%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA044-2 : 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 : n017.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 09:31:24 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 13 unt; 3 def)
% Number of atoms : 75 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 39 ~; 36 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : c_lessequals(c_0,v_l(X0,X1),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : c_lessequals(c_0,v_h(X0),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f4,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f5,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(f6,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(f7,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(f8,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(f9,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f10,plain,
! [X0] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f17,definition,
( spl0_2
<=> class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f19,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f25,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_2 ),
inference(resolution,[],[f19,f8]) ).
fof(f26,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f25,f4]) ).
fof(f27,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f26]) ).
fof(f28,plain,
! [X2,X0,X1] :
( c_lessequals(c_0,c_times(X2,X0,X1),X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(resolution,[],[f9,f10]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_times(X0,X2,X1) = c_HOL_Oabs(c_times(X0,X2,X1),X1) ),
inference(resolution,[],[f28,f5]) ).
fof(f30,plain,
! [X0,X1] :
( ~ c_lessequals(c_0,X1,t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_times(X1,v_h(X0),t_b) = c_HOL_Oabs(c_times(X1,v_h(X0),t_b),t_b) ),
inference(resolution,[],[f29,f2]) ).
fof(f40,definition,
( spl0_4
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f42,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_4 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f56,definition,
( spl0_8
<=> ! [X0,X1] :
( ~ c_lessequals(c_0,X1,t_b)
| c_times(X1,v_h(X0),t_b) = c_HOL_Oabs(c_times(X1,v_h(X0),t_b),t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f57,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_0,X1,t_b)
| c_times(X1,v_h(X0),t_b) = c_HOL_Oabs(c_times(X1,v_h(X0),t_b),t_b) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_8 ),
inference(avatar_split_clause,[],[f30,f56,f40,f17]) ).
fof(f59,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f42,f4]) ).
fof(f60,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f59]) ).
fof(f69,plain,
( ! [X2,X0,X1] : c_times(v_l(X0,X1),v_h(X2),t_b) = c_HOL_Oabs(c_times(v_l(X0,X1),v_h(X2),t_b),t_b)
| ~ spl0_8 ),
inference(resolution,[],[f57,f1]) ).
fof(f75,plain,
( c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b)
| ~ spl0_8 ),
inference(superposition,[],[f3,f69]) ).
fof(f76,plain,
( $false
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f75]) ).
fof(f77,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f76]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f27]) ).
cnf(s7,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f58]) ).
cnf(s8,plain,
spl0_4,
inference(sat_conversion,[],[f60]) ).
cnf(s11,plain,
~ spl0_8,
inference(sat_conversion,[],[f77]) ).
cnf(s12,plain,
~ spl0_2,
inference(rat,[],[s7,s11,s8]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s3,s12]) ).
fof(f78,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n017.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 20:29:36 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 % (3969983)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (3969994)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2671824813:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.26 % (3969994) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3969983-3969994"...
% 0.09/0.26 % (3969994)...printing done.
% 0.09/0.26 % (3969989)% WARNING: option uhcvi not known.
% 0.09/0.26 % (3969994)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 % (3969994)------------------------------
% 0.09/0.26 % (3969994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3969994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3969994)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3969994)Termination reason: Refutation
% 0.09/0.26 % (3969994)Time elapsed: 0.002 s
% 0.09/0.26 % (3969994)Peak memory usage: 12 MB
% 0.09/0.26 % (3969994)Instructions burned: 3 (million)
% 0.09/0.26 % (3969983)Success in time 0.026 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------