%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT143-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 11:46:04 AM UTC 2026
% Result : Unsatisfiable 3.40s 1.37s
% Output : Refutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 66 ( 37 unt; 6 def)
% Number of atoms : 95 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 54 ( 25 ~; 23 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : meet(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
fof(f2,axiom,
! [X0] : join(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
fof(f4,axiom,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
fof(f6,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
fof(f7,axiom,
! [X2,X0,X1] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
fof(f8,axiom,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
fof(f9,axiom,
! [X2,X0,X1] : join(meet(X0,X1),meet(X1,X2)) = join(meet(X0,X1),meet(X1,join(meet(X0,X1),meet(X2,join(X0,X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H24) ).
fof(f10,negated_conjecture,
meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_H15) ).
fof(f12,definition,
( spl0_1
<=> meet(a,join(meet(a,b),meet(a,c))) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f14,plain,
( meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))
| spl0_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f15,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f10,f12]) ).
fof(f23,plain,
! [X0,X1] : join(X1,meet(X0,X1)) = X1,
inference(superposition,[],[f4,f5]) ).
fof(f24,plain,
( meet(a,join(meet(b,a),meet(a,c))) != meet(a,join(meet(b,a),join(meet(a,c),meet(c,join(a,b)))))
| spl0_1 ),
inference(superposition,[],[f14,f5]) ).
fof(f32,definition,
( spl0_3
<=> meet(a,join(meet(b,a),meet(a,c))) = meet(a,join(meet(b,a),join(meet(a,c),meet(c,join(a,b))))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f34,plain,
( meet(a,join(meet(b,a),meet(a,c))) != meet(a,join(meet(b,a),join(meet(a,c),meet(c,join(a,b)))))
| spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
( ~ spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f24,f12,f32]) ).
fof(f102,plain,
! [X2,X0,X1] : meet(X0,meet(join(X0,X1),X2)) = meet(X0,X2),
inference(superposition,[],[f7,f3]) ).
fof(f113,plain,
! [X2,X0,X1] : meet(X0,X1) = meet(X0,meet(X1,join(meet(X0,X1),X2))),
inference(superposition,[],[f3,f7]) ).
fof(f148,plain,
( meet(a,join(meet(b,a),meet(a,c))) != meet(a,join(meet(b,a),join(meet(c,join(a,b)),meet(a,c))))
| spl0_3 ),
inference(superposition,[],[f34,f6]) ).
fof(f150,definition,
( spl0_9
<=> meet(a,join(meet(b,a),meet(a,c))) = meet(a,join(meet(b,a),join(meet(c,join(a,b)),meet(a,c)))) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f152,plain,
( meet(a,join(meet(b,a),meet(a,c))) != meet(a,join(meet(b,a),join(meet(c,join(a,b)),meet(a,c))))
| spl0_9 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( ~ spl0_9
| spl0_3 ),
inference(avatar_split_clause,[],[f148,f32,f150]) ).
fof(f223,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f6,f8]) ).
fof(f356,plain,
! [X2,X0,X1] : join(meet(X1,X0),meet(X0,X2)) = join(meet(X1,X0),meet(X0,join(meet(X1,X0),meet(X2,join(X0,X1))))),
inference(superposition,[],[f9,f6]) ).
fof(f467,plain,
! [X2,X0,X1] : meet(X1,X0) = meet(X1,meet(X0,join(X1,X2))),
inference(superposition,[],[f102,f5]) ).
fof(f856,plain,
! [X2,X0,X1] : join(X1,X0) = join(meet(X0,X2),join(X1,X0)),
inference(superposition,[],[f223,f4]) ).
fof(f1544,plain,
! [X2,X0,X1] : meet(X1,join(X0,X2)) = join(meet(X1,join(X0,X2)),meet(X0,X1)),
inference(superposition,[],[f23,f467]) ).
fof(f1568,plain,
( meet(a,join(meet(b,a),meet(a,c))) != meet(a,join(meet(b,a),meet(c,join(a,b))))
| spl0_9 ),
inference(backward_demodulation,[],[f152,f1544]) ).
fof(f1600,definition,
( spl0_23
<=> meet(a,join(meet(b,a),meet(a,c))) = meet(a,join(meet(b,a),meet(c,join(a,b)))) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f1602,plain,
( meet(a,join(meet(b,a),meet(a,c))) != meet(a,join(meet(b,a),meet(c,join(a,b))))
| spl0_23 ),
inference(avatar_component_clause,[],[f1600]) ).
fof(f1603,plain,
( ~ spl0_23
| spl0_9 ),
inference(avatar_split_clause,[],[f1568,f150,f1600]) ).
fof(f2501,plain,
( meet(a,join(meet(b,a),meet(c,a))) != meet(a,join(meet(b,a),meet(c,join(a,b))))
| spl0_23 ),
inference(superposition,[],[f1602,f5]) ).
fof(f2503,definition,
( spl0_25
<=> meet(a,join(meet(b,a),meet(c,a))) = meet(a,join(meet(b,a),meet(c,join(a,b)))) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f2505,plain,
( meet(a,join(meet(b,a),meet(c,a))) != meet(a,join(meet(b,a),meet(c,join(a,b))))
| spl0_25 ),
inference(avatar_component_clause,[],[f2503]) ).
fof(f2506,plain,
( ~ spl0_25
| spl0_23 ),
inference(avatar_split_clause,[],[f2501,f1600,f2503]) ).
fof(f3102,plain,
! [X0,X1] : join(meet(X0,X1),X0) = X0,
inference(superposition,[],[f856,f2]) ).
fof(f3407,plain,
! [X0,X1] : join(meet(X0,X1),X1) = X1,
inference(superposition,[],[f3102,f5]) ).
fof(f3525,plain,
! [X2,X0,X1] : meet(X1,join(meet(X0,X1),X2)) = join(meet(X0,X1),meet(X1,join(meet(X0,X1),X2))),
inference(superposition,[],[f3407,f113]) ).
fof(f3552,plain,
! [X2,X0,X1] : join(meet(meet(X1,X0),X0),meet(X0,X2)) = join(meet(meet(X1,X0),X0),meet(X0,join(meet(meet(X1,X0),X0),meet(X2,X0)))),
inference(superposition,[],[f9,f3407]) ).
fof(f3595,plain,
! [X2,X0,X1] : join(meet(X1,meet(X0,X0)),meet(X0,X2)) = join(meet(X1,meet(X0,X0)),meet(X0,join(meet(X1,meet(X0,X0)),meet(X2,X0)))),
inference(forward_demodulation,[],[f3552,f7]) ).
fof(f3604,plain,
! [X2,X0,X1] : join(meet(X1,X0),meet(X0,X2)) = meet(X0,join(meet(X1,X0),meet(X2,join(X0,X1)))),
inference(backward_demodulation,[],[f356,f3525]) ).
fof(f3619,plain,
! [X2,X0,X1] : join(meet(X1,X0),meet(X0,X2)) = join(meet(X1,X0),meet(X0,join(meet(X1,X0),meet(X2,X0)))),
inference(forward_demodulation,[],[f3595,f1]) ).
fof(f3621,plain,
( join(meet(b,a),meet(a,c)) != meet(a,join(meet(b,a),meet(c,a)))
| spl0_25 ),
inference(backward_demodulation,[],[f2505,f3604]) ).
fof(f3633,plain,
! [X2,X0,X1] : join(meet(X1,X0),meet(X0,X2)) = meet(X0,join(meet(X1,X0),meet(X2,X0))),
inference(forward_demodulation,[],[f3619,f3525]) ).
fof(f3640,definition,
( spl0_29
<=> join(meet(b,a),meet(a,c)) = meet(a,join(meet(b,a),meet(c,a))) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f3642,plain,
( join(meet(b,a),meet(a,c)) != meet(a,join(meet(b,a),meet(c,a)))
| spl0_29 ),
inference(avatar_component_clause,[],[f3640]) ).
fof(f3643,plain,
( ~ spl0_29
| spl0_25 ),
inference(avatar_split_clause,[],[f3621,f2503,f3640]) ).
fof(f3662,plain,
( join(meet(b,a),meet(a,c)) != join(meet(b,a),meet(a,c))
| spl0_29 ),
inference(forward_demodulation,[],[f3642,f3633]) ).
fof(f3663,plain,
( $false
| spl0_29 ),
inference(trivial_inequality_removal,[],[f3662]) ).
fof(f3664,plain,
spl0_29,
inference(avatar_contradiction_clause,[],[f3663]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f15]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s16,plain,
( spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f153]) ).
cnf(s39,plain,
( spl0_9
| ~ spl0_23 ),
inference(sat_conversion,[],[f1603]) ).
cnf(s41,plain,
( spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f2506]) ).
cnf(s48,plain,
( spl0_25
| ~ spl0_29 ),
inference(sat_conversion,[],[f3643]) ).
cnf(s51,plain,
spl0_29,
inference(sat_conversion,[],[f3664]) ).
cnf(s52,plain,
spl0_25,
inference(rat,[],[s48,s51]) ).
cnf(s53,plain,
spl0_23,
inference(rat,[],[s41,s52]) ).
cnf(s54,plain,
spl0_9,
inference(rat,[],[s39,s53]) ).
cnf(s55,plain,
spl0_3,
inference(rat,[],[s16,s54]) ).
cnf(s56,plain,
spl0_1,
inference(rat,[],[s3,s55]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s1,s56]) ).
fof(f3665,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT143-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.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 : Sun Sep 27 14:07:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.40/1.37 % (2672088)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.40/1.37 % (2672196)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3696020329:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.40/1.37 % (2672194)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2026387900:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.40/1.37 % (2672195)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2263529407:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.40/1.37 % (2672200)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=362216347:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.40/1.37 % (2672199)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3772788420:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.40/1.37 % (2672198)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3751169305:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.40/1.37 % (2672198)Refutation not found, incomplete strategy
% 3.40/1.37 % (2672198)------------------------------
% 3.40/1.37 % (2672198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.37 % (2672198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.37 % (2672198)CaDiCaL version: 2.1.3
% 3.40/1.37 % (2672198)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.37 % (2672198)Time elapsed: 0.001 s
% 3.40/1.37 % (2672198)Peak memory usage: 87 MB
% 3.40/1.37 % (2672198)Instructions burned: 1 (million)
% 3.40/1.37 % (2672197)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2366239441:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.40/1.37 % (2672199)First to succeed.
% 3.40/1.37 % (2672197)Instruction limit reached!
% 3.40/1.37 % (2672197)------------------------------
% 3.40/1.37 % (2672197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.37 % (2672197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.37 % (2672197)CaDiCaL version: 2.1.3
% 3.40/1.37 % (2672197)Termination reason: Instruction limit
% 3.40/1.37 % (2672197)Termination phase: Saturation
% 3.40/1.37 % (2672197)Time elapsed: 0.084 s
% 3.40/1.37 % (2672197)Peak memory usage: 89 MB
% 3.40/1.37 % (2672197)Instructions burned: 137 (million)
% 3.40/1.37 % (2672199)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2672088"
% 3.40/1.37 % (2672198)------------------------------
% 3.40/1.37 % (2672198)------------------------------
% 3.40/1.37 % (2672221)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3896639749:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.40/1.37 % (2672199)Refutation found. Thanks to Tanya!
% 3.40/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.40/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 4.26/1.57 % (2672199)------------------------------
% 4.26/1.57 % (2672199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.26/1.57 % (2672199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.26/1.57 % (2672199)CaDiCaL version: 2.1.3
% 4.26/1.57 % (2672199)Termination reason: Refutation
% 4.26/1.57 % (2672199)Time elapsed: 0.111 s
% 4.26/1.57 % (2672199)Peak memory usage: 90 MB
% 4.26/1.57 % (2672199)Instructions burned: 146 (million)
% 4.26/1.57 % (2672199)------------------------------
% 4.26/1.57 % (2672199)------------------------------
% 4.26/1.57 % (2672088)Success in time 0.515 s
% 4.26/1.57 % Vampire exiting
%------------------------------------------------------------------------------