%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV408+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 : n004.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 01:09:08 PM UTC 2026
% Result : Theorem 3.61s 1.29s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 2 def)
% Number of atoms : 125 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 133 ( 58 ~; 50 |; 18 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 69 ( 1 sgn 56 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f16,axiom,
! [X0] : update_slb(create_slb,X0) = create_slb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f39,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(f42,axiom,
! [X0,X1,X2] :
( ( contains_slb(X0,X1)
& strictly_less_than(X1,X2) )
=> ( pair_in_list(update_slb(X0,X2),X1,X2)
| ? [X3] :
( pair_in_list(update_slb(X0,X2),X1,X3)
& less_than(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l44_l45) ).
fof(f43,conjecture,
! [X0,X1,X2,X3] :
( ( contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) )
=> ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
| ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l44_co) ).
fof(f44,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) )
=> ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
| ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
inference(rectify,[],[f39]) ).
fof(f49,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ? [X3] :
( pair_in_list(update_slb(X0,X2),X1,X3)
& less_than(X2,X3) )
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f50,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ? [X3] :
( pair_in_list(update_slb(X0,X2),X1,X3)
& less_than(X2,X3) )
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
? [X0,X1,X2,X3] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& ! [X4] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
| ~ less_than(findmin_pqp_res(X0),X4) )
& contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f44]) ).
fof(f52,plain,
? [X0,X1,X2,X3] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& ! [X4] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
| ~ less_than(findmin_pqp_res(X0),X4) )
& contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ),
inference(flattening,[],[f51]) ).
fof(f57,plain,
! [X0,X1,X2] :
( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0)
| create_slb = X1 ),
inference(ennf_transformation,[],[f45]) ).
fof(f64,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ( pair_in_list(update_slb(X0,X2),X1,sK0(X0,X1,X2))
& less_than(X2,sK0(X0,X1,X2)) )
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f50]) ).
fof(f65,plain,
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
& ! [X4] :
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4)
| ~ less_than(findmin_pqp_res(sK1),X4) )
& contains_slb(sK2,sK4)
& strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f52]) ).
fof(f70,plain,
! [X2,X0,X1] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| less_than(X2,sK0(X0,X1,X2))
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f71,plain,
! [X2,X0,X1] :
( pair_in_list(update_slb(X0,X2),X1,sK0(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f72,plain,
strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))),
inference(cnf_transformation,[],[f65]) ).
fof(f73,plain,
contains_slb(sK2,sK4),
inference(cnf_transformation,[],[f65]) ).
fof(f74,plain,
! [X4] :
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4)
| ~ less_than(findmin_pqp_res(sK1),X4) ),
inference(cnf_transformation,[],[f65]) ).
fof(f75,plain,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
inference(cnf_transformation,[],[f10]) ).
fof(f89,plain,
! [X0] : create_slb = update_slb(create_slb,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f90,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f57]) ).
fof(f98,plain,
( strictly_less_than(sK4,findmin_pqp_res(sK1))
| create_slb = sK2 ),
inference(superposition,[],[f72,f90]) ).
fof(f100,definition,
( spl5_1
<=> create_slb = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f102,plain,
( create_slb = sK2
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f104,definition,
( spl5_2
<=> strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f106,plain,
( strictly_less_than(sK4,findmin_pqp_res(sK1))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f98,f104,f100]) ).
fof(f113,plain,
( less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ contains_slb(sK2,sK4)
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
inference(resolution,[],[f70,f75]) ).
fof(f120,plain,
( less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
inference(forward_subsumption_resolution,[],[f113,f73]) ).
fof(f122,plain,
( less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f120,f106]) ).
fof(f126,plain,
( pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
| ~ contains_slb(sK2,sK4)
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1))
| ~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1))) ),
inference(resolution,[],[f71,f74]) ).
fof(f129,plain,
! [X0,X1] :
( pair_in_list(create_slb,X1,sK0(create_slb,X1,X0))
| pair_in_list(create_slb,X1,X0)
| ~ contains_slb(create_slb,X1)
| ~ strictly_less_than(X1,X0) ),
inference(superposition,[],[f71,f89]) ).
fof(f130,plain,
! [X0,X1] :
( pair_in_list(create_slb,X1,X0)
| ~ contains_slb(create_slb,X1)
| ~ strictly_less_than(X1,X0) ),
inference(forward_subsumption_resolution,[],[f129,f87]) ).
fof(f131,plain,
( ~ contains_slb(sK2,sK4)
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1))
| ~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1))) ),
inference(forward_subsumption_resolution,[],[f126,f75]) ).
fof(f132,plain,
! [X0,X1] :
( ~ contains_slb(create_slb,X1)
| ~ strictly_less_than(X1,X0) ),
inference(forward_subsumption_resolution,[],[f130,f87]) ).
fof(f133,plain,
( ~ strictly_less_than(sK4,findmin_pqp_res(sK1))
| ~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1))) ),
inference(forward_subsumption_resolution,[],[f131,f73]) ).
fof(f134,plain,
( ~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f133,f106]) ).
fof(f135,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f134,f122]) ).
fof(f136,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f135]) ).
fof(f141,plain,
( contains_slb(create_slb,sK4)
| ~ spl5_1 ),
inference(superposition,[],[f73,f102]) ).
fof(f150,plain,
( ! [X0] : ~ strictly_less_than(sK4,X0)
| ~ spl5_1 ),
inference(resolution,[],[f132,f141]) ).
fof(f151,plain,
( $false
| ~ spl5_1 ),
inference(resolution,[],[f150,f72]) ).
fof(f152,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f151]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f107]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f136]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f152]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f153,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 10:50:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.61/1.29 % (279735)Detected formulas, will run a generic FOF schedule.
% 3.61/1.29 % (279742)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=3260735681:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.29 % (279740)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=3408192921:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.29 % (279745)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3807756949:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.29 % (279743)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3638132352:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.29 % (279744)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1235314760:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.29 % (279746)dis-21_1_sil=8000:lcm=predicate:random_seed=1894504626: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)
% 3.61/1.29 % (279741)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=3383475378:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.29 % (279743)First to succeed.
% 3.61/1.29 % (279743)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-279735"
% 3.61/1.29 % (279744)Also succeeded, but the first one will report.
% 3.61/1.29 % (279745)Also succeeded, but the first one will report.
% 3.61/1.29 % (279746)Instruction limit reached!
% 3.61/1.29 % (279746)------------------------------
% 3.61/1.29 % (279746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.29 % (279746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.29 % (279746)CaDiCaL version: 2.1.3
% 3.61/1.29 % (279746)Termination reason: Instruction limit
% 3.61/1.29 % (279746)Termination phase: Saturation
% 3.61/1.29 % (279746)Time elapsed: 0.051 s
% 3.61/1.29 % (279746)Peak memory usage: 88 MB
% 3.61/1.29 % (279746)Instructions burned: 130 (million)
% 3.61/1.29 % (279754)lrs+10_1_sil=8000:sp=occurrence:random_seed=1984554423:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.61/1.29 % (279754)Also succeeded, but the first one will report.
% 3.61/1.29 % (279743)Refutation found. Thanks to Tanya!
% 3.61/1.29 % SZS status Theorem for theBenchmark
% 3.61/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.29 % (279743)------------------------------
% 3.61/1.29 % (279743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.29 % (279743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.29 % (279743)CaDiCaL version: 2.1.3
% 3.61/1.29 % (279743)Termination reason: Refutation
% 3.61/1.29 % (279743)Time elapsed: 0.005 s
% 3.61/1.29 % (279743)Peak memory usage: 89 MB
% 3.61/1.29 % (279743)Instructions burned: 5 (million)
% 3.61/1.29 % (279743)------------------------------
% 3.61/1.29 % (279743)------------------------------
% 3.61/1.29 % (279735)Success in time 0.428 s
% 3.61/1.29 % Vampire exiting
%------------------------------------------------------------------------------