%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA012-2 : 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 : n004.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 0.27s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 12 unt; 2 def)
% Number of atoms : 63 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 27 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_1,c_times(X0,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X1,X0) != c_0
| X1 = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f5,plain,
! [X0,X1] :
( c_0 != c_HOL_Oabs(X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X1 ),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = c_0
| c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f8,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X1
| c_1 = c_times(c_HOL_Oinverse(X1,X0),X1,X0) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f11,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
fof(f12,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[],[f9,f3]) ).
fof(f13,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f10,f3]) ).
fof(f14,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[],[f11,f3]) ).
fof(f15,plain,
! [X0] :
( c_1 = c_times(c_HOL_Oinverse(X0,t_a),X0,t_a)
| c_0 = X0 ),
inference(resolution,[],[f8,f12]) ).
fof(f16,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| c_0 = c_HOL_Oabs(v_c,t_a) ),
inference(superposition,[],[f2,f15]) ).
fof(f18,definition,
( spl0_1
<=> c_0 = c_HOL_Oabs(v_c,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f20,plain,
( c_0 = c_HOL_Oabs(v_c,t_a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f22,definition,
( spl0_2
<=> c_lessequals(c_1,c_1,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f24,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f16,f22,f18]) ).
fof(f26,plain,
( ~ class_Orderings_Oorder(t_a)
| spl0_2 ),
inference(resolution,[],[f24,f6]) ).
fof(f27,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f26,f14]) ).
fof(f28,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f27]) ).
fof(f30,plain,
( c_0 != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| v_c = c_0
| ~ spl0_1 ),
inference(superposition,[],[f5,f20]) ).
fof(f31,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| v_c = c_0
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f30]) ).
fof(f32,plain,
( v_c = c_0
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f31,f13]) ).
fof(f33,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f32,f1]) ).
fof(f34,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f33]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f35,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:28:22 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.09/0.27 % (722129)Will run a generic schedule for satisfiability detection.
% 0.09/0.27 % (722136)% WARNING: option uhcvi not known.
% 0.09/0.27 % (722138)dis+10_1_sil=32000:sp=arity:random_seed=698506334:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.27 % (722136)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1277438464:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.27 % (722137)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1891357371:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.27 % (722139)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3922789079:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.27 % (722138) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-722129-722138"...
% 0.09/0.27 % (722136) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-722129-722136"...
% 0.09/0.27 % (722139) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-722129-722139"...
% 0.09/0.27 % (722138)...printing done.
% 0.09/0.27 % (722136)...printing done.
% 0.09/0.27 % (722139)...printing done.
% 0.09/0.27 % (722135)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2586252121_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.27 % (722137) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-722129-722137"...
% 0.09/0.27 % (722138)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.27 % (722138)------------------------------
% 0.09/0.27 % (722138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.27 % (722138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.27 % (722138)CaDiCaL version: 2.1.3
% 0.09/0.27 % (722138)Termination reason: Refutation
% 0.09/0.27 % (722138)Time elapsed: 0.002 s
% 0.09/0.27 % (722138)Peak memory usage: 12 MB
% 0.09/0.27 % (722138)Instructions burned: 1 (million)
% 0.09/0.27 % (722129)Success in time 0.026 s
% 0.09/0.27 % Vampire exiting
%------------------------------------------------------------------------------