%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 3.64s 1.28s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 64 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 30 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,plain,
c_0 = v_f(c_0),
inference(reorient_equations,[],[f1]) ).
fof(f3,negated_conjecture,
c_less(c_0,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5,negated_conjecture,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X0)),t_a),c_times(X0,c_HOL_Oabs(v_h(v_xa(X0)),t_a),t_a),t_a)
| ~ c_less(c_0,X0,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f6,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f7,axiom,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| X0 = c_Suc(c_minus(X0,c_1,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
fof(f8,plain,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| c_Suc(c_minus(X0,c_1,tc_nat)) = X0 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] :
( c_less(c_0,X0,tc_nat)
| X0 = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f10,plain,
! [X0] :
( c_less(c_0,X0,tc_nat)
| c_0 = X0 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(c_0,X0) = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f12,plain,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f14,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(f15,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f16,axiom,
! [X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f17,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_LOrder_Ojoin__semilorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f18,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f19,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f20,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(resolution,[],[f17,f6]) ).
fof(f21,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(resolution,[],[f18,f6]) ).
fof(f22,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[],[f20,f16]) ).
fof(f23,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f19,f6]) ).
fof(f24,plain,
c_0 = c_HOL_Oabs(c_0,t_a),
inference(resolution,[],[f12,f23]) ).
fof(f27,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_x,t_a) ),
inference(resolution,[],[f14,f3]) ).
fof(f37,plain,
c_lessequals(c_0,v_x,t_a),
inference(forward_subsumption_resolution,[],[f27,f22]) ).
fof(f38,plain,
! [X0] :
( c_Suc(c_minus(X0,c_1,tc_nat)) = X0
| c_0 = X0 ),
inference(resolution,[],[f8,f10]) ).
fof(f39,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| c_0 = X0 ),
inference(superposition,[],[f4,f38]) ).
fof(f40,plain,
( c_0 = v_xa(v_x)
| ~ c_less(c_0,v_x,t_a) ),
inference(resolution,[],[f39,f5]) ).
fof(f41,plain,
c_0 = v_xa(v_x),
inference(forward_subsumption_resolution,[],[f40,f3]) ).
fof(f42,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| ~ c_less(c_0,v_x,t_a) ),
inference(superposition,[],[f5,f41]) ).
fof(f43,plain,
~ c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(forward_subsumption_resolution,[],[f42,f3]) ).
fof(f44,plain,
~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(forward_demodulation,[],[f43,f2]) ).
fof(f45,plain,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(forward_demodulation,[],[f44,f24]) ).
fof(f46,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ c_lessequals(c_0,v_x,t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(resolution,[],[f45,f15]) ).
fof(f47,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(forward_subsumption_resolution,[],[f46,f37]) ).
fof(f48,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a),
inference(forward_subsumption_resolution,[],[f47,f21]) ).
fof(f49,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f48,f13]) ).
fof(f50,plain,
$false,
inference(forward_subsumption_resolution,[],[f49,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n011.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 20:29:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/1.28 % (3732957)Input is clausal, will run a generic CNF schedule.
% 3.64/1.28 % (3732966)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1688338076:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.64/1.28 % (3732966)Refutation not found, incomplete strategy
% 3.64/1.28 % (3732966)------------------------------
% 3.64/1.28 % (3732966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.28 % (3732966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.28 % (3732966)CaDiCaL version: 2.1.3
% 3.64/1.28 % (3732966)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.28 % (3732966)Time elapsed: 0.001 s
% 3.64/1.28 % (3732966)Peak memory usage: 88 MB
% 3.64/1.28 % (3732967)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1151928299:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.64/1.28 % (3732962)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=2573478452:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.64/1.28 % (3732965)lrs+10_1_sil=8000:sp=occurrence:random_seed=3263562754:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.64/1.28 % (3732964)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3631557683:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.64/1.28 % (3732963)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4286282789:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.64/1.28 % (3732968)dis-21_1_sil=8000:lcm=predicate:random_seed=3523812767: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)
% 3.64/1.28 % (3732968)Refutation not found, incomplete strategy
% 3.64/1.28 % (3732968)------------------------------
% 3.64/1.28 % (3732968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.28 % (3732968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.28 % (3732968)CaDiCaL version: 2.1.3
% 3.64/1.28 % (3732968)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.28 % (3732968)Time elapsed: 0.001 s
% 3.64/1.28 % (3732968)Peak memory usage: 88 MB
% 3.64/1.28 % (3732968)Instructions burned: 1 (million)
% 3.64/1.28 % (3732965)First to succeed.
% 3.64/1.28 % (3732967)Also succeeded, but the first one will report.
% 3.64/1.28 % (3732965)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3732957"
% 3.64/1.28 % (3732966)------------------------------
% 3.64/1.28 % (3732966)------------------------------
% 3.64/1.28 % (3732968)------------------------------
% 3.64/1.28 % (3732968)------------------------------
% 3.64/1.28 % (3732977)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=2542653542:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.64/1.28 % (3732977)Also succeeded, but the first one will report.
% 3.64/1.28 % (3732965)Refutation found. Thanks to Tanya!
% 3.64/1.28 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.28 % (3732965)------------------------------
% 3.64/1.28 % (3732965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.28 % (3732965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.28 % (3732965)CaDiCaL version: 2.1.3
% 3.64/1.28 % (3732965)Termination reason: Refutation
% 3.64/1.28 % (3732965)Time elapsed: 0.003 s
% 3.64/1.28 % (3732965)Peak memory usage: 88 MB
% 3.64/1.28 % (3732965)Instructions burned: 2 (million)
% 3.64/1.28 % (3732965)------------------------------
% 3.64/1.28 % (3732965)------------------------------
% 3.64/1.28 % (3732957)Success in time 0.43 s
% 3.64/1.28 % Vampire exiting
%------------------------------------------------------------------------------