%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC198-1 : 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 : n002.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 01:02:54 PM UTC 2026
% Result : Unsatisfiable 5.25s 1.71s
% Output : Refutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 10 unt; 4 def)
% Number of atoms : 133 ( 22 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 161 ( 80 ~; 77 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f30,axiom,
! [X0] : ssItem(skaf65(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f173,axiom,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X2 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X0 = X2 ),
inference(reorient_equations,[],[f173]) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0] :
( ssItem(sk5(X0))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( memberP(sk1,sk5(X0))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| X0 != sk5(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
! [X0] :
( sk5(X0) != X0
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f208]) ).
fof(f211,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f216,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f217,plain,
( sk3 = cons(sk6,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f216]) ).
fof(f240,definition,
( spl0_1
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f242,plain,
( nil = sk3
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f253,definition,
( spl0_4
<=> sk3 = cons(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f255,plain,
( sk3 = cons(sk6,nil)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f217,f253,f240]) ).
fof(f265,definition,
( spl0_6
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f267,plain,
( ssItem(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f268,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f211,f265,f240]) ).
fof(f273,plain,
! [X0] :
( memberP(sk3,sk5(X0))
| ~ ssItem(X0) ),
inference(superposition,[],[f207,f205]) ).
fof(f274,plain,
( ! [X0] :
( memberP(cons(sk6,nil),sk5(X0))
| ~ ssItem(X0) )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f273,f255]) ).
fof(f276,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssItem(sk5(X0))
| memberP(nil,sk5(X0))
| sk5(X0) = sk6 )
| ~ spl0_4 ),
inference(resolution,[],[f274,f174]) ).
fof(f277,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssItem(sk6)
| ~ ssItem(sk5(X0))
| memberP(nil,sk5(X0))
| sk5(X0) = sk6 )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f276,f8]) ).
fof(f278,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssItem(sk5(X0))
| memberP(nil,sk5(X0))
| sk5(X0) = sk6 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f277,f267]) ).
fof(f279,plain,
( ! [X0] :
( memberP(nil,sk5(X0))
| ~ ssItem(X0)
| sk5(X0) = sk6 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f278,f206]) ).
fof(f280,plain,
( ! [X0] :
( ~ ssItem(X0)
| sk5(X0) = sk6
| ~ ssItem(sk5(X0)) )
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f279,f71]) ).
fof(f281,plain,
( ! [X0] :
( sk5(X0) = sk6
| ~ ssItem(X0) )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f280,f206]) ).
fof(f283,plain,
( ! [X0] :
( sk6 != X0
| ~ ssItem(X0)
| ~ ssItem(X0) )
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f209,f281]) ).
fof(f288,plain,
( ! [X0] :
( sk6 != X0
| ~ ssItem(X0) )
| ~ spl0_4
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f283]) ).
fof(f292,definition,
( spl0_7
<=> ! [X0] : ~ ssItem(X0) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f293,plain,
( ! [X0] : ~ ssItem(X0)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f301,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f293,f30]) ).
fof(f317,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f318,plain,
( ~ ssItem(sk6)
| ~ spl0_4
| ~ spl0_6 ),
inference(equality_resolution,[],[f288]) ).
fof(f319,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f318,f267]) ).
fof(f320,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f322,plain,
( ! [X0] :
( memberP(nil,sk5(X0))
| ~ ssItem(X0) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f273,f242]) ).
fof(f333,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssItem(sk5(X0)) )
| ~ spl0_1 ),
inference(resolution,[],[f322,f71]) ).
fof(f334,plain,
( ! [X0] : ~ ssItem(X0)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f333,f206]) ).
fof(f335,plain,
( spl0_7
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f334,f240,f292]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s7,plain,
( spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f268]) ).
cnf(s17,plain,
~ spl0_7,
inference(sat_conversion,[],[f317]) ).
cnf(s18,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f320]) ).
cnf(s20,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f335]) ).
cnf(s21,plain,
~ spl0_1,
inference(rat,[],[s20,s17]) ).
cnf(s24,plain,
spl0_6,
inference(rat,[],[s7,s21]) ).
cnf(s25,plain,
~ spl0_4,
inference(rat,[],[s18,s24]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s3,s25,s21]) ).
fof(f336,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC198-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 08:28:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 4.31/1.51 % (208686)Input is clausal, will run a generic CNF schedule.
% 4.31/1.51 % (208691)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=2138723066:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.31/1.51 % (208693)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2297011451:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.31/1.51 % (208695)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2069584567:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.31/1.51 % (208696)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1130027248:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.31/1.51 % (208694)lrs+10_1_sil=8000:sp=occurrence:random_seed=541360562:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.31/1.51 % (208692)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1770051481:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.31/1.51 % (208697)dis-21_1_sil=8000:lcm=predicate:random_seed=1990209099: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)
% 4.31/1.51 % (208695)Instruction limit reached!
% 4.31/1.51 % (208695)------------------------------
% 4.31/1.51 % (208695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.51 % (208695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.51 % (208695)CaDiCaL version: 2.1.3
% 4.31/1.51 % (208695)Termination reason: Instruction limit
% 4.31/1.51 % (208695)Termination phase: Saturation
% 4.31/1.51 % (208695)Time elapsed: 0.052 s
% 4.31/1.51 % (208695)Peak memory usage: 88 MB
% 4.31/1.51 % (208695)Instructions burned: 114 (million)
% 4.31/1.51 % (208694)Instruction limit reached!
% 4.31/1.51 % (208694)------------------------------
% 4.31/1.51 % (208694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.51 % (208694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.51 % (208694)CaDiCaL version: 2.1.3
% 4.31/1.51 % (208694)Termination reason: Instruction limit
% 4.31/1.51 % (208694)Termination phase: Saturation
% 4.31/1.51 % (208694)Time elapsed: 0.057 s
% 4.31/1.51 % (208694)Peak memory usage: 89 MB
% 4.31/1.51 % (208694)Instructions burned: 109 (million)
% 4.31/1.51 % (208697)Instruction limit reached!
% 4.31/1.51 % (208697)------------------------------
% 4.31/1.51 % (208697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.51 % (208697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.51 % (208697)CaDiCaL version: 2.1.3
% 4.31/1.51 % (208697)Termination reason: Instruction limit
% 4.31/1.51 % (208697)Termination phase: Saturation
% 4.31/1.51 % (208697)Time elapsed: 0.067 s
% 4.31/1.51 % (208697)Peak memory usage: 90 MB
% 4.31/1.51 % (208697)Instructions burned: 119 (million)
% 4.31/1.51 % (208696)Instruction limit reached!
% 4.31/1.51 % (208696)------------------------------
% 4.31/1.51 % (208696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.51 % (208696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.51 % (208696)CaDiCaL version: 2.1.3
% 4.31/1.51 % (208696)Termination reason: Instruction limit
% 4.31/1.51 % (208696)Termination phase: Saturation
% 4.31/1.51 % (208696)Time elapsed: 0.123 s
% 4.31/1.51 % (208696)Peak memory usage: 90 MB
% 4.31/1.51 % (208696)Instructions burned: 180 (million)
% 4.31/1.51 % (208705)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=1440942876:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.31/1.51 % (208705)Refutation not found, incomplete strategy
% 4.31/1.51 % (208705)------------------------------
% 4.31/1.51 % (208705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.51 % (208705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.51 % (208705)CaDiCaL version: 2.1.3
% 4.31/1.51 % (208705)Termination reason: Refutation not found, incomplete strategy
% 4.31/1.51 % (208705)Time elapsed: 0.005 s
% 4.31/1.51 % (208705)Peak memory usage: 89 MB
% 4.31/1.51 % (208705)Instructions burned: 5 (million)
% 4.31/1.51 % (208707)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3446216110:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.25/1.71 % (208706)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=558722758: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)
% 5.25/1.71 % (208707)First to succeed.
% 5.25/1.71 % (208707)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-208686"
% 5.25/1.71 % (208708)lrs+10_64_to=lpo:sil=8000:random_seed=2691961524:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.25/1.71 % (208706)Instruction limit reached!
% 5.25/1.71 % (208706)------------------------------
% 5.25/1.71 % (208706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.71 % (208706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.71 % (208706)CaDiCaL version: 2.1.3
% 5.25/1.71 % (208706)Termination reason: Instruction limit
% 5.25/1.71 % (208706)Termination phase: Saturation
% 5.25/1.71 % (208706)Time elapsed: 0.098 s
% 5.25/1.71 % (208706)Peak memory usage: 91 MB
% 5.25/1.71 % (208706)Instructions burned: 191 (million)
% 5.25/1.71 % (208708)Instruction limit reached!
% 5.25/1.71 % (208708)------------------------------
% 5.25/1.71 % (208708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.71 % (208708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.71 % (208708)CaDiCaL version: 2.1.3
% 5.25/1.71 % (208708)Termination reason: Instruction limit
% 5.25/1.71 % (208708)Termination phase: Saturation
% 5.25/1.71 % (208708)Time elapsed: 0.068 s
% 5.25/1.71 % (208708)Peak memory usage: 90 MB
% 5.25/1.71 % (208708)Instructions burned: 128 (million)
% 5.25/1.71 % (208691)Also succeeded, but the first one will report.
% 5.25/1.71 % (208705)------------------------------
% 5.25/1.71 % (208705)------------------------------
% 5.25/1.71 % (208707)Refutation found. Thanks to Tanya!
% 5.25/1.71 % SZS status Unsatisfiable for theBenchmark
% 5.25/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 5.25/1.71 % (208707)------------------------------
% 5.25/1.71 % (208707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.71 % (208707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.71 % (208707)CaDiCaL version: 2.1.3
% 5.25/1.71 % (208707)Termination reason: Refutation
% 5.25/1.71 % (208707)Time elapsed: 0.007 s
% 5.25/1.71 % (208707)Peak memory usage: 89 MB
% 5.25/1.71 % (208707)Instructions burned: 8 (million)
% 5.25/1.71 % (208707)------------------------------
% 5.25/1.71 % (208707)------------------------------
% 5.25/1.71 % (208686)Success in time 0.66 s
% 5.25/1.71 % Vampire exiting
%------------------------------------------------------------------------------