%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV399+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:09:07 PM UTC 2026
% Result : Theorem 2.69s 1.14s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 8 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 55 ~; 43 |; 18 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 78 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X0,X1)
& less_than(X1,X2) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f2,axiom,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( less_than(X0,X1)
& ~ less_than(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f19,axiom,
! [X0,X1,X2,X3] :
( ( pair_in_list(X0,X1,X2)
& less_than(X3,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l35_li3637) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( ( pair_in_list(X0,X1,X2)
& strictly_less_than(X2,X3) )
=> pair_in_list(update_slb(X0,X3),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l35_li3839) ).
fof(f21,conjecture,
! [X0] :
( ? [X1,X2] :
( pair_in_list(X0,X1,X2)
& strictly_less_than(X1,X2) )
=> ! [X3] :
? [X4,X5] :
( pair_in_list(update_slb(X0,X3),X4,X5)
& strictly_less_than(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l35_co) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( ? [X1,X2] :
( pair_in_list(X0,X1,X2)
& strictly_less_than(X1,X2) )
=> ! [X3] :
? [X4,X5] :
( pair_in_list(update_slb(X0,X3),X4,X5)
& strictly_less_than(X4,X5) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X2,X3) ),
inference(ennf_transformation,[],[f20]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X2,X3) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
? [X0] :
( ? [X3] :
! [X4,X5] :
( ~ pair_in_list(update_slb(X0,X3),X4,X5)
| ~ strictly_less_than(X4,X5) )
& ? [X1,X2] :
( pair_in_list(X0,X1,X2)
& strictly_less_than(X1,X2) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f28,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X0,X1)
| ~ less_than(X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X0,X1)
| ~ less_than(X1,X2) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
? [X0] :
( ? [X1] :
! [X2,X3] :
( ~ pair_in_list(update_slb(X0,X1),X2,X3)
| ~ strictly_less_than(X2,X3) )
& ? [X4,X5] :
( pair_in_list(X0,X4,X5)
& strictly_less_than(X4,X5) ) ),
inference(rectify,[],[f27]) ).
fof(f33,plain,
( ! [X2,X3] :
( ~ pair_in_list(update_slb(sK0,sK1),X2,X3)
| ~ strictly_less_than(X2,X3) )
& pair_in_list(sK0,sK2,sK3)
& strictly_less_than(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2),skolemize(X5,sK3)],[f32]) ).
fof(f36,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) )
& ( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
| ~ strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) )
& ( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
| ~ strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f40,plain,
strictly_less_than(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f41,plain,
pair_in_list(sK0,sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f42,plain,
! [X2,X3] :
( ~ pair_in_list(update_slb(sK0,sK1),X2,X3)
| ~ strictly_less_than(X2,X3) ),
inference(cnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f45,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X0,X1)
| ~ less_than(X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ less_than(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
~ less_than(sK3,sK2),
inference(resolution,[],[f52,f40]) ).
fof(f60,plain,
! [X0] :
( ~ less_than(sK3,X0)
| ~ less_than(X0,sK2) ),
inference(resolution,[],[f45,f57]) ).
fof(f64,plain,
! [X0] :
( less_than(X0,sK3)
| ~ less_than(X0,sK2) ),
inference(resolution,[],[f60,f44]) ).
fof(f65,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(forward_subsumption_resolution,[],[f54,f44]) ).
fof(f81,plain,
! [X0,X1] :
( ~ pair_in_list(sK0,X0,X1)
| ~ less_than(sK1,X1)
| ~ strictly_less_than(X0,X1) ),
inference(resolution,[],[f38,f42]) ).
fof(f82,plain,
! [X0,X1] :
( ~ pair_in_list(sK0,X0,X1)
| ~ strictly_less_than(X1,sK1)
| ~ strictly_less_than(X0,sK1) ),
inference(resolution,[],[f39,f42]) ).
fof(f83,plain,
( ~ less_than(sK1,sK3)
| ~ strictly_less_than(sK2,sK3) ),
inference(resolution,[],[f81,f41]) ).
fof(f84,plain,
~ less_than(sK1,sK3),
inference(forward_subsumption_resolution,[],[f83,f40]) ).
fof(f86,plain,
~ less_than(sK1,sK2),
inference(resolution,[],[f84,f64]) ).
fof(f120,plain,
( ~ strictly_less_than(sK3,sK1)
| ~ strictly_less_than(sK2,sK1) ),
inference(resolution,[],[f82,f41]) ).
fof(f124,plain,
( ~ strictly_less_than(sK2,sK1)
| less_than(sK1,sK3) ),
inference(resolution,[],[f120,f65]) ).
fof(f125,plain,
~ strictly_less_than(sK2,sK1),
inference(forward_subsumption_resolution,[],[f124,f84]) ).
fof(f130,plain,
less_than(sK1,sK2),
inference(resolution,[],[f125,f65]) ).
fof(f131,plain,
$false,
inference(forward_subsumption_resolution,[],[f130,f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV399+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.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 10:53:32 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.69/1.14 % (2539550)Detected formulas, will run a generic FOF schedule.
% 2.69/1.14 % (2539559)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1826222013:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.14 % (2539559)First to succeed.
% 2.69/1.14 % (2539559)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2539550"
% 2.69/1.14 % (2539556)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=2768899171:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.14 % (2539558)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=269182132:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.14 % (2539557)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=878941235:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.14 % (2539555)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=3928415244:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.14 % (2539558)Also succeeded, but the first one will report.
% 2.69/1.14 % (2539560)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3330295012:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.14 % (2539561)dis-21_1_sil=8000:lcm=predicate:random_seed=225252552: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)
% 2.69/1.14 % (2539560)Also succeeded, but the first one will report.
% 2.69/1.14 % (2539561)Instruction limit reached!
% 2.69/1.14 % (2539561)------------------------------
% 2.69/1.14 % (2539561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.14 % (2539561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.14 % (2539561)CaDiCaL version: 2.1.3
% 2.69/1.14 % (2539561)Termination reason: Instruction limit
% 2.69/1.14 % (2539561)Termination phase: Saturation
% 2.69/1.14 % (2539561)Time elapsed: 0.070 s
% 2.69/1.14 % (2539561)Peak memory usage: 89 MB
% 2.69/1.14 % (2539561)Instructions burned: 129 (million)
% 2.69/1.14 % (2539559)Refutation found. Thanks to Tanya!
% 2.69/1.14 % SZS status Theorem for theBenchmark
% 2.69/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.14 % (2539559)------------------------------
% 2.69/1.14 % (2539559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.14 % (2539559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.14 % (2539559)CaDiCaL version: 2.1.3
% 2.69/1.14 % (2539559)Termination reason: Refutation
% 2.69/1.14 % (2539559)Time elapsed: 0.003 s
% 2.69/1.14 % (2539559)Peak memory usage: 88 MB
% 2.69/1.14 % (2539559)Instructions burned: 5 (million)
% 2.69/1.14 % (2539559)------------------------------
% 2.69/1.14 % (2539559)------------------------------
% 2.69/1.14 % (2539550)Success in time 0.287 s
% 2.69/1.14 % Vampire exiting
%------------------------------------------------------------------------------