%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 09:31:22 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 53 ( 20 unt; 3 def)
% Number of atoms : 115 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 65 ~; 59 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [X2,X3,X0,X1,X4] :
( c_lessequals(c_times(X3,X1,X0),c_times(X4,X2,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X4,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f5,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(f6,negated_conjecture,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f7,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f8,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f9,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f10,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f12,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f13,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f14,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f15,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f16,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(resolution,[],[f13,f11]) ).
fof(f17,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolution,[],[f14,f11]) ).
fof(f18,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f15,f11]) ).
fof(f19,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[],[f18,f12]) ).
fof(f20,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_c,t_b) ),
inference(resolution,[],[f4,f6]) ).
fof(f21,plain,
c_lessequals(c_0,v_c,t_b),
inference(forward_subsumption_resolution,[],[f20,f19]) ).
fof(f22,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,[],[f1,f11]) ).
fof(f28,definition,
( spl0_1
<=> c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f30,plain,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f40,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| ~ c_lessequals(c_0,v_c,t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_1 ),
inference(resolution,[],[f30,f3]) ).
fof(f41,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f40,f21]) ).
fof(f42,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f41,f16]) ).
fof(f45,plain,
! [X0,X1] :
( c_lessequals(c_times(X0,X1,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(superposition,[],[f2,f9]) ).
fof(f54,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_1 ),
inference(resolution,[],[f42,f5]) ).
fof(f55,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f54,f18]) ).
fof(f56,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( c_lessequals(c_times(X0,X1,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
inference(forward_subsumption_resolution,[],[f45,f17]) ).
fof(f59,definition,
( spl0_5
<=> ! [X0,X1] :
( c_lessequals(c_times(X0,X1,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f60,plain,
( ! [X0,X1] :
( c_lessequals(c_times(X0,X1,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f57,f59,f28]) ).
fof(f74,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) )
| ~ spl0_5 ),
inference(superposition,[],[f60,f22]) ).
fof(f126,definition,
( spl0_16
<=> c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f128,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| spl0_16 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f139,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ spl0_5 ),
inference(resolution,[],[f74,f10]) ).
fof(f155,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f139,f7]) ).
fof(f156,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f155,f8]) ).
fof(f157,plain,
( ~ spl0_16
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f156,f59,f126]) ).
fof(f158,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_16 ),
inference(resolution,[],[f128,f5]) ).
fof(f159,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f158,f18]) ).
fof(f160,plain,
spl0_16,
inference(avatar_contradiction_clause,[],[f159]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f61]) ).
cnf(s13,plain,
( ~ spl0_5
| ~ spl0_16 ),
inference(sat_conversion,[],[f157]) ).
cnf(s14,plain,
spl0_16,
inference(sat_conversion,[],[f160]) ).
cnf(s15,plain,
~ spl0_5,
inference(rat,[],[s13,s14]) ).
cnf(s19,plain,
~ spl0_1,
inference(rat,[],[s4,s15]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s3,s19]) ).
fof(f161,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.26 % Computer : n014.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Mon Sep 28 20:32:46 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.30 Running first-order model finding
% 0.25/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.34 % (2134473)Will run a generic schedule for satisfiability detection.
% 0.25/0.34 % (2134478)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=80557657_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.34 % TRYING [1]
% 0.25/0.34 % TRYING [2]
% 0.25/0.34 % TRYING [3]
% 0.25/0.34 % (2134479)% WARNING: option uhcvi not known.
% 0.25/0.34 % (2134480)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3716676883:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.34 % (2134479)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2225758972:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.34 % (2134483)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=886718650:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.34 % (2134482)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3908937129:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.34 % (2134481)dis+10_1_sil=32000:sp=arity:random_seed=220590393:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.34 % (2134484)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3226869843:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.34 % (2134483) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2134473-2134483"...
% 0.25/0.34 % (2134481) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2134473-2134481"...
% 0.25/0.34 % (2134483)...printing done.
% 0.25/0.34 % (2134482) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2134473-2134482"...
% 0.25/0.34 % (2134481)...printing done.
% 0.25/0.34 % (2134484) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2134473-2134484"...
% 0.25/0.34 % (2134481)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.34 % (2134481)------------------------------
% 0.25/0.34 % (2134481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (2134481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (2134481)CaDiCaL version: 2.1.3
% 0.25/0.34 % (2134481)Termination reason: Refutation
% 0.25/0.34 % (2134481)Time elapsed: 0.006 s
% 0.25/0.34 % (2134481)Peak memory usage: 12 MB
% 0.25/0.34 % (2134481)Instructions burned: 7 (million)
% 0.25/0.34 % (2134473)Success in time 0.03 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------