%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA018-2 : 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 : n004.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 09:30:53 AM UTC 2026
% Result : Unsatisfiable 5.52s 1.69s
% Output : Refutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 51 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2,negated_conjecture,
c_less(c_0,v_ca,t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f5,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
fof(f7,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(f8,axiom,
! [X2,X0,X1] :
( ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
fof(f10,axiom,
! [X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f11,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f12,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_LOrder_Ojoin__semilorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f13,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f14,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolution,[],[f11,f5]) ).
fof(f15,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[],[f12,f5]) ).
fof(f16,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolution,[],[f13,f5]) ).
fof(f17,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[],[f15,f10]) ).
fof(f18,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_ca,t_b) ),
inference(resolution,[],[f8,f2]) ).
fof(f19,plain,
c_lessequals(c_0,v_ca,t_b),
inference(forward_subsumption_resolution,[],[f18,f17]) ).
fof(f21,plain,
! [X0,X1] :
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),X1,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_HOL_Oabs(v_x(X0),t_b),X1,t_b) ),
inference(resolution,[],[f7,f3]) ).
fof(f22,plain,
! [X0,X1] :
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),X1,t_b)
| c_lessequals(c_HOL_Oabs(v_x(X0),t_b),X1,t_b) ),
inference(forward_subsumption_resolution,[],[f21,f17]) ).
fof(f24,plain,
! [X2,X0,X1] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(resolution,[],[f6,f14]) ).
fof(f28,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,X1,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(X0),t_b),X1,t_b)
| ~ c_lessequals(c_0,v_ca,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(resolution,[],[f22,f9]) ).
fof(f29,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,X1,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(X0),t_b),X1,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(forward_subsumption_resolution,[],[f28,f19]) ).
fof(f30,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,X1,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(X0),t_b),X1,t_b) ),
inference(forward_subsumption_resolution,[],[f29,f16]) ).
fof(f32,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(superposition,[],[f4,f24]) ).
fof(f57,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_xa),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(resolution,[],[f30,f32]) ).
fof(f60,plain,
$false,
inference(forward_subsumption_resolution,[],[f57,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 % Computer : n004.cluster.edu
% 0.24/0.28 % Model : x86_64 x86_64
% 0.24/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.28 % Memory : 8046.5625MB
% 0.24/0.28 % OS : Linux 6.8.0-71-generic
% 0.24/0.28 % CPULimit : 300
% 0.24/0.28 % WCLimit : 300
% 0.24/0.28 % DateTime : Mon Sep 28 20:28:52 UTC 2026
% 0.24/0.28 % CPUTime :
% 0.24/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.33 Running first-order theorem proving
% 0.24/0.33 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
% 5.52/1.69 % (723516)Input is clausal, will run a generic CNF schedule.
% 5.52/1.69 % (723527)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2444952220:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.52/1.69 % (723530)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2360476126:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.52/1.69 % (723531)dis-21_1_sil=8000:lcm=predicate:random_seed=68433712: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)
% 5.52/1.69 % (723525)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=239246659:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.52/1.69 % (723528)lrs+10_1_sil=8000:sp=occurrence:random_seed=3041698048:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.52/1.69 % (723526)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4221260287:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.52/1.69 % (723529)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=762145000:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.52/1.69 % (723528)First to succeed.
% 5.52/1.69 % (723528)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-723516"
% 5.52/1.69 % (723530)Also succeeded, but the first one will report.
% 5.52/1.69 % (723529)Instruction limit reached!
% 5.52/1.69 % (723529)------------------------------
% 5.52/1.69 % (723529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.69 % (723529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.69 % (723529)CaDiCaL version: 2.1.3
% 5.52/1.69 % (723529)Termination reason: Instruction limit
% 5.52/1.69 % (723529)Termination phase: Saturation
% 5.52/1.69 % (723529)Time elapsed: 0.107 s
% 5.52/1.69 % (723529)Peak memory usage: 88 MB
% 5.52/1.69 % (723529)Instructions burned: 114 (million)
% 5.52/1.69 % (723531)Instruction limit reached!
% 5.52/1.69 % (723531)------------------------------
% 5.52/1.69 % (723531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.69 % (723531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.69 % (723531)CaDiCaL version: 2.1.3
% 5.52/1.69 % (723531)Termination reason: Instruction limit
% 5.52/1.69 % (723531)Termination phase: Saturation
% 5.52/1.69 % (723531)Time elapsed: 0.111 s
% 5.52/1.69 % (723531)Peak memory usage: 88 MB
% 5.52/1.69 % (723531)Instructions burned: 117 (million)
% 5.52/1.69 % (723527)Also succeeded, but the first one will report.
% 5.52/1.69 % (723540)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2641337087:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 5.52/1.69 % (723539)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=3728119302:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 5.52/1.69 % (723539)Also succeeded, but the first one will report.
% 5.52/1.69 % (723540)Also succeeded, but the first one will report.
% 5.52/1.69 % (723528)Refutation found. Thanks to Tanya!
% 5.52/1.69 % SZS status Unsatisfiable for theBenchmark
% 5.52/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 5.52/1.69 % (723528)------------------------------
% 5.52/1.69 % (723528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.69 % (723528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.69 % (723528)CaDiCaL version: 2.1.3
% 5.52/1.69 % (723528)Termination reason: Refutation
% 5.52/1.69 % (723528)Time elapsed: 0.005 s
% 5.52/1.69 % (723528)Peak memory usage: 88 MB
% 5.52/1.69 % (723528)Instructions burned: 3 (million)
% 5.52/1.69 % (723528)------------------------------
% 5.52/1.69 % (723528)------------------------------
% 5.52/1.69 % (723516)Success in time 0.676 s
% 5.52/1.69 % Vampire exiting
%------------------------------------------------------------------------------