%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV381+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:09:04 PM UTC 2026
% Result : Theorem 0.66s 0.70s
% Output : Refutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 15 unt; 3 def)
% Number of atoms : 158 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 147 ( 62 ~; 60 |; 9 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 112 ( 1 sgn 107 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X0,X1)
& less_than(X1,X2) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f2,axiom,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
fof(f3,axiom,
! [X0] : less_than(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( less_than(X0,X1)
& ~ less_than(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f5,axiom,
! [X0] : less_than(bottom,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
fof(f10,axiom,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
<=> ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
fof(f50,axiom,
! [X0,X1] : findmin_cpq_res(triple(X0,create_slb,X1)) = bottom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f51,axiom,
! [X0,X1,X2,X3] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f63,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_pq(i(triple(X0,X1,X2)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_li56) ).
fof(f64,axiom,
! [X0,X1,X2] :
( ? [X3] :
( contains_cpq(triple(X0,X1,X2),X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) )
=> ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_l18) ).
fof(f65,conjecture,
! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_co) ).
fof(f66,negated_conjecture,
~ ! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f74,plain,
! [X0,X1,X2] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
inference(rectify,[],[f51]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) )
=> issmallestelement_pq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f76,plain,
! [X0,X1] :
( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f77,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X0,X1)
| ~ less_than(X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f78,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X0,X1)
| ~ less_than(X1,X2) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f80,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f116,plain,
! [X0,X1,X2] :
( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0)
| create_slb = X1 ),
inference(ennf_transformation,[],[f74]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ! [X3] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f118,plain,
? [X0,X1,X2] :
( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
& phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f121,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ( ~ less_than(X1,sK0(X0,X1))
& contains_pq(X0,sK0(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f81]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) )
& ( contains_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f132,plain,
( ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4)))
& phi(findmin_cpq_eff(triple(sK2,sK3,sK4))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f118]) ).
fof(f133,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X0,X1)
| ~ less_than(X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f134,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f135,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f136,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f137,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f144,plain,
! [X0,X1] :
( contains_pq(X0,sK0(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f145,plain,
! [X0,X1] :
( ~ less_than(X1,sK0(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f192,plain,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f50]) ).
fof(f193,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f116]) ).
fof(f203,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[],[f131]) ).
fof(f204,plain,
! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ),
inference(cnf_transformation,[],[f117]) ).
fof(f205,plain,
phi(findmin_cpq_eff(triple(sK2,sK3,sK4))),
inference(cnf_transformation,[],[f132]) ).
fof(f206,plain,
~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4))),
inference(cnf_transformation,[],[f132]) ).
fof(f212,plain,
! [X0] : issmallestelement_pq(X0,bottom),
inference(resolution,[],[f145,f137]) ).
fof(f221,plain,
( ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_pqp_res(sK2))
| create_slb = sK3 ),
inference(superposition,[],[f206,f193]) ).
fof(f224,definition,
( spl5_1
<=> create_slb = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f226,plain,
( create_slb = sK3
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f228,definition,
( spl5_2
<=> issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_pqp_res(sK2)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f230,plain,
( ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_pqp_res(sK2))
| spl5_2 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f221,f228,f224]) ).
fof(f234,plain,
! [X2,X0,X1] :
( issmallestelement_pq(X2,X0)
| ~ less_than(X1,sK0(X2,X0))
| ~ less_than(X0,X1) ),
inference(resolution,[],[f133,f145]) ).
fof(f236,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(forward_subsumption_resolution,[],[f136,f134]) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(resolution,[],[f204,f203]) ).
fof(f355,plain,
( ! [X0] :
( ~ less_than(findmin_pqp_res(sK2),X0)
| ~ less_than(X0,sK0(i(triple(sK2,sK3,sK4)),findmin_pqp_res(sK2))) )
| spl5_2 ),
inference(resolution,[],[f234,f230]) ).
fof(f357,plain,
( ~ less_than(findmin_pqp_res(sK2),sK0(i(triple(sK2,sK3,sK4)),findmin_pqp_res(sK2)))
| spl5_2 ),
inference(resolution,[],[f355,f135]) ).
fof(f424,plain,
! [X0] :
( ~ contains_pq(i(triple(sK2,sK3,sK4)),X0)
| ~ strictly_less_than(X0,findmin_cpq_res(triple(sK2,sK3,sK4))) ),
inference(resolution,[],[f252,f205]) ).
fof(f429,plain,
! [X0] :
( ~ strictly_less_than(sK0(i(triple(sK2,sK3,sK4)),X0),findmin_cpq_res(triple(sK2,sK3,sK4)))
| issmallestelement_pq(i(triple(sK2,sK3,sK4)),X0) ),
inference(resolution,[],[f424,f144]) ).
fof(f493,plain,
! [X0] :
( ~ strictly_less_than(sK0(i(triple(sK2,sK3,sK4)),X0),findmin_pqp_res(sK2))
| issmallestelement_pq(i(triple(sK2,sK3,sK4)),X0)
| create_slb = sK3 ),
inference(superposition,[],[f429,f193]) ).
fof(f495,definition,
( spl5_7
<=> ! [X0] :
( ~ strictly_less_than(sK0(i(triple(sK2,sK3,sK4)),X0),findmin_pqp_res(sK2))
| issmallestelement_pq(i(triple(sK2,sK3,sK4)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f496,plain,
( ! [X0] :
( ~ strictly_less_than(sK0(i(triple(sK2,sK3,sK4)),X0),findmin_pqp_res(sK2))
| issmallestelement_pq(i(triple(sK2,sK3,sK4)),X0) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f497,plain,
( spl5_1
| spl5_7 ),
inference(avatar_split_clause,[],[f493,f495,f224]) ).
fof(f499,plain,
( ~ issmallestelement_pq(i(triple(sK2,create_slb,sK4)),findmin_cpq_res(triple(sK2,create_slb,sK4)))
| ~ spl5_1 ),
inference(superposition,[],[f206,f226]) ).
fof(f528,plain,
( ~ issmallestelement_pq(i(triple(sK2,create_slb,sK4)),bottom)
| ~ spl5_1 ),
inference(forward_demodulation,[],[f499,f192]) ).
fof(f538,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f528,f212]) ).
fof(f539,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f546,plain,
( ! [X0] :
( issmallestelement_pq(i(triple(sK2,sK3,sK4)),X0)
| less_than(findmin_pqp_res(sK2),sK0(i(triple(sK2,sK3,sK4)),X0)) )
| ~ spl5_7 ),
inference(resolution,[],[f496,f236]) ).
fof(f551,plain,
( less_than(findmin_pqp_res(sK2),sK0(i(triple(sK2,sK3,sK4)),findmin_pqp_res(sK2)))
| spl5_2
| ~ spl5_7 ),
inference(resolution,[],[f546,f230]) ).
fof(f552,plain,
( $false
| spl5_2
| ~ spl5_7 ),
inference(forward_subsumption_resolution,[],[f551,f357]) ).
fof(f553,plain,
( spl5_2
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f552]) ).
cnf(s1,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f231]) ).
cnf(s5,plain,
( spl5_1
| spl5_7 ),
inference(sat_conversion,[],[f497]) ).
cnf(s8,plain,
~ spl5_1,
inference(sat_conversion,[],[f539]) ).
cnf(s9,plain,
( spl5_2
| ~ spl5_7 ),
inference(sat_conversion,[],[f553]) ).
cnf(s11,plain,
spl5_7,
inference(rat,[],[s5,s8]) ).
cnf(s13,plain,
spl5_2,
inference(rat,[],[s9,s11]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s13,s8]) ).
fof(f556,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV381+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 10:46:01 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 0.66/0.70 % (1701469)Detected formulas, will run a generic FOF schedule.
% 0.66/0.70 % (1701479)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=769694982:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.66/0.70 % (1701479)First to succeed.
% 0.66/0.70 % (1701479)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1701469"
% 0.66/0.70 % (1701478)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3682852992:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.66/0.70 % (1701480)dis-21_1_sil=8000:lcm=predicate:random_seed=2952820897:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.66/0.70 % (1701476)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2137821736:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.66/0.70 % (1701477)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2006275824:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.66/0.70 % (1701475)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3061773988:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.66/0.70 % (1701474)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=929201115:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.66/0.70 % (1701477)Refutation not found, incomplete strategy
% 0.66/0.70 % (1701477)------------------------------
% 0.66/0.70 % (1701477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.70 % (1701477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.70 % (1701477)CaDiCaL version: 2.1.3
% 0.66/0.70 % (1701477)Termination reason: Refutation not found, incomplete strategy
% 0.66/0.70 % (1701477)Time elapsed: 0.002 s
% 0.66/0.70 % (1701477)Peak memory usage: 88 MB
% 0.66/0.70 % (1701477)Instructions burned: 1 (million)
% 0.66/0.70 % (1701480)Also succeeded, but the first one will report.
% 0.66/0.70 % (1701478)Also succeeded, but the first one will report.
% 0.66/0.70 % (1701479)Refutation found. Thanks to Tanya!
% 0.66/0.70 % SZS status Theorem for theBenchmark
% 0.66/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.66/0.80 % (1701479)------------------------------
% 0.66/0.80 % (1701479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.80 % (1701479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.80 % (1701479)CaDiCaL version: 2.1.3
% 0.66/0.80 % (1701479)Termination reason: Refutation
% 0.66/0.80 % (1701479)Time elapsed: 0.012 s
% 0.66/0.80 % (1701479)Peak memory usage: 90 MB
% 0.66/0.80 % (1701479)Instructions burned: 27 (million)
% 0.66/0.80 % (1701479)------------------------------
% 0.66/0.80 % (1701479)------------------------------
% 0.66/0.80 % (1701469)Success in time 0.295 s
% 0.66/0.80 % Vampire exiting
%------------------------------------------------------------------------------