%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC378-1 : 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 : n004.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 01:03:43 PM UTC 2026
% Result : Unsatisfiable 2.82s 1.07s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 15 unt; 4 def)
% Number of atoms : 219 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 254 ( 117 ~; 133 |; 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
fof(f170,axiom,
! [X2,X0,X1] :
( ~ memberP(app(X0,X1),X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| memberP(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
app(sk5,sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
sk4 = app(sk5,sk6),
inference(reorient_equations,[],[f208]) ).
fof(f210,negated_conjecture,
app(sk6,sk5) = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,plain,
sk3 = app(sk6,sk5),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
ssItem(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
( memberP(sk2,sk7)
| memberP(sk1,sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f214,negated_conjecture,
( ~ memberP(sk2,sk7)
| ~ memberP(sk1,sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f217,plain,
( memberP(sk4,sk7)
| memberP(sk3,sk7) ),
inference(definition_unfolding,[],[f213,f204,f205]) ).
fof(f218,plain,
( ~ memberP(sk4,sk7)
| ~ memberP(sk3,sk7) ),
inference(definition_unfolding,[],[f214,f204,f205]) ).
fof(f226,definition,
( spl0_1
<=> memberP(sk3,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f227,plain,
( memberP(sk3,sk7)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( ~ memberP(sk3,sk7)
| spl0_1 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f230,definition,
( spl0_2
<=> memberP(sk4,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f231,plain,
( memberP(sk4,sk7)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f232,plain,
( ~ memberP(sk4,sk7)
| spl0_2 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f218,f230,f226]) ).
fof(f234,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f217,f230,f226]) ).
fof(f307,plain,
! [X0] :
( memberP(sk4,X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ),
inference(superposition,[],[f151,f209]) ).
fof(f309,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(superposition,[],[f151,f211]) ).
fof(f311,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(forward_subsumption_resolution,[],[f309,f206]) ).
fof(f312,plain,
! [X0] :
( memberP(sk4,X0)
| ~ ssList(sk5)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f307,f207]) ).
fof(f313,plain,
! [X0] :
( ~ memberP(sk6,X0)
| ~ ssItem(X0)
| memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[],[f311,f207]) ).
fof(f314,plain,
! [X0] :
( ~ memberP(sk5,X0)
| ~ ssItem(X0)
| memberP(sk4,X0) ),
inference(forward_subsumption_resolution,[],[f312,f206]) ).
fof(f321,plain,
! [X0] :
( memberP(sk4,X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(superposition,[],[f152,f209]) ).
fof(f323,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ),
inference(superposition,[],[f152,f211]) ).
fof(f325,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f323,f206]) ).
fof(f326,plain,
! [X0] :
( memberP(sk4,X0)
| ~ ssList(sk5)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(forward_subsumption_resolution,[],[f321,f207]) ).
fof(f327,plain,
! [X0] :
( ~ memberP(sk5,X0)
| ~ ssItem(X0)
| memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[],[f325,f207]) ).
fof(f328,plain,
! [X0] :
( ~ memberP(sk6,X0)
| ~ ssItem(X0)
| memberP(sk4,X0) ),
inference(forward_subsumption_resolution,[],[f326,f206]) ).
fof(f500,plain,
! [X0] :
( ~ memberP(sk4,X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssItem(X0)
| memberP(sk6,X0)
| memberP(sk5,X0) ),
inference(superposition,[],[f170,f209]) ).
fof(f502,plain,
! [X0] :
( ~ memberP(sk3,X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssItem(X0)
| memberP(sk5,X0)
| memberP(sk6,X0) ),
inference(superposition,[],[f170,f211]) ).
fof(f506,plain,
! [X0] :
( ~ memberP(sk3,X0)
| ~ ssList(sk6)
| ~ ssItem(X0)
| memberP(sk5,X0)
| memberP(sk6,X0) ),
inference(forward_subsumption_resolution,[],[f502,f206]) ).
fof(f507,plain,
! [X0] :
( ~ memberP(sk4,X0)
| ~ ssList(sk5)
| ~ ssItem(X0)
| memberP(sk6,X0)
| memberP(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f500,f207]) ).
fof(f508,plain,
! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| memberP(sk5,X0)
| memberP(sk6,X0) ),
inference(forward_subsumption_resolution,[],[f506,f207]) ).
fof(f509,plain,
! [X0] :
( ~ memberP(sk4,X0)
| ~ ssItem(X0)
| memberP(sk6,X0)
| memberP(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f507,f206]) ).
fof(f638,plain,
( ~ ssItem(sk7)
| memberP(sk6,sk7)
| memberP(sk5,sk7)
| ~ spl0_2 ),
inference(resolution,[],[f509,f231]) ).
fof(f639,plain,
( memberP(sk6,sk7)
| memberP(sk5,sk7)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f638,f212]) ).
fof(f641,definition,
( spl0_17
<=> memberP(sk5,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f643,plain,
( memberP(sk5,sk7)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f645,definition,
( spl0_18
<=> memberP(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f647,plain,
( memberP(sk6,sk7)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f648,plain,
( spl0_17
| spl0_18
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f639,f230,f645,f641]) ).
fof(f649,plain,
( ~ ssItem(sk7)
| memberP(sk5,sk7)
| memberP(sk6,sk7)
| ~ spl0_1 ),
inference(resolution,[],[f227,f508]) ).
fof(f650,plain,
( memberP(sk5,sk7)
| memberP(sk6,sk7)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f649,f212]) ).
fof(f651,plain,
( spl0_18
| spl0_17
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f650,f226,f641,f645]) ).
fof(f663,plain,
( ~ ssItem(sk7)
| memberP(sk3,sk7)
| ~ spl0_17 ),
inference(resolution,[],[f643,f327]) ).
fof(f665,plain,
( memberP(sk3,sk7)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f663,f212]) ).
fof(f666,plain,
( $false
| spl0_1
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f665,f228]) ).
fof(f667,plain,
( spl0_1
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f666]) ).
fof(f688,plain,
( ~ ssItem(sk7)
| memberP(sk4,sk7)
| ~ spl0_18 ),
inference(resolution,[],[f647,f328]) ).
fof(f689,plain,
( ~ ssItem(sk7)
| memberP(sk3,sk7)
| ~ spl0_18 ),
inference(resolution,[],[f647,f313]) ).
fof(f690,plain,
( memberP(sk3,sk7)
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f689,f212]) ).
fof(f691,plain,
( $false
| spl0_1
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f690,f228]) ).
fof(f692,plain,
( spl0_1
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f691]) ).
fof(f693,plain,
( memberP(sk4,sk7)
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f688,f212]) ).
fof(f694,plain,
( $false
| spl0_2
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f693,f232]) ).
fof(f695,plain,
( spl0_2
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f708,plain,
( ~ ssItem(sk7)
| memberP(sk4,sk7)
| ~ spl0_17 ),
inference(resolution,[],[f643,f314]) ).
fof(f709,plain,
( memberP(sk4,sk7)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f708,f212]) ).
fof(f710,plain,
( $false
| spl0_2
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f709,f232]) ).
fof(f711,plain,
( spl0_2
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f710]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f233]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f234]) ).
cnf(s18,plain,
( ~ spl0_2
| spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f648]) ).
cnf(s19,plain,
( ~ spl0_1
| spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f651]) ).
cnf(s20,plain,
( spl0_1
| ~ spl0_17 ),
inference(sat_conversion,[],[f667]) ).
cnf(s21,plain,
( spl0_1
| ~ spl0_18 ),
inference(sat_conversion,[],[f692]) ).
cnf(s22,plain,
( spl0_2
| ~ spl0_18 ),
inference(sat_conversion,[],[f695]) ).
cnf(s23,plain,
( spl0_2
| ~ spl0_17 ),
inference(sat_conversion,[],[f711]) ).
cnf(s26,plain,
spl0_1,
inference(rat,[],[s18,s2,s20,s21]) ).
cnf(s27,plain,
~ spl0_2,
inference(rat,[],[s1,s26]) ).
cnf(s28,plain,
~ spl0_17,
inference(rat,[],[s23,s27]) ).
cnf(s29,plain,
~ spl0_18,
inference(rat,[],[s22,s27]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s19,s26,s28,s29]) ).
fof(f712,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC378-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 09:21:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.82/1.07 % (226185)Input is clausal, will run a generic CNF schedule.
% 2.82/1.07 % (226196)dis-21_1_sil=8000:lcm=predicate:random_seed=4140070054: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)
% 2.82/1.07 % (226196)Instruction limit reached!
% 2.82/1.07 % (226196)------------------------------
% 2.82/1.07 % (226196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.07 % (226196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.07 % (226196)CaDiCaL version: 2.1.3
% 2.82/1.07 % (226196)Termination reason: Instruction limit
% 2.82/1.07 % (226196)Termination phase: Saturation
% 2.82/1.07 % (226196)Time elapsed: 0.030 s
% 2.82/1.07 % (226196)Peak memory usage: 89 MB
% 2.82/1.07 % (226196)Instructions burned: 122 (million)
% 2.82/1.07 % (226193)lrs+10_1_sil=8000:sp=occurrence:random_seed=1949713327:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.82/1.07 % (226190)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=549644125:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.82/1.07 % (226195)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4192031746:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.82/1.07 % (226191)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=210960982:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.82/1.07 % (226194)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3641134895:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.82/1.07 % (226192)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3501831795:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.82/1.07 % (226193)First to succeed.
% 2.82/1.07 % (226193)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-226185"
% 2.82/1.07 % (226194)Also succeeded, but the first one will report.
% 2.82/1.07 % (226198)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=2350692790:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.82/1.07 % (226198)Also succeeded, but the first one will report.
% 2.82/1.07 % (226195)Instruction limit reached!
% 2.82/1.07 % (226195)------------------------------
% 2.82/1.07 % (226195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.07 % (226195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.07 % (226195)CaDiCaL version: 2.1.3
% 2.82/1.07 % (226195)Termination reason: Instruction limit
% 2.82/1.07 % (226195)Termination phase: Saturation
% 2.82/1.07 % (226195)Time elapsed: 0.115 s
% 2.82/1.07 % (226195)Peak memory usage: 90 MB
% 2.82/1.07 % (226195)Instructions burned: 180 (million)
% 2.82/1.07 % (226206)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3126906675: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)
% 2.82/1.07 % (226193)Refutation found. Thanks to Tanya!
% 2.82/1.07 % SZS status Unsatisfiable for theBenchmark
% 2.82/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.17 % (226193)------------------------------
% 3.47/1.17 % (226193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.17 % (226193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.17 % (226193)CaDiCaL version: 2.1.3
% 3.47/1.17 % (226193)Termination reason: Refutation
% 3.47/1.17 % (226193)Time elapsed: 0.012 s
% 3.47/1.17 % (226193)Peak memory usage: 90 MB
% 3.47/1.17 % (226193)Instructions burned: 17 (million)
% 3.47/1.17 % (226193)------------------------------
% 3.47/1.17 % (226193)------------------------------
% 3.47/1.17 % (226185)Success in time 0.42 s
% 3.47/1.17 % Vampire exiting
%------------------------------------------------------------------------------