%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG104+2 : 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 : n019.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 3.56s 1.48s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 20 unt; 3 def)
% Number of atoms : 124 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 121 ( 51 ~; 42 |; 23 &)
% ( 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 32 !; 4 ?)
% 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,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xy )
& 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,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X1] :
( aElement0(X1)
& xy = sdtasdt0(xc,X1) )
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
inference(rectify,[],[f39]) ).
fof(f46,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(f63,plain,
( aElement0(sK0)
& xx = sdtasdt0(xc,sK0)
& aElementOf0(xx,slsdtgt0(xc))
& aElement0(sK1)
& xy = sdtasdt0(xc,sK1)
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f45]) ).
fof(f68,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f69,plain,
aElement0(xz),
inference(cnf_transformation,[],[f63]) ).
fof(f74,plain,
xx = sdtasdt0(xc,sK0),
inference(cnf_transformation,[],[f63]) ).
fof(f76,plain,
xx = sdtasdt0(xc,xu),
inference(cnf_transformation,[],[f40]) ).
fof(f77,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f81,plain,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[],[f46]) ).
fof(f82,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(f83,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f84,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f97,definition,
~ sP5(sdtasdt0(xz,xx)),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f98,plain,
sP5(sdtasdt0(xc,sdtasdt0(xu,xz))),
inference(inequality_splitting,[],[f81,f97]) ).
fof(f104,plain,
( ~ sP5(sdtasdt0(xx,xz))
| ~ aElement0(xx)
| ~ aElement0(xz) ),
inference(superposition,[],[f97,f83]) ).
fof(f107,plain,
( ~ sP5(sdtasdt0(xx,xz))
| ~ aElement0(xx) ),
inference(forward_subsumption_resolution,[],[f104,f69]) ).
fof(f109,plain,
( ~ sP5(sdtasdt0(sdtasdt0(xc,sK0),xz))
| ~ aElement0(xx) ),
inference(forward_demodulation,[],[f107,f74]) ).
fof(f111,plain,
( ~ aElement0(sdtasdt0(xc,sK0))
| ~ sP5(sdtasdt0(sdtasdt0(xc,sK0),xz)) ),
inference(forward_demodulation,[],[f109,f74]) ).
fof(f113,definition,
( spl6_1
<=> sP5(sdtasdt0(sdtasdt0(xc,sK0),xz)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f115,plain,
( ~ sP5(sdtasdt0(sdtasdt0(xc,sK0),xz))
| spl6_1 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f117,definition,
( spl6_2
<=> aElement0(sdtasdt0(xc,sK0)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f121,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f111,f117,f113]) ).
fof(f175,plain,
( aElement0(xx)
| ~ aElement0(xc)
| ~ aElement0(xu) ),
inference(superposition,[],[f84,f76]) ).
fof(f176,plain,
! [X0] :
( sdtasdt0(xc,sdtasdt0(xu,X0)) = sdtasdt0(xx,X0)
| ~ aElement0(xc)
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(superposition,[],[f82,f76]) ).
fof(f177,plain,
! [X0] :
( sdtasdt0(xc,sdtasdt0(xu,X0)) = sdtasdt0(xx,X0)
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f176,f68]) ).
fof(f178,plain,
( aElement0(xx)
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[],[f175,f68]) ).
fof(f180,plain,
! [X0] :
( sdtasdt0(xc,sdtasdt0(xu,X0)) = sdtasdt0(xx,X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f177,f77]) ).
fof(f181,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f178,f77]) ).
fof(f183,plain,
! [X0] :
( sdtasdt0(xc,sdtasdt0(xu,X0)) = sdtasdt0(sdtasdt0(xc,sK0),X0)
| ~ aElement0(X0) ),
inference(forward_demodulation,[],[f180,f74]) ).
fof(f184,plain,
aElement0(sdtasdt0(xc,sK0)),
inference(forward_demodulation,[],[f181,f74]) ).
fof(f186,plain,
spl6_2,
inference(avatar_split_clause,[],[f184,f117]) ).
fof(f446,plain,
( sP5(sdtasdt0(sdtasdt0(xc,sK0),xz))
| ~ aElement0(xz) ),
inference(superposition,[],[f98,f183]) ).
fof(f457,plain,
( ~ aElement0(xz)
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f446,f115]) ).
fof(f463,plain,
( $false
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f457,f69]) ).
fof(f464,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f463]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f121]) ).
cnf(s3,plain,
spl6_2,
inference(sat_conversion,[],[f186]) ).
cnf(s12,plain,
spl6_1,
inference(sat_conversion,[],[f464]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s2,s3,s12]) ).
fof(f467,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG104+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n019.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 23:16:34 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.56/1.48 % (3516660)Detected formulas, will run a generic FOF schedule.
% 3.56/1.48 % (3516671)dis-21_1_sil=8000:lcm=predicate:random_seed=3869090924: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)
% 3.56/1.48 % (3516666)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=1406416441:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.56/1.48 % (3516671)Instruction limit reached!
% 3.56/1.48 % (3516671)------------------------------
% 3.56/1.48 % (3516671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (3516671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (3516671)CaDiCaL version: 2.1.3
% 3.56/1.48 % (3516671)Termination reason: Instruction limit
% 3.56/1.48 % (3516671)Termination phase: Saturation
% 3.56/1.48 % (3516671)Time elapsed: 0.039 s
% 3.56/1.48 % (3516671)Peak memory usage: 89 MB
% 3.56/1.48 % (3516671)Instructions burned: 132 (million)
% 3.56/1.48 % (3516667)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=3308434502:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.56/1.48 % (3516665)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=3007141181:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.56/1.48 % (3516670)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3999874636:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.56/1.48 % (3516668)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=93392729:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.56/1.48 % (3516669)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2103867086:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.56/1.48 % (3516668)First to succeed.
% 3.56/1.48 % (3516668)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3516660"
% 3.56/1.48 % (3516669)Also succeeded, but the first one will report.
% 3.56/1.48 % (3516670)Instruction limit reached!
% 3.56/1.48 % (3516670)------------------------------
% 3.56/1.48 % (3516670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (3516670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (3516670)CaDiCaL version: 2.1.3
% 3.56/1.48 % (3516670)Termination reason: Instruction limit
% 3.56/1.48 % (3516670)Termination phase: Saturation
% 3.56/1.48 % (3516670)Time elapsed: 0.047 s
% 3.56/1.48 % (3516670)Peak memory usage: 90 MB
% 3.56/1.48 % (3516670)Instructions burned: 142 (million)
% 3.56/1.48 % (3516677)lrs+10_1_sil=8000:sp=occurrence:random_seed=774624186:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.56/1.48 % (3516680)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2013091046:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 3.56/1.48 % (3516680)Instruction limit reached!
% 3.56/1.48 % (3516680)------------------------------
% 3.56/1.48 % (3516680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (3516680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (3516680)CaDiCaL version: 2.1.3
% 3.56/1.48 % (3516680)Termination reason: Instruction limit
% 3.56/1.48 % (3516680)Termination phase: Saturation
% 3.56/1.48 % (3516680)Time elapsed: 0.038 s
% 3.56/1.48 % (3516680)Peak memory usage: 90 MB
% 3.56/1.48 % (3516680)Instructions burned: 157 (million)
% 3.56/1.48 % (3516683)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2560353941:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.56/1.48 % (3516668)Refutation found. Thanks to Tanya!
% 3.56/1.48 % SZS status Theorem for theBenchmark
% 3.56/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.48 % (3516668)------------------------------
% 3.56/1.48 % (3516668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (3516668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (3516668)CaDiCaL version: 2.1.3
% 3.56/1.48 % (3516668)Termination reason: Refutation
% 3.56/1.48 % (3516668)Time elapsed: 0.010 s
% 3.56/1.48 % (3516668)Peak memory usage: 89 MB
% 3.56/1.48 % (3516668)Instructions burned: 12 (million)
% 3.56/1.48 % (3516668)------------------------------
% 3.56/1.48 % (3516668)------------------------------
% 3.56/1.48 % (3516660)Success in time 0.421 s
% 3.56/1.48 % Vampire exiting
%------------------------------------------------------------------------------