%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC384-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:03:44 PM UTC 2026
% Result : Unsatisfiable 3.59s 1.25s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 79 ( 18 unt; 8 def)
% Number of atoms : 185 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 89 ~; 98 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f119,axiom,
! [X0,X1] :
( cons(X0,nil) != X1
| ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
( ssList(sk6)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( ssList(sk7)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f212,plain,
( sk3 = cons(sk5,nil)
| nil = sk4 ),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
( app(app(sk6,sk3),sk7) = sk4
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f214,plain,
( sk4 = app(app(sk6,sk3),sk7)
| nil = sk4 ),
inference(reorient_equations,[],[f213]) ).
fof(f225,negated_conjecture,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_22) ).
fof(f228,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f229,plain,
( ~ singletonP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f225,f205,f204,f205]) ).
fof(f231,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f237,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(equality_resolution,[],[f119]) ).
fof(f238,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f243,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f246,definition,
( spl0_1
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f248,plain,
( ~ segmentP(sk4,sk3)
| spl0_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl0_2
<=> singletonP(sk3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f252,plain,
( ~ singletonP(sk3)
| spl0_2 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f229,f250,f246]) ).
fof(f267,definition,
( spl0_6
<=> sk4 = app(app(sk6,sk3),sk7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f269,plain,
( sk4 = app(app(sk6,sk3),sk7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f272,definition,
( spl0_7
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f274,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f277,definition,
( spl0_8
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f279,plain,
( ssList(sk7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f282,definition,
( spl0_9
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f284,plain,
( ssList(sk6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f287,definition,
( spl0_10
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f289,plain,
( nil = sk4
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f292,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f214,f267,f287]) ).
fof(f293,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f212,f272,f287]) ).
fof(f294,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f210,f277,f287]) ).
fof(f295,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f209,f282,f287]) ).
fof(f297,definition,
( spl0_11
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f299,plain,
( ssItem(sk5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f301,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f207,f297,f287]) ).
fof(f304,plain,
( neq(nil,nil)
| ~ spl0_10 ),
inference(superposition,[],[f228,f289]) ).
fof(f306,plain,
( ~ ssList(nil)
| ~ spl0_10 ),
inference(resolution,[],[f243,f304]) ).
fof(f307,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f306,f8]) ).
fof(f308,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f365,plain,
( ~ ssList(sk3)
| ~ ssItem(sk5)
| singletonP(sk3)
| ~ spl0_7 ),
inference(superposition,[],[f237,f274]) ).
fof(f367,plain,
( ~ ssItem(sk5)
| singletonP(sk3)
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f365,f202]) ).
fof(f369,plain,
( singletonP(sk3)
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f367,f299]) ).
fof(f370,plain,
( $false
| spl0_2
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f369,f252]) ).
fof(f371,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f370]) ).
fof(f880,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk7)
| ~ spl0_6 ),
inference(superposition,[],[f238,f269]) ).
fof(f885,plain,
( ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk7)
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f880,f248]) ).
fof(f900,plain,
( ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk7)
| spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f885,f284]) ).
fof(f914,plain,
( ~ ssList(sk4)
| ~ ssList(sk7)
| spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f900,f202]) ).
fof(f923,plain,
( ~ ssList(sk7)
| spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f914,f203]) ).
fof(f924,plain,
( $false
| spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f923,f279]) ).
fof(f925,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f924]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s10,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f292]) ).
cnf(s11,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f293]) ).
cnf(s12,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f294]) ).
cnf(s13,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f295]) ).
cnf(s15,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f301]) ).
cnf(s16,plain,
~ spl0_10,
inference(sat_conversion,[],[f308]) ).
cnf(s18,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_11 ),
inference(sat_conversion,[],[f371]) ).
cnf(s25,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f925]) ).
cnf(s26,plain,
spl0_11,
inference(rat,[],[s15,s16]) ).
cnf(s27,plain,
spl0_9,
inference(rat,[],[s13,s16]) ).
cnf(s29,plain,
spl0_8,
inference(rat,[],[s12,s16]) ).
cnf(s30,plain,
spl0_7,
inference(rat,[],[s11,s16]) ).
cnf(s31,plain,
spl0_2,
inference(rat,[],[s18,s26,s30]) ).
cnf(s35,plain,
spl0_6,
inference(rat,[],[s10,s16]) ).
cnf(s36,plain,
spl0_1,
inference(rat,[],[s25,s27,s29,s35]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s1,s31,s36]) ).
fof(f926,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC384-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 09:29:48 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.59/1.25 % (241580)Input is clausal, will run a generic CNF schedule.
% 3.59/1.25 % (241585)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=2377216733:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.59/1.25 % (241586)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=79239774:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.59/1.25 % (241590)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3730164339:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.59/1.25 % (241588)lrs+10_1_sil=8000:sp=occurrence:random_seed=396488314:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.59/1.25 % (241589)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=654150973:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.59/1.25 % (241591)dis-21_1_sil=8000:lcm=predicate:random_seed=248150816: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)
% 3.59/1.25 % (241587)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2755456028:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.59/1.25 % (241588)First to succeed.
% 3.59/1.25 % (241588)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-241580"
% 3.59/1.25 % (241589)Also succeeded, but the first one will report.
% 3.59/1.25 % (241590)Also succeeded, but the first one will report.
% 3.59/1.25 % (241591)Instruction limit reached!
% 3.59/1.25 % (241591)------------------------------
% 3.59/1.25 % (241591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.25 % (241591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.25 % (241591)CaDiCaL version: 2.1.3
% 3.59/1.25 % (241591)Termination reason: Instruction limit
% 3.59/1.25 % (241591)Termination phase: Saturation
% 3.59/1.25 % (241591)Time elapsed: 0.065 s
% 3.59/1.25 % (241591)Peak memory usage: 90 MB
% 3.59/1.25 % (241591)Instructions burned: 117 (million)
% 3.59/1.25 % (241599)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=3871851474:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.59/1.25 % (241599)Also succeeded, but the first one will report.
% 3.59/1.25 % (241588)Refutation found. Thanks to Tanya!
% 3.59/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.59/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.25 % (241588)------------------------------
% 3.59/1.25 % (241588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.25 % (241588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.25 % (241588)CaDiCaL version: 2.1.3
% 3.59/1.25 % (241588)Termination reason: Refutation
% 3.59/1.25 % (241588)Time elapsed: 0.016 s
% 3.59/1.25 % (241588)Peak memory usage: 90 MB
% 3.59/1.25 % (241588)Instructions burned: 23 (million)
% 3.59/1.25 % (241588)------------------------------
% 3.59/1.25 % (241588)------------------------------
% 3.59/1.25 % (241580)Success in time 0.428 s
% 3.59/1.25 % Vampire exiting
%------------------------------------------------------------------------------