%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG104+1 : TPTP v9.3.1. Released v4.0.0.
% 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 12:35:32 PM UTC 2026
% Result : Theorem 2.64s 1.34s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 17 unt; 3 def)
% Number of atoms : 104 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 104 ( 49 ~; 43 |; 7 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f39,axiom,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
fof(f40,axiom,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1956) ).
fof(f43,conjecture,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(flattening,[],[f44]) ).
fof(f48,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f49,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f51,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f52]) ).
fof(f66,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
aElement0(xz),
inference(cnf_transformation,[],[f39]) ).
fof(f70,plain,
xx = sdtasdt0(xc,xu),
inference(cnf_transformation,[],[f40]) ).
fof(f71,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f75,plain,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[],[f45]) ).
fof(f83,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f84,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f85,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f91,definition,
~ sP3(sdtasdt0(xz,xx)),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f92,plain,
sP3(sdtasdt0(xc,sdtasdt0(xu,xz))),
inference(inequality_splitting,[],[f75,f91]) ).
fof(f98,plain,
( ~ sP3(sdtasdt0(xx,xz))
| ~ aElement0(xx)
| ~ aElement0(xz) ),
inference(superposition,[],[f91,f84]) ).
fof(f101,plain,
( ~ sP3(sdtasdt0(xx,xz))
| ~ aElement0(xx) ),
inference(forward_subsumption_resolution,[],[f98,f67]) ).
fof(f103,definition,
( spl4_1
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f105,plain,
( ~ aElement0(xx)
| spl4_1 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f107,definition,
( spl4_2
<=> sP3(sdtasdt0(xx,xz)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f109,plain,
( ~ sP3(sdtasdt0(xx,xz))
| spl4_2 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f111,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f101,f107,f103]) ).
fof(f116,plain,
( aElement0(xx)
| ~ aElement0(xc)
| ~ aElement0(xu) ),
inference(superposition,[],[f85,f70]) ).
fof(f117,plain,
! [X0] :
( sdtasdt0(xc,sdtasdt0(xu,X0)) = sdtasdt0(xx,X0)
| ~ aElement0(xc)
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(superposition,[],[f83,f70]) ).
fof(f121,plain,
! [X0] :
( sdtasdt0(xc,sdtasdt0(xu,X0)) = sdtasdt0(xx,X0)
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f117,f66]) ).
fof(f122,plain,
( ~ aElement0(xc)
| ~ aElement0(xu)
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f116,f105]) ).
fof(f124,plain,
! [X0] :
( sdtasdt0(xc,sdtasdt0(xu,X0)) = sdtasdt0(xx,X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f121,f71]) ).
fof(f125,plain,
( ~ aElement0(xu)
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f122,f66]) ).
fof(f126,plain,
( $false
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f125,f71]) ).
fof(f127,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f264,plain,
( sP3(sdtasdt0(xx,xz))
| ~ aElement0(xz) ),
inference(superposition,[],[f92,f124]) ).
fof(f275,plain,
( ~ aElement0(xz)
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f264,f109]) ).
fof(f281,plain,
( $false
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f275,f67]) ).
fof(f282,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f281]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f111]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f127]) ).
cnf(s12,plain,
spl4_2,
inference(sat_conversion,[],[f282]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s2,s12,s3]) ).
fof(f285,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG104+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n016.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 23:21:18 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.64/1.34 % (3103809)Detected formulas, will run a generic FOF schedule.
% 2.64/1.34 % (3103817)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3329769695:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.34 % (3103817)First to succeed.
% 2.64/1.34 % (3103817)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3103809"
% 2.64/1.34 % (3103820)dis-21_1_sil=8000:lcm=predicate:random_seed=2105173981: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)
% 2.64/1.34 % (3103818)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4030754294:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.34 % (3103814)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=2991354943:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.34 % (3103815)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=1712253821:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.34 % (3103816)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=3607601255:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.34 % (3103819)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1909564795:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.34 % (3103818)Also succeeded, but the first one will report.
% 2.64/1.34 % (3103820)Instruction limit reached!
% 2.64/1.34 % (3103820)------------------------------
% 2.64/1.34 % (3103820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.34 % (3103820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.34 % (3103820)CaDiCaL version: 2.1.3
% 2.64/1.34 % (3103820)Termination reason: Instruction limit
% 2.64/1.34 % (3103820)Termination phase: Saturation
% 2.64/1.34 % (3103820)Time elapsed: 0.073 s
% 2.64/1.34 % (3103820)Peak memory usage: 89 MB
% 2.64/1.34 % (3103820)Instructions burned: 130 (million)
% 2.64/1.34 % (3103819)Instruction limit reached!
% 2.64/1.34 % (3103819)------------------------------
% 2.64/1.34 % (3103819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.34 % (3103819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.34 % (3103819)CaDiCaL version: 2.1.3
% 2.64/1.34 % (3103819)Termination reason: Instruction limit
% 2.64/1.34 % (3103819)Termination phase: Saturation
% 2.64/1.34 % (3103819)Time elapsed: 0.088 s
% 2.64/1.34 % (3103819)Peak memory usage: 90 MB
% 2.64/1.34 % (3103819)Instructions burned: 140 (million)
% 2.64/1.34 % (3103817)Refutation found. Thanks to Tanya!
% 2.64/1.34 % SZS status Theorem for theBenchmark
% 2.64/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.34 % (3103817)------------------------------
% 2.64/1.34 % (3103817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.34 % (3103817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.34 % (3103817)CaDiCaL version: 2.1.3
% 2.64/1.34 % (3103817)Termination reason: Refutation
% 2.64/1.34 % (3103817)Time elapsed: 0.004 s
% 2.64/1.34 % (3103817)Peak memory usage: 89 MB
% 2.64/1.34 % (3103817)Instructions burned: 7 (million)
% 2.64/1.34 % (3103817)------------------------------
% 2.64/1.34 % (3103817)------------------------------
% 2.64/1.34 % (3103809)Success in time 0.285 s
% 2.64/1.34 % Vampire exiting
%------------------------------------------------------------------------------