%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA020-2 : 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 : n005.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 09:31:18 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 25 unt; 3 def)
% Number of atoms : 85 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 40 ~; 32 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,plain,
c_0 = v_f(c_0),
inference(reorient_equations,[],[f1]) ).
fof(f3,negated_conjecture,
c_less(c_0,v_c,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
v_x = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,plain,
c_0 = v_x,
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f8,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(c_0,X0) = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f9,plain,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,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(f11,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(f12,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f13,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f14,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(f15,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(f16,plain,
v_x = v_f(v_x),
inference(definition_unfolding,[],[f2,f5,f5]) ).
fof(f17,plain,
c_less(v_x,v_c,t_a),
inference(definition_unfolding,[],[f3,f5]) ).
fof(f18,plain,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| v_x = c_HOL_Oabs(v_x,X0) ),
inference(definition_unfolding,[],[f9,f5,f5]) ).
fof(f19,plain,
! [X0,X1] :
( c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(definition_unfolding,[],[f10,f5]) ).
fof(f20,plain,
! [X2,X0,X1] :
( c_lessequals(v_x,c_times(X2,X1,X0),X0)
| ~ c_lessequals(v_x,X1,X0)
| ~ c_lessequals(v_x,X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(definition_unfolding,[],[f12,f5,f5,f5]) ).
fof(f21,plain,
~ c_lessequals(c_HOL_Oabs(v_x,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(superposition,[],[f6,f16]) ).
fof(f48,definition,
( spl0_6
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f49,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl0_7
<=> c_lessequals(v_x,v_c,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f53,plain,
( c_lessequals(v_x,v_c,t_a)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f56,definition,
( spl0_8
<=> c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f58,plain,
( ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| spl0_8 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f66,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(resolution,[],[f13,f7]) ).
fof(f71,plain,
spl0_6,
inference(avatar_split_clause,[],[f66,f48]) ).
fof(f75,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[],[f14,f7]) ).
fof(f86,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f15,f7]) ).
fof(f87,plain,
v_x = c_HOL_Oabs(v_x,t_a),
inference(resolution,[],[f86,f18]) ).
fof(f112,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(v_x,v_c,t_a) ),
inference(resolution,[],[f11,f17]) ).
fof(f113,plain,
c_lessequals(v_x,v_c,t_a),
inference(forward_subsumption_resolution,[],[f112,f75]) ).
fof(f119,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_8 ),
inference(resolution,[],[f58,f19]) ).
fof(f122,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f119,f86]) ).
fof(f123,plain,
spl0_8,
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f126,plain,
spl0_7,
inference(avatar_split_clause,[],[f113,f52]) ).
fof(f127,plain,
~ c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(superposition,[],[f21,f87]) ).
fof(f130,plain,
( ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ c_lessequals(v_x,v_c,t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(resolution,[],[f127,f20]) ).
fof(f131,plain,
( ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f130,f53]) ).
fof(f134,plain,
( ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f131,f49]) ).
fof(f135,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f134,f52,f48,f56]) ).
cnf(s56,plain,
spl0_6,
inference(sat_conversion,[],[f71]) ).
cnf(s104,plain,
spl0_8,
inference(sat_conversion,[],[f123]) ).
cnf(s110,plain,
spl0_7,
inference(sat_conversion,[],[f126]) ).
cnf(s121,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f135]) ).
cnf(s123,plain,
~ spl0_6,
inference(rat,[],[s121,s110,s104]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s56,s123]) ).
fof(f136,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:29:17 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (1118800)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (1118807)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1767472078:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (1118807) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1118800-1118807"...
% 0.09/0.25 % (1118807)...printing done.
% 0.09/0.25 % (1118806)% WARNING: option uhcvi not known.
% 0.09/0.25 % (1118807)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (1118807)------------------------------
% 0.09/0.25 % (1118807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1118807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1118807)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1118807)Termination reason: Refutation
% 0.09/0.25 % (1118807)Time elapsed: 0.002 s
% 0.09/0.25 % (1118807)Peak memory usage: 12 MB
% 0.09/0.25 % (1118807)Instructions burned: 4 (million)
% 0.09/0.25 % (1118800)Success in time 0.027 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------