%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA014-2 : 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 09:30:52 AM UTC 2026
% Result : Unsatisfiable 0.17s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 45 ( 14 unt; 2 def)
% Number of atoms : 83 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 38 ~; 36 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
fof(f6,axiom,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f8,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = c_0
| c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f9,plain,
! [X0,X1] :
( c_1 = c_times(c_HOL_Oinverse(X1,X0),X1,X0)
| c_0 = X1
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
fof(f11,axiom,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f12,axiom,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f13,axiom,
! [X0] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f14,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
fof(f15,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_1,X0,X1) = X0 ),
inference(resolution,[],[f4,f10]) ).
fof(f16,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| c_times(c_1,X0,X1) = X0 ),
inference(resolution,[],[f15,f12]) ).
fof(f17,plain,
! [X0] : c_times(c_1,X0,t_a) = X0,
inference(resolution,[],[f16,f3]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X2)
| c_times(c_times(X0,X1,X2),X3,X2) = c_times(X0,c_times(X1,X3,X2),X2) ),
inference(resolution,[],[f5,f11]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X2)
| c_HOL_Oabs(c_times(X0,X1,X2),X2) = c_times(c_HOL_Oabs(X0,X2),c_HOL_Oabs(X1,X2),X2) ),
inference(resolution,[],[f7,f13]) ).
fof(f21,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,[],[f20,f3]) ).
fof(f22,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_HOL_Oabs(c_times(v_c,v_f(v_x(X0)),t_a),t_a),t_a),t_a),
inference(superposition,[],[f2,f21]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X2)
| c_times(c_times(X0,X1,X2),X3,X2) = c_times(X0,c_times(X1,X3,X2),X2) ),
inference(resolution,[],[f18,f12]) ).
fof(f25,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),c_HOL_Oabs(c_times(X0,c_times(v_c,v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),t_a),t_a),t_a),
inference(superposition,[],[f22,f21]) ).
fof(f28,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,[],[f24,f3]) ).
fof(f29,plain,
! [X0,X1] :
( c_times(c_HOL_Oinverse(X0,t_a),c_times(X0,X1,t_a),t_a) = c_times(c_1,X1,t_a)
| c_0 = X0
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(superposition,[],[f28,f9]) ).
fof(f38,plain,
! [X0,X1] :
( c_times(c_HOL_Oinverse(X0,t_a),c_times(X0,X1,t_a),t_a) = X1
| c_0 = X0
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(forward_demodulation,[],[f29,f17]) ).
fof(f41,definition,
( spl0_1
<=> class_Ring__and__Field_Ofield(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f43,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl0_2
<=> ! [X0,X1] :
( c_times(c_HOL_Oinverse(X0,t_a),c_times(X0,X1,t_a),t_a) = X1
| c_0 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f46,plain,
( ! [X0,X1] :
( c_times(c_HOL_Oinverse(X0,t_a),c_times(X0,X1,t_a),t_a) = X1
| c_0 = X0 )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f38,f45,f41]) ).
fof(f48,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| spl0_1 ),
inference(resolution,[],[f43,f12]) ).
fof(f49,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f48,f3]) ).
fof(f50,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f49]) ).
fof(f59,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| v_c = c_0
| ~ spl0_2 ),
inference(superposition,[],[f25,f46]) ).
fof(f62,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f59,f1]) ).
fof(f187,plain,
( ~ class_Orderings_Oorder(t_a)
| ~ spl0_2 ),
inference(resolution,[],[f62,f6]) ).
fof(f189,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| ~ spl0_2 ),
inference(resolution,[],[f187,f14]) ).
fof(f190,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f189,f3]) ).
fof(f191,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f190]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f50]) ).
cnf(s5,plain,
~ spl0_2,
inference(sat_conversion,[],[f191]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s2]) ).
fof(f192,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:26:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.17/1.30 % (2765496)Input is clausal, will run a generic CNF schedule.
% 0.17/1.30 % (2765507)dis-21_1_sil=8000:lcm=predicate:random_seed=3280957059: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)
% 0.17/1.30 % (2765507)Refutation not found, incomplete strategy
% 0.17/1.30 % (2765507)------------------------------
% 0.17/1.30 % (2765507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.30 % (2765507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.30 % (2765507)CaDiCaL version: 2.1.3
% 0.17/1.30 % (2765507)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.30 % (2765507)Time elapsed: 0.001 s
% 0.17/1.30 % (2765507)Peak memory usage: 88 MB
% 0.17/1.30 % (2765505)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2102313196:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.30 % (2765504)lrs+10_1_sil=8000:sp=occurrence:random_seed=2922481015:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.30 % (2765501)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=3442645934:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.30 % (2765502)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1916001975:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.30 % (2765503)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1166615862:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.30 % (2765506)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1055191017:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.30 % (2765505)Refutation not found, incomplete strategy
% 0.17/1.30 % (2765505)------------------------------
% 0.17/1.30 % (2765505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.30 % (2765505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.30 % (2765505)CaDiCaL version: 2.1.3
% 0.17/1.30 % (2765505)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.30 % (2765505)Time elapsed: 0.002 s
% 0.17/1.30 % (2765505)Peak memory usage: 88 MB
% 0.17/1.30 % (2765505)Instructions burned: 1 (million)
% 0.17/1.30 % (2765506)First to succeed.
% 0.17/1.30 % (2765504)Also succeeded, but the first one will report.
% 0.17/1.30 % (2765506)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2765496"
% 0.17/1.30 % (2765507)------------------------------
% 0.17/1.30 % (2765507)------------------------------
% 0.17/1.30 % (2765515)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=3908945627:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.17/1.30 % (2765505)------------------------------
% 0.17/1.30 % (2765505)------------------------------
% 0.17/1.30 % (2765506)Refutation found. Thanks to Tanya!
% 0.17/1.30 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.30 % (2765506)------------------------------
% 0.17/1.30 % (2765506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.30 % (2765506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.30 % (2765506)CaDiCaL version: 2.1.3
% 0.17/1.30 % (2765506)Termination reason: Refutation
% 0.17/1.30 % (2765506)Time elapsed: 0.008 s
% 0.17/1.30 % (2765506)Peak memory usage: 89 MB
% 0.17/1.30 % (2765506)Instructions burned: 10 (million)
% 0.17/1.30 % (2765506)------------------------------
% 0.17/1.30 % (2765506)------------------------------
% 0.17/1.30 % (2765496)Success in time 0.445 s
% 0.17/1.30 % Vampire exiting
%------------------------------------------------------------------------------