%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA029-2 : 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 : n014.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 09:31:21 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 85 ( 42 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 57 ( 57 !; 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_2) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,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(f7,axiom,
! [X2,X0,X1] :
( c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f9,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(f10,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(f11,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f12,axiom,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f13,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f14,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f15,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_HOL_Oabs(X0,X1),X1) ),
inference(resolution,[],[f4,f13]) ).
fof(f16,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[],[f15,f3]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0) ),
inference(resolution,[],[f10,f7]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X1,X2)
| c_lessequals(X1,X0,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(resolution,[],[f17,f11]) ).
fof(f20,plain,
! [X2,X0,X1] :
( c_lessequals(X0,X1,X2)
| c_lessequals(X1,X0,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(resolution,[],[f18,f12]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X1,X0,X2)
| c_lessequals(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f20,f14]) ).
fof(f23,plain,
! [X0,X1] :
( c_lessequals(X0,X1,t_b)
| c_lessequals(X1,X0,t_b) ),
inference(resolution,[],[f21,f3]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X3,X0,X2)
| c_lessequals(X3,X1,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[],[f9,f11]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(X3,X1,X2)
| c_lessequals(c_Orderings_Omax(X3,X0,X2),X1,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[],[f8,f12]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X1,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[],[f24,f14]) ).
fof(f36,plain,
! [X2,X0,X1] :
( c_lessequals(c_Orderings_Omax(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,X1,t_b)
| ~ c_lessequals(X2,X1,t_b) ),
inference(resolution,[],[f28,f3]) ).
fof(f37,plain,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(resolution,[],[f36,f2]) ).
fof(f38,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[],[f37,f16]) ).
fof(f39,plain,
! [X2,X0,X1] :
( c_lessequals(X0,X1,t_b)
| ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X0,X2,t_b) ),
inference(resolution,[],[f34,f3]) ).
fof(f50,plain,
! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(X1,c_0,t_b) ),
inference(resolution,[],[f39,f16]) ).
fof(f64,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(resolution,[],[f50,f38]) ).
fof(f69,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(resolution,[],[f64,f23]) ).
fof(f70,plain,
$false,
inference(forward_subsumption_resolution,[],[f69,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA029-2 : 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 : n014.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 20:32:00 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 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
% 0.20/0.28 % (2131739)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (2131745)% WARNING: option uhcvi not known.
% 0.20/0.28 % (2131746)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1943861417:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (2131744)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4271883286_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (2131745)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=110504145:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (2131747)dis+10_1_sil=32000:sp=arity:random_seed=2669026076:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (2131748)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2655678561:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % TRYING [1]
% 0.20/0.28 % TRYING [2]
% 0.20/0.28 % TRYING [3]
% 0.20/0.28 % (2131748) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2131739-2131748"...
% 0.20/0.28 % TRYING [4]
% 0.20/0.28 % (2131747) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2131739-2131747"...
% 0.20/0.28 % (2131750)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1136011912:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (2131745) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2131739-2131745"...
% 0.20/0.28 % (2131748)...printing done.
% 0.20/0.28 % (2131749)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=940504873:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (2131747)...printing done.
% 0.20/0.28 % (2131748)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2131748)------------------------------
% 0.20/0.28 % (2131748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2131748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2131748)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2131748)Termination reason: Refutation
% 0.20/0.28 % (2131748)Time elapsed: 0.003 s
% 0.20/0.28 % (2131748)Peak memory usage: 11 MB
% 0.20/0.28 % (2131748)Instructions burned: 4 (million)
% 0.20/0.28 % (2131739)Success in time 0.048 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------