%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 09:31:20 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.24s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 61 ( 18 unt; 6 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 128 ( 62 ~; 60 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f4,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f6,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,axiom,
! [X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f9,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| class_LOrder_Ojoin__semilorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f11,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f12,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f13,plain,
! [X0,X1] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f14,plain,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f15,plain,
! [X0] :
( class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Olinorder(X0) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f16,plain,
! [X0] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f17,plain,
~ class_Ring__and__Field_Oordered__idom(t_b),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f18,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(resolution,[],[f14,f8]) ).
fof(f19,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[],[f15,f17]) ).
fof(f20,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f16,f17]) ).
fof(f21,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[],[f13,f20]) ).
fof(f22,plain,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Oorder(X0) ),
inference(resolution,[],[f5,f2]) ).
fof(f26,definition,
( spl0_1
<=> class_Orderings_Oorder(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f28,plain,
( ~ class_Orderings_Oorder(t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f30,definition,
( spl0_2
<=> class_Orderings_Olinorder(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f32,plain,
( ~ class_Orderings_Olinorder(t_b)
| spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f43,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_1 ),
inference(resolution,[],[f28,f18]) ).
fof(f44,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f32,f19]) ).
fof(f45,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f46,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f43,f20]) ).
fof(f47,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ~ c_lessequals(X0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[],[f4,f6]) ).
fof(f55,definition,
( spl0_6
<=> ! [X0] :
( ~ c_lessequals(X0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f56,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f48,f55,f26]) ).
fof(f117,definition,
( spl0_14
<=> c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f119,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| spl0_14 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f125,plain,
( $false
| spl0_14 ),
inference(resolution,[],[f119,f21]) ).
fof(f129,plain,
spl0_14,
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f152,definition,
( spl0_20
<=> c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f153,plain,
( c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f154,plain,
( ~ c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
| spl0_20 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f170,plain,
( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ class_Orderings_Oorder(t_b)
| spl0_20 ),
inference(resolution,[],[f154,f22]) ).
fof(f172,definition,
( spl0_22
<=> c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f175,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_22
| spl0_20 ),
inference(avatar_split_clause,[],[f170,f152,f172,f30,f26]) ).
fof(f181,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ spl0_6
| ~ spl0_20 ),
inference(resolution,[],[f153,f56]) ).
fof(f188,plain,
( ~ spl0_14
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f181,f152,f55,f117]) ).
fof(f201,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(resolution,[],[f3,f7]) ).
fof(f217,plain,
( ~ spl0_2
| ~ spl0_22
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f201,f117,f172,f30]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f47]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f57]) ).
cnf(s18,plain,
spl0_14,
inference(sat_conversion,[],[f129]) ).
cnf(s27,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_20
| spl0_22 ),
inference(sat_conversion,[],[f175]) ).
cnf(s30,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_20 ),
inference(sat_conversion,[],[f188]) ).
cnf(s38,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f217]) ).
cnf(s40,plain,
spl0_6,
inference(rat,[],[s6,s4]) ).
cnf(s42,plain,
~ spl0_20,
inference(rat,[],[s30,s18,s40]) ).
cnf(s46,plain,
~ spl0_22,
inference(rat,[],[s38,s18,s3]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s27,s42,s4,s46,s3]) ).
fof(f218,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n010.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 20:31:03 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.24 % (2275008)Will run a generic schedule for satisfiability detection.
% 0.06/0.24 % (2275019)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=374705204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.24 % (2275019) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2275008-2275019"...
% 0.06/0.24 % (2275019)...printing done.
% 0.06/0.24 % (2275019)Refutation found. Thanks to Tanya!
% 0.06/0.24 % SZS status Unsatisfiable for theBenchmark
% 0.06/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.24 % (2275019)------------------------------
% 0.06/0.24 % (2275019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.24 % (2275019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.24 % (2275019)CaDiCaL version: 2.1.3
% 0.06/0.24 % (2275019)Termination reason: Refutation
% 0.06/0.24 % (2275019)Time elapsed: 0.002 s
% 0.06/0.24 % (2275019)Peak memory usage: 12 MB
% 0.06/0.24 % (2275019)Instructions burned: 4 (million)
% 0.06/0.24 % (2275008)Success in time 0.029 s
% 0.06/0.24 % Vampire exiting
%------------------------------------------------------------------------------