%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA017-2 : 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 : n020.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 09:30:53 AM UTC 2026
% Result : Unsatisfiable 3.54s 1.26s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 32 ( 15 unt; 1 def)
% Number of atoms : 54 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 21 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_b(X0),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(X0)),t_b),t_b),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
fof(f8,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f10,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(f11,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolution,[],[f8,f3]) ).
fof(f12,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolution,[],[f9,f3]) ).
fof(f13,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f10,f3]) ).
fof(f14,plain,
! [X2,X0,X1] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(resolution,[],[f5,f11]) ).
fof(f15,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(resolution,[],[f6,f3]) ).
fof(f17,plain,
! [X2,X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(c_HOL_Oabs(X0,t_b),X2,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),X2,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(superposition,[],[f7,f15]) ).
fof(f20,plain,
! [X2,X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(c_HOL_Oabs(X0,t_b),X2,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),X2,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b) ),
inference(forward_subsumption_resolution,[],[f17,f12]) ).
fof(f23,plain,
! [X0,X1] : ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X0,X1,t_b))),t_b),t_b),c_times(X0,c_times(X1,c_HOL_Oabs(v_f(v_x(c_times(X0,X1,t_b))),t_b),t_b),t_b),t_b),
inference(superposition,[],[f2,f14]) ).
fof(f58,definition,
( spl0_1
<=> c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f59,plain,
( c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f66,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_1 ),
inference(resolution,[],[f60,f4]) ).
fof(f67,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f66,f13]) ).
fof(f68,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),X0,t_b))),t_b),c_times(X0,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),X0,t_b))),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b) ),
inference(resolution,[],[f23,f20]) ).
fof(f82,plain,
( ! [X0] : ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),X0,t_b))),t_b),c_times(X0,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),X0,t_b))),t_b),t_b),t_b)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f69,f59]) ).
fof(f106,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f82,f1]) ).
fof(f111,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f106]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f68]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f111]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f115,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA017-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:29:34 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 3.54/1.25 % (500332)Input is clausal, will run a generic CNF schedule.
% 3.54/1.25 % (500343)dis-21_1_sil=8000:lcm=predicate:random_seed=1174152215: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)
% 3.54/1.25 % (500343)Refutation not found, incomplete strategy
% 3.54/1.25 % (500343)------------------------------
% 3.54/1.25 % (500343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.25 % (500343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.25 % (500343)CaDiCaL version: 2.1.3
% 3.54/1.25 % (500343)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.25 % (500343)Time elapsed: 0.001 s
% 3.54/1.25 % (500343)Peak memory usage: 88 MB
% 3.54/1.25 % (500338)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1561543647:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.54/1.25 % (500340)lrs+10_1_sil=8000:sp=occurrence:random_seed=1076264545:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.54/1.25 % (500341)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1201436175:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.54/1.25 % (500337)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=551043583:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.54/1.25 % (500339)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1168722764:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.54/1.25 % (500341)Refutation not found, incomplete strategy
% 3.54/1.25 % (500341)------------------------------
% 3.54/1.25 % (500341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.25 % (500341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.25 % (500341)CaDiCaL version: 2.1.3
% 3.54/1.25 % (500341)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.25 % (500341)Time elapsed: 0.001 s
% 3.54/1.25 % (500341)Peak memory usage: 87 MB
% 3.54/1.25 % (500340)First to succeed.
% 3.54/1.25 % (500340)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-500332"
% 3.54/1.25 % (500342)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1034139611:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.54/1.25 % (500342)Also succeeded, but the first one will report.
% 3.54/1.25 % (500343)------------------------------
% 3.54/1.25 % (500343)------------------------------
% 3.54/1.25 % (500351)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=790368119:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.54/1.25 % (500341)------------------------------
% 3.54/1.25 % (500341)------------------------------
% 3.54/1.25 % (500351)Instruction limit reached!
% 3.54/1.25 % (500351)------------------------------
% 3.54/1.25 % (500351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.25 % (500351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.25 % (500351)CaDiCaL version: 2.1.3
% 3.54/1.25 % (500351)Termination reason: Instruction limit
% 3.54/1.26 % (500351)Termination phase: Saturation
% 3.54/1.26 % (500351)Time elapsed: 0.043 s
% 3.54/1.26 % (500351)Peak memory usage: 89 MB
% 3.54/1.26 % (500351)Instructions burned: 145 (million)
% 3.54/1.26 % (500340)Refutation found. Thanks to Tanya!
% 3.54/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.54/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.26 % (500340)------------------------------
% 3.54/1.26 % (500340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.26 % (500340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.26 % (500340)CaDiCaL version: 2.1.3
% 3.54/1.26 % (500340)Termination reason: Refutation
% 3.54/1.26 % (500340)Time elapsed: 0.006 s
% 3.54/1.26 % (500340)Peak memory usage: 89 MB
% 3.54/1.26 % (500340)Instructions burned: 6 (million)
% 3.54/1.26 % (500340)------------------------------
% 3.54/1.26 % (500340)------------------------------
% 3.54/1.26 % (500332)Success in time 0.412 s
% 3.54/1.26 % Vampire exiting
%------------------------------------------------------------------------------