%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA012-1 : 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 : 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 09:30:51 AM UTC 2026
% Result : Unsatisfiable 5.58s 1.63s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 13 unt; 3 def)
% Number of atoms : 94 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 94 ( 47 ~; 44 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1425,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f1428,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(c_HOL_Oabs(X1,X0),c_0,X0)
| X1 = c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f1429,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oabs(X1,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X1 ),
inference(reorient_equations,[],[f1428]) ).
fof(f1759,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = c_0
| c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f1760,plain,
! [X0,X1] :
( c_1 = c_times(c_HOL_Oinverse(X1,X0),X1,X0)
| c_0 = X1
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f1759]) ).
fof(f2262,axiom,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f2456,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f2937,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f2979,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f2985,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_LOrder_Ojoin__semilorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_52) ).
fof(f3365,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3366,plain,
c_0 != v_c,
inference(reorient_equations,[],[f3365]) ).
fof(f3367,negated_conjecture,
! [X0] : ~ c_lessequals(c_1,c_times(X0,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3368,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3370,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[],[f3368,f2937]) ).
fof(f3399,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(resolution,[],[f3368,f2985]) ).
fof(f3446,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| c_0 = c_HOL_Oabs(v_c,t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(superposition,[],[f3367,f1760]) ).
fof(f3456,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| c_0 = c_HOL_Oabs(v_c,t_a) ),
inference(forward_subsumption_resolution,[],[f3446,f3370]) ).
fof(f3464,definition,
( spl0_3
<=> class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f3465,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f3464]) ).
fof(f3466,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| spl0_3 ),
inference(avatar_component_clause,[],[f3464]) ).
fof(f3484,definition,
( spl0_8
<=> c_0 = c_HOL_Oabs(v_c,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f3486,plain,
( c_0 = c_HOL_Oabs(v_c,t_a)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f3484]) ).
fof(f3488,definition,
( spl0_9
<=> c_lessequals(c_1,c_1,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f3490,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| spl0_9 ),
inference(avatar_component_clause,[],[f3488]) ).
fof(f3491,plain,
( spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f3456,f3488,f3484]) ).
fof(f3710,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| spl0_3 ),
inference(resolution,[],[f3466,f2979]) ).
fof(f3715,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f3710,f3368]) ).
fof(f3716,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f3715]) ).
fof(f3738,plain,
( ~ class_Orderings_Oorder(t_a)
| spl0_9 ),
inference(resolution,[],[f3490,f2262]) ).
fof(f3741,plain,
( ~ class_LOrder_Ojoin__semilorder(t_a)
| spl0_9 ),
inference(resolution,[],[f3738,f2456]) ).
fof(f3766,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f3741,f3399]) ).
fof(f3767,plain,
spl0_9,
inference(avatar_contradiction_clause,[],[f3766]) ).
fof(f3776,plain,
( c_lessequals(c_0,c_0,t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_8 ),
inference(superposition,[],[f1425,f3486]) ).
fof(f3778,plain,
( ~ c_lessequals(c_0,c_0,t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_0 = v_c
| ~ spl0_8 ),
inference(superposition,[],[f1429,f3486]) ).
fof(f3795,plain,
( ~ c_lessequals(c_0,c_0,t_a)
| c_0 = v_c
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f3778,f3465]) ).
fof(f3796,plain,
( c_lessequals(c_0,c_0,t_a)
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f3776,f3465]) ).
fof(f3820,plain,
( ~ c_lessequals(c_0,c_0,t_a)
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f3795,f3366]) ).
fof(f3831,plain,
( $false
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f3820,f3796]) ).
fof(f3832,plain,
( ~ spl0_3
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f3831]) ).
cnf(s4,plain,
( spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f3491]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f3716]) ).
cnf(s14,plain,
spl0_9,
inference(sat_conversion,[],[f3767]) ).
cnf(s22,plain,
( ~ spl0_3
| ~ spl0_8 ),
inference(sat_conversion,[],[f3832]) ).
cnf(s23,plain,
~ spl0_8,
inference(rat,[],[s22,s6]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s4,s14,s23]) ).
fof(f3833,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA012-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:28:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.43/1.44 % (3731221)Input is clausal, will run a generic CNF schedule.
% 4.43/1.44 % (3731226)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=3692780246:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.43/1.44 % (3731227)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=330176817:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.43/1.44 % (3731228)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3358150360:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.43/1.44 % (3731231)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4133331309:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.43/1.44 % (3731230)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4211931991:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.43/1.44 % (3731229)lrs+10_1_sil=8000:sp=occurrence:random_seed=2598571061:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.43/1.44 % (3731232)dis-21_1_sil=8000:lcm=predicate:random_seed=3719538886: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)
% 4.43/1.44 % (3731230)Instruction limit reached!
% 4.43/1.44 % (3731230)------------------------------
% 4.43/1.44 % (3731230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.44 % (3731230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.44 % (3731230)CaDiCaL version: 2.1.3
% 4.43/1.44 % (3731230)Termination reason: Instruction limit
% 4.43/1.44 % (3731230)Termination phase: Saturation
% 4.43/1.44 % (3731230)Time elapsed: 0.067 s
% 4.43/1.44 % (3731230)Peak memory usage: 90 MB
% 4.43/1.44 % (3731230)Instructions burned: 114 (million)
% 4.43/1.44 % (3731229)Instruction limit reached!
% 4.43/1.44 % (3731229)------------------------------
% 4.43/1.44 % (3731229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.44 % (3731229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.44 % (3731229)CaDiCaL version: 2.1.3
% 4.43/1.44 % (3731229)Termination reason: Instruction limit
% 4.43/1.44 % (3731229)Termination phase: Saturation
% 4.43/1.44 % (3731229)Time elapsed: 0.074 s
% 4.43/1.44 % (3731229)Peak memory usage: 91 MB
% 4.43/1.44 % (3731229)Instructions burned: 108 (million)
% 4.43/1.44 % (3731232)Instruction limit reached!
% 4.43/1.44 % (3731232)------------------------------
% 4.43/1.44 % (3731232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.44 % (3731232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.44 % (3731232)CaDiCaL version: 2.1.3
% 4.43/1.44 % (3731232)Termination reason: Instruction limit
% 4.43/1.44 % (3731232)Termination phase: Saturation
% 4.43/1.44 % (3731232)Time elapsed: 0.058 s
% 4.43/1.44 % (3731232)Peak memory usage: 90 MB
% 4.43/1.44 % (3731232)Instructions burned: 117 (million)
% 4.43/1.44 % (3731231)Instruction limit reached!
% 4.43/1.44 % (3731231)------------------------------
% 4.43/1.44 % (3731231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.44 % (3731231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.44 % (3731231)CaDiCaL version: 2.1.3
% 4.43/1.44 % (3731231)Termination reason: Instruction limit
% 4.43/1.44 % (3731231)Termination phase: Saturation
% 4.43/1.44 % (3731231)Time elapsed: 0.113 s
% 4.43/1.44 % (3731231)Peak memory usage: 91 MB
% 4.43/1.44 % (3731231)Instructions burned: 180 (million)
% 4.43/1.44 % (3731242)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1833234546:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 4.43/1.44 % (3731241)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=758664355: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)
% 4.43/1.44 % (3731240)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=2939532267:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 4.43/1.44 % (3731240)Refutation not found, incomplete strategy
% 4.43/1.44 % (3731240)------------------------------
% 4.43/1.44 % (3731240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.58/1.63 % (3731240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.63 % (3731240)CaDiCaL version: 2.1.3
% 5.58/1.63 % (3731240)Termination reason: Refutation not found, incomplete strategy
% 5.58/1.63 % (3731240)Time elapsed: 0.013 s
% 5.58/1.63 % (3731240)Peak memory usage: 90 MB
% 5.58/1.63 % (3731240)Instructions burned: 17 (million)
% 5.58/1.63 % (3731242)First to succeed.
% 5.58/1.63 % (3731242)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3731221"
% 5.58/1.63 % (3731243)lrs+10_64_to=lpo:sil=8000:random_seed=1868582728:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.58/1.63 % (3731241)Instruction limit reached!
% 5.58/1.63 % (3731241)------------------------------
% 5.58/1.63 % (3731241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.58/1.63 % (3731241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.63 % (3731241)CaDiCaL version: 2.1.3
% 5.58/1.63 % (3731241)Termination reason: Instruction limit
% 5.58/1.63 % (3731241)Termination phase: Saturation
% 5.58/1.63 % (3731241)Time elapsed: 0.108 s
% 5.58/1.63 % (3731241)Peak memory usage: 93 MB
% 5.58/1.63 % (3731241)Instructions burned: 191 (million)
% 5.58/1.63 % (3731243)Instruction limit reached!
% 5.58/1.63 % (3731243)------------------------------
% 5.58/1.63 % (3731243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.58/1.63 % (3731243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.63 % (3731243)CaDiCaL version: 2.1.3
% 5.58/1.63 % (3731243)Termination reason: Instruction limit
% 5.58/1.63 % (3731243)Termination phase: Saturation
% 5.58/1.63 % (3731243)Time elapsed: 0.071 s
% 5.58/1.63 % (3731243)Peak memory usage: 92 MB
% 5.58/1.63 % (3731243)Instructions burned: 127 (million)
% 5.58/1.63 % (3731240)------------------------------
% 5.58/1.63 % (3731240)------------------------------
% 5.58/1.63 % (3731248)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1335328643:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.58/1.63 % (3731242)Refutation found. Thanks to Tanya!
% 5.58/1.63 % SZS status Unsatisfiable for theBenchmark
% 5.58/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 5.58/1.63 % (3731242)------------------------------
% 5.58/1.63 % (3731242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.58/1.63 % (3731242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.63 % (3731242)CaDiCaL version: 2.1.3
% 5.58/1.63 % (3731242)Termination reason: Refutation
% 5.58/1.63 % (3731242)Time elapsed: 0.042 s
% 5.58/1.63 % (3731242)Peak memory usage: 92 MB
% 5.58/1.63 % (3731242)Instructions burned: 69 (million)
% 5.58/1.63 % (3731242)------------------------------
% 5.58/1.63 % (3731242)------------------------------
% 5.58/1.63 % (3731221)Success in time 0.764 s
% 5.58/1.63 % Vampire exiting
%------------------------------------------------------------------------------