%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV413+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 : n008.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 01:09:09 PM UTC 2026
% Result : Theorem 2.26s 0.86s
% Output : Refutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 53 ( 21 ~; 13 |; 16 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 40 ( 30 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',l49_li3637) ).
fof(f20,conjecture,
! [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',l49_co) ).
fof(f21,negated_conjecture,
~ ! [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) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f32,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(f33,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,[],[f32]) ).
fof(f40,plain,
( ! [X4] :
( ~ pair_in_list(update_slb(sK0,sK3),sK1,X4)
| ~ less_than(sK3,X4) )
& pair_in_list(sK0,sK1,sK2)
& strictly_less_than(sK1,sK3)
& less_than(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f33]) ).
fof(f66,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,[],[f31]) ).
fof(f67,plain,
less_than(sK3,sK2),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
pair_in_list(sK0,sK1,sK2),
inference(cnf_transformation,[],[f40]) ).
fof(f70,plain,
! [X4] :
( ~ pair_in_list(update_slb(sK0,sK3),sK1,X4)
| ~ less_than(sK3,X4) ),
inference(cnf_transformation,[],[f40]) ).
fof(f89,plain,
! [X0] :
( ~ pair_in_list(sK0,sK1,X0)
| ~ less_than(sK3,X0)
| ~ less_than(sK3,X0) ),
inference(resolution,[],[f66,f70]) ).
fof(f91,plain,
! [X0] :
( ~ pair_in_list(sK0,sK1,X0)
| ~ less_than(sK3,X0) ),
inference(duplicate_literal_removal,[],[f89]) ).
fof(f103,plain,
~ less_than(sK3,sK2),
inference(resolution,[],[f91,f69]) ).
fof(f104,plain,
$false,
inference(forward_subsumption_resolution,[],[f103,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV413+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n008.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 10:53:10 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 2.26/0.86 % (2168990)Detected formulas, will run a generic FOF schedule.
% 2.26/0.86 % (2169000)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=731176811:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.26/0.86 % (2169000)First to succeed.
% 2.26/0.86 % (2169000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2168990"
% 2.26/0.86 % (2168999)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1561763817:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.26/0.86 % (2168998)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1648870227:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.26/0.86 % (2168997)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=2710680544:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.26/0.86 % (2168995)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=506694247:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.26/0.86 % (2168996)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=4206820044:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.26/0.86 % (2168998)Also succeeded, but the first one will report.
% 2.26/0.86 % (2168999)Also succeeded, but the first one will report.
% 2.26/0.86 % (2169001)dis-21_1_sil=8000:lcm=predicate:random_seed=1257655525: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)
% 2.26/0.86 % (2169001)Also succeeded, but the first one will report.
% 2.26/0.86 % (2169000)Refutation found. Thanks to Tanya!
% 2.26/0.86 % SZS status Theorem for theBenchmark
% 2.26/0.86 % SZS output start Proof for theBenchmark
% See solution above
% 2.26/0.86 % (2169000)------------------------------
% 2.26/0.86 % (2169000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.26/0.86 % (2169000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.86 % (2169000)CaDiCaL version: 2.1.3
% 2.26/0.86 % (2169000)Termination reason: Refutation
% 2.26/0.86 % (2169000)Time elapsed: 0.002 s
% 2.26/0.86 % (2169000)Peak memory usage: 89 MB
% 2.26/0.86 % (2169000)Instructions burned: 3 (million)
% 2.26/0.86 % (2169000)------------------------------
% 2.26/0.86 % (2169000)------------------------------
% 2.26/0.86 % (2168990)Success in time 0.266 s
% 2.26/0.86 % Vampire exiting
%------------------------------------------------------------------------------