%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA039-1 : 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 : n003.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 09:30:59 AM UTC 2026
% Result : Unsatisfiable 3.77s 1.33s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 38 ( 14 unt; 2 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 32 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1018,axiom,
! [X0] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f1045,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f1052,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f1147,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f1166,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Olordered__ring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f1487,axiom,
! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
fof(f1488,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(f1489,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f1490,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
fof(f1491,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1494,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1495,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f1682,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(t_a),
inference(resolution,[],[f1147,f1495]) ).
fof(f1687,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[],[f1682,f1045]) ).
fof(f1692,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(resolution,[],[f1682,f1052]) ).
fof(f1721,plain,
class_Ring__and__Field_Olordered__ring(t_a),
inference(resolution,[],[f1166,f1495]) ).
fof(f1736,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[],[f1721,f1018]) ).
fof(f2159,plain,
! [X0,X1] :
( ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),X1,t_a)
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_HOL_Oabs(v_h(X0),t_a),X1,t_a) ),
inference(resolution,[],[f1489,f1491]) ).
fof(f2169,plain,
! [X0,X1] :
( ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),X1,t_a)
| c_lessequals(c_HOL_Oabs(v_h(X0),t_a),X1,t_a) ),
inference(forward_subsumption_resolution,[],[f2159,f1687]) ).
fof(f2173,plain,
! [X0,X1] :
( ~ c_lessequals(v_c,X0,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(X1),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| c_lessequals(c_HOL_Oabs(v_h(X1),t_a),c_times(X0,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a) ),
inference(resolution,[],[f1490,f2169]) ).
fof(f2192,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Oabs(v_h(X1),t_a),c_times(X0,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(X1),t_a),t_a)
| ~ c_lessequals(v_c,X0,t_a) ),
inference(forward_subsumption_resolution,[],[f2173,f1692]) ).
fof(f2307,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
inference(resolution,[],[f2192,f1494]) ).
fof(f2313,definition,
( spl0_1
<=> c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f2315,plain,
( ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| spl0_1 ),
inference(avatar_component_clause,[],[f2313]) ).
fof(f2317,definition,
( spl0_2
<=> c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f2319,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| spl0_2 ),
inference(avatar_component_clause,[],[f2317]) ).
fof(f2320,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f2307,f2317,f2313]) ).
fof(f2321,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_1 ),
inference(resolution,[],[f2315,f1487]) ).
fof(f2322,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f2321,f1736]) ).
fof(f2323,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f2322]) ).
fof(f2352,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_2 ),
inference(resolution,[],[f2319,f1488]) ).
fof(f2353,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2352,f1736]) ).
fof(f2354,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2353]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f2320]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f2323]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f2354]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f2355,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA039-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 20:35:42 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 3.77/1.33 % (1955999)Input is clausal, will run a generic CNF schedule.
% 3.77/1.33 % (1956127)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1047367014:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.77/1.33 % (1956128)lrs+10_1_sil=8000:sp=occurrence:random_seed=3082320122:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.77/1.33 % (1956126)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=305501843:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.77/1.33 % (1956129)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1516109630:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.77/1.33 % (1956125)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=1946719456:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.77/1.33 % (1956128)First to succeed.
% 3.77/1.33 % (1956128)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1955999"
% 3.77/1.33 % (1956131)dis-21_1_sil=8000:lcm=predicate:random_seed=908410548: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)
% 3.77/1.33 % (1956129)Also succeeded, but the first one will report.
% 3.77/1.33 % (1956130)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2743460904:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.77/1.33 % (1956131)Instruction limit reached!
% 3.77/1.33 % (1956131)------------------------------
% 3.77/1.33 % (1956131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.33 % (1956131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.33 % (1956131)CaDiCaL version: 2.1.3
% 3.77/1.33 % (1956131)Termination reason: Instruction limit
% 3.77/1.33 % (1956131)Termination phase: Saturation
% 3.77/1.33 % (1956131)Time elapsed: 0.068 s
% 3.77/1.33 % (1956131)Peak memory usage: 90 MB
% 3.77/1.33 % (1956131)Instructions burned: 118 (million)
% 3.77/1.33 % (1956130)Also succeeded, but the first one will report.
% 3.77/1.33 % (1956139)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=2051755397:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.77/1.33 % (1956139)Refutation not found, incomplete strategy
% 3.77/1.33 % (1956139)------------------------------
% 3.77/1.33 % (1956139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.33 % (1956139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.33 % (1956139)CaDiCaL version: 2.1.3
% 3.77/1.33 % (1956139)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.33 % (1956139)Time elapsed: 0.004 s
% 3.77/1.33 % (1956139)Peak memory usage: 89 MB
% 3.77/1.33 % (1956139)Instructions burned: 4 (million)
% 3.77/1.33 % (1956128)Refutation found. Thanks to Tanya!
% 3.77/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.77/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.33 % (1956128)------------------------------
% 3.77/1.33 % (1956128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.33 % (1956128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.33 % (1956128)CaDiCaL version: 2.1.3
% 3.77/1.33 % (1956128)Termination reason: Refutation
% 3.77/1.33 % (1956128)Time elapsed: 0.018 s
% 3.77/1.33 % (1956128)Peak memory usage: 90 MB
% 3.77/1.33 % (1956128)Instructions burned: 25 (million)
% 3.77/1.33 % (1956128)------------------------------
% 3.77/1.33 % (1956128)------------------------------
% 3.77/1.33 % (1955999)Success in time 0.468 s
% 3.77/1.33 % Vampire exiting
%------------------------------------------------------------------------------