%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA027-2 : 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 : n016.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 09:30:56 AM UTC 2026
% Result : Unsatisfiable 3.52s 1.25s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 49 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 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(f1,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox2/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/sandbox2/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/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_Ocomm__monoid__add(X0)
| c_plus(c_0,X1,X0) = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,plain,
! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| c_lessequals(v_g(v_x),X0,t_b) ),
inference(forward_subsumption_resolution,[],[f20,f19]) ).
fof(f24,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(f25,plain,
c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b),
inference(forward_subsumption_resolution,[],[f24,f17]) ).
fof(f26,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(forward_demodulation,[],[f25,f18]) ).
fof(f29,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[],[f23,f26]) ).
fof(f30,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(f31,plain,
! [X0,X1] :
( c_lessequals(c_0,c_minus(X1,X0,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(forward_subsumption_resolution,[],[f30,f17]) ).
fof(f34,plain,
~ c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[],[f31,f3]) ).
fof(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f34,f29]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n016.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 20:35:49 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 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
% 3.52/1.25 % (3955001)Input is clausal, will run a generic CNF schedule.
% 3.52/1.25 % (3955010)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2222366758:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.52/1.25 % (3955010)Instruction limit reached!
% 3.52/1.25 % (3955010)------------------------------
% 3.52/1.25 % (3955010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.25 % (3955010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.25 % (3955010)CaDiCaL version: 2.1.3
% 3.52/1.25 % (3955010)Termination reason: Instruction limit
% 3.52/1.25 % (3955010)Termination phase: Saturation
% 3.52/1.25 % (3955010)Time elapsed: 0.042 s
% 3.52/1.25 % (3955010)Peak memory usage: 89 MB
% 3.52/1.25 % (3955010)Instructions burned: 116 (million)
% 3.52/1.25 % (3955011)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2285685008:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.52/1.25 % (3955009)lrs+10_1_sil=8000:sp=occurrence:random_seed=1352304884:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.52/1.25 % (3955006)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=3412577409:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.52/1.25 % (3955007)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3153983489:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.52/1.25 % (3955008)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3384849019:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.52/1.25 % (3955009)First to succeed.
% 3.52/1.25 % (3955009)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3955001"
% 3.52/1.25 % (3955011)Also succeeded, but the first one will report.
% 3.52/1.25 % (3955012)dis-21_1_sil=8000:lcm=predicate:random_seed=1601666201: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)
% 3.52/1.25 % (3955012)Instruction limit reached!
% 3.52/1.25 % (3955012)------------------------------
% 3.52/1.25 % (3955012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.25 % (3955012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.25 % (3955012)CaDiCaL version: 2.1.3
% 3.52/1.25 % (3955012)Termination reason: Instruction limit
% 3.52/1.25 % (3955012)Termination phase: Saturation
% 3.52/1.25 % (3955012)Time elapsed: 0.068 s
% 3.52/1.25 % (3955012)Peak memory usage: 88 MB
% 3.52/1.25 % (3955012)Instructions burned: 117 (million)
% 3.52/1.25 % (3955019)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=1730350743:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.52/1.25 % (3955019)Instruction limit reached!
% 3.52/1.25 % (3955019)------------------------------
% 3.52/1.25 % (3955019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.25 % (3955019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.25 % (3955019)CaDiCaL version: 2.1.3
% 3.52/1.25 % (3955019)Termination reason: Instruction limit
% 3.52/1.25 % (3955019)Termination phase: Saturation
% 3.52/1.25 % (3955019)Time elapsed: 0.047 s
% 3.52/1.25 % (3955019)Peak memory usage: 88 MB
% 3.52/1.25 % (3955019)Instructions burned: 145 (million)
% 3.52/1.25 % (3955021)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4256805040: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)
% 3.52/1.25 % (3955021)Also succeeded, but the first one will report.
% 3.52/1.25 % (3955023)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3336589248:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.52/1.25 % (3955023)Refutation not found, incomplete strategy
% 3.52/1.25 % (3955023)------------------------------
% 3.52/1.25 % (3955023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.25 % (3955023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.25 % (3955023)CaDiCaL version: 2.1.3
% 3.52/1.25 % (3955023)Termination reason: Refutation not found, incomplete strategy
% 3.52/1.25 % (3955023)Time elapsed: 0.001 s
% 3.52/1.25 % (3955023)Peak memory usage: 88 MB
% 3.52/1.25 % (3955023)Instructions burned: 1 (million)
% 3.52/1.25 % (3955009)Refutation found. Thanks to Tanya!
% 3.52/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.52/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.25 % (3955009)------------------------------
% 3.52/1.25 % (3955009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.25 % (3955009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.25 % (3955009)CaDiCaL version: 2.1.3
% 3.52/1.25 % (3955009)Termination reason: Refutation
% 3.52/1.25 % (3955009)Time elapsed: 0.002 s
% 3.52/1.25 % (3955009)Peak memory usage: 88 MB
% 3.52/1.25 % (3955009)Instructions burned: 2 (million)
% 3.52/1.25 % (3955009)------------------------------
% 3.52/1.25 % (3955009)------------------------------
% 3.52/1.25 % (3955001)Success in time 0.407 s
% 3.52/1.25 % Vampire exiting
%------------------------------------------------------------------------------