%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA009-2 : 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 : n011.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 5.65s 1.83s
% Output : Refutation 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 22 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_plus(X1,X3,X0),c_plus(X2,X3,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X1,c_uminus(X1,X0),X0) = c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f3,negated_conjecture,
! [X0] : c_lessequals(v_lb(X0),v_f(X0),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f4,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f6,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f7,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f8,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(resolution,[],[f5,f7]) ).
fof(f9,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[],[f6,f7]) ).
fof(f10,plain,
! [X0] : c_0 = c_plus(X0,c_uminus(X0,t_b),t_b),
inference(resolution,[],[f2,f9]) ).
fof(f11,plain,
! [X0,X1] :
( c_lessequals(c_0,c_plus(X1,c_uminus(X0,t_b),t_b),t_b)
| ~ c_lessequals(X0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(superposition,[],[f1,f10]) ).
fof(f14,plain,
! [X0,X1] :
( c_lessequals(c_0,c_plus(X1,c_uminus(X0,t_b),t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(forward_subsumption_resolution,[],[f11,f8]) ).
fof(f24,plain,
~ c_lessequals(v_lb(v_x),v_f(v_x),t_b),
inference(resolution,[],[f14,f4]) ).
fof(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f24,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n011.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Mon Sep 28 20:27:01 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running first-order theorem proving
% 0.09/0.27 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
% 5.65/1.83 % (3730113)Input is clausal, will run a generic CNF schedule.
% 5.65/1.83 % (3730120)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=2198841454:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.65/1.83 % (3730126)dis-21_1_sil=8000:lcm=predicate:random_seed=3086293859: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)
% 5.65/1.83 % (3730126)Refutation not found, incomplete strategy
% 5.65/1.83 % (3730126)------------------------------
% 5.65/1.83 % (3730126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.65/1.83 % (3730126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.83 % (3730126)CaDiCaL version: 2.1.3
% 5.65/1.83 % (3730126)Termination reason: Refutation not found, incomplete strategy
% 5.65/1.83 % (3730126)Time elapsed: 0.002 s
% 5.65/1.83 % (3730126)Peak memory usage: 88 MB
% 5.65/1.83 % (3730123)lrs+10_1_sil=8000:sp=occurrence:random_seed=4162202637:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.65/1.83 % (3730121)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2699830917:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.65/1.83 % (3730124)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2204801861:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.65/1.83 % (3730125)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3651594401:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.65/1.83 % (3730122)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=370126666:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.65/1.83 % (3730124)Refutation not found, incomplete strategy
% 5.65/1.83 % (3730124)------------------------------
% 5.65/1.83 % (3730124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.65/1.83 % (3730124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.83 % (3730124)CaDiCaL version: 2.1.3
% 5.65/1.83 % (3730124)Termination reason: Refutation not found, incomplete strategy
% 5.65/1.83 % (3730124)Time elapsed: 0.001 s
% 5.65/1.83 % (3730124)Peak memory usage: 87 MB
% 5.65/1.83 % (3730123)First to succeed.
% 5.65/1.83 % (3730123)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3730113"
% 5.65/1.83 % (3730125)Also succeeded, but the first one will report.
% 5.65/1.83 % (3730126)------------------------------
% 5.65/1.83 % (3730126)------------------------------
% 5.65/1.83 % (3730124)------------------------------
% 5.65/1.83 % (3730124)------------------------------
% 5.65/1.83 % (3730123)Refutation found. Thanks to Tanya!
% 5.65/1.83 % SZS status Unsatisfiable for theBenchmark
% 5.65/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 5.65/1.83 % (3730123)------------------------------
% 5.65/1.83 % (3730123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.65/1.83 % (3730123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.83 % (3730123)CaDiCaL version: 2.1.3
% 5.65/1.83 % (3730123)Termination reason: Refutation
% 5.65/1.83 % (3730123)Time elapsed: 0.003 s
% 5.65/1.83 % (3730123)Peak memory usage: 88 MB
% 5.65/1.83 % (3730123)Instructions burned: 1 (million)
% 5.65/1.83 % (3730123)------------------------------
% 5.65/1.83 % (3730123)------------------------------
% 5.65/1.83 % (3730113)Success in time 0.655 s
% 5.65/1.83 % Vampire exiting
%------------------------------------------------------------------------------