%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA037-1 : 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 : n010.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 09:30:58 AM UTC 2026
% Result : Unsatisfiable 0.35s 2.40s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 42 ( 14 unt; 4 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 95 ( 51 ~; 40 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2655,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f3025,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f3035,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f3365,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,c_Orderings_Omax(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI1_0) ).
fof(f3367,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f3369,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
fof(f3376,negated_conjecture,
c_lessequals(c_0,v_f(v_xa),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3378,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(v_c,v_f(v_xa),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3382,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(c_Orderings_Omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
fof(f3383,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3409,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[],[f3383,f3025]) ).
fof(f3490,plain,
! [X0] :
( ~ c_lessequals(X0,c_times(c_Orderings_Omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),X0,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[],[f3382,f3367]) ).
fof(f3494,definition,
( spl0_6
<=> class_Orderings_Oorder(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f3496,plain,
( ~ class_Orderings_Oorder(t_b)
| spl0_6 ),
inference(avatar_component_clause,[],[f3494]) ).
fof(f3498,definition,
( spl0_7
<=> ! [X0] :
( ~ c_lessequals(X0,c_times(c_Orderings_Omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),X0,t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f3499,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_times(c_Orderings_Omax(v_c,v_ca,t_b),v_f(v_xa),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),X0,t_b) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f3498]) ).
fof(f3500,plain,
( ~ spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f3490,f3498,f3494]) ).
fof(f3693,plain,
( ~ class_Orderings_Olinorder(t_b)
| spl0_6 ),
inference(resolution,[],[f3496,f2655]) ).
fof(f3699,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f3693,f3409]) ).
fof(f3700,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f3699]) ).
fof(f3769,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(X0,v_f(v_xa),t_b),t_b)
| ~ c_lessequals(X0,c_Orderings_Omax(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_0,v_f(v_xa),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
| ~ spl0_7 ),
inference(resolution,[],[f3499,f3369]) ).
fof(f3772,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(X0,v_f(v_xa),t_b),t_b)
| ~ c_lessequals(X0,c_Orderings_Omax(v_c,v_ca,t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f3769,f3376]) ).
fof(f3777,definition,
( spl0_22
<=> class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f3779,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| spl0_22 ),
inference(avatar_component_clause,[],[f3777]) ).
fof(f3781,definition,
( spl0_23
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(X0,v_f(v_xa),t_b),t_b)
| ~ c_lessequals(X0,c_Orderings_Omax(v_c,v_ca,t_b),t_b) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f3782,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(X0,v_f(v_xa),t_b),t_b)
| ~ c_lessequals(X0,c_Orderings_Omax(v_c,v_ca,t_b),t_b) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f3781]) ).
fof(f3783,plain,
( ~ spl0_22
| spl0_23
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f3772,f3498,f3781,f3777]) ).
fof(f3794,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_22 ),
inference(resolution,[],[f3779,f3035]) ).
fof(f3797,plain,
( $false
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f3794,f3383]) ).
fof(f3798,plain,
spl0_22,
inference(avatar_contradiction_clause,[],[f3797]) ).
fof(f3970,plain,
( ~ c_lessequals(v_c,c_Orderings_Omax(v_c,v_ca,t_b),t_b)
| ~ spl0_23 ),
inference(resolution,[],[f3782,f3378]) ).
fof(f4143,plain,
( ~ class_Orderings_Olinorder(t_b)
| ~ spl0_23 ),
inference(resolution,[],[f3970,f3365]) ).
fof(f4146,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f4143,f3409]) ).
fof(f4147,plain,
~ spl0_23,
inference(avatar_contradiction_clause,[],[f4146]) ).
cnf(s3,plain,
( ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f3500]) ).
cnf(s12,plain,
spl0_6,
inference(sat_conversion,[],[f3700]) ).
cnf(s19,plain,
( ~ spl0_7
| ~ spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f3783]) ).
cnf(s21,plain,
spl0_22,
inference(sat_conversion,[],[f3798]) ).
cnf(s36,plain,
~ spl0_23,
inference(sat_conversion,[],[f4147]) ).
cnf(s39,plain,
~ spl0_7,
inference(rat,[],[s19,s36,s21]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s3,s39,s12]) ).
fof(f4148,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA037-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.29 % Computer : n010.cluster.edu
% 0.13/0.29 % Model : x86_64 x86_64
% 0.13/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.29 % Memory : 8046.5625MB
% 0.13/0.29 % OS : Linux 6.8.0-71-generic
% 0.13/0.29 % CPULimit : 300
% 0.13/0.29 % WCLimit : 300
% 0.13/0.29 % DateTime : Mon Sep 28 20:33:47 UTC 2026
% 0.13/0.29 % CPUTime :
% 0.13/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.31/0.35 Running first-order theorem proving
% 0.31/0.35 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
% 7.14/2.05 % (2278005)Input is clausal, will run a generic CNF schedule.
% 7.14/2.05 % (2278010)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=2799919690:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.14/2.05 % (2278011)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3921731984:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.14/2.05 % (2278012)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1881724117:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.14/2.05 % (2278015)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2857122417:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.14/2.05 % (2278013)lrs+10_1_sil=8000:sp=occurrence:random_seed=2797318767:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.14/2.05 % (2278014)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3363839193:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.14/2.05 % (2278016)dis-21_1_sil=8000:lcm=predicate:random_seed=1034731456: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)
% 7.14/2.05 % (2278016)Instruction limit reached!
% 7.14/2.05 % (2278016)------------------------------
% 7.14/2.05 % (2278016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.14/2.05 % (2278016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/2.05 % (2278016)CaDiCaL version: 2.1.3
% 7.14/2.05 % (2278016)Termination reason: Instruction limit
% 7.14/2.05 % (2278016)Termination phase: Saturation
% 7.14/2.05 % (2278016)Time elapsed: 0.100 s
% 7.14/2.05 % (2278016)Peak memory usage: 90 MB
% 7.14/2.05 % (2278016)Instructions burned: 117 (million)
% 7.14/2.05 % (2278014)Instruction limit reached!
% 7.14/2.05 % (2278014)------------------------------
% 7.14/2.05 % (2278014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.14/2.05 % (2278014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/2.05 % (2278014)CaDiCaL version: 2.1.3
% 7.14/2.05 % (2278014)Termination reason: Instruction limit
% 7.14/2.05 % (2278014)Termination phase: Saturation
% 7.14/2.05 % (2278014)Time elapsed: 0.116 s
% 7.14/2.05 % (2278014)Peak memory usage: 90 MB
% 7.14/2.05 % (2278014)Instructions burned: 114 (million)
% 7.14/2.05 % (2278013)Instruction limit reached!
% 7.14/2.05 % (2278013)------------------------------
% 7.14/2.05 % (2278013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.14/2.05 % (2278013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/2.05 % (2278013)CaDiCaL version: 2.1.3
% 7.14/2.05 % (2278013)Termination reason: Instruction limit
% 7.14/2.05 % (2278013)Termination phase: Saturation
% 7.14/2.05 % (2278013)Time elapsed: 0.117 s
% 7.14/2.05 % (2278013)Peak memory usage: 91 MB
% 7.14/2.05 % (2278013)Instructions burned: 108 (million)
% 7.14/2.05 % (2278015)Instruction limit reached!
% 7.14/2.05 % (2278015)------------------------------
% 7.14/2.05 % (2278015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.14/2.05 % (2278015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/2.05 % (2278015)CaDiCaL version: 2.1.3
% 7.14/2.05 % (2278015)Termination reason: Instruction limit
% 7.14/2.05 % (2278015)Termination phase: Saturation
% 7.14/2.05 % (2278015)Time elapsed: 0.178 s
% 7.14/2.05 % (2278015)Peak memory usage: 91 MB
% 7.14/2.05 % (2278015)Instructions burned: 181 (million)
% 7.14/2.05 % (2278032)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=569129469:i=143:sd=2:aac=none:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/143Mi)
% 7.14/2.05 % (2278032)Refutation not found, incomplete strategy
% 7.14/2.05 % (2278032)------------------------------
% 7.14/2.05 % (2278032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.14/2.05 % (2278032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/2.05 % (2278032)CaDiCaL version: 2.1.3
% 7.14/2.05 % (2278032)Termination reason: Refutation not found, incomplete strategy
% 7.14/2.05 % (2278032)Time elapsed: 0.018 s
% 7.14/2.05 % (2278032)Peak memory usage: 90 MB
% 7.14/2.05 % (2278032)Instructions burned: 22 (million)
% 7.14/2.05 % (2278033)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=432979814:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 0.35/2.40 % (2278034)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3050799203:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 0.35/2.40 % (2278035)lrs+10_64_to=lpo:sil=8000:random_seed=2870807245:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 0.35/2.40 % (2278034)First to succeed.
% 0.35/2.40 % (2278034)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2278005"
% 0.35/2.40 % (2278033)Instruction limit reached!
% 0.35/2.40 % (2278033)------------------------------
% 0.35/2.40 % (2278033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.40 % (2278033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.40 % (2278033)CaDiCaL version: 2.1.3
% 0.35/2.40 % (2278033)Termination reason: Instruction limit
% 0.35/2.40 % (2278033)Termination phase: Saturation
% 0.35/2.40 % (2278033)Time elapsed: 0.191 s
% 0.35/2.40 % (2278033)Peak memory usage: 92 MB
% 0.35/2.40 % (2278033)Instructions burned: 189 (million)
% 0.35/2.40 % (2278035)Instruction limit reached!
% 0.35/2.40 % (2278035)------------------------------
% 0.35/2.40 % (2278035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.40 % (2278035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.40 % (2278035)CaDiCaL version: 2.1.3
% 0.35/2.40 % (2278035)Termination reason: Instruction limit
% 0.35/2.40 % (2278035)Termination phase: Saturation
% 0.35/2.40 % (2278035)Time elapsed: 0.116 s
% 0.35/2.40 % (2278035)Peak memory usage: 92 MB
% 0.35/2.40 % (2278035)Instructions burned: 129 (million)
% 0.35/2.40 % (2278032)------------------------------
% 0.35/2.40 % (2278032)------------------------------
% 0.35/2.40 % (2278041)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3398406312:i=157:gtg=all_2990 on theBenchmark for (2990ds/157Mi)
% 0.35/2.40 % (2278040)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2926986053:avsq=on:i=194:fgj=on:bd=preordered_2990 on theBenchmark for (2990ds/194Mi)
% 0.35/2.40 % (2278034)Refutation found. Thanks to Tanya!
% 0.35/2.40 % SZS status Unsatisfiable for theBenchmark
% 0.35/2.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/2.40 % (2278034)------------------------------
% 0.35/2.40 % (2278034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.40 % (2278034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.40 % (2278034)CaDiCaL version: 2.1.3
% 0.35/2.40 % (2278034)Termination reason: Refutation
% 0.35/2.40 % (2278034)Time elapsed: 0.099 s
% 0.35/2.40 % (2278034)Peak memory usage: 93 MB
% 0.35/2.40 % (2278034)Instructions burned: 89 (million)
% 0.35/2.40 % (2278034)------------------------------
% 0.35/2.40 % (2278034)------------------------------
% 0.35/2.40 % (2278005)Success in time 1.303 s
% 0.35/2.40 % Vampire exiting
%------------------------------------------------------------------------------