%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC244-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:03:06 PM UTC 2026
% Result : Unsatisfiable 3.55s 1.19s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 11 unt; 1 def)
% Number of atoms : 174 ( 45 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 270 ( 142 ~; 127 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f112,axiom,
! [X0] :
( cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f200,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
fof(f208,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ssItem(sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
! [X2,X0,X1] :
( ssItem(sk5(X2,X1,X0))
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| memberP(X1,sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f213,plain,
! [X2,X0,X1] :
( sk1 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| memberP(X1,sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f212]) ).
fof(f255,definition,
( spl0_2
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f256,plain,
( ssList(nil)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f291,plain,
spl0_2,
inference(avatar_split_clause,[],[f8,f255]) ).
fof(f310,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) != sk1
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(X0)
| memberP(nil,sk5(X1,nil,X0))
| ~ ssList(cons(X0,nil)) ),
inference(superposition,[],[f213,f74]) ).
fof(f312,plain,
( ! [X0,X1] :
( ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| ~ ssItem(X0)
| memberP(nil,sk5(X1,nil,X0))
| app(cons(X0,nil),X1) != sk1 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f310,f256]) ).
fof(f351,plain,
( ! [X0,X1] :
( ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X0)
| memberP(nil,sk5(X1,nil,X0))
| app(cons(X0,nil),X1) != sk1 )
| ~ spl0_2 ),
inference(resolution,[],[f86,f312]) ).
fof(f354,plain,
( ! [X0,X1] :
( ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| memberP(nil,sk5(X1,nil,X0))
| app(cons(X0,nil),X1) != sk1 )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f351]) ).
fof(f360,plain,
( ! [X0,X1] :
( memberP(nil,sk5(X1,nil,X0))
| ~ ssList(X1)
| ~ ssItem(X0)
| app(cons(X0,nil),X1) != sk1 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f354,f256]) ).
fof(f365,plain,
( ! [X0,X1] :
( ~ ssItem(sk5(X0,nil,X1))
| ~ ssItem(X1)
| sk1 != app(cons(X1,nil),X0)
| ~ ssList(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f360,f71]) ).
fof(f366,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| app(cons(X0,nil),X1) != sk1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X1)
| sk1 != app(app(nil,cons(X0,nil)),X1)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f365,f211]) ).
fof(f367,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| app(cons(X0,nil),X1) != sk1
| ~ ssList(X1)
| ~ ssList(nil)
| sk1 != app(app(nil,cons(X0,nil)),X1) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f366]) ).
fof(f368,plain,
( ! [X0,X1] :
( app(cons(X0,nil),X1) != sk1
| ~ ssItem(X0)
| ~ ssList(X1)
| sk1 != app(app(nil,cons(X0,nil)),X1) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f367,f256]) ).
fof(f440,plain,
( ! [X0,X1] :
( cons(X0,X1) != sk1
| ~ ssItem(X0)
| ~ ssList(X1)
| sk1 != app(app(nil,cons(X0,nil)),X1)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(superposition,[],[f368,f126]) ).
fof(f456,plain,
( ! [X0,X1] :
( sk1 != app(app(nil,cons(X0,nil)),X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != sk1 )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f440]) ).
fof(f465,plain,
( ! [X0,X1] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != sk1
| app(cons(X0,nil),X1) != sk1 )
| ~ spl0_2 ),
inference(superposition,[],[f456,f74]) ).
fof(f468,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != sk1
| app(cons(X0,nil),X1) != sk1
| ~ ssList(nil)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f465,f86]) ).
fof(f470,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != sk1
| app(cons(X0,nil),X1) != sk1
| ~ ssList(nil) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f468]) ).
fof(f471,plain,
( ! [X0,X1] :
( app(cons(X0,nil),X1) != sk1
| ~ ssList(X1)
| cons(X0,X1) != sk1
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f470,f256]) ).
fof(f473,plain,
( ! [X0,X1] :
( cons(X0,X1) != sk1
| ~ ssList(X1)
| cons(X0,X1) != sk1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(superposition,[],[f471,f126]) ).
fof(f474,plain,
( ! [X0,X1] :
( cons(X0,X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f473]) ).
fof(f486,plain,
( ! [X0] :
( sk1 != X0
| ~ ssList(skaf82(X0))
| ~ ssItem(skaf83(X0))
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f474,f112]) ).
fof(f487,plain,
( ! [X0] :
( sk1 != X0
| ~ ssItem(skaf83(X0))
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f486,f13]) ).
fof(f489,plain,
( ! [X0] :
( sk1 != X0
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f487,f12]) ).
fof(f519,plain,
( ~ ssList(sk1)
| nil = sk1
| ~ spl0_2 ),
inference(equality_resolution,[],[f489]) ).
fof(f520,plain,
( nil = sk1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f519,f200]) ).
fof(f521,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f520,f208]) ).
fof(f522,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f521]) ).
cnf(s10,plain,
spl0_2,
inference(sat_conversion,[],[f291]) ).
cnf(s12,plain,
~ spl0_2,
inference(sat_conversion,[],[f522]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s10,s12]) ).
fof(f523,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC244-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n006.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 08:40:56 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 3.55/1.19 % (3821582)Input is clausal, will run a generic CNF schedule.
% 3.55/1.19 % (3821588)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=492717939:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.55/1.19 % (3821590)lrs+10_1_sil=8000:sp=occurrence:random_seed=2706416921:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.55/1.19 % (3821589)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=622667353:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.55/1.19 % (3821593)dis-21_1_sil=8000:lcm=predicate:random_seed=2108521477:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.55/1.19 % (3821587)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=1263380375:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.55/1.19 % (3821592)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1446800050:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.55/1.19 % (3821591)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1005757369:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.55/1.19 % (3821592)First to succeed.
% 3.55/1.19 % (3821592)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3821582"
% 3.55/1.19 % (3821593)Instruction limit reached!
% 3.55/1.19 % (3821593)------------------------------
% 3.55/1.19 % (3821593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.19 % (3821593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.19 % (3821593)CaDiCaL version: 2.1.3
% 3.55/1.19 % (3821593)Termination reason: Instruction limit
% 3.55/1.19 % (3821593)Termination phase: Saturation
% 3.55/1.19 % (3821593)Time elapsed: 0.065 s
% 3.55/1.19 % (3821593)Peak memory usage: 89 MB
% 3.55/1.19 % (3821593)Instructions burned: 118 (million)
% 3.55/1.19 % (3821590)Instruction limit reached!
% 3.55/1.19 % (3821590)------------------------------
% 3.55/1.19 % (3821590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.19 % (3821590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.19 % (3821590)CaDiCaL version: 2.1.3
% 3.55/1.19 % (3821590)Termination reason: Instruction limit
% 3.55/1.19 % (3821590)Termination phase: Saturation
% 3.55/1.19 % (3821590)Time elapsed: 0.068 s
% 3.55/1.19 % (3821590)Peak memory usage: 90 MB
% 3.55/1.19 % (3821590)Instructions burned: 108 (million)
% 3.55/1.19 % (3821591)Instruction limit reached!
% 3.55/1.19 % (3821591)------------------------------
% 3.55/1.19 % (3821591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.19 % (3821591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.19 % (3821591)CaDiCaL version: 2.1.3
% 3.55/1.19 % (3821591)Termination reason: Instruction limit
% 3.55/1.19 % (3821591)Termination phase: Saturation
% 3.55/1.19 % (3821591)Time elapsed: 0.062 s
% 3.55/1.19 % (3821591)Peak memory usage: 89 MB
% 3.55/1.19 % (3821591)Instructions burned: 114 (million)
% 3.55/1.19 % (3821601)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=150141149:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.55/1.19 % (3821602)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1123269092:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.55/1.19 % (3821603)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=817264492:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.55/1.19 % (3821603)Also succeeded, but the first one will report.
% 3.55/1.19 % (3821592)Refutation found. Thanks to Tanya!
% 3.55/1.19 % SZS status Unsatisfiable for theBenchmark
% 3.55/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.19 % (3821592)------------------------------
% 3.55/1.19 % (3821592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.19 % (3821592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.19 % (3821592)CaDiCaL version: 2.1.3
% 3.55/1.19 % (3821592)Termination reason: Refutation
% 3.55/1.19 % (3821592)Time elapsed: 0.015 s
% 3.55/1.19 % (3821592)Peak memory usage: 89 MB
% 3.55/1.19 % (3821592)Instructions burned: 21 (million)
% 3.55/1.19 % (3821592)------------------------------
% 3.55/1.19 % (3821592)------------------------------
% 3.55/1.19 % (3821582)Success in time 0.429 s
% 3.55/1.19 % Vampire exiting
%------------------------------------------------------------------------------