%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:30:55 AM UTC 2026
% Result : Unsatisfiable 3.38s 0.97s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 51 ( 14 unt; 4 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 50 ~; 52 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f6,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,axiom,
! [X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f9,axiom,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f11,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f12,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f13,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(resolution,[],[f9,f8]) ).
fof(f14,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[],[f10,f12]) ).
fof(f15,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f11,f12]) ).
fof(f16,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[],[f1,f15]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0) ),
inference(resolution,[],[f5,f2]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X1,X2)
| c_lessequals(X1,X0,X2)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
inference(resolution,[],[f17,f13]) ).
fof(f19,plain,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| ~ c_lessequals(X3,X0,X2)
| c_lessequals(X3,X1,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[],[f4,f13]) ).
fof(f20,plain,
! [X0,X1] :
( c_lessequals(X0,X1,t_b)
| c_lessequals(X1,X0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(resolution,[],[f18,f14]) ).
fof(f22,definition,
( spl0_1
<=> class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f23,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,definition,
( spl0_2
<=> ! [X0,X1] :
( c_lessequals(X0,X1,t_b)
| c_lessequals(X1,X0,t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f26,plain,
( ! [X0,X1] :
( c_lessequals(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f20,f25,f22]) ).
fof(f28,plain,
! [X2,X0,X1] :
( c_lessequals(c_Orderings_Omax(X2,X0,t_b),X1,t_b)
| ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[],[f3,f14]) ).
fof(f29,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f23,f15]) ).
fof(f30,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f31,plain,
( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ spl0_2 ),
inference(resolution,[],[f26,f6]) ).
fof(f33,plain,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(resolution,[],[f28,f7]) ).
fof(f35,definition,
( spl0_3
<=> 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_3])],[avatar_definition]) ).
fof(f36,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_3 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,definition,
( spl0_4
<=> c_lessequals(c_minus(v_k(v_x),v_g(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_4])],[avatar_definition]) ).
fof(f39,plain,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| spl0_4 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f33,f38,f35]) ).
fof(f41,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f36,f16]) ).
fof(f43,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f41]) ).
fof(f45,plain,
! [X2,X0,X1] :
( c_lessequals(X0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b)
| ~ c_lessequals(X1,X2,t_b) ),
inference(resolution,[],[f19,f15]) ).
fof(f48,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_minus(v_k(v_x),v_g(v_x),t_b),X0,t_b) )
| spl0_4 ),
inference(resolution,[],[f45,f39]) ).
fof(f51,plain,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| spl0_4 ),
inference(resolution,[],[f48,f16]) ).
fof(f53,plain,
( $false
| ~ spl0_2
| spl0_4 ),
inference(resolution,[],[f51,f31]) ).
fof(f56,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
~ spl0_4,
inference(rat,[],[s3,s4]) ).
cnf(s7,plain,
~ spl0_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s2]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 20:30:19 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 3.38/0.97 % (3708261)Input is clausal, will run a generic CNF schedule.
% 3.38/0.97 % (3708358)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3564843118:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 3.38/0.97 % (3708355)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=3832537528:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 3.38/0.97 % (3708359)lrs+10_1_sil=8000:sp=occurrence:random_seed=3144026217:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 3.38/0.97 % (3708357)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4030238379:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 3.38/0.97 % (3708361)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1825300151:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 3.38/0.97 % (3708363)dis-21_1_sil=8000:lcm=predicate:random_seed=4114523100: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)
% 3.38/0.97 % (3708362)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1379821395:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 3.38/0.97 % (3708363)First to succeed.
% 3.38/0.97 % (3708362)Also succeeded, but the first one will report.
% 3.38/0.97 % (3708361)Also succeeded, but the first one will report.
% 3.38/0.97 % (3708363)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3708261"
% 3.38/0.97 % (3708359)Also succeeded, but the first one will report.
% 3.38/0.97 % (3708363)Refutation found. Thanks to Tanya!
% 3.38/0.97 % SZS status Unsatisfiable for theBenchmark
% 3.38/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/0.97 % (3708363)------------------------------
% 3.38/0.97 % (3708363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/0.97 % (3708363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.97 % (3708363)CaDiCaL version: 2.1.3
% 3.38/0.97 % (3708363)Termination reason: Refutation
% 3.38/0.97 % (3708363)Time elapsed: 0.003 s
% 3.38/0.97 % (3708363)Peak memory usage: 89 MB
% 3.38/0.97 % (3708363)Instructions burned: 2 (million)
% 3.38/0.97 % (3708363)------------------------------
% 3.38/0.97 % (3708363)------------------------------
% 3.38/0.97 % (3708261)Success in time 0.437 s
% 3.38/0.97 % Vampire exiting
%------------------------------------------------------------------------------