%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:31:00 AM UTC 2026
% Result : Unsatisfiable 3.62s 1.28s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 31 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 21 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : c_lessequals(c_0,v_l(X0,X1),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : c_lessequals(c_0,v_h(X0),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f4,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f5,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(c_0,X1,X0)
| c_HOL_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f6,axiom,
! [X2,X0,X1] :
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f7,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f8,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f9,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(X0,X1) = X0
| ~ c_lessequals(c_0,X0,X1) ),
inference(resolution,[],[f5,f8]) ).
fof(f10,plain,
! [X0] :
( c_HOL_Oabs(X0,t_b) = X0
| ~ c_lessequals(c_0,X0,t_b) ),
inference(resolution,[],[f9,f4]) ).
fof(f11,plain,
( c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b)
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
inference(superposition,[],[f3,f10]) ).
fof(f12,plain,
~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(trivial_inequality_removal,[],[f11]) ).
fof(f13,plain,
( ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(resolution,[],[f12,f6]) ).
fof(f14,plain,
( ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(forward_subsumption_resolution,[],[f13,f2]) ).
fof(f15,plain,
~ class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(forward_subsumption_resolution,[],[f14,f1]) ).
fof(f16,plain,
~ class_Ring__and__Field_Oordered__idom(t_b),
inference(resolution,[],[f15,f7]) ).
fof(f17,plain,
$false,
inference(forward_subsumption_resolution,[],[f16,f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:36:52 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.62/1.28 % (708238)Input is clausal, will run a generic CNF schedule.
% 3.62/1.28 % (708245)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3866828560:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.62/1.28 % (708247)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3491281176:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.62/1.28 % (708246)lrs+10_1_sil=8000:sp=occurrence:random_seed=2902069807:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.62/1.28 % (708244)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1606212290:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.62/1.28 % (708243)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1172527220:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.62/1.28 % (708249)dis-21_1_sil=8000:lcm=predicate:random_seed=62048696:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.62/1.28 % (708248)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=596877483:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.62/1.28 % (708248)First to succeed.
% 3.62/1.28 % (708247)Also succeeded, but the first one will report.
% 3.62/1.28 % (708249)Also succeeded, but the first one will report.
% 3.62/1.28 % (708248)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-708238"
% 3.62/1.28 % (708246)Also succeeded, but the first one will report.
% 3.62/1.28 % (708248)Refutation found. Thanks to Tanya!
% 3.62/1.28 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.28 % (708248)------------------------------
% 3.62/1.28 % (708248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.28 % (708248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.28 % (708248)CaDiCaL version: 2.1.3
% 3.62/1.28 % (708248)Termination reason: Refutation
% 3.62/1.28 % (708248)Time elapsed: 0.002 s
% 3.62/1.28 % (708248)Peak memory usage: 88 MB
% 3.62/1.28 % (708248)Instructions burned: 1 (million)
% 3.62/1.28 % (708248)------------------------------
% 3.62/1.28 % (708248)------------------------------
% 3.62/1.28 % (708238)Success in time 0.432 s
% 3.62/1.28 % Vampire exiting
%------------------------------------------------------------------------------