%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV409+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 : 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 01:09:08 PM UTC 2026
% Result : Theorem 3.63s 1.29s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 155 ( 68 ~; 55 |; 26 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 88 ( 75 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f19,axiom,
! [X0,X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( ( pair_in_list(X0,X1,X2)
& strictly_less_than(X1,X3)
& strictly_less_than(X2,X3) )
=> pair_in_list(update_slb(X0,X3),X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).
fof(f21,axiom,
! [X0,X1,X2,X3] :
( ( pair_in_list(X0,X1,X2)
& strictly_less_than(X1,X3)
& less_than(X3,X2) )
=> ? [X4] :
( pair_in_list(update_slb(X0,X3),X1,X4)
& less_than(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).
fof(f22,conjecture,
! [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',l45_co) ).
fof(f23,negated_conjecture,
~ ! [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) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
| ~ contains_slb(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
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(X1,X3)
| ~ 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(X1,X3)
| ~ strictly_less_than(X2,X3) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( pair_in_list(update_slb(X0,X3),X1,X4)
& less_than(X3,X4) )
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,X3)
| ~ less_than(X3,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( pair_in_list(update_slb(X0,X3),X1,X4)
& less_than(X3,X4) )
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,X3)
| ~ less_than(X3,X2) ),
inference(flattening,[],[f27]) ).
fof(f29,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,[],[f23]) ).
fof(f30,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,[],[f29]) ).
fof(f35,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f24]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ( pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3))
& less_than(X3,sK1(X0,X1,X3)) )
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,X3)
| ~ less_than(X3,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X4,sK1(X0,X1,X3))],[f28]) ).
fof(f37,plain,
( ~ pair_in_list(update_slb(sK2,sK4),sK3,sK4)
& ! [X3] :
( ~ pair_in_list(update_slb(sK2,sK4),sK3,X3)
| ~ less_than(sK4,X3) )
& contains_slb(sK2,sK3)
& strictly_less_than(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f30]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,X3)
| ~ strictly_less_than(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( less_than(X3,sK1(X0,X1,X3))
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,X3)
| ~ less_than(X3,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3))
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,X3)
| ~ less_than(X3,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
strictly_less_than(sK3,sK4),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
contains_slb(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X3] :
( ~ pair_in_list(update_slb(sK2,sK4),sK3,X3)
| ~ less_than(sK4,X3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f51,plain,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK4),
inference(cnf_transformation,[],[f37]) ).
fof(f62,plain,
! [X0,X1] :
( ~ less_than(X0,X1)
| strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f65,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f94,plain,
! [X0] :
( ~ pair_in_list(sK2,sK3,X0)
| ~ strictly_less_than(sK3,sK4)
| ~ strictly_less_than(X0,sK4) ),
inference(resolution,[],[f45,f51]) ).
fof(f99,plain,
! [X0] :
( ~ pair_in_list(sK2,sK3,X0)
| ~ strictly_less_than(X0,sK4) ),
inference(forward_subsumption_resolution,[],[f94,f48]) ).
fof(f106,plain,
! [X0] :
( ~ pair_in_list(sK2,sK3,X0)
| ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,X0)
| ~ less_than(sK4,sK1(sK2,sK3,sK4)) ),
inference(resolution,[],[f47,f50]) ).
fof(f109,plain,
! [X0] :
( ~ pair_in_list(sK2,sK3,X0)
| ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,X0) ),
inference(forward_subsumption_resolution,[],[f106,f46]) ).
fof(f110,plain,
! [X0] :
( ~ pair_in_list(sK2,sK3,X0)
| ~ less_than(sK4,X0) ),
inference(forward_subsumption_resolution,[],[f109,f48]) ).
fof(f111,plain,
( ~ strictly_less_than(sK0(sK2,sK3),sK4)
| ~ contains_slb(sK2,sK3) ),
inference(resolution,[],[f99,f44]) ).
fof(f112,plain,
~ strictly_less_than(sK0(sK2,sK3),sK4),
inference(forward_subsumption_resolution,[],[f111,f49]) ).
fof(f113,plain,
( ~ less_than(sK4,sK0(sK2,sK3))
| ~ contains_slb(sK2,sK3) ),
inference(resolution,[],[f110,f44]) ).
fof(f114,plain,
~ less_than(sK4,sK0(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f113,f49]) ).
fof(f117,plain,
less_than(sK0(sK2,sK3),sK4),
inference(resolution,[],[f114,f65]) ).
fof(f124,plain,
( strictly_less_than(sK0(sK2,sK3),sK4)
| less_than(sK4,sK0(sK2,sK3)) ),
inference(resolution,[],[f117,f62]) ).
fof(f125,plain,
less_than(sK4,sK0(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f124,f112]) ).
fof(f126,plain,
$false,
inference(forward_subsumption_resolution,[],[f125,f114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/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 10:54:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.63/1.29 % (2542130)Detected formulas, will run a generic FOF schedule.
% 3.63/1.29 % (2542175)dis-21_1_sil=8000:lcm=predicate:random_seed=3057621624: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)
% 3.63/1.29 % (2542175)Instruction limit reached!
% 3.63/1.29 % (2542175)------------------------------
% 3.63/1.29 % (2542175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.29 % (2542175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.29 % (2542175)CaDiCaL version: 2.1.3
% 3.63/1.29 % (2542175)Termination reason: Instruction limit
% 3.63/1.29 % (2542175)Termination phase: Saturation
% 3.63/1.29 % (2542175)Time elapsed: 0.034 s
% 3.63/1.29 % (2542175)Peak memory usage: 88 MB
% 3.63/1.29 % (2542175)Instructions burned: 134 (million)
% 3.63/1.29 % (2542174)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1628413428:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.29 % (2542171)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=991690949:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.29 % (2542173)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2174153163:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.29 % (2542170)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=2965655109:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.29 % (2542172)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1303217409:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.29 % (2542169)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=3574706403:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.29 % (2542172)First to succeed.
% 3.63/1.29 % (2542173)Also succeeded, but the first one will report.
% 3.63/1.29 % (2542172)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2542130"
% 3.63/1.29 % (2542174)Also succeeded, but the first one will report.
% 3.63/1.29 % (2542201)lrs+10_1_sil=8000:sp=occurrence:random_seed=2284723653:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.63/1.29 % (2542201)Also succeeded, but the first one will report.
% 3.63/1.29 % (2542172)Refutation found. Thanks to Tanya!
% 3.63/1.29 % SZS status Theorem for theBenchmark
% 3.63/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.29 % (2542172)------------------------------
% 3.63/1.29 % (2542172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.29 % (2542172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.29 % (2542172)CaDiCaL version: 2.1.3
% 3.63/1.29 % (2542172)Termination reason: Refutation
% 3.63/1.29 % (2542172)Time elapsed: 0.005 s
% 3.63/1.29 % (2542172)Peak memory usage: 89 MB
% 3.63/1.29 % (2542172)Instructions burned: 5 (million)
% 3.63/1.29 % (2542172)------------------------------
% 3.63/1.29 % (2542172)------------------------------
% 3.63/1.29 % (2542130)Success in time 0.428 s
% 3.63/1.29 % Vampire exiting
%------------------------------------------------------------------------------