%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:30:51 AM UTC 2026
% Result : Unsatisfiable 3.26s 1.05s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 12 unt; 2 def)
% Number of atoms : 63 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 27 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_1,c_times(X0,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X1,X0) != c_0
| X1 = c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f5,plain,
! [X0,X1] :
( c_0 != c_HOL_Oabs(X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X1 ),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = c_0
| c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f8,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X1
| c_1 = c_times(c_HOL_Oinverse(X1,X0),X1,X0) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f11,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
fof(f12,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[],[f9,f3]) ).
fof(f13,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f10,f3]) ).
fof(f14,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[],[f11,f3]) ).
fof(f15,plain,
! [X0] :
( c_1 = c_times(c_HOL_Oinverse(X0,t_a),X0,t_a)
| c_0 = X0 ),
inference(resolution,[],[f8,f12]) ).
fof(f16,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| c_0 = c_HOL_Oabs(v_c,t_a) ),
inference(superposition,[],[f2,f15]) ).
fof(f18,definition,
( spl0_1
<=> c_0 = c_HOL_Oabs(v_c,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f20,plain,
( c_0 = c_HOL_Oabs(v_c,t_a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f22,definition,
( spl0_2
<=> c_lessequals(c_1,c_1,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f24,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f16,f22,f18]) ).
fof(f26,plain,
( ~ class_Orderings_Oorder(t_a)
| spl0_2 ),
inference(resolution,[],[f24,f6]) ).
fof(f27,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f26,f14]) ).
fof(f28,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f27]) ).
fof(f30,plain,
( c_0 != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| v_c = c_0
| ~ spl0_1 ),
inference(superposition,[],[f5,f20]) ).
fof(f31,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| v_c = c_0
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f30]) ).
fof(f32,plain,
( v_c = c_0
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f31,f13]) ).
fof(f33,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f32,f1]) ).
fof(f34,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f33]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f35,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 20:28:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 3.26/1.05 % (3703587)Input is clausal, will run a generic CNF schedule.
% 3.26/1.05 % (3703624)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=1775236507:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 3.26/1.05 % (3703629)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=550920933:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 3.26/1.05 % (3703627)lrs+10_1_sil=8000:sp=occurrence:random_seed=2759615850:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 3.26/1.05 % (3703628)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1440926023:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 3.26/1.05 % (3703626)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2357912173:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 3.26/1.05 % (3703625)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=415625769:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 3.26/1.05 % (3703628)Refutation not found, incomplete strategy
% 3.26/1.05 % (3703628)------------------------------
% 3.26/1.05 % (3703628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.05 % (3703628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.05 % (3703628)CaDiCaL version: 2.1.3
% 3.26/1.05 % (3703628)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.05 % (3703628)Time elapsed: 0.001 s
% 3.26/1.05 % (3703628)Peak memory usage: 87 MB
% 3.26/1.05 % (3703627)First to succeed.
% 3.26/1.05 % (3703629)Also succeeded, but the first one will report.
% 3.26/1.05 % (3703627)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3703587"
% 3.26/1.05 % (3703630)dis-21_1_sil=8000:lcm=predicate:random_seed=3709886942:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 3.26/1.05 % (3703630)Refutation not found, incomplete strategy
% 3.26/1.05 % (3703630)------------------------------
% 3.26/1.05 % (3703630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.05 % (3703630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.05 % (3703630)CaDiCaL version: 2.1.3
% 3.26/1.05 % (3703630)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.05 % (3703630)Time elapsed: 0.001 s
% 3.26/1.05 % (3703630)Peak memory usage: 88 MB
% 3.26/1.05 % (3703628)------------------------------
% 3.26/1.05 % (3703628)------------------------------
% 3.26/1.05 % (3703627)Refutation found. Thanks to Tanya!
% 3.26/1.05 % SZS status Unsatisfiable for theBenchmark
% 3.26/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.26/1.05 % (3703627)------------------------------
% 3.26/1.05 % (3703627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.05 % (3703627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.05 % (3703627)CaDiCaL version: 2.1.3
% 3.26/1.05 % (3703627)Termination reason: Refutation
% 3.26/1.05 % (3703627)Time elapsed: 0.002 s
% 3.26/1.05 % (3703627)Peak memory usage: 89 MB
% 3.26/1.05 % (3703627)Instructions burned: 1 (million)
% 3.26/1.05 % (3703627)------------------------------
% 3.26/1.05 % (3703627)------------------------------
% 3.26/1.05 % (3703587)Success in time 0.399 s
% 3.26/1.05 % Vampire exiting
%------------------------------------------------------------------------------