%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA015-2 : 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 09:30:52 AM UTC 2026
% Result : Unsatisfiable 2.54s 0.86s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 36 ( 17 unt; 1 def)
% Number of atoms : 60 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 28 ~; 23 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,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_Osemigroup__mult__class_Omult__assoc_0) ).
fof(f3,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(f4,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(f5,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_g(X0),t_a),c_times(v_d,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X0)),t_a),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f8,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
fof(f11,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f12,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f13,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[],[f8,f12]) ).
fof(f14,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[],[f9,f12]) ).
fof(f15,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[],[f13,f7]) ).
fof(f16,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(resolution,[],[f10,f12]) ).
fof(f17,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f11,f12]) ).
fof(f18,plain,
! [X2,X0,X1] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(resolution,[],[f15,f2]) ).
fof(f19,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_a),t_a) = c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a),
inference(resolution,[],[f3,f14]) ).
fof(f21,plain,
! [X2,X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_a),t_a),c_times(c_HOL_Oabs(X0,t_a),X2,t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(X1,t_a),X2,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(superposition,[],[f4,f19]) ).
fof(f24,plain,
! [X2,X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_a),t_a),c_times(c_HOL_Oabs(X0,t_a),X2,t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(X1,t_a),X2,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a) ),
inference(forward_subsumption_resolution,[],[f21,f16]) ).
fof(f27,plain,
! [X0,X1] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(X0,X1,t_a))),t_a),t_a),c_times(X0,c_times(X1,c_HOL_Oabs(v_f(v_x(c_times(X0,X1,t_a))),t_a),t_a),t_a),t_a),
inference(superposition,[],[f6,f18]) ).
fof(f62,definition,
( spl0_1
<=> c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f63,plain,
( c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
| spl0_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f70,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_1 ),
inference(resolution,[],[f64,f1]) ).
fof(f71,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f70,f17]) ).
fof(f72,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f71]) ).
fof(f102,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X0,t_a))),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X0,t_a))),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
inference(resolution,[],[f27,f24]) ).
fof(f115,plain,
( ! [X0] : ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X0,t_a))),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X0,t_a))),t_a),t_a),t_a)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f102,f63]) ).
fof(f133,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f115,f5]) ).
fof(f138,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f133]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f72]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f138]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f142,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA015-2 : 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
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 20:28:19 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running first-order theorem proving
% 0.09/0.12 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
% 2.54/0.86 % (3704421)Input is clausal, will run a generic CNF schedule.
% 2.54/0.86 % (3704496)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=2853549470:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.54/0.86 % (3704499)lrs+10_1_sil=8000:sp=occurrence:random_seed=1152385356:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.54/0.86 % (3704500)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3230117114:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.54/0.86 % (3704498)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2665221610:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.54/0.86 % (3704497)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3671031091:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.54/0.86 % (3704500)Refutation not found, incomplete strategy
% 2.54/0.86 % (3704500)------------------------------
% 2.54/0.86 % (3704500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/0.86 % (3704500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.86 % (3704500)CaDiCaL version: 2.1.3
% 2.54/0.86 % (3704500)Termination reason: Refutation not found, incomplete strategy
% 2.54/0.86 % (3704500)Time elapsed: 0.0000 s
% 2.54/0.86 % (3704500)Peak memory usage: 87 MB
% 2.54/0.86 % (3704499)First to succeed.
% 2.54/0.86 % (3704499)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3704421"
% 2.54/0.86 % (3704501)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4225535636:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.54/0.86 % (3704501)Also succeeded, but the first one will report.
% 2.54/0.86 % (3704502)dis-21_1_sil=8000:lcm=predicate:random_seed=1453380385: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)
% 2.54/0.86 % (3704502)Refutation not found, incomplete strategy
% 2.54/0.86 % (3704502)------------------------------
% 2.54/0.86 % (3704502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/0.86 % (3704502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.86 % (3704502)CaDiCaL version: 2.1.3
% 2.54/0.86 % (3704502)Termination reason: Refutation not found, incomplete strategy
% 2.54/0.86 % (3704502)Time elapsed: 0.005 s
% 2.54/0.86 % (3704502)Peak memory usage: 88 MB
% 2.54/0.86 % (3704502)Instructions burned: 1 (million)
% 2.54/0.86 % (3704500)------------------------------
% 2.54/0.86 % (3704500)------------------------------
% 2.54/0.86 % (3704499)Refutation found. Thanks to Tanya!
% 2.54/0.86 % SZS status Unsatisfiable for theBenchmark
% 2.54/0.86 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/0.86 % (3704499)------------------------------
% 2.54/0.86 % (3704499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/0.86 % (3704499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.86 % (3704499)CaDiCaL version: 2.1.3
% 2.54/0.86 % (3704499)Termination reason: Refutation
% 2.54/0.86 % (3704499)Time elapsed: 0.004 s
% 2.54/0.86 % (3704499)Peak memory usage: 89 MB
% 2.54/0.86 % (3704499)Instructions burned: 8 (million)
% 2.54/0.86 % (3704499)------------------------------
% 2.54/0.86 % (3704499)------------------------------
% 2.54/0.86 % (3704421)Success in time 0.334 s
% 2.54/0.86 % Vampire exiting
%------------------------------------------------------------------------------