%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA028-1 : 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 : n012.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 5.95s 1.55s
% Output : Refutation 5.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 13 unt; 2 def)
% Number of atoms : 67 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 37 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1439,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_plus(X3,X1,X0),c_plus(X3,X2,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f1495,axiom,
! [X2,X0,X1] :
( c_lessequals(c_uminus(X2,X0),c_uminus(X1,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f3029,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f3032,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f3048,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f3385,axiom,
! [X2,X0,X1] :
( c_minus(X1,X2,X0) = c_plus(X1,c_uminus(X2,X0),X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
fof(f3391,negated_conjecture,
! [X0] : c_lessequals(v_g(X0),v_k(X0),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3393,negated_conjecture,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3394,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3421,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[],[f3394,f3032]) ).
fof(f3474,plain,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b)
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(superposition,[],[f3393,f3385]) ).
fof(f3475,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[],[f3474,f3421]) ).
fof(f3481,definition,
( spl0_1
<=> class_OrderedGroup_Opordered__ab__group__add(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f3482,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f3481]) ).
fof(f3483,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f3481]) ).
fof(f3628,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_1 ),
inference(resolution,[],[f3483,f3048]) ).
fof(f3629,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f3628,f3394]) ).
fof(f3630,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f3629]) ).
fof(f3707,plain,
( ~ c_lessequals(c_plus(v_f(v_x),c_uminus(v_k(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b)
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(superposition,[],[f3475,f3385]) ).
fof(f3710,plain,
~ c_lessequals(c_plus(v_f(v_x),c_uminus(v_k(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[],[f3707,f3421]) ).
fof(f3953,definition,
( spl0_17
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f3954,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f3953]) ).
fof(f3955,plain,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| spl0_17 ),
inference(avatar_component_clause,[],[f3953]) ).
fof(f3961,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_17 ),
inference(resolution,[],[f3955,f3029]) ).
fof(f3968,plain,
( $false
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f3961,f3394]) ).
fof(f3969,plain,
spl0_17,
inference(avatar_contradiction_clause,[],[f3968]) ).
fof(f4005,plain,
( ~ c_lessequals(c_uminus(v_k(v_x),t_b),c_uminus(v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(resolution,[],[f3710,f1439]) ).
fof(f4013,plain,
( ~ c_lessequals(c_uminus(v_k(v_x),t_b),c_uminus(v_g(v_x),t_b),t_b)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f4005,f3954]) ).
fof(f4014,plain,
( ~ c_lessequals(v_g(v_x),v_k(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ spl0_17 ),
inference(resolution,[],[f4013,f1495]) ).
fof(f4021,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f4014,f3391]) ).
fof(f4022,plain,
( $false
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f4021,f3482]) ).
fof(f4023,plain,
( ~ spl0_1
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f4022]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f3630]) ).
cnf(s16,plain,
spl0_17,
inference(sat_conversion,[],[f3969]) ).
cnf(s18,plain,
( ~ spl0_1
| ~ spl0_17 ),
inference(sat_conversion,[],[f4023]) ).
cnf(s19,plain,
~ spl0_1,
inference(rat,[],[s18,s16]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s4,s19]) ).
fof(f4024,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA028-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.14 % Computer : n012.cluster.edu
% 0.09/0.14 % Model : x86_64 x86_64
% 0.09/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.14 % Memory : 8046.5625MB
% 0.09/0.14 % OS : Linux 6.8.0-71-generic
% 0.09/0.14 % CPULimit : 300
% 0.09/0.14 % WCLimit : 300
% 0.09/0.14 % DateTime : Mon Sep 28 20:30:34 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 Running first-order theorem proving
% 0.09/0.17 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
% 3.37/1.40 % (3708855)Input is clausal, will run a generic CNF schedule.
% 3.37/1.40 % (3708863)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=2812577654:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.37/1.40 % (3708869)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2030096478:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.37/1.40 % (3708865)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1239782082:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.37/1.40 % (3708868)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1582208527:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.37/1.40 % (3708866)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3555575076:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.37/1.40 % (3708867)lrs+10_1_sil=8000:sp=occurrence:random_seed=3799842449:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.37/1.40 % (3708870)dis-21_1_sil=8000:lcm=predicate:random_seed=3507705565: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)
% 3.37/1.40 % (3708870)Instruction limit reached!
% 3.37/1.40 % (3708870)------------------------------
% 3.37/1.40 % (3708870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.40 % (3708870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.40 % (3708870)CaDiCaL version: 2.1.3
% 3.37/1.40 % (3708870)Termination reason: Instruction limit
% 3.37/1.40 % (3708870)Termination phase: Saturation
% 3.37/1.40 % (3708870)Time elapsed: 0.055 s
% 3.37/1.40 % (3708870)Peak memory usage: 90 MB
% 3.37/1.40 % (3708870)Instructions burned: 117 (million)
% 3.37/1.40 % (3708868)Instruction limit reached!
% 3.37/1.40 % (3708868)------------------------------
% 3.37/1.40 % (3708868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.40 % (3708868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.40 % (3708868)CaDiCaL version: 2.1.3
% 3.37/1.40 % (3708868)Termination reason: Instruction limit
% 3.37/1.40 % (3708868)Termination phase: Saturation
% 3.37/1.40 % (3708868)Time elapsed: 0.059 s
% 3.37/1.40 % (3708868)Peak memory usage: 90 MB
% 3.37/1.40 % (3708868)Instructions burned: 115 (million)
% 3.37/1.40 % (3708867)Instruction limit reached!
% 3.37/1.40 % (3708867)------------------------------
% 3.37/1.40 % (3708867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.40 % (3708867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.40 % (3708867)CaDiCaL version: 2.1.3
% 3.37/1.40 % (3708867)Termination reason: Instruction limit
% 3.37/1.40 % (3708867)Termination phase: Saturation
% 3.37/1.40 % (3708867)Time elapsed: 0.062 s
% 3.37/1.40 % (3708867)Peak memory usage: 90 MB
% 3.37/1.40 % (3708867)Instructions burned: 110 (million)
% 3.37/1.40 % (3708869)Instruction limit reached!
% 3.37/1.40 % (3708869)------------------------------
% 3.37/1.40 % (3708869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.40 % (3708869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.40 % (3708869)CaDiCaL version: 2.1.3
% 3.37/1.40 % (3708869)Termination reason: Instruction limit
% 3.37/1.40 % (3708869)Termination phase: Saturation
% 3.37/1.40 % (3708869)Time elapsed: 0.096 s
% 3.37/1.40 % (3708869)Peak memory usage: 91 MB
% 3.37/1.40 % (3708869)Instructions burned: 182 (million)
% 3.37/1.40 % (3708879)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2323766014: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)
% 3.37/1.40 % (3708880)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=622988781:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 3.37/1.40 % (3708878)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=3288495211:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 3.37/1.40 % (3708878)Refutation not found, incomplete strategy
% 3.37/1.40 % (3708878)------------------------------
% 3.37/1.40 % (3708878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.55 % (3708878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.55 % (3708878)CaDiCaL version: 2.1.3
% 5.95/1.55 % (3708878)Termination reason: Refutation not found, incomplete strategy
% 5.95/1.55 % (3708878)Time elapsed: 0.008 s
% 5.95/1.55 % (3708878)Peak memory usage: 89 MB
% 5.95/1.55 % (3708878)Instructions burned: 12 (million)
% 5.95/1.55 % (3708881)lrs+10_64_to=lpo:sil=8000:random_seed=714880886:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.95/1.55 % (3708880)First to succeed.
% 5.95/1.55 % (3708880)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3708855"
% 5.95/1.55 % (3708879)Instruction limit reached!
% 5.95/1.55 % (3708879)------------------------------
% 5.95/1.55 % (3708879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.55 % (3708879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.55 % (3708879)CaDiCaL version: 2.1.3
% 5.95/1.55 % (3708879)Termination reason: Instruction limit
% 5.95/1.55 % (3708879)Termination phase: Saturation
% 5.95/1.55 % (3708879)Time elapsed: 0.094 s
% 5.95/1.55 % (3708879)Peak memory usage: 92 MB
% 5.95/1.55 % (3708879)Instructions burned: 189 (million)
% 5.95/1.55 % (3708881)Instruction limit reached!
% 5.95/1.55 % (3708881)------------------------------
% 5.95/1.55 % (3708881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.55 % (3708881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.55 % (3708881)CaDiCaL version: 2.1.3
% 5.95/1.55 % (3708881)Termination reason: Instruction limit
% 5.95/1.55 % (3708881)Termination phase: Saturation
% 5.95/1.55 % (3708881)Time elapsed: 0.068 s
% 5.95/1.55 % (3708881)Peak memory usage: 91 MB
% 5.95/1.55 % (3708881)Instructions burned: 126 (million)
% 5.95/1.55 % (3708878)------------------------------
% 5.95/1.55 % (3708878)------------------------------
% 5.95/1.55 % (3708887)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2635694674:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 5.95/1.55 % (3708886)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1691902605:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 5.95/1.55 % (3708880)Refutation found. Thanks to Tanya!
% 5.95/1.55 % SZS status Unsatisfiable for theBenchmark
% 5.95/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.95/1.55 % (3708880)------------------------------
% 5.95/1.55 % (3708880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.55 % (3708880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.55 % (3708880)CaDiCaL version: 2.1.3
% 5.95/1.55 % (3708880)Termination reason: Refutation
% 5.95/1.55 % (3708880)Time elapsed: 0.048 s
% 5.95/1.55 % (3708880)Peak memory usage: 92 MB
% 5.95/1.55 % (3708880)Instructions burned: 82 (million)
% 5.95/1.55 % (3708880)------------------------------
% 5.95/1.55 % (3708880)------------------------------
% 5.95/1.55 % (3708855)Success in time 0.841 s
% 5.95/1.55 % Vampire exiting
%------------------------------------------------------------------------------