%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA039-2 : 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 : n007.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 09:30:59 AM UTC 2026
% Result : Unsatisfiable 3.49s 1.25s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 12 unt; 4 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 48 ~; 41 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
fof(f5,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(f6,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/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
fof(f8,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f9,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f10,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f11,plain,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(X3,X0,X2)
| c_lessequals(X3,X1,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[],[f6,f9]) ).
fof(f12,plain,
! [X2,X0,X1] :
( c_lessequals(X0,X2,t_a)
| ~ c_lessequals(X0,X1,t_a)
| ~ c_lessequals(X1,X2,t_a) ),
inference(resolution,[],[f11,f3]) ).
fof(f13,plain,
! [X0] :
( ~ c_lessequals(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),X0,t_a) ),
inference(resolution,[],[f12,f2]) ).
fof(f15,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(resolution,[],[f13,f7]) ).
fof(f17,definition,
( spl0_1
<=> class_Ring__and__Field_Opordered__semiring(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f19,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_a)
| spl0_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f21,definition,
( spl0_2
<=> c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f23,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| spl0_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl0_3
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f26,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f15,f25,f21,f17]) ).
fof(f28,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| spl0_1 ),
inference(resolution,[],[f19,f8]) ).
fof(f29,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f28,f3]) ).
fof(f30,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f31,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_2 ),
inference(resolution,[],[f23,f5]) ).
fof(f33,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| spl0_2 ),
inference(resolution,[],[f31,f10]) ).
fof(f34,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f33,f3]) ).
fof(f35,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f34]) ).
fof(f36,plain,
( ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ spl0_3 ),
inference(resolution,[],[f26,f1]) ).
fof(f44,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_3 ),
inference(resolution,[],[f36,f4]) ).
fof(f60,definition,
( spl0_6
<=> class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f62,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_6 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f67,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f44,f25,f60]) ).
fof(f68,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| spl0_6 ),
inference(resolution,[],[f62,f10]) ).
fof(f69,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f68,f3]) ).
fof(f70,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f69]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f35]) ).
cnf(s6,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s7,plain,
spl0_6,
inference(sat_conversion,[],[f70]) ).
cnf(s8,plain,
~ spl0_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s3,s2]) ).
fof(f71,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:31:56 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.49/1.25 % (2766812)Input is clausal, will run a generic CNF schedule.
% 3.49/1.25 % (2766821)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2335063313:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.25 % (2766821)Refutation not found, incomplete strategy
% 3.49/1.25 % (2766821)------------------------------
% 3.49/1.25 % (2766821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.25 % (2766821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.25 % (2766821)CaDiCaL version: 2.1.3
% 3.49/1.25 % (2766821)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.25 % (2766821)Time elapsed: 0.0000 s
% 3.49/1.25 % (2766821)Peak memory usage: 87 MB
% 3.49/1.25 % (2766822)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=152837356:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.25 % (2766822)First to succeed.
% 3.49/1.25 % (2766822)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2766812"
% 3.49/1.25 % (2766817)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=85716805:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.25 % (2766819)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1854889256:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.25 % (2766823)dis-21_1_sil=8000:lcm=predicate:random_seed=4158731162: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)
% 3.49/1.25 % (2766820)lrs+10_1_sil=8000:sp=occurrence:random_seed=1194631838:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.25 % (2766818)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1705966518:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.25 % (2766823)Also succeeded, but the first one will report.
% 3.49/1.25 % (2766820)Also succeeded, but the first one will report.
% 3.49/1.25 % (2766821)------------------------------
% 3.49/1.25 % (2766821)------------------------------
% 3.49/1.25 % (2766831)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=2564726475:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.49/1.25 % (2766831)Also succeeded, but the first one will report.
% 3.49/1.25 % (2766822)Refutation found. Thanks to Tanya!
% 3.49/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.25 % (2766822)------------------------------
% 3.49/1.25 % (2766822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.25 % (2766822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.25 % (2766822)CaDiCaL version: 2.1.3
% 3.49/1.25 % (2766822)Termination reason: Refutation
% 3.49/1.25 % (2766822)Time elapsed: 0.004 s
% 3.49/1.25 % (2766822)Peak memory usage: 89 MB
% 3.49/1.25 % (2766822)Instructions burned: 3 (million)
% 3.49/1.25 % (2766822)------------------------------
% 3.49/1.25 % (2766822)------------------------------
% 3.49/1.25 % (2766812)Success in time 0.403 s
% 3.49/1.25 % Vampire exiting
%------------------------------------------------------------------------------