%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:33:41 PM UTC 2026
% Result : Theorem 6.92s 1.76s
% Output : Refutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 24 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 17 ~; 6 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 47 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2)
& join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2)
& join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( composition(X1,X2) != join(composition(X0,X2),composition(X1,X2))
| composition(X2,X1) != join(composition(X2,X0),composition(X2,X1)) )
& join(X0,X1) = X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( ( composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2))
| composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1)) )
& sK1 = join(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f21,plain,
sK1 = join(sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f22,plain,
( composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2))
| composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f24,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f30,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f35,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f44,plain,
sK1 = join(sK1,sK0),
inference(forward_demodulation,[],[f21,f24]) ).
fof(f45,plain,
( composition(sK1,sK2) != join(composition(sK1,sK2),composition(sK0,sK2))
| composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1)) ),
inference(forward_demodulation,[],[f22,f24]) ).
fof(f46,plain,
( composition(sK1,sK2) != composition(join(sK1,sK0),sK2)
| composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1)) ),
inference(forward_demodulation,[],[f45,f30]) ).
fof(f47,plain,
( composition(sK1,sK2) != composition(sK1,sK2)
| composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1)) ),
inference(forward_demodulation,[],[f46,f44]) ).
fof(f48,plain,
composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1)),
inference(trivial_inequality_removal,[],[f47]) ).
fof(f49,plain,
composition(sK2,sK1) != join(composition(sK2,sK1),composition(sK2,sK0)),
inference(forward_demodulation,[],[f48,f24]) ).
fof(f55,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f30,f29]) ).
fof(f135,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f55,f29]) ).
fof(f144,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f135,f35]) ).
fof(f153,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f144,f35]) ).
fof(f159,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f153,f29]) ).
fof(f179,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f36,f159]) ).
fof(f183,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f179,f36]) ).
fof(f225,plain,
composition(sK2,sK1) != composition(sK2,join(sK1,sK0)),
inference(superposition,[],[f49,f183]) ).
fof(f230,plain,
composition(sK2,sK1) != composition(sK2,sK1),
inference(forward_demodulation,[],[f225,f44]) ).
fof(f231,plain,
$false,
inference(trivial_inequality_removal,[],[f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 22:49:37 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.40 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
% 5.63/1.57 % (633643)Detected formulas, will run a generic FOF schedule.
% 5.63/1.57 % (633663)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4225528757:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.63/1.57 % (633665)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1964050410:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.63/1.57 % (633664)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=233745691:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.63/1.57 % (633667)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=891399966:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.63/1.57 % (633662)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=1937493809:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.63/1.57 % (633666)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1448088135:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.63/1.57 % (633668)dis-21_1_sil=8000:lcm=predicate:random_seed=3607281636:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.63/1.57 % (633668)Refutation not found, incomplete strategy
% 5.63/1.57 % (633668)------------------------------
% 5.63/1.57 % (633668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.57 % (633668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.57 % (633668)CaDiCaL version: 2.1.3
% 5.63/1.57 % (633668)Termination reason: Refutation not found, incomplete strategy
% 5.63/1.57 % (633668)Time elapsed: 0.003 s
% 5.63/1.57 % (633668)Peak memory usage: 88 MB
% 5.63/1.57 % (633668)Instructions burned: 1 (million)
% 5.63/1.57 % (633665)Instruction limit reached!
% 5.63/1.57 % (633665)------------------------------
% 5.63/1.57 % (633665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.57 % (633665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.57 % (633665)CaDiCaL version: 2.1.3
% 5.63/1.57 % (633665)Termination reason: Instruction limit
% 5.63/1.57 % (633665)Termination phase: Saturation
% 5.63/1.57 % (633665)Time elapsed: 0.067 s
% 5.63/1.57 % (633665)Peak memory usage: 89 MB
% 5.63/1.57 % (633665)Instructions burned: 110 (million)
% 5.63/1.57 % (633666)Instruction limit reached!
% 5.63/1.57 % (633666)------------------------------
% 5.63/1.57 % (633666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.57 % (633666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.57 % (633666)CaDiCaL version: 2.1.3
% 5.63/1.57 % (633666)Termination reason: Instruction limit
% 5.63/1.57 % (633666)Termination phase: Saturation
% 5.63/1.57 % (633666)Time elapsed: 0.105 s
% 5.63/1.57 % (633666)Peak memory usage: 88 MB
% 5.63/1.57 % (633666)Instructions burned: 119 (million)
% 5.63/1.57 % (633667)Instruction limit reached!
% 5.63/1.57 % (633667)------------------------------
% 5.63/1.57 % (633667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.57 % (633667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.57 % (633667)CaDiCaL version: 2.1.3
% 5.63/1.57 % (633667)Termination reason: Instruction limit
% 5.63/1.57 % (633667)Termination phase: Saturation
% 5.63/1.57 % (633667)Time elapsed: 0.114 s
% 5.63/1.57 % (633667)Peak memory usage: 90 MB
% 5.63/1.57 % (633667)Instructions burned: 140 (million)
% 5.63/1.57 % (633680)lrs+10_1_sil=8000:sp=occurrence:random_seed=2259123612:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.63/1.57 % (633681)lrs+10_1_sil=32000:urr=on:br=off:random_seed=191122908:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.63/1.57 % (633682)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3432427386:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.63/1.57 % (633668)------------------------------
% 5.63/1.57 % (633668)------------------------------
% 5.63/1.57 % (633680)Instruction limit reached!
% 5.63/1.57 % (633680)------------------------------
% 5.63/1.57 % (633680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.57 % (633680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.76 % (633680)CaDiCaL version: 2.1.3
% 6.92/1.76 % (633680)Termination reason: Instruction limit
% 6.92/1.76 % (633680)Termination phase: Saturation
% 6.92/1.76 % (633680)Time elapsed: 0.211 s
% 6.92/1.76 % (633680)Peak memory usage: 89 MB
% 6.92/1.76 % (633680)Instructions burned: 286 (million)
% 6.92/1.76 % (633681)Instruction limit reached!
% 6.92/1.76 % (633681)------------------------------
% 6.92/1.76 % (633681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.76 % (633681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.76 % (633681)CaDiCaL version: 2.1.3
% 6.92/1.76 % (633681)Termination reason: Instruction limit
% 6.92/1.76 % (633681)Termination phase: Saturation
% 6.92/1.76 % (633681)Time elapsed: 0.141 s
% 6.92/1.76 % (633681)Peak memory usage: 89 MB
% 6.92/1.76 % (633681)Instructions burned: 157 (million)
% 6.92/1.76 % (633663)First to succeed.
% 6.92/1.76 % (633663)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-633643"
% 6.92/1.76 % (633682)Instruction limit reached!
% 6.92/1.76 % (633682)------------------------------
% 6.92/1.76 % (633682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.76 % (633682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.76 % (633682)CaDiCaL version: 2.1.3
% 6.92/1.76 % (633682)Termination reason: Instruction limit
% 6.92/1.76 % (633682)Termination phase: Saturation
% 6.92/1.76 % (633682)Time elapsed: 0.229 s
% 6.92/1.76 % (633682)Peak memory usage: 92 MB
% 6.92/1.76 % (633682)Instructions burned: 326 (million)
% 6.92/1.76 % (633692)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=269611272:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 6.92/1.76 % (633693)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2040147806:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 6.92/1.76 % (633695)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3279599770:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 6.92/1.76 % (633693)Also succeeded, but the first one will report.
% 6.92/1.76 % (633696)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=681766631:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 6.92/1.76 % (633663)Refutation found. Thanks to Tanya!
% 6.92/1.76 % SZS status Theorem for theBenchmark
% 6.92/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 6.92/1.76 % (633663)------------------------------
% 6.92/1.76 % (633663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.76 % (633663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.76 % (633663)CaDiCaL version: 2.1.3
% 6.92/1.76 % (633663)Termination reason: Refutation
% 6.92/1.76 % (633663)Time elapsed: 0.593 s
% 6.92/1.76 % (633663)Peak memory usage: 129 MB
% 6.92/1.76 % (633663)Instructions burned: 943 (million)
% 6.92/1.76 % (633663)------------------------------
% 6.92/1.76 % (633663)------------------------------
% 6.92/1.76 % (633643)Success in time 0.922 s
% 6.92/1.76 % Vampire exiting
%------------------------------------------------------------------------------