%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET031-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:39:42 PM UTC 2026
% Result : Unsatisfiable 1.45s 1.40s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 10 unt; 3 def)
% Number of atoms : 72 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 27 ~; 32 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X0 != ordered_pair(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
fof(f16,plain,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair(X1,X2) != X0 ),
inference(reorient_equations,[],[f15]) ).
fof(f89,axiom,
! [X0] :
( member(f18(X0),X0)
| relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',relation2) ).
fof(f90,axiom,
! [X0] :
( ~ ordered_pair_predicate(f18(X0))
| relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',relation3) ).
fof(f146,axiom,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| little_set(f29(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f147,axiom,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| little_set(f30(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
fof(f149,axiom,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| X0 = ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose4) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2)) = X0 ),
inference(reorient_equations,[],[f149]) ).
fof(f178,negated_conjecture,
~ relation(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_composition_is_a_relation) ).
fof(f180,plain,
! [X2,X1] :
( ordered_pair_predicate(ordered_pair(X1,X2))
| ~ little_set(X1)
| ~ little_set(X2) ),
inference(equality_resolution,[],[f16]) ).
fof(f186,plain,
! [X0,X1] :
( little_set(f29(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) ),
inference(resolution,[],[f146,f89]) ).
fof(f187,plain,
! [X0,X1] :
( little_set(f30(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) ),
inference(resolution,[],[f147,f89]) ).
fof(f193,plain,
! [X0,X1] :
( relation(compose(X0,X1))
| f18(compose(X0,X1)) = ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f30(f18(compose(X0,X1)),X0,X1)) ),
inference(resolution,[],[f150,f89]) ).
fof(f230,plain,
f18(compose(a,b)) = ordered_pair(f29(f18(compose(a,b)),a,b),f30(f18(compose(a,b)),a,b)),
inference(resolution,[],[f193,f178]) ).
fof(f238,plain,
( ordered_pair_predicate(f18(compose(a,b)))
| ~ little_set(f29(f18(compose(a,b)),a,b))
| ~ little_set(f30(f18(compose(a,b)),a,b)) ),
inference(superposition,[],[f180,f230]) ).
fof(f241,definition,
( spl0_1
<=> little_set(f29(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f243,plain,
( ~ little_set(f29(f18(compose(a,b)),a,b))
| spl0_1 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f245,definition,
( spl0_2
<=> little_set(f30(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f247,plain,
( ~ little_set(f30(f18(compose(a,b)),a,b))
| spl0_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f253,definition,
( spl0_4
<=> ordered_pair_predicate(f18(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f255,plain,
( ordered_pair_predicate(f18(compose(a,b)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( ~ spl0_2
| ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f238,f253,f241,f245]) ).
fof(f289,plain,
( relation(compose(a,b))
| spl0_1 ),
inference(resolution,[],[f243,f186]) ).
fof(f290,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f289,f178]) ).
fof(f291,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f292,plain,
( relation(compose(a,b))
| spl0_2 ),
inference(resolution,[],[f247,f187]) ).
fof(f293,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f292,f178]) ).
fof(f294,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f293]) ).
fof(f319,plain,
( relation(compose(a,b))
| ~ spl0_4 ),
inference(resolution,[],[f255,f90]) ).
fof(f321,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f319,f178]) ).
fof(f322,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f321]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s9,plain,
spl0_1,
inference(sat_conversion,[],[f291]) ).
cnf(s10,plain,
spl0_2,
inference(sat_conversion,[],[f294]) ).
cnf(s12,plain,
~ spl0_4,
inference(sat_conversion,[],[f322]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s12,s10,s9]) ).
fof(f323,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET031-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:16:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 1.45/1.40 % (3910767)Input is clausal, will run a generic CNF schedule.
% 1.45/1.40 % (3910774)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4052794318:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.45/1.40 % (3910772)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=2188861219:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.45/1.40 % (3910776)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3401159371:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.45/1.40 % (3910773)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3845674085:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.45/1.40 % (3910775)lrs+10_1_sil=8000:sp=occurrence:random_seed=3560289383:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.45/1.40 % (3910778)dis-21_1_sil=8000:lcm=predicate:random_seed=3030494548: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)
% 1.45/1.40 % (3910777)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3472561770:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.45/1.40 % (3910775)First to succeed.
% 1.45/1.40 % (3910775)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3910767"
% 1.45/1.40 % (3910777)Also succeeded, but the first one will report.
% 1.45/1.40 % (3910778)Instruction limit reached!
% 1.45/1.40 % (3910778)------------------------------
% 1.45/1.40 % (3910778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.45/1.40 % (3910778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/1.40 % (3910778)CaDiCaL version: 2.1.3
% 1.45/1.40 % (3910778)Termination reason: Instruction limit
% 1.45/1.40 % (3910778)Termination phase: Saturation
% 1.45/1.40 % (3910778)Time elapsed: 0.050 s
% 1.45/1.40 % (3910778)Peak memory usage: 90 MB
% 1.45/1.40 % (3910778)Instructions burned: 118 (million)
% 1.45/1.40 % (3910776)Instruction limit reached!
% 1.45/1.40 % (3910776)------------------------------
% 1.45/1.40 % (3910776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.45/1.40 % (3910776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/1.40 % (3910776)CaDiCaL version: 2.1.3
% 1.45/1.40 % (3910776)Termination reason: Instruction limit
% 1.45/1.40 % (3910776)Termination phase: Saturation
% 1.45/1.40 % (3910776)Time elapsed: 0.066 s
% 1.45/1.40 % (3910776)Peak memory usage: 88 MB
% 1.45/1.40 % (3910776)Instructions burned: 114 (million)
% 1.45/1.40 % (3910786)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=1357817445:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.45/1.40 % (3910786)Refutation not found, incomplete strategy
% 1.45/1.40 % (3910786)------------------------------
% 1.45/1.40 % (3910786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.45/1.40 % (3910786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/1.40 % (3910786)CaDiCaL version: 2.1.3
% 1.45/1.40 % (3910786)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.40 % (3910786)Time elapsed: 0.002 s
% 1.45/1.40 % (3910786)Peak memory usage: 88 MB
% 1.45/1.40 % (3910786)Instructions burned: 1 (million)
% 1.45/1.40 % (3910787)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=43916590: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)
% 1.45/1.40 % (3910787)Also succeeded, but the first one will report.
% 1.45/1.40 % (3910775)Refutation found. Thanks to Tanya!
% 1.45/1.40 % SZS status Unsatisfiable for theBenchmark
% 1.45/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 1.45/1.40 % (3910775)------------------------------
% 1.45/1.40 % (3910775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.45/1.40 % (3910775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/1.40 % (3910775)CaDiCaL version: 2.1.3
% 1.45/1.40 % (3910775)Termination reason: Refutation
% 1.45/1.40 % (3910775)Time elapsed: 0.007 s
% 1.45/1.40 % (3910775)Peak memory usage: 89 MB
% 1.45/1.40 % (3910775)Instructions burned: 8 (million)
% 1.45/1.40 % (3910775)------------------------------
% 1.45/1.40 % (3910775)------------------------------
% 1.45/1.40 % (3910767)Success in time 0.445 s
% 1.45/1.40 % Vampire exiting
%------------------------------------------------------------------------------