%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA020-2 : 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 : n006.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 09:30:54 AM UTC 2026
% Result : Unsatisfiable 2.74s 1.17s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 21 unt; 6 def)
% Number of atoms : 120 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 108 ( 52 ~; 50 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,plain,
c_0 = v_f(c_0),
inference(reorient_equations,[],[f1]) ).
fof(f3,negated_conjecture,
c_less(c_0,v_c,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
v_x = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,plain,
c_0 = v_x,
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f8,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(c_0,X0) = c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f9,plain,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f11,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| c_lessequals(c_0,c_times(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f13,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f14,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(f15,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(f16,plain,
v_x = v_f(v_x),
inference(definition_unfolding,[],[f2,f5,f5]) ).
fof(f17,plain,
c_less(v_x,v_c,t_a),
inference(definition_unfolding,[],[f3,f5]) ).
fof(f18,plain,
! [X0] :
( v_x = c_HOL_Oabs(v_x,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(definition_unfolding,[],[f9,f5,f5]) ).
fof(f19,plain,
! [X0,X1] :
( c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(definition_unfolding,[],[f10,f5]) ).
fof(f20,plain,
! [X2,X0,X1] :
( c_lessequals(v_x,c_times(X2,X1,X0),X0)
| ~ c_lessequals(v_x,X1,X0)
| ~ c_lessequals(v_x,X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(definition_unfolding,[],[f12,f5,f5,f5]) ).
fof(f23,plain,
~ c_lessequals(c_HOL_Oabs(v_x,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(superposition,[],[f6,f16]) ).
fof(f24,plain,
( ~ c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(superposition,[],[f23,f18]) ).
fof(f26,definition,
( spl0_1
<=> class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f27,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,definition,
( spl0_2
<=> c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f30,plain,
( ~ c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| spl0_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f24,f29,f26]) ).
fof(f32,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| spl0_1 ),
inference(resolution,[],[f15,f27]) ).
fof(f33,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f32,f7]) ).
fof(f34,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f33]) ).
fof(f38,definition,
( spl0_3
<=> class_Orderings_Oorder(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f39,plain,
( ~ class_Orderings_Oorder(t_a)
| spl0_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f48,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| spl0_3 ),
inference(resolution,[],[f39,f14]) ).
fof(f49,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f48,f7]) ).
fof(f50,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f49]) ).
fof(f53,plain,
( ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ c_lessequals(v_x,v_c,t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| spl0_2 ),
inference(resolution,[],[f30,f20]) ).
fof(f60,definition,
( spl0_7
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f61,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| spl0_7 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_8
<=> c_lessequals(v_x,v_c,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f64,plain,
( ~ c_lessequals(v_x,v_c,t_a)
| spl0_8 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,definition,
( spl0_9
<=> c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f67,plain,
( ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| spl0_9 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| spl0_2 ),
inference(avatar_split_clause,[],[f53,f29,f66,f63,f60]) ).
fof(f71,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| spl0_7 ),
inference(resolution,[],[f61,f13]) ).
fof(f72,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f71,f7]) ).
fof(f73,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f74,plain,
( ~ c_less(v_x,v_c,t_a)
| ~ class_Orderings_Oorder(t_a)
| spl0_8 ),
inference(resolution,[],[f64,f11]) ).
fof(f75,plain,
( ~ class_Orderings_Oorder(t_a)
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f74,f17]) ).
fof(f76,plain,
( ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f75,f63,f38]) ).
fof(f77,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_9 ),
inference(resolution,[],[f67,f19]) ).
fof(f83,plain,
( ~ spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f77,f66,f26]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f34]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f50]) ).
cnf(s8,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f68]) ).
cnf(s10,plain,
spl0_7,
inference(sat_conversion,[],[f73]) ).
cnf(s11,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f76]) ).
cnf(s13,plain,
( ~ spl0_1
| spl0_9 ),
inference(sat_conversion,[],[f83]) ).
cnf(s14,plain,
( spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(rat,[],[s8,s10]) ).
cnf(s15,plain,
spl0_8,
inference(rat,[],[s11,s5]) ).
cnf(s18,plain,
spl0_9,
inference(rat,[],[s13,s2]) ).
cnf(s20,plain,
spl0_2,
inference(rat,[],[s14,s15,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s20,s2]) ).
fof(f84,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:28:55 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 2.74/1.17 % (141003)Input is clausal, will run a generic CNF schedule.
% 2.74/1.17 % (141012)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3979904442:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.17 % (141012)First to succeed.
% 2.74/1.17 % (141012)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-141003"
% 2.74/1.17 % (141009)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=634783414:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.17 % (141014)dis-21_1_sil=8000:lcm=predicate:random_seed=2797869728: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)
% 2.74/1.17 % (141011)lrs+10_1_sil=8000:sp=occurrence:random_seed=577052437:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.17 % (141010)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=368762534:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.17 % (141013)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1999274872:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.17 % (141008)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=2157526198:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.17 % (141014)Refutation not found, incomplete strategy
% 2.74/1.17 % (141014)------------------------------
% 2.74/1.17 % (141014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.17 % (141014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.17 % (141014)CaDiCaL version: 2.1.3
% 2.74/1.17 % (141014)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.17 % (141014)Time elapsed: 0.002 s
% 2.74/1.17 % (141014)Peak memory usage: 87 MB
% 2.74/1.17 % (141014)Instructions burned: 1 (million)
% 2.74/1.17 % (141011)Also succeeded, but the first one will report.
% 2.74/1.17 % (141013)Also succeeded, but the first one will report.
% 2.74/1.17 % (141012)Refutation found. Thanks to Tanya!
% 2.74/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.17 % (141012)------------------------------
% 2.74/1.17 % (141012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.17 % (141012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.17 % (141012)CaDiCaL version: 2.1.3
% 2.74/1.17 % (141012)Termination reason: Refutation
% 2.74/1.17 % (141012)Time elapsed: 0.002 s
% 2.74/1.17 % (141012)Peak memory usage: 89 MB
% 2.74/1.17 % (141012)Instructions burned: 3 (million)
% 2.74/1.17 % (141012)------------------------------
% 2.74/1.17 % (141012)------------------------------
% 2.74/1.17 % (141003)Success in time 0.297 s
% 2.74/1.17 % Vampire exiting
%------------------------------------------------------------------------------