%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA015-2 : 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 : n019.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 09:31:17 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 53 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f4,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(X3,X1,X0),c_times(X3,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
fof(f5,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_g(X0),t_a),c_times(v_d,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X0)),t_a),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f8,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(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
fof(f11,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(f12,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| class_Ring__and__Field_Opordered__semiring(X0)
| c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f14,plain,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f15,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f16,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f17,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[],[f9,f12]) ).
fof(f18,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f11,f12]) ).
fof(f19,plain,
~ class_Ring__and__Field_Ofield(t_a),
inference(resolution,[],[f15,f12]) ).
fof(f20,plain,
~ class_Ring__and__Field_Opordered__semiring(t_a),
inference(resolution,[],[f16,f12]) ).
fof(f21,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[],[f19,f14]) ).
fof(f22,plain,
! [X2,X0,X1] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(resolution,[],[f2,f21]) ).
fof(f23,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_a),t_a) = c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a),
inference(resolution,[],[f3,f17]) ).
fof(f27,plain,
! [X0,X1] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(X0,X1,t_a))),t_a),t_a),c_times(X0,c_times(X1,c_HOL_Oabs(v_f(v_x(c_times(X0,X1,t_a))),t_a),t_a),t_a),t_a),
inference(superposition,[],[f6,f22]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| class_Ring__and__Field_Opordered__semiring(X2)
| c_lessequals(c_times(c_HOL_Oabs(X3,X2),X0,X2),c_times(c_HOL_Oabs(X3,X2),X1,X2),X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[],[f13,f1]) ).
fof(f38,plain,
! [X2,X0,X1] :
( class_Ring__and__Field_Opordered__semiring(t_a)
| c_lessequals(c_times(c_HOL_Oabs(X0,t_a),X1,t_a),c_times(c_HOL_Oabs(X0,t_a),X2,t_a),t_a)
| ~ c_lessequals(X1,X2,t_a) ),
inference(resolution,[],[f37,f18]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,t_a)
| c_lessequals(c_times(c_HOL_Oabs(X0,t_a),X1,t_a),c_times(c_HOL_Oabs(X0,t_a),X2,t_a),t_a) ),
inference(forward_subsumption_resolution,[],[f38,f20]) ).
fof(f40,plain,
! [X0,X1] : c_lessequals(c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(v_g(X1),t_a),t_a),c_times(c_HOL_Oabs(X0,t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),t_a),
inference(resolution,[],[f39,f5]) ).
fof(f43,plain,
! [X0,X1] : c_lessequals(c_HOL_Oabs(c_times(X0,v_g(X1),t_a),t_a),c_times(c_HOL_Oabs(X0,t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),t_a),
inference(forward_demodulation,[],[f40,f23]) ).
fof(f94,plain,
$false,
inference(resolution,[],[f27,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 20:28:33 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.22/0.29 % (195274)Will run a generic schedule for satisfiability detection.
% 0.22/0.29 % (195281)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1169209800:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.29 % (195280)% WARNING: option uhcvi not known.
% 0.22/0.29 % (195285)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2269996932:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.29 % (195282)dis+10_1_sil=32000:sp=arity:random_seed=2881917570:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.29 % (195280)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1925405313:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.29 % (195279)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=674805758_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.29 % (195283)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1211918000:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.29 % (195284)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1735550416:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.29 % TRYING [1]
% 0.22/0.29 % TRYING [2]
% 0.22/0.29 % (195280) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-195274-195280"...
% 0.22/0.29 % (195284) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-195274-195284"...
% 0.22/0.29 % (195282) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-195274-195282"...
% 0.22/0.29 % (195280)...printing done.
% 0.22/0.29 % (195284)...printing done.
% 0.22/0.29 % TRYING [3]
% 0.22/0.29 % (195280)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (195280)------------------------------
% 0.22/0.29 % (195280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (195280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (195280)CaDiCaL version: 2.1.3
% 0.22/0.29 % (195280)Termination reason: Refutation
% 0.22/0.29 % (195280)Time elapsed: 0.005 s
% 0.22/0.29 % (195280)Peak memory usage: 11 MB
% 0.22/0.29 % (195280)Instructions burned: 6 (million)
% 0.22/0.29 % (195274)Success in time 0.046 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------