%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL003+1 : 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 : n015.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 12:33:36 PM UTC 2026
% Result : Theorem 0.15s 1.61s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 10 unt; 2 def)
% Number of atoms : 79 ( 39 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 29 ~; 28 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
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(f14,conjecture,
! [X0,X1] :
( ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) )
& ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) )
& ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( ( converse(X1) != join(converse(X0),converse(X1))
& join(X0,X1) = X1 )
| ( join(X0,X1) != X1
& join(converse(X0),converse(X1)) = converse(X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( ( converse(sK1) != join(converse(sK0),converse(sK1))
& sK1 = join(sK0,sK1) )
| ( sK1 != join(sK0,sK1)
& converse(sK1) = join(converse(sK0),converse(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f31,plain,
( sK1 = join(sK0,sK1)
| converse(sK1) = join(converse(sK0),converse(sK1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
( converse(sK1) != join(converse(sK0),converse(sK1))
| sK1 != join(sK0,sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,definition,
( spl2_1
<=> converse(sK1) = join(converse(sK0),converse(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f37,plain,
( converse(sK1) != join(converse(sK0),converse(sK1))
| spl2_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f38,plain,
( converse(sK1) = join(converse(sK0),converse(sK1))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl2_2
<=> sK1 = join(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f41,plain,
( sK1 != join(sK0,sK1)
| spl2_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( sK1 = join(sK0,sK1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f31,f40,f36]) ).
fof(f44,plain,
( ~ spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f34,f36,f40]) ).
fof(f64,plain,
( converse(sK1) != converse(join(sK0,sK1))
| spl2_1 ),
inference(superposition,[],[f37,f26]) ).
fof(f67,plain,
( converse(sK1) != converse(sK1)
| spl2_1
| ~ spl2_2 ),
inference(forward_demodulation,[],[f64,f42]) ).
fof(f68,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f67]) ).
fof(f69,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f70,plain,
( converse(sK1) = join(converse(sK1),converse(sK0))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f38,f18]) ).
fof(f71,plain,
( sK1 != join(sK1,sK0)
| spl2_2 ),
inference(forward_demodulation,[],[f41,f18]) ).
fof(f72,plain,
( converse(sK1) = converse(join(sK1,sK0))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f70,f26]) ).
fof(f75,plain,
( join(sK1,sK0) = converse(converse(sK1))
| ~ spl2_1 ),
inference(superposition,[],[f25,f72]) ).
fof(f76,plain,
( sK1 = join(sK1,sK0)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f75,f25]) ).
fof(f79,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f76,f71]) ).
fof(f80,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[],[f79]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f80]) ).
cnf(s5,plain,
spl2_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl2_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f81,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 22:53:31 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.40 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
% 0.15/1.61 % (2099798)Detected formulas, will run a generic FOF schedule.
% 0.15/1.61 % (2099816)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=1279236326:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.61 % (2099821)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3235987765:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.61 % (2099817)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=578494481:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.61 % (2099821)First to succeed.
% 0.15/1.61 % (2099818)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=3455365281:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.61 % (2099819)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=657436588:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.61 % (2099821)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2099798"
% 0.15/1.61 % (2099820)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=89583633:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.61 % (2099819)Also succeeded, but the first one will report.
% 0.15/1.61 % (2099820)Also succeeded, but the first one will report.
% 0.15/1.61 % (2099822)dis-21_1_sil=8000:lcm=predicate:random_seed=1306257051: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)
% 0.15/1.61 % (2099822)Refutation not found, incomplete strategy
% 0.15/1.61 % (2099822)------------------------------
% 0.15/1.61 % (2099822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.61 % (2099822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.61 % (2099822)CaDiCaL version: 2.1.3
% 0.15/1.61 % (2099822)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.61 % (2099822)Time elapsed: 0.002 s
% 0.15/1.61 % (2099822)Peak memory usage: 88 MB
% 0.15/1.61 % (2099822)Instructions burned: 1 (million)
% 0.15/1.61 % (2099822)------------------------------
% 0.15/1.61 % (2099822)------------------------------
% 0.15/1.61 % (2099821)Refutation found. Thanks to Tanya!
% 0.15/1.61 % SZS status Theorem for theBenchmark
% 0.15/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.61 % (2099821)------------------------------
% 0.15/1.61 % (2099821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.61 % (2099821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.61 % (2099821)CaDiCaL version: 2.1.3
% 0.15/1.61 % (2099821)Termination reason: Refutation
% 0.15/1.61 % (2099821)Time elapsed: 0.004 s
% 0.15/1.61 % (2099821)Peak memory usage: 90 MB
% 0.15/1.61 % (2099821)Instructions burned: 4 (million)
% 0.15/1.61 % (2099821)------------------------------
% 0.15/1.61 % (2099821)------------------------------
% 0.15/1.61 % (2099798)Success in time 0.543 s
% 0.15/1.61 % Vampire exiting
%------------------------------------------------------------------------------