%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA010-2 : 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 : n018.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 09:31:16 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 37 ( 14 unt; 3 def)
% Number of atoms : 72 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 73 ( 38 ~; 32 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ c_lessequals(c_0,X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f4,negated_conjecture,
! [X0] : c_lessequals(c_0,v_f(X0),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5,negated_conjecture,
! [X0] : c_lessequals(v_f(X0),c_times(v_c,v_g(X0),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0] : ~ c_lessequals(v_f(v_x(X0)),c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f8,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(f9,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f10,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f8,f9]) ).
fof(f16,definition,
( spl0_2
<=> class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f18,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f20,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f18,f10]) ).
fof(f21,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f20]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_0,X0,X2)
| ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| c_HOL_Oabs(X1,X2) = X1 ),
inference(resolution,[],[f2,f1]) ).
fof(f25,definition,
( spl0_3
<=> class_Orderings_Oorder(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f27,plain,
( ~ class_Orderings_Oorder(t_b)
| spl0_3 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f32,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_3 ),
inference(resolution,[],[f27,f7]) ).
fof(f33,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f32,f25,f16]) ).
fof(f118,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,[],[f3,f9]) ).
fof(f126,plain,
! [X0] : ~ c_lessequals(v_f(v_x(c_HOL_Oabs(X0,t_b))),c_HOL_Oabs(c_times(X0,v_g(v_x(c_HOL_Oabs(X0,t_b))),t_b),t_b),t_b),
inference(superposition,[],[f6,f118]) ).
fof(f215,plain,
! [X0] :
( ~ c_lessequals(c_0,v_f(X0),t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_times(v_c,v_g(X0),t_b) = c_HOL_Oabs(c_times(v_c,v_g(X0),t_b),t_b) ),
inference(resolution,[],[f23,f5]) ).
fof(f221,definition,
( spl0_10
<=> ! [X0] :
( ~ c_lessequals(c_0,v_f(X0),t_b)
| c_times(v_c,v_g(X0),t_b) = c_HOL_Oabs(c_times(v_c,v_g(X0),t_b),t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f222,plain,
( ! [X0] :
( ~ c_lessequals(c_0,v_f(X0),t_b)
| c_times(v_c,v_g(X0),t_b) = c_HOL_Oabs(c_times(v_c,v_g(X0),t_b),t_b) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f223,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f215,f221,f25,f16]) ).
fof(f224,plain,
( ! [X0] : c_times(v_c,v_g(X0),t_b) = c_HOL_Oabs(c_times(v_c,v_g(X0),t_b),t_b)
| ~ spl0_10 ),
inference(resolution,[],[f222,f4]) ).
fof(f233,plain,
( ~ c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b)
| ~ spl0_10 ),
inference(superposition,[],[f126,f224]) ).
fof(f247,plain,
( $false
| ~ spl0_10 ),
inference(resolution,[],[f233,f5]) ).
fof(f249,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f247]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f21]) ).
cnf(s4,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s25,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f223]) ).
cnf(s27,plain,
~ spl0_10,
inference(sat_conversion,[],[f249]) ).
cnf(s28,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(rat,[],[s25,s27]) ).
cnf(s29,plain,
~ spl0_3,
inference(rat,[],[s28,s2]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s4,s29,s2]) ).
fof(f250,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA010-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n018.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 20:30:26 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.09/0.26 % (3730529)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (3730540)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1691394687:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.26 % (3730535)% WARNING: option uhcvi not known.
% 0.09/0.26 % (3730540) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3730529-3730540"...
% 0.09/0.26 % (3730540)...printing done.
% 0.09/0.26 % (3730534)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1265027609_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.26 % (3730540)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (3730540)------------------------------
% 0.09/0.26 % (3730540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3730540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3730540)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3730540)Termination reason: Refutation
% 0.09/0.26 % (3730540)Time elapsed: 0.006 s
% 0.09/0.26 % (3730540)Peak memory usage: 12 MB
% 0.09/0.26 % (3730540)Instructions burned: 15 (million)
% 0.09/0.26 % (3730529)Success in time 0.031 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------