%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA027-2 : 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 : n026.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 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 18 unt; 4 def)
% Number of atoms : 92 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 89 ( 45 ~; 40 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2,negated_conjecture,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f4,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f5,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,c_minus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_plus(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_minus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f9,axiom,
! [X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f10,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f11,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(f12,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f13,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(f14,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolution,[],[f12,f4]) ).
fof(f15,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f13,f4]) ).
fof(f16,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[],[f15,f11]) ).
fof(f17,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[],[f15,f10]) ).
fof(f18,plain,
! [X0] : c_plus(c_0,X0,t_b) = X0,
inference(resolution,[],[f5,f14]) ).
fof(f19,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[],[f16,f9]) ).
fof(f20,plain,
! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_g(v_x),X0,t_b) ),
inference(resolution,[],[f8,f2]) ).
fof(f23,definition,
( spl0_1
<=> class_Orderings_Oorder(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f31,definition,
( spl0_3
<=> ! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| c_lessequals(v_g(v_x),X0,t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f32,plain,
( ! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| c_lessequals(v_g(v_x),X0,t_b) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f33,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f20,f31,f23]) ).
fof(f34,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ),
inference(resolution,[],[f6,f1]) ).
fof(f36,definition,
( spl0_4
<=> c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f38,plain,
( c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl0_5
<=> class_OrderedGroup_Opordered__ab__group__add(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f41,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
( spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f34,f40,f36]) ).
fof(f46,plain,
spl0_5,
inference(avatar_split_clause,[],[f17,f40]) ).
fof(f49,plain,
spl0_1,
inference(avatar_split_clause,[],[f19,f23]) ).
fof(f50,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(X1,X0,t_b),t_b) ),
inference(superposition,[],[f7,f18]) ).
fof(f51,plain,
( ! [X0,X1] :
( c_lessequals(c_0,c_minus(X1,X0,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f50,f41]) ).
fof(f52,plain,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f38,f18]) ).
fof(f55,plain,
( c_lessequals(v_g(v_x),v_f(v_x),t_b)
| ~ spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f32,f52]) ).
fof(f58,plain,
( ~ c_lessequals(v_g(v_x),v_f(v_x),t_b)
| ~ spl0_5 ),
inference(resolution,[],[f51,f3]) ).
fof(f63,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f58,f55]) ).
fof(f64,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f63]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
( spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f46]) ).
cnf(s7,plain,
spl0_1,
inference(sat_conversion,[],[f49]) ).
cnf(s8,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f64]) ).
cnf(s9,plain,
spl0_4,
inference(rat,[],[s3,s5]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s8,s5,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s10,s7]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:33:42 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.19/0.26 % (13913)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (13921)dis+10_1_sil=32000:sp=arity:random_seed=4220140456:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (13921) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-13913-13921"...
% 0.19/0.26 % (13919)% WARNING: option uhcvi not known.
% 0.19/0.26 % (13921)...printing done.
% 0.19/0.26 % (13921)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (13921)------------------------------
% 0.19/0.26 % (13921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (13921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (13921)CaDiCaL version: 2.1.3
% 0.19/0.26 % (13921)Termination reason: Refutation
% 0.19/0.26 % (13921)Time elapsed: 0.002 s
% 0.19/0.26 % (13921)Peak memory usage: 12 MB
% 0.19/0.26 % (13921)Instructions burned: 2 (million)
% 0.19/0.26 % (13913)Success in time 0.036 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------