.59/1.31 % (243974)dis-21_1_sil=8000:lcm=predicate:random_seed=1119155024: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)
% 2.59/1.31 % (243968)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=1674891839:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.59/1.31 % (243969)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3619169931:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.59/1.31 % (243970)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2190808640:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.59/1.31 % (243971)lrs+10_1_sil=8000:sp=occurrence:random_seed=601343411:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.59/1.31 % (243972)Instruction limit reached!
% 2.59/1.31 % (243972)------------------------------
% 2.59/1.31 % (243972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.31 % (243972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.31 % (243972)CaDiCaL version: 2.1.3
% 2.59/1.31 % (243972)Termination reason: Instruction limit
% 2.59/1.31 % (243972)Termination phase: Saturation
% 2.59/1.31 % (243972)Time elapsed: 0.030 s
% 2.59/1.31 % (243972)Peak memory usage: 88 MB
% 2.59/1.31 % (243972)Instructions burned: 115 (million)
% 2.59/1.31 % (243973)First to succeed.
% 2.59/1.31 % (243973)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-243963"
% 2.59/1.31 % (243971)Instruction limit reached!
% 2.59/1.31 % (243971)------------------------------
% 2.59/1.31 % (243971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.31 % (243971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.31 % (243971)CaDiCaL version: 2.1.3
% 2.59/1.31 % (243971)Termination reason: Instruction limit
% 2.59/1.31 % (243971)Termination phase: Saturation
% 2.59/1.31 % (243971)Time elapsed: 0.061 s
% 2.59/1.31 % (243971)Peak memory usage: 88 MB
% 2.59/1.31 % (243971)Instructions burned: 107 (million)
% 2.59/1.31 % (243974)Instruction limit reached!
% 2.59/1.31 % (243974)------------------------------
% 2.59/1.31 % (243974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.31 % (243974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.31 % (243974)CaDiCaL version: 2.1.3
% 2.59/1.31 % (243974)Termination reason: Instruction limit
% 2.59/1.31 % (243974)Termination phase: Saturation
% 2.59/1.31 % (243974)Time elapsed: 0.079 s
% 2.59/1.31 % (243974)Peak memory usage: 88 MB
% 2.59/1.31 % (243974)Instructions burned: 117 (million)
% 2.59/1.31 % (243982)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=962537888:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.59/1.31 % (243982)Instruction limit reached!
% 2.59/1.31 % (243982)------------------------------
% 2.59/1.31 % (243982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.31 % (243982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.31 % (243982)CaDiCaL version: 2.1.3
% 2.59/1.31 % (243982)Termination reason: Instruction limit
% 2.59/1.31 % (243982)Termination phase: Saturation
% 2.59/1.31 % (243982)Time elapsed: 0.041 s
% 2.59/1.31 % (243982)Peak memory usage: 88 MB
% 2.59/1.31 % (243982)Instructions burned: 147 (million)
% 2.59/1.31 % (243983)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4002654469: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)
% 2.59/1.31 % (243983)Refutation not found, incomplete strategy
% 2.59/1.31 % (243983)------------------------------
% 2.59/1.31 % (243983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.31 % (243983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.31 % (243983)CaDiCaL version: 2.1.3
% 2.59/1.31 % (243983)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.31 % (243983)Time elapsed: 0.002 s
% 2.59/1.31 % (243983)Peak memory usage: 87 MB
% 2.59/1.31 % (243983)Instructions burned: 1 (million)
% 2.59/1.31 % (243984)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2108160796:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 2.59/1.31 % (243973)Refutation found. Thanks to Tanya!
% 2.59/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.59/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (243973)------------------------------
% 0.16/1.50 % (243973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (243973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (243973)CaDiCaL version: 2.1.3
% 0.16/1.50 % (243973)Termination reason: Refutation
% 0.16/1.50 % (243973)Time elapsed: 0.027 s
% 0.16/1.50 % (243973)Peak memory usage: 89 MB
% 0.16/1.50 % (243973)Instructions burned: 38 (million)
% 0.16/1.50 % (243973)------------------------------
% 0.16/1.50 % (243973)------------------------------
% 0.16/1.50 % (243963)Success in time 0.446 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------