%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA029-2 : 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 : 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 09:30:56 AM UTC 2026
% Result : Unsatisfiable 2.48s 1.12s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 42 ( 12 unt; 2 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 96 ( 46 ~; 48 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f7,axiom,
! [X2,X0,X1] :
( c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f11,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f12,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f13,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f14,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f15,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[],[f12,f3]) ).
fof(f16,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f13,f3]) ).
fof(f17,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[],[f14,f3]) ).
fof(f18,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[],[f17,f11]) ).
fof(f19,plain,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Oorder(X0) ),
inference(resolution,[],[f10,f7]) ).
fof(f51,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(resolution,[],[f8,f2]) ).
fof(f55,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(forward_subsumption_resolution,[],[f51,f15]) ).
fof(f57,definition,
( spl0_1
<=> c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f59,plain,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl0_2
<=> c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f55,f61,f57]) ).
fof(f87,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_2 ),
inference(resolution,[],[f63,f4]) ).
fof(f88,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f87,f16]) ).
fof(f89,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f88]) ).
fof(f90,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,X0,t_b) )
| ~ spl0_2 ),
inference(resolution,[],[f62,f9]) ).
fof(f91,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X0,t_b)
| c_lessequals(c_0,X0,t_b) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f90,f18]) ).
fof(f116,plain,
( ! [X0] :
( c_lessequals(c_0,X0,t_b)
| c_lessequals(X0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ class_Orderings_Oorder(t_b) )
| ~ spl0_2 ),
inference(resolution,[],[f91,f19]) ).
fof(f118,plain,
( ! [X0] :
( c_lessequals(c_0,X0,t_b)
| c_lessequals(X0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f116,f15]) ).
fof(f120,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| c_lessequals(c_0,X0,t_b) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f118,f18]) ).
fof(f132,plain,
( c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| spl0_1
| ~ spl0_2 ),
inference(resolution,[],[f120,f59]) ).
fof(f143,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f132,f1]) ).
fof(f144,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f143]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f89]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f144]) ).
cnf(s5,plain,
spl0_1,
inference(rat,[],[s4,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f146,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n014.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 20:32:01 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 2.48/1.12 % (2131984)Input is clausal, will run a generic CNF schedule.
% 2.48/1.12 % (2132046)lrs+10_1_sil=8000:sp=occurrence:random_seed=3476804712:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.48/1.12 % (2132046)First to succeed.
% 2.48/1.12 % (2132046)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2131984"
% 2.48/1.12 % (2132049)dis-21_1_sil=8000:lcm=predicate:random_seed=3775092002: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)
% 2.48/1.12 % (2132044)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=671922064:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.48/1.12 % (2132047)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4164243787:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.48/1.12 % (2132045)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=754015026:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.48/1.12 % (2132043)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=1431908180:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.48/1.12 % (2132048)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3996675440:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.48/1.12 % (2132049)Also succeeded, but the first one will report.
% 2.48/1.12 % (2132047)Also succeeded, but the first one will report.
% 2.48/1.12 % (2132048)Also succeeded, but the first one will report.
% 2.48/1.12 % (2132046)Refutation found. Thanks to Tanya!
% 2.48/1.12 % SZS status Unsatisfiable for theBenchmark
% 2.48/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.48/1.12 % (2132046)------------------------------
% 2.48/1.12 % (2132046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.12 % (2132046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.12 % (2132046)CaDiCaL version: 2.1.3
% 2.48/1.12 % (2132046)Termination reason: Refutation
% 2.48/1.12 % (2132046)Time elapsed: 0.003 s
% 2.48/1.12 % (2132046)Peak memory usage: 89 MB
% 2.48/1.12 % (2132046)Instructions burned: 5 (million)
% 2.48/1.12 % (2132046)------------------------------
% 2.48/1.12 % (2132046)------------------------------
% 2.48/1.12 % (2131984)Success in time 0.267 s
% 2.48/1.12 % Vampire exiting
%------------------------------------------------------------------------------