%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA039-2 : 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 : n016.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 09:31:23 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.29s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 15 unt; 3 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 42 ~; 42 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(X1,c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
fof(f5,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(f6,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
fof(f8,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f10,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(f11,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f12,plain,
c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ~ c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( ~ c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(X3,X2,X0) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(c_0,X3,X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f17,plain,
! [X0] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f18,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[],[f9,f3]) ).
fof(f19,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f10,f3]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,t_a)
| c_lessequals(X2,X0,t_a)
| c_lessequals(X0,X1,t_a) ),
inference(resolution,[],[f15,f18]) ).
fof(f21,plain,
! [X0] :
( c_lessequals(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),X0,t_a) ),
inference(resolution,[],[f20,f12]) ).
fof(f23,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a)
| c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(resolution,[],[f21,f16]) ).
fof(f25,definition,
( spl0_1
<=> class_Ring__and__Field_Opordered__semiring(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f27,plain,
( class_Ring__and__Field_Opordered__semiring(t_a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl0_2
<=> c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f31,plain,
( c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl0_3
<=> ! [X0] :
( c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f34,plain,
( ! [X0] :
( c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f35,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f23,f33,f29,f25]) ).
fof(f36,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_2 ),
inference(resolution,[],[f31,f14]) ).
fof(f38,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f36,f19]) ).
fof(f39,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f40,plain,
( c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ spl0_3 ),
inference(resolution,[],[f34,f11]) ).
fof(f42,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_3 ),
inference(resolution,[],[f40,f13]) ).
fof(f44,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f42,f19]) ).
fof(f45,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f46,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ spl0_1 ),
inference(resolution,[],[f27,f17]) ).
fof(f47,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f46,f3]) ).
fof(f48,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f47]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s2,s4]) ).
fof(f49,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : 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 : n016.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 20:38:33 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 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
% 0.24/0.29 % (3957377)Will run a generic schedule for satisfiability detection.
% 0.24/0.29 % (3957383)% WARNING: option uhcvi not known.
% 0.24/0.29 % (3957383)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1703912531:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.29 % (3957383) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3957377-3957383"...
% 0.24/0.29 % (3957383)...printing done.
% 0.24/0.29 % (3957383)Refutation found. Thanks to Tanya!
% 0.24/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.24/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.29 % (3957383)------------------------------
% 0.24/0.29 % (3957383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.29 % (3957383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.29 % (3957383)CaDiCaL version: 2.1.3
% 0.24/0.29 % (3957383)Termination reason: Refutation
% 0.24/0.29 % (3957383)Time elapsed: 0.001 s
% 0.24/0.29 % (3957383)Peak memory usage: 12 MB
% 0.24/0.29 % (3957383)Instructions burned: 2 (million)
% 0.24/0.29 % (3957377)Success in time 0.028 s
% 0.24/0.29 % Vampire exiting
%------------------------------------------------------------------------------