%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 01:21:11 PM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 176 ( 79 ~; 65 |; 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 : 94 ( 81 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( less_than(X0,X1)
& ~ less_than(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(f19,axiom,
! [X0,X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f32,plain,
! [X0,X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
| ~ contains_slb(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f33,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(f34,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,[],[f33]) ).
fof(f35,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(f36,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,[],[f35]) ).
fof(f37,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(f38,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,[],[f37]) ).
fof(f39,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(f40,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,[],[f39]) ).
fof(f45,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))],[f32]) ).
fof(f46,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))],[f36]) ).
fof(f47,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)],[f38]) ).
fof(f49,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f53,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f73,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X1,X3)
| ~ strictly_less_than(X2,X3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ pair_in_list(X0,X1,X2)
| less_than(X3,sK1(X0,X1,X3))
| ~ strictly_less_than(X1,X3)
| ~ less_than(X3,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3))
| ~ strictly_less_than(X1,X3)
| ~ less_than(X3,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f77,plain,
strictly_less_than(sK3,sK4),
inference(cnf_transformation,[],[f47]) ).
fof(f78,plain,
contains_slb(sK2,sK3),
inference(cnf_transformation,[],[f47]) ).
fof(f79,plain,
! [X3] :
( ~ pair_in_list(update_slb(sK2,sK4),sK3,X3)
| ~ less_than(sK4,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f80,plain,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK4),
inference(cnf_transformation,[],[f47]) ).
fof(f109,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(forward_subsumption_resolution,[],[f53,f49]) ).
fof(f148,plain,
! [X2,X0,X1] :
( pair_in_list(update_slb(X0,X1),X2,X1)
| ~ strictly_less_than(X2,X1)
| ~ strictly_less_than(sK0(X0,X2),X1)
| ~ contains_slb(X0,X2) ),
inference(resolution,[],[f74,f73]) ).
fof(f157,plain,
! [X2,X0,X1] :
( less_than(X0,sK1(X1,X2,X0))
| ~ strictly_less_than(X2,X0)
| ~ less_than(X0,sK0(X1,X2))
| ~ contains_slb(X1,X2) ),
inference(resolution,[],[f75,f73]) ).
fof(f232,plain,
! [X2,X0,X1] :
( pair_in_list(update_slb(X0,X1),X2,sK1(X0,X2,X1))
| ~ strictly_less_than(X2,X1)
| ~ less_than(X1,sK0(X0,X2))
| ~ contains_slb(X0,X2) ),
inference(resolution,[],[f76,f73]) ).
fof(f415,plain,
( ~ strictly_less_than(sK3,sK4)
| ~ strictly_less_than(sK0(sK2,sK3),sK4)
| ~ contains_slb(sK2,sK3) ),
inference(resolution,[],[f148,f80]) ).
fof(f426,plain,
( ~ strictly_less_than(sK0(sK2,sK3),sK4)
| ~ contains_slb(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f415,f77]) ).
fof(f428,plain,
~ strictly_less_than(sK0(sK2,sK3),sK4),
inference(forward_subsumption_resolution,[],[f426,f78]) ).
fof(f430,plain,
less_than(sK4,sK0(sK2,sK3)),
inference(resolution,[],[f428,f109]) ).
fof(f558,plain,
( ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,sK0(sK2,sK3))
| ~ contains_slb(sK2,sK3)
| ~ less_than(sK4,sK1(sK2,sK3,sK4)) ),
inference(resolution,[],[f232,f79]) ).
fof(f570,plain,
( ~ less_than(sK4,sK0(sK2,sK3))
| ~ contains_slb(sK2,sK3)
| ~ less_than(sK4,sK1(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[],[f558,f77]) ).
fof(f571,plain,
( ~ contains_slb(sK2,sK3)
| ~ less_than(sK4,sK1(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[],[f570,f430]) ).
fof(f572,plain,
~ less_than(sK4,sK1(sK2,sK3,sK4)),
inference(forward_subsumption_resolution,[],[f571,f78]) ).
fof(f583,plain,
( ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,sK0(sK2,sK3))
| ~ contains_slb(sK2,sK3) ),
inference(resolution,[],[f572,f157]) ).
fof(f586,plain,
( ~ less_than(sK4,sK0(sK2,sK3))
| ~ contains_slb(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f583,f77]) ).
fof(f587,plain,
~ contains_slb(sK2,sK3),
inference(forward_subsumption_resolution,[],[f586,f430]) ).
fof(f588,plain,
$false,
inference(forward_subsumption_resolution,[],[f587,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n015.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 10:54:16 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.31 % (2541919)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (2541935)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4047091639:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (2541931)% WARNING: option uhcvi not known.
% 0.20/0.31 % (2541933)dis+10_1_sil=32000:sp=arity:random_seed=1991646766:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (2541932)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2005289812:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (2541930)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2683530581_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (2541931)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=321272764:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (2541934)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2648698783:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % (2541936)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2928831931:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % TRYING [1]
% 0.20/0.31 % TRYING [2]
% 0.20/0.31 % TRYING [3]
% 0.20/0.31 % TRYING [4]
% 0.20/0.31 % (2541933) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2541919-2541933"...
% 0.20/0.31 % (2541933)...printing done.
% 0.20/0.31 % (2541933)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.31 % (2541933)------------------------------
% 0.20/0.31 % (2541933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2541933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2541933)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2541933)Termination reason: Refutation
% 0.20/0.31 % (2541933)Time elapsed: 0.021 s
% 0.20/0.31 % (2541933)Peak memory usage: 12 MB
% 0.20/0.31 % (2541933)Instructions burned: 33 (million)
% 0.20/0.31 % (2541919)Success in time 0.07 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------