%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA043-2 : 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 : n003.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 09:31:00 AM UTC 2026
% Result : Unsatisfiable 3.61s 1.39s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 13 unt; 4 def)
% Number of atoms : 83 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 83 ( 41 ~; 38 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(X0),t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(X0),v_xa(X0)),t_b),c_HOL_Oabs(v_f(v_k(v_x(X0),v_xa(X0))),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_l(v_x(X0),v_xa(X0)),t_b),c_HOL_Oabs(v_h(v_k(v_x(X0),v_xa(X0))),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_times(X1,c_times(X2,X3,X0),X0) = c_times(X2,c_times(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__left__commute_0) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
fof(f7,axiom,
! [X0] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
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_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(f10,plain,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(X0,c_times(X1,X2,X3),X3) = c_times(X1,c_times(X0,X2,X3),X3) ),
inference(resolution,[],[f5,f7]) ).
fof(f11,plain,
! [X2,X0,X1] : c_times(X0,c_times(X1,X2,t_b),t_b) = c_times(X1,c_times(X0,X2,t_b),t_b),
inference(resolution,[],[f10,f3]) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X1,X3,t_b),c_times(X0,c_times(X1,X2,t_b),t_b),t_b)
| ~ c_lessequals(X3,c_times(X0,X2,t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(superposition,[],[f6,f11]) ).
fof(f21,definition,
( spl0_1
<=> class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f23,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f29,definition,
( spl0_3
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_times(X1,X3,t_b),c_times(X0,c_times(X1,X2,t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(X3,c_times(X0,X2,t_b),t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f30,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_0,X1,t_b)
| c_lessequals(c_times(X1,X3,t_b),c_times(X0,c_times(X1,X2,t_b),t_b),t_b)
| ~ c_lessequals(X3,c_times(X0,X2,t_b),t_b) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f16,f29,f21]) ).
fof(f34,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_1 ),
inference(resolution,[],[f23,f8]) ).
fof(f35,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f34,f3]) ).
fof(f36,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f35]) ).
fof(f77,definition,
( spl0_4
<=> class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f84,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_4 ),
inference(resolution,[],[f79,f9]) ).
fof(f85,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f84,f3]) ).
fof(f86,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f85]) ).
fof(f87,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_times(c_HOL_Oabs(X0,t_b),X1,t_b),c_times(X2,c_times(c_HOL_Oabs(X0,t_b),X3,t_b),t_b),t_b)
| ~ c_lessequals(X1,c_times(X2,X3,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
| ~ spl0_3 ),
inference(resolution,[],[f30,f4]) ).
fof(f90,definition,
( spl0_6
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_times(c_HOL_Oabs(X0,t_b),X1,t_b),c_times(X2,c_times(c_HOL_Oabs(X0,t_b),X3,t_b),t_b),t_b)
| ~ c_lessequals(X1,c_times(X2,X3,t_b),t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f91,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,c_times(X2,X3,t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(X0,t_b),X1,t_b),c_times(X2,c_times(c_HOL_Oabs(X0,t_b),X3,t_b),t_b),t_b) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f87,f29,f90,f77]) ).
fof(f243,plain,
( ! [X0,X1] : c_lessequals(c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(v_f(X1),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(v_h(X1),t_b),t_b),t_b),t_b)
| ~ spl0_6 ),
inference(resolution,[],[f91,f1]) ).
fof(f418,plain,
( $false
| ~ spl0_6 ),
inference(resolution,[],[f243,f2]) ).
fof(f421,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f418]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f36]) ).
cnf(s7,plain,
spl0_4,
inference(sat_conversion,[],[f86]) ).
cnf(s8,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f92]) ).
cnf(s9,plain,
~ spl0_6,
inference(sat_conversion,[],[f421]) ).
cnf(s10,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
~ spl0_3,
inference(rat,[],[s10,s7]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s4,s11,s5]) ).
fof(f423,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA043-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:35:43 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.61/1.39 % (1956120)Input is clausal, will run a generic CNF schedule.
% 3.61/1.39 % (1956145)lrs+10_1_sil=8000:sp=occurrence:random_seed=929758518:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.61/1.39 % (1956145)Instruction limit reached!
% 3.61/1.39 % (1956145)------------------------------
% 3.61/1.39 % (1956145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.39 % (1956145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.39 % (1956145)CaDiCaL version: 2.1.3
% 3.61/1.39 % (1956145)Termination reason: Instruction limit
% 3.61/1.39 % (1956145)Termination phase: Saturation
% 3.61/1.39 % (1956145)Time elapsed: 0.029 s
% 3.61/1.39 % (1956145)Peak memory usage: 88 MB
% 3.61/1.39 % (1956145)Instructions burned: 110 (million)
% 3.61/1.39 % (1956143)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3822698603:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.61/1.39 % (1956144)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3190157351:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.61/1.39 % (1956142)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=3065619582:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.61/1.39 % (1956146)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3553601853:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.61/1.39 % (1956148)dis-21_1_sil=8000:lcm=predicate:random_seed=228655295: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)
% 3.61/1.39 % (1956147)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2632001549:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.61/1.39 % (1956146)Refutation not found, incomplete strategy
% 3.61/1.39 % (1956146)------------------------------
% 3.61/1.39 % (1956146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.39 % (1956146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.39 % (1956146)CaDiCaL version: 2.1.3
% 3.61/1.39 % (1956146)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.39 % (1956146)Time elapsed: 0.001 s
% 3.61/1.39 % (1956146)Peak memory usage: 87 MB
% 3.61/1.39 % (1956148)Refutation not found, incomplete strategy
% 3.61/1.39 % (1956148)------------------------------
% 3.61/1.39 % (1956148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.39 % (1956148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.39 % (1956148)CaDiCaL version: 2.1.3
% 3.61/1.39 % (1956148)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.39 % (1956148)Time elapsed: 0.001 s
% 3.61/1.39 % (1956148)Peak memory usage: 87 MB
% 3.61/1.39 % (1956147)First to succeed.
% 3.61/1.39 % (1956147)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1956120"
% 3.61/1.39 % (1956150)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=144325783:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.61/1.39 % (1956150)Refutation not found, incomplete strategy
% 3.61/1.39 % (1956150)------------------------------
% 3.61/1.39 % (1956150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.39 % (1956150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.39 % (1956150)CaDiCaL version: 2.1.3
% 3.61/1.39 % (1956150)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.39 % (1956150)Time elapsed: 0.001 s
% 3.61/1.39 % (1956150)Peak memory usage: 87 MB
% 3.61/1.39 % (1956150)Instructions burned: 1 (million)
% 3.61/1.39 % (1956150)------------------------------
% 3.61/1.39 % (1956150)------------------------------
% 3.61/1.39 % (1956146)------------------------------
% 3.61/1.39 % (1956146)------------------------------
% 3.61/1.39 % (1956148)------------------------------
% 3.61/1.39 % (1956148)------------------------------
% 3.61/1.39 % (1956147)Refutation found. Thanks to Tanya!
% 3.61/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.61/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.39 % (1956147)------------------------------
% 3.61/1.39 % (1956147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.39 % (1956147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.39 % (1956147)CaDiCaL version: 2.1.3
% 3.61/1.39 % (1956147)Termination reason: Refutation
% 3.61/1.39 % (1956147)Time elapsed: 0.016 s
% 3.61/1.39 % (1956147)Peak memory usage: 89 MB
% 3.61/1.39 % (1956147)Instructions burned: 29 (million)
% 3.61/1.39 % (1956147)------------------------------
% 3.61/1.39 % (1956147)------------------------------
% 3.61/1.39 % (1956120)Success in time 0.397 s
% 3.61/1.39 % Vampire exiting
%------------------------------------------------------------------------------