%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA009-1 : 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 : n007.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 09:30:51 AM UTC 2026
% Result : Unsatisfiable 0.19s 1.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 35 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1455,axiom,
! [X2,X0,X1] :
( c_lessequals(c_minus(X1,X2,X0),c_0,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f1458,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X1,c_uminus(X2,X0),X0) = c_plus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f1459,plain,
! [X2,X0,X1] :
( c_plus(X1,X2,X0) = c_minus(X1,c_uminus(X2,X0),X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(reorient_equations,[],[f1458]) ).
fof(f1475,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_minus(X1,X2,X0),X0) = c_minus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f1476,plain,
! [X2,X0,X1] :
( c_minus(X2,X1,X0) = c_uminus(c_minus(X1,X2,X0),X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(reorient_equations,[],[f1475]) ).
fof(f1477,axiom,
! [X0,X1] :
( c_uminus(c_uminus(X1,X0),X0) = X1
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f1483,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_uminus(X1,X0),X0)
| ~ c_lessequals(X1,c_0,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f3032,axiom,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f3048,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f3364,negated_conjecture,
! [X0] : c_lessequals(v_lb(X0),v_f(X0),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3366,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3367,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3477,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(unit_resulting_resolution,[],[f3032,f3367]) ).
fof(f3480,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unit_resulting_resolution,[],[f3048,f3367]) ).
fof(f3570,plain,
( ~ c_lessequals(c_0,c_minus(v_f(v_x),c_uminus(c_uminus(v_lb(v_x),t_b),t_b),t_b),t_b)
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(superposition,[],[f3366,f1459]) ).
fof(f3571,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),c_uminus(c_uminus(v_lb(v_x),t_b),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[],[f3570,f3477]) ).
fof(f3868,plain,
! [X0,X1] : c_minus(X0,X1,t_b) = c_uminus(c_minus(X1,X0,t_b),t_b),
inference(unit_resulting_resolution,[],[f1476,f3477]) ).
fof(f3869,plain,
! [X0] : c_uminus(c_uminus(X0,t_b),t_b) = X0,
inference(unit_resulting_resolution,[],[f1477,f3477]) ).
fof(f3929,plain,
~ c_lessequals(c_0,c_uminus(c_minus(c_uminus(c_uminus(v_lb(v_x),t_b),t_b),v_f(v_x),t_b),t_b),t_b),
inference(backward_demodulation,[],[f3571,f3868]) ).
fof(f3942,plain,
~ c_lessequals(c_0,c_uminus(c_minus(v_lb(v_x),v_f(v_x),t_b),t_b),t_b),
inference(forward_demodulation,[],[f3929,f3869]) ).
fof(f4057,plain,
! [X0] : c_lessequals(c_minus(v_lb(X0),v_f(X0),t_b),c_0,t_b),
inference(unit_resulting_resolution,[],[f1455,f3364,f3480]) ).
fof(f4489,plain,
~ c_lessequals(c_minus(v_lb(v_x),v_f(v_x),t_b),c_0,t_b),
inference(unit_resulting_resolution,[],[f1483,f3480,f3942]) ).
fof(f4494,plain,
$false,
inference(forward_subsumption_resolution,[],[f4489,f4057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA009-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:26:21 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 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
% 0.19/1.50 % (2765054)Input is clausal, will run a generic CNF schedule.
% 0.19/1.50 % (2765061)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1844154113:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.50 % (2765064)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4241812201:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.50 % (2765062)lrs+10_1_sil=8000:sp=occurrence:random_seed=1584935775:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.50 % (2765060)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2722998271:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.50 % (2765063)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4094399449:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.50 % (2765059)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=2088057731:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.50 % (2765065)dis-21_1_sil=8000:lcm=predicate:random_seed=2676263804: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)
% 0.19/1.50 % (2765065)Instruction limit reached!
% 0.19/1.50 % (2765065)------------------------------
% 0.19/1.50 % (2765065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765065)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765065)Termination reason: Instruction limit
% 0.19/1.50 % (2765065)Termination phase: Saturation
% 0.19/1.50 % (2765065)Time elapsed: 0.058 s
% 0.19/1.50 % (2765065)Peak memory usage: 90 MB
% 0.19/1.50 % (2765065)Instructions burned: 117 (million)
% 0.19/1.50 % (2765062)Instruction limit reached!
% 0.19/1.50 % (2765062)------------------------------
% 0.19/1.50 % (2765062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765062)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765062)Termination reason: Instruction limit
% 0.19/1.50 % (2765062)Termination phase: Saturation
% 0.19/1.50 % (2765062)Time elapsed: 0.063 s
% 0.19/1.50 % (2765062)Peak memory usage: 90 MB
% 0.19/1.50 % (2765062)Instructions burned: 109 (million)
% 0.19/1.50 % (2765063)Instruction limit reached!
% 0.19/1.50 % (2765063)------------------------------
% 0.19/1.50 % (2765063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765063)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765063)Termination reason: Instruction limit
% 0.19/1.50 % (2765063)Termination phase: Saturation
% 0.19/1.50 % (2765063)Time elapsed: 0.068 s
% 0.19/1.50 % (2765063)Peak memory usage: 91 MB
% 0.19/1.50 % (2765063)Instructions burned: 114 (million)
% 0.19/1.50 % (2765064)Instruction limit reached!
% 0.19/1.50 % (2765064)------------------------------
% 0.19/1.50 % (2765064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765064)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765064)Termination reason: Instruction limit
% 0.19/1.50 % (2765064)Termination phase: Saturation
% 0.19/1.50 % (2765064)Time elapsed: 0.105 s
% 0.19/1.50 % (2765064)Peak memory usage: 91 MB
% 0.19/1.50 % (2765064)Instructions burned: 181 (million)
% 0.19/1.50 % (2765075)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3089544099:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.19/1.50 % (2765073)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2396233630:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.19/1.50 % (2765074)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4071997688:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.19/1.50 % (2765073)Refutation not found, incomplete strategy
% 0.19/1.50 % (2765073)------------------------------
% 0.19/1.50 % (2765073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765073)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765073)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.50 % (2765073)Time elapsed: 0.008 s
% 0.19/1.50 % (2765073)Peak memory usage: 90 MB
% 0.19/1.50 % (2765073)Instructions burned: 10 (million)
% 0.19/1.50 % (2765075)Refutation not found, incomplete strategy
% 0.19/1.50 % (2765075)------------------------------
% 0.19/1.50 % (2765075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765075)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765075)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.50 % (2765075)Time elapsed: 0.041 s
% 0.19/1.50 % (2765075)Peak memory usage: 91 MB
% 0.19/1.50 % (2765075)Instructions burned: 67 (million)
% 0.19/1.50 % (2765076)lrs+10_64_to=lpo:sil=8000:random_seed=2482142667:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 0.19/1.50 % (2765074)First to succeed.
% 0.19/1.50 % (2765074)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2765054"
% 0.19/1.50 % (2765076)Instruction limit reached!
% 0.19/1.50 % (2765076)------------------------------
% 0.19/1.50 % (2765076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765076)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765076)Termination reason: Instruction limit
% 0.19/1.50 % (2765076)Termination phase: Saturation
% 0.19/1.50 % (2765076)Time elapsed: 0.072 s
% 0.19/1.50 % (2765076)Peak memory usage: 92 MB
% 0.19/1.50 % (2765076)Instructions burned: 126 (million)
% 0.19/1.50 % (2765073)------------------------------
% 0.19/1.50 % (2765073)------------------------------
% 0.19/1.50 % (2765081)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=255749369:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 0.19/1.50 % (2765075)------------------------------
% 0.19/1.50 % (2765075)------------------------------
% 0.19/1.50 % (2765074)Refutation found. Thanks to Tanya!
% 0.19/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.50 % (2765074)------------------------------
% 0.19/1.50 % (2765074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2765074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2765074)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2765074)Termination reason: Refutation
% 0.19/1.50 % (2765074)Time elapsed: 0.077 s
% 0.19/1.50 % (2765074)Peak memory usage: 92 MB
% 0.19/1.50 % (2765074)Instructions burned: 131 (million)
% 0.19/1.50 % (2765074)------------------------------
% 0.19/1.50 % (2765074)------------------------------
% 0.19/1.50 % (2765054)Success in time 0.751 s
% 0.19/1.50 % Vampire exiting
%------------------------------------------------------------------------------