%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV411+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 : n010.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 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 9 unt; 2 def)
% Number of atoms : 100 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 40 ~; 36 |; 17 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 69 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
<=> ( contains_slb(X0,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax21) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax23) ).
fof(f19,conjecture,
! [X0] :
( ! [X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) )
=> ! [X3,X4,X5] :
( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
=> ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l47_co) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) )
=> ! [X3,X4,X5] :
( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
=> ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f32,plain,
? [X0] :
( ? [X3,X4,X5] :
( ! [X6] : ~ pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6)
& contains_slb(insert_slb(X0,pair(X4,X5)),X3) )
& ! [X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
| ~ contains_slb(X0,X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( ~ contains_slb(X0,X2)
& X1 != X2 ) )
& ( contains_slb(X0,X2)
| X1 = X2
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( ~ contains_slb(X0,X2)
& X1 != X2 ) )
& ( contains_slb(X0,X2)
| X1 = X2
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ~ pair_in_list(X0,X2,X4)
& ( X1 != X2
| X3 != X4 ) ) )
& ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ~ pair_in_list(X0,X2,X4)
& ( X1 != X2
| X3 != X4 ) ) )
& ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
? [X0] :
( ? [X1,X2,X3] :
( ! [X4] : ~ pair_in_list(insert_slb(X0,pair(X2,X3)),X1,X4)
& contains_slb(insert_slb(X0,pair(X2,X3)),X1) )
& ! [X5] :
( ? [X6] : pair_in_list(X0,X5,X6)
| ~ contains_slb(X0,X5) ) ),
inference(rectify,[],[f32]) ).
fof(f38,plain,
( ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK2,sK3)),sK1,X4)
& contains_slb(insert_slb(sK0,pair(sK2,sK3)),sK1)
& ! [X5] :
( pair_in_list(sK0,X5,sK4(X5))
| ~ contains_slb(sK0,X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X6,sK4(X5))],[f37]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
! [X2,X3,X0,X1,X4] :
( X1 != X2
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 != X4 ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(X0,X2,X4)
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f62,plain,
! [X5] :
( ~ contains_slb(sK0,X5)
| pair_in_list(sK0,X5,sK4(X5)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f63,plain,
contains_slb(insert_slb(sK0,pair(sK2,sK3)),sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f64,plain,
! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK2,sK3)),sK1,X4),
inference(cnf_transformation,[],[f38]) ).
fof(f85,plain,
( sK1 = sK2
| contains_slb(sK0,sK1) ),
inference(resolution,[],[f47,f63]) ).
fof(f90,definition,
( spl5_1
<=> contains_slb(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f92,plain,
( contains_slb(sK0,sK1)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl5_2
<=> sK1 = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f96,plain,
( sK1 = sK2
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f85,f94,f90]) ).
fof(f100,plain,
( ! [X0] : ~ pair_in_list(insert_slb(sK0,pair(sK1,sK3)),sK1,X0)
| ~ spl5_2 ),
inference(superposition,[],[f64,f96]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( X2 != X3
| pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X3) ),
inference(equality_resolution,[],[f53]) ).
fof(f150,plain,
! [X2,X0,X1] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(equality_resolution,[],[f102]) ).
fof(f164,plain,
( $false
| ~ spl5_2 ),
inference(resolution,[],[f150,f100]) ).
fof(f168,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f164]) ).
fof(f169,plain,
( pair_in_list(sK0,sK1,sK4(sK1))
| ~ spl5_1 ),
inference(resolution,[],[f92,f62]) ).
fof(f173,plain,
( ! [X0,X1] : pair_in_list(insert_slb(sK0,pair(X0,X1)),sK1,sK4(sK1))
| ~ spl5_1 ),
inference(resolution,[],[f169,f54]) ).
fof(f178,plain,
( $false
| ~ spl5_1 ),
inference(resolution,[],[f173,f64]) ).
fof(f182,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f178]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f97]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f168]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f182]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f183,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n010.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 10:51:47 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.25 % (1845630)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (1845640)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2064324038:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (1845640) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1845630-1845640"...
% 0.08/0.25 % (1845640)...printing done.
% 0.08/0.25 % (1845640)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (1845640)------------------------------
% 0.08/0.25 % (1845640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (1845640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (1845640)CaDiCaL version: 2.1.3
% 0.08/0.25 % (1845640)Termination reason: Refutation
% 0.08/0.25 % (1845640)Time elapsed: 0.005 s
% 0.08/0.25 % (1845640)Peak memory usage: 12 MB
% 0.08/0.25 % (1845640)Instructions burned: 12 (million)
% 0.08/0.25 % (1845630)Success in time 0.036 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------